Science, Art and Nature in Medieval and Modern Thought

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V E N E T I I S , Apud Thomam Baglionum. M DC X. Superiorum Permiffu, & Privilegio. Galileo Galilei, Sidereus mincius (1610): title page. This little book marks a turning-point in Galileo's life. Here he published his first telescopic discoveries, notably of the mountainous surface of the Moon and the satellites of Jupiter, which he named the Medicean stars after the Grand Duke of Tuscany. Here also he showed a serious commitment to the Gopernican system.

SCIENCE, ART AND NATURE IN MEDIEVAL AND MODERN THOUGHT

A.C. CROMBIE

THE HAMBLEDON PRESS LONDON

AND

RIO GRANDE

Published by Hambledon Press 1996 102 Gloucester Avenue, London NW1 8HX (UK) PO Box 102, Rio Grande, Ohio 45674 (USA) ISBN 1 85285 067 1 © Alistair Cameron Crombie 1996 A description of this book is available from the British Library and from the Library of Congress

Printed on acid-free paper and bound in Great Britain by Cambridge University Press

Contents

Acknowledgements Illustrations Preface Further Bibliography of A.C. Crombie 1 Designed in the Mind: Western visions of Science, Nature and Humankind 2 The Western Experience of Scientific Objectivity 3 Historical Perceptions of Medieval Science 4 Robert Grosseteste (c. 1168-1253) 5 Roger Bacon (c. 1219-1292) [with J.D. North] 6 Infinite Power and the Laws of Nature: A Medieval Speculation 7 Experimental Science and the Rational Artist in Early Modern Europe 8 Mathematics and Platonism in the Sixteenth-Century Italian Universities and in Jesuit Educational Policy 9 Sources of Galileo Galilei's Early Natural Philosophy 10 The Jesuits and Galileo's Ideas of Science and of Nature [with A. Carugo] 11 Galileo and the Art of Rhetoric [with A. Carugo] 12 Galileo Galilei: A Philosophical Symbol 13 Alexandre Koyré and Great Britain: Galileo and Mersenne 14 Marin Mersenne and the Origins of Language 15 Le Corps à la Renaissance: Theories of Perceiver and Perceived in Hearing 16 Expectation, Modelling and Assent in the History of Optics: i, Alhazen and the Medieval Tradition; ii, Kepler and Descartes 17 Contingent Expectation and Uncertain Choice: Historical Contexts of Arguments from Probabilities 18 P.-L. Moreau de Maupertuis, F.R.S. (1698-1759): Précurseur du Transformisme 19 The Public and Private Faces of Charles Darwin 20 The Language of Science

vii ix xi xiii

1 13 31 39 51 67 89 115 149 165 231 257 263 275 291 301 357 407 429 439

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Science, Art and Nature in Medieval and Modern Thought

21 Some Historical Questions about Disease 22 Historians and the Scientific Revolution 23 The Origins of Western Science

443 451 465

Appendix to Chapter 10: 479 (a) Sources and Dates of Galileos Writings [with A. Carugo] (b) Pietro Redondi, Galileo eretico (Torino, 1983) [with A. Carugo] (c) Mario Biagioli, Galileo, Courtier (Chicago, 1993) Corrections to Science, Optics and Music in Medieval and Early Modern Thought (1990) 495 Index 497

Acknowledgements

The articles reprinted here first appeared in the following places and are reprinted by kind permission of the original publishers. 1

History of Science, xxvi (1988), pp. 1-12.

2

Proceedings of the 3rd International Humanistic Symposium 1975: The Case of Objectivity (Athenai: Hellenistic Society for Humanistic Studies, 1977), pp. 428-55.

3

In Italian in Federico II e le Scienze: Proceedings of the International Seminar on Frederick II and the Mediterranean World (1990), a cura di A. Paravicini Bagliani (Palermo: Sellerio, 1995).

4

Dictionary of Scientific Biography, ed. C.C. Gillispie, v (New York: Charles Scriber's Sons, 1972), pp. 548-54.

5

Ibid., i (1970), pp. 377-85.

6

L'infinito nella scienza, a cura di G. Toraldo di Francia (Roma: Enciclopedia Italiana, 1987), pp. 223-43.

7

Daedalus, cxv (1986), pp. 49-74.

8

Prismata: Naturwissenschaftsgeschichtliche Studien: Festchrift fur Willy Hartner, hrsg. Y. Maeyama aund W.G. Salzer (Wiesbaden: Franz Steiner Verlag GmbH, 1977), pp. 63-94.

9

Reason, Experiment and Mysticism in the Scientific Revolution, ed. M.L. Righini Bonelli and W.R. Shea (New York: Science History Publications, 1975), pp. 157-75.

10 Annali dell' Istituto e Museo di Storia della Scienza di Firenze, viii.2 (1983), pp. 1-68. 11 Nouvelles de la république des lettres (1988) ii, pp. 7-31. 12 Actes du VIIle Congrés International d'Histoire des Sciences (Florence, 1956), pp. 1089-95.

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Science, Art and Nature in Medieval and Modern Thought

13 The Renaissance of a History: Proceedings of the International Conference Alexandre Koyré, Paris, 1986, ed. P Redondi: History and Technology, iv (London, 1987), pp. 81-92. 14 In French in Nature, histoire, société: Essais en hommage à Jacques Roger, éd. C. Blanckaert, J.-L. Fischer, R. Rey (Paris: Editions Klincksieck, 1995); Appendix: The Times Literary Supplement, 2 October 1992, p. 23. 15 Le Corps à la Renaissance: Actes du XXXe Colloque de Tours 1987, sous la direction de J. Céard, M.M. Fontaine, J.-C. Margolin (Paris: Aux Amateurs de Livres, 1990), pp. 379-87. 16 Studies in History and Philosophy of Science, xxi (1990), pp. 605-32, xxii (1991), pp. 89-115. 17 The Rational Arts of Living, ed. A.C. Crombie and N.G. Siraisi, Smith College Studies in History, vol. 50 (Northampton, Mass., 1987), pp. 53101; first version published in French in Médecine et Probabilités: Actes de la Journée d'Etudes du 15 December 1979, éd. A. Fagot (Paris: I'Université Paris-Val de Marne, 1982). 18 Revue de synthèse, lxxviii (1957), pp. 35-56. 19 First published as 'Darwin's Scientific Method' in Actes du IXe Congrès International d'Histoire des Sciences, Barcelona-Madrid 1959 (Barcelona/ Paris, 1960), pp. 354-62; reprinted in The Listener (London: B.B.C., November 1959). 20 Presented at the Forum de la communication scientifique et technique: Quelles langues pour la science?, organise a l'initiative du Ministère de la Francophonie; published in French in Alliage: Culture - Science Technique, no. 4 (Eté, 1990), pp. 39-42. 21 Sida: Epidémies et sociétés, 20 et 21 juin 1987, éd. C. Mérieux (Lyon, 1987), pp. 115-21. 22 Physis, xi (1969), pp. 167-80. 23 Metascience, n.s.ii (1993), pp. 1-16.

Illustrations

Galileo Galilei, Sidereus nuncius (1610): title page

ii

Figure illustrating Roger Bacon's fifth rule

56

Galileo Galilei, from // Saggiatore (1623) : frontispiece

88

The beginning of Galileo's autograph Disputationes

152

Autograph page of Galileo's Tractatio de Caelo

154

Watermark showing a backward-looking lamb

157

Diagram of the Copernican system, with the Sun in the centre, from Galileo's Dialogo (1632)

164

Pope Urban VIII facing Galileo

165

Galileo Galilei by Mario Leoni (1624)

230

Galileo Galilei, Dialogo (1632): title page

256

Vincenzo Galilei, Dialogo della musica antica (1581): title page

274

Rene Descartes, by an unknown artist

300

Euclid: the geometry of vision

302

Euclidian vision: from Robert Fludd, Utriusque cosmi. . . historia: Microcosmus (Oppenheim, 1618)

303

The anatomy of the eye (1572)

306

Diagram of the eye, from Roger Bacon, Opus Majus

307

Light rays and the eye, from Roger Bacon, Opus Majus

312

Alberti's grid (1435)

318

A painting of a cross-section of the visual pyramid: from Fludd (1618)

318

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Science, Art and Nature in Medieval and Modern Thought

Leonardo da Vinci, Codex Atlanticus, f. 337, illustrating his comparison of the eye with a camera obscura

321

Leonardo da Vinci, Codex D, f. 3v

322

Observing a solar eclipse in a camera obscura (1545)

323

Kepler, Ad Vitellionem paralipomena (Frankfurt, 1604), after Plater, De corporis humani structura et usu (Basel, 1583)

333

Descartes, La dioptrique (Leiden, 1637), illustrating Kepler's ocular dioptrics

337

Kepler, Ad Vitellionem paralipomena (Frankfurt, 1604), vol. 3, prop, xxiii

340

Scheiner, Rosa ursina (Bracciani, 1630), comparing the eye and a camera obscura with a lens system, and the effects on each of using further lenses

346

Descartes, La dioptrique (Leiden, 1637), illustrating the transmission of light

351

Scheiner, Oculus (Oeniponti, 1619), showing the structure of the eye

353

Preface

This second volume of essays forms a coherent set of studies like the first volume Science, Optics and Music in Medieval and Early Modern Thought published in 1990. Both volumes complement my books Augustine to Galileo: Medieval and Early Modern Science and Robert Grosseteste and the Origins of Experimental Science 1100-1700 and lead into my Styles of Scientific Thinking in the European Tradition: The History of Argument and Explanation Especially in the Mathematical and Biomedical Sciences and Arts (3 volumes, published by Gerald Duckworth & Co. Ltd, London, 1994), and forthcoming Galileo's Arguments and Disputes in Natural Philosophy (with the collaboration of Adriano Carugo), and Marin Mersenne: Science, Music and Language. The history of Western science is the history of a vision and an argument, initiated by the ancient Greeks in their search for principles at once of nature and of argument itself. This scientific vision, explored and controlled by argument, and the diversification of both vision and argument by scientific experience and by interaction with the wider contexts of intellectual culture, constitute the long history of European scientific thought. Underlying that development have been specific commitments to conceptions of nature and of science with its intellectual and moral assumptions, accompanied by a recurrent critique. Their diversification has generated a series of different styles of scientific thinking and of making theoretical and practical decisions. These styles are described and analysed in the opening chapter and exemplified in more detail in those that follow. These deal with scientific objectivity, the historiography of medieval science, Robert Grosseteste and Roger Bacon (Chapter 5 in collaboration with John North), the medieval conception of laws of nature, and the historical relation between rational design in scientific experimentation and in the arts exemplified especially by perspective painting. After a chapter on the place of mathematics in sixteenthcentury Italian universities and in Jesuit educational policy, there are five substantial studies of Galileo and his ideals of scientific demonstration and experimentation, of his use of rhetoric, and of his reputation. Two of them, Chapters 10 and 11, were written in collaboration with my colleague Adriano Carugo. Central to them are our discoveries of the use by Galileo of works by Jesuit philosophers at the Collegio Romano or associated therewith, which

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Science, Art and Nature in Medieval and Modern Thought

have thrown an entirely new and very influential light on Galileo's intellectual biography. These chapters contain the original and authentic account of these discoveries. Next come studies of Mersenne and the origins of language, and of the role of hypothetical modelling in the investigation of hearing and more particularly of vision, with a detailed analysis of the theories and researches of Alhazen, Kepler and Descartes. These complement and bring up to date my long monograph on the subject (1967) republished in Science, Optics and Music. There is a further substantial analysis of historical contexts of arguments from probabilities, from the qualitative treatment found in ancient medicine, ethics and law, through the quantification of probabilities initiated with insurance and commerce in fifteenth-century Italy, given mathematical elegance especially by Pascal, Huygens and Leibniz, developed further in the fields of demography and economics, and applied to a form of evolution by natural selection in the eighteenth century by Maupertuis and finally in crucial detail by Darwin. Concluding chapters deal with scientific language, conceptions of disease, and the historiography of science. Some of the papers included in this volume (chs. 3,10 appendix (a), 14, 20) have not been published in English before. The others have been left as they were first printed except for minor corrections. Thus they record stages in the process of discovery and interpretation, as in the chapters on Galileo, especially when dealing with problems of dating, many of them still unsolved. They have been reprinted with continuous pagination, with footnotes at the bottom of the page, and with appropriate revision of internal references. Immediately relevant further bibliography has been added as required at the ends of chapters. An extensive bibliography for the whole subject is included in my Styles of Scientific Thinking. Additions to my own publications, beyond those included in the bibliography of my writings in Science, Optics and Music, are listed below. Finally, once again it is a pleasure to thank all those who provided the occasions for these papers, in Belagio, Athens, Erice, Rome, Cambridge, Mass., Capri, Florence, Paris, Tours, Smith College, Barcelona and Annecy. A.C. Crombie 30 November 1994 Trinity College, Oxford

Further Bibliography of A.C. Crombie

Acknowledgements should have been made in Science, Optics and Music to the bibliography published in The Light of Nature: Essays in the History and Philosophy of Science Presented to A.C. Crombie, ed. J.D. North and J.J. Roche. Dordrecht, Martinus Nijhoff Publishers, 1985. (a) Books on the History of Science

1992

Stili di pensiero scientifico agli inizi dell' Europa moderna. Napoli, Bibliopolis. Spanish translation by J.L. Barona, Valencia, 1994.

1994

Styles of Scientific Thinking in the European Tradition: The History of Argument and Explanation Especially in the Mathematical and Biomedical Sciences and Arts, 3 vols. London, Gerald Duckworth & Co. Ltd., 1994. (b) Papers on the History of Science

1990

'Le corps a la Renaissance: Theories of Perceiver and Perceived in Hearing' in Le Corps a la Renaissance: Actes du xxxe Colloque de Tours 1987, sous la direction de J. Céard, M.M. Fontaine, J.-C. Margolin. Paris, Aux Amateurs de Livres, pp. 379-87. 'Expectation and Assent in Seventeenth-Century Scientific Argument: Galileo and Others' (Banfi Lecture, 1989), Istituto Antonio Banfi Annali, iii (1989-90), pp. 11-54 'La Langue maternelle de la science', Alliage: Culture - Science Technique, no. 4 (Eté, 1990), pp. 39-42. Review of E. Grant and J.E. Murdoch (ed.), Mathematics and its Applications to Science and Natural Philosophy in the Middle Ages (Cambridge, 1987) in English Historical Review, cv (1990), pp. 1007-8.

1990/91 'Expectation, Modelling and Assent in the History of Optics, i: Alhazen and the Medieval Tradition; ii: Kepler and Descartes',

xiv

Science, Art and Nature in Medieval and Modern Thought Studies in History and Philosophy of Science, xxi (1990), pp. 605-32, xxii (1991), pp. 89-115

1992

Review of Nicolas-Claude Fabri de Peiresc, Lettres à Claude Saumaise et à son entourage (1620-1637), éd. Agnes Bresson. Firenze, Leo S. Olschki, 1992, Times Literary Supplement, 2 October 1992, p. 23.

1993

The Origins of Western Science', Metascience, n.s. ii, pp. 1-16. Presentation of Lessico filosofico dei secoli xvii e xviii, Sezione latina, a cura di Marta Fattori con la collaborazione di M.L. Bianchi, fasc.i (Roma, 1992) at the Warburg Institute, London, 3 May 1993, in Nouvelles de la Republique des Lettres, (1993)-ii, 102-4.

1994

Reviews of Elspeth Whitney, Paradise Restored: The Mechanical Arts from Antiquity through the Thirteenth Century (Philadelphia: American Philosophical Society, Transactions lxxx.1, 1990) and Georges Minois, L'Eglise et la Science: Histoire d'un malentendu. De Saint Augustine a Galilee (Paris, 1990) in English Historical Review, cix (1994), pp. 136-8; and of Guiseppe Olmi, L'inventario del mondo: Catalogazione della natura a luoghi delsapere nella prima etá moderna (Bologna, 1992) in Journal of the History of Collections, forthcoming. 'The Greek Origins of European Scientific Styles', Ad familiares: The journal of the Friends of Classics, vii (1994), pp. xii-xiv. 'The History of European Science', New European: European Business Review, xciv (1994), pp. ii-v. 'Historical Perceptions of Medieval Science' in Federico II e le Scienze: Proceedings of the International Seminar on Frederick II and the Mediterranean World, a cura di A. Paravicini Bagliani. Palermo, Sellerio, pp. 15-24. 'Marin Mersenne et les origines du langage' in Nature, histoire, société: Essais en hommage a Jacques Roger, prés. par C. Blanckaert, J.-L. Fischer, J. Rey. Paris, Editions Klincksieck, pp. 35-46.

1995

'Boundaries of normality' in Malatia i cultura: Seminari d'Estudis sobre la Ciència, ed. J.L. Barona (Valencia, 1995), pp. 11-17. 'Per una antropologia històrica del saber científic', interview by Marc Borràs in Mètode: Revista de difusió de la investigació de la Universitat de València, ix (1995), pp. 14-17. 'Commitments and Styles of European Scientific Thinking' in History of Science, xxiii (1995), pp. 225-38.

'Univers' (with J.D. North) in Les caractères originaux de I'Occident medieval, éd. J. Le Goff, J.-C. Schmitt. Paris, Librairie Arthème Fayard, forthcoming.

Bibliography

xv

"Philosophical Commitments and Scientific Progress" in The Idea of Progress (Academia Europea conference 1994), forthcoming. (c) Editorships Editor, 1949-54 of The British Journal for the Philosophy of Science. Joint founder and editor of History of Science: A Review of Literature, Research and Teaching, Cambridge, W. Heffer and Sons, 1962-72; Science History Publications 1973- . (d) Scientific Papers Papers on (i) interspecific competition (an experimental and mathematical analysis on some aspects of ecology and natural selection) and (ii) the physiology of the chemical sense-organs in insects. 1941

On Oviposition, Olfactory Conditioning and Host Selection in Rhizopertha dominica Fab. (Insecta, coleoptera)', Journal of Experimental Biology, 18, pp. 62-79.

1942

'The Effect of Crowding upon the Oviposition of Grain-Infesting Insects',/. Exp. Biol., 19, pp. 311-40.

1943

'The Effect of Crowding upon the Natality of Grain-Infesting Insects', Proceedings of the Zoological Society of London, A, 113, pp. 77-98.

1944

'On Intraspecific and Interspecific Competition in Larvae of Graminivorous Insects', 7. Exp. BioL, 20, pp. 135-51. 'On the Measurement and Modification of the Olfactory Responses of Blow-Flies', /. Exp. BioL, 20, pp. 159-66. 'Sensillae of the Adults and larvae of the Beetle Rhizopertha dominica Fab. (Bostrichidae)', Proceedings of the Royal Entomological Society of London A, 19, pp. 131-2.

1945

'On Competition between Different Species of Graminivorous Insects', Proceedings of the Royal Society, B, 132, pp. 362-95.

1946

'Further Experiments on Insect Competition', Proc. Roy. Soc., B, 133, pp. 76-109.

1947

'The Behaviour of Wireworms in Response to Chemical Stimulation' [with W.H. Thorpe, R. Hill and J.H. Darrah], /. Exp. BioL, 23, pp. 234-66. 'The Chemoreceptors of the Wire worm (Agriotes spp.) and the Relation of Activity to Chemical Composition' [with J.H. Darrah], J. Exp. Biol. 24, pp. 95-109. 'Interspecific Competition', Journal of Animal Ecology, 16, pp. 44-73.

In nature's infinite book of secrecy A little I can read. (Shakespeare, Antony and Cleopatra i.l 1)

1 Designed in the Mind: Western Visions of Science, Nature and Humankind When we speak today of natural science we mean a specific vision created within Western culture, at once of knowledge and of the object of that knowledge, a vision at once of natural science and of nature.1 We may trace the characteristically Western tradition of rational science and philosophy to the commitment of the ancient Greeks, for whatever reason, to the decision of questions by argument and evidence, as distinct from custom, edict, authority, revelation, rule-of-thumb, on some other principle or practice. They developed thereby the notion of a problem as distinct from a doctrine, and the consequent habit of envisaging thought and action in all situations as the perception and solving of problems. By deciding at the same time that among many possible worlds as envisaged in other cultures, the one world that existed was a world of exclusively self-consistent and discoverable rational causality, the Greek philosophers, mathematicians and medical men committed their scientific successors exclusively to this effective direction of thinking. They closed for Western scientific vision the elsewhere open questions of what kind of world people found themselves inhabiting and so of what methods they should use to explore and explain and control it. They introduced in this way the conception of a rational scientific system, a system in which formal reasoning matched natural causation, so that natural events must follow exactly from scientific principles, just as logical and mathematical conclusions must follow from their premises. Thus they introduced, in parallel with their conception of causal demonstration, the equally fundamental conception of formal proof. From these two conceptions all the essential character and style of Western philosophy, mathematics and natural science have followed. The exclusive rationality so defined supplied the presuppositions and came to supply the methods of reasoning alike in purely formal discourse and in the experiential exploration of nature. Hence it offered rational control of subjectmatters of all kinds, from mathematical to material, from ideas to things. A similar characteristic style is evident over the whole range of Western intellectual and practical enterprise. We have then in Western scientific culture, as an object of study to which we its students at the same time inextricably belong, a highly intellectualized and integrated whole, designed in

2

Science, Art and Nature in Medieval and Modern Thought

the mind like a work of art, not all at once but over many generations of interaction between creative thinking and testing, between programmes and their realization or modification or rejection. But if we insist upon the cultural specificity of the Western scientific tradition in its origins and initial development, and upon its enduring identity in diffusion to other cultures, we do not have to look far below the surface of scientific inquiry and its immediate results to see that the whole historical process has gone on in a context of intellectual and moral commitments, expectations, dispositions and memories that have varied greatly with different periods, societies and also individuals. These have affected both the problems perceived and the solutions found acceptable, and also the evaluations of desirable or undesirable ends and their motivations. The whole historical experience of scientific thinking is an invitation to treat the history of science, both in its development in the West and in its complex diffusion through other cultures, as a kind of comparative historical anthropology of thought. An historical anthropology of science must be concerned before all with people and their vision. The scientific movement offers an invitation to examine the,identity of natural science within an intellectual culture, to distinguishrihat from the identities of other intellectual and practical activities in the arts, scholarship, philosophy, law, government, commerce and so on, and to relate them all in a taxonomy of styles. It is an invitation to analyse the various elements that make up an intellectual style in the study and treatment of nature: conceptions of nature and of science, methods of scientific inquiry and demonstration diversified according to the subject-matter, evaluations of scientific goals with consequent motivations, and intellectual and moral commitments and expectations generating attitudes to innovation and change. The scientific thinking found in a particular period or society or individual gets its vision and style from different but closely related intellectual or moral commitments or dispositions. We may distinguish three. (1) First there have been conceptions of nature within the general scheme of existence and of its knowability to man. These in turn have been conditioned by language. The original Greek commitment entailed the replacement of conceptions of nature as an arbitrary sociological order maintained by personified agents, found in all ancient cosmologies and cosmogonies, with the conception of an inevitable order established by an exclusive natural causality. In the succession competing for dominance in subsequent Western thought, nature has been conceived as a product of divine economy or art with appropriate characteristics of simplicity and harmony, as a consequence of atomic chance, as a causal continuum, as a workshop of active substantial powers, as a passive system of mechanisms, as an evolutionary generation of novelty, as a manifestation of probabilities.

Western Visions of Science, Nature and Humankind

3

Any language itself embodies a theory of meaning, a logic, a classification of experience in names, a conception of both perceiver and perceived and their relation, and of relations in space and time. Philology can be an indispensable guide to theoretical ideas and real actions. The expression of a system of science in a language may not entail an immediate critique of the fundamental structure of that language, yet its vocabulary and syntax may have to be modified to provide for the conceptual and technical precision required by the science developing within it. Thus a new terminology had to be devised in medieval and early modern Latin to accommodate the new kinematic and dynamic conceptions, especially of functions, of instantaneous change and of rates of change, which could scarcely be expressed in the classical logic and syntax of subject and predicate. Terminology may have had to be revised to detach its specific scientific meaning from its source in common but inadequate or misleading analogies. "The word current", wrote Michael Faraday,2 "is so expressive in common language that when applied in the consideration of electrical phenomena, we can hardly divest it sufficiently of its meaning, or prevent our minds from being prejudiced by it". For the same reason he replaced "pole", inconveniently suggesting attraction, with the neutral "electrode", in a new terminology devised with the aid of William Whewell to fit the precise context of electro-chemistry. John Tyndall3 in his attractive account of Faraday as a discoverer exemplified a familiar historical process when he described how, in this new science, "prompted by certain analogies we ascribe electrical phenomena to the action of a peculiar fluid, sometimes flowing, sometimes at rest. Such conceptions have their advantages and their disadvantages; they afford peaceful lodging to the intellect for a time, but they also circumscribe it, and by-and-by, when the mind has grown too large for its lodging, it often finds difficulty in breaking down the walls of what has become its prison instead of its home." Thus a radically new technical language may be made up, precisely symbolized as first for mathematics and music and later for many other sciences and arts. The result may be a special language fundamentally different in intention from that implicit in the common language of the society from which it originated, but still a language that may be learned and understood in any society and may convey to it objectively communicable knowledge. Must science in different linguistic cultures always acquire differences of logical form, and must the grammatical structure of a language always impose its ontological presuppositions on the science developing within it? While the technical language of science has often been developed partly to escape from just such impositions, philology can be an accurate guide to implicit or explicit intellectual commitments of this kind and to their changes. The West learnt from the Greeks to look for causal continuity in events both physical and moral, and this has structured its natural and moral philosophy

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Science, Art and Nature in Medieval and Modern Thought

alike and its whole tradition of dramatic literature and music since Antiquity. Japanese thinking, now in exemplary possession of Western science and music, seems traditionally by contrast to have accepted events in their individual existential discontinuity, impressionistically unrelated to before and after, with no general abstract term for nature, but each thing the subject of personal knowledge and companionship, not of mastery either by thought or action. The whole question might throw an interesting light in our philosophical anthropology upon a question central to the whole Western debate: that of distinguishing the argument giving rational control of subject-matter from an implication of the existence of entities appearing in the language used, or, more generally, that of distinguishing a rational structure of nature from that of the organizing human mind. (2) A second kind of intellectual commitment affecting scientific style has been to a conception of science and of the organization of scientific inquiry. Two different traditions of scientific organization and method began in Antiquity. The dominant Greek mathematicians saw as their goal the reduction of every scientific field to the axiomatic model of their most powerful intellectual invention, geometry. At once alternative and complementary to this was the much older medical and technological practice of exploring and recording by piecemeal observation, measurement and trial. The medieval and early modern experimental natural philosophers combined both traditions, to transform the geometrical pattern by an increasing preoccupation with quantitative experimental analysis of causal connections and functional relations. Yet a different pattern came from intellectual satisfaction in mathematical harmonies rather than causal processes. Other modes of intellectual organization assimilated analysis for scientific investigation to that for artistic construction, or looked for probabilities or for genetic origins and derivations. All generated scientific systems made up of theories and laws and statements of observations, providing particular explanations and solutions of problems within the framework of a general conception of nature and science, along with scientific methods diversified by the diversity both of general commitments and of particular subject-matters of varying complexity. The commitments of a period or group or individual to general beliefs about nature and about science, combined with the technical possibilities available, have regulated the problems seen, the questions put to nature, and the acceptability of both questions and answers. Such commitments have directed research towards certain types of problem and towards certain types of discovery and explanation, but away from others. They have both guided inquiry and supplied its ultimate irreducible explanatory principles. By taking us beneath the surface of immediate scientific results, they help us to identify the conceptual and technical conditions, frontiers and horizons making certain discoveries possible and explanations acceptable to a generation or group, but

Western Visions of Science, Nature and Humankind

5

others not, and the same not to others. More specifically a discovery or a theory or even a presentation of research may open fresh horizons but at the same time close others hitherto held possible. Dominant intellectual commitments have made certain kinds of question appear cogent and given certain kinds of explanation their power to convince, and excluded others. They established, in anticipation of any particular research, the kind of world that was supposed to exist and the appropriate methods of inquiry. Such beliefs, taken from the more general intellectual context of natural science, have regulated the expectations both of questions and of answers, the form of theories and the kinds of explanatory entities taken into them, and the acceptability of the explanations they offered. They established in advance the kind of explanation that would give satisfaction when the supposedly discoverable had been discovered. They have been challenged not usually by observation, but by re-examining the metaphysics or theology or other general beliefs assumed. In this process the cogency of such worlds might change from generation to generation as each nevertheless added to enduringly valid scientific knowledge. (3) A third kind of intellectual and moral commitment has concerned what could and should be done. This in its diverse modes has followed from diverse evaluations of the nature and purpose of existence and hence of right human action. It has been linked with dispositions generating an habitual response to events, both internally within scientific thinking itself, and externally in the responses of society: dispositions to expect to master or to be mastered by or simply to contemplate events, to change or to resist change, to anticipate innovation or conservation, to be ready or not to reject theories and to rethink accepted beliefs and to alter habits. Such dispositions have been both psychological and social. They may be specified by habitual styles and methods both of opposition and of acceptance. They may characterize a society over the whole range of its intellectual and moral behaviour, of which its natural science is simply a part. The primary focus, for example, of medieval and early modern Christian as of Islamic culture and society on the teaching and preservation of theological truth could scarcely fail to condition all human inquiries. Sensitive implications of natural philosophical and metaphysical questions and doctrines placed the whole of intellectual life within the political framework and control of a moral cosmology.The medieval Christian theological hierarchy of dignity within that cosmology, as also Islamic attitudes to the visual representation of natural objects, took that control as far as aesthetic style. Given the dual source of human knowledge in the divine gifts of true reason and of undeniable revelation, the whole enterprise made an urgent issue then of error, of the possibility of error in good faith, of the attitude to be taken to

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unpersuadable infidels and irredeemable heretics, of the commitments and expectations of disagreement as well as agreement. In all this, and in the whole scientific movement considered in the context of society and of communication, persuasion has been as important as proof. The use of persuasive arguments to reinforce or to create the power of ideas to convince, especially when the ideas were new and the audience uncertain or unsympathetic, has been well understood by some of the greatest scientific innovators. Galileo and Descartes were both masters of the current rhetorical techniques of persuasion. Galileo devoted at least as much energy to trying to establish the identity of natural science within contemporary intellectual culture as to solving particular physical problems. He conducted all his controversies at two levels: one was concerned with the particular physical problem in question; the other was concerned with an eloquent advocacy of his conception of natural science as an enterprise in solving problems and finding scientific explanations distinct from the philosophical or theological exegesis of authorities and texts, from a literary exercise, from a commercial or legal negotiation, from magic, and so on. His test of a general explanation was its ability to incorporate the solution of particular problems. Descartes argued likewise at two levels, and this indeed was a general necessity in a period when the intellectual identity of the contemporary scientific movement was still open to misunderstanding by the learned world at large and when its methods and accepted styles of reasoning were still to some extent being established. Again, Charles Lyell, himself a lawyer, set out like a skilful lawyer to present his uniformitarian conception of geology as the only acceptable one and to discredit its hitherto accepted catastrophic rival. Charles Darwin similarly set out his argument in the Origin of species for evolution by natural selection like a legal brief: marshalling the evidence, demolishing rival explanations, proposing his own solution, raising difficulties against it, meeting them one by one, and finally concluding that his was the only plausible and acceptable explanation that could account for all the various categories of fact that had to be considered. By presenting his arguments in the wake of the statistical analysis of human economics which provided the persuasive analogy, Darwin was able to establish at one and the same time his scientific explanation by natural selection and a statistical conception of the economy of nature which belief in providential design had hitherto made widely unacceptable in biology. Persuasion has obviously been aimed at the diffusion of scientific ideas, both at the sophisticated level of the scientific community and also among the general public. Change in ideas has come about more easily in some scientific situations, periods and societies than in others. It has been easier to reject particular theories within an accepted system of general doctrine than to take the drastic step of rejecting the whole doctrine. The disposition to change, which has been

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so marked a characteristic of the whole modern history of the West, became within the same culture an essential part of the scientific movement over a period when innovation and improvement were also becoming the intellectual habit in art, theology, philosophy, law, government, commerce and many other activities. It was a matter of individual as well as collective behaviour: Kepler, for example, contrasts notably with some of his contemporaries and opponents in controversy by his readiness to sacrifice a favourite theory to contrary evidence. The conscious cultivation and reward of a disposition towards innovation began in Western society perhaps first in the technical arts and philosophy, but it has been transmitted elsewhere mainly with Western commerce and science. A comprehensive historical inquiry into the sciences and arts mediating man's experience of nature as perceiver and knower and agent would include questions at different levels, in part given by nature, in part made by man. These correspond to the three kinds of commitment. Thus at the level of nature there is historical ecology: the reconstruction of the physical and biomedical environment and of what people made of it. The sources and problems of historical ecology, both human and physical, range from those of archaeology and palaeopathology to those of the history of climate, technology, medicine, agriculture, travel and art. Historical problems at all levels require scientific and linguistic knowledge to control the view of any present recorded through the eyes and language of those who saw it. They may require also historical knowledge of religion and of artistic style, economic theory, and other analytical disciplines. At all levels comparative historical studies of the intellectual and social commitments, dispositions and habits, and of the material conditions, that might make scientific activity and its practical applications intellectually or socially or materially easy for one society, but difficult or impossible for another, have an immediate relevance for the diverse cultures brought into contact with the science, medicine, technology and commerce of our contemporary world. It is only comparatively recently, and only in highly industrialized societies, that science and technology have risen to a dominant position among the vastly various concerns and interests that throughout history have moved men to thought and action. What have been the numbers, social position, education, occupations, institutions, private and public habits, motives, opportunities, persuasions and means of communication of the individuals taking part in scientific activities in different periods and societies? What critical audience has there been to be convinced by, use, transmit, develop, revise or reject their arguments? Where scientific and analogous inquiries have interested only a scattered minority, what opportunities have existed for establishing agreement on principles and methods, or even continuity between generations? How, for example, were these maintained in the ancient Mediterranean, or in China or

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Science, Art and Nature in Medieval and Modern Thought

India? In comparison, what intellectual or moral or practical commitments motivated the teaching and learned institutions of medieval Islam and of medieval and early modern Christendom, and came in the last to establish effective conditions of education and research for an explicit scientific community? How have the conditions for science and for technology differed? What intellectual needs or habits or intentions or social pressures have there been within different philosophical or scientific or technical groups to bring about a consensus of opinion in favour of innovation or of conservation? How have scientific ideas and activities been located within the values of society at large? What has been the intellectual or moral or practical value given to science in different societies, within a range of interests so divergent as those indicated, for example, by a predominant concern with a theological scheme of human responsibility and destiny, by the cultivation of the arts or of literary learning or of logic and philosophy, by the pressures and expediencies of politics, by the needs of war, trade, industry, transport or medicine? What has been the appeal of pure intellectual curiosity and philosophical satisfaction, of a religious search for God in nature, of a desire for intellectual or moral or social or political reform, of utility in the senses either of the material improvement of the human condition or of industrial or commercial or political or military power or gain? What social or commercial or political interests have promoted or resisted scientific research and technical innovation, and the diffusion and application of ideas, discoveries and inventions? To what extent does innovation breed innovation? What was the costeffectiveness of the inventions described in histories of technology, who used them, and with what consequences? It would be relevant to compare the criteria of evidence and decision used in science or in medical diagnosis and prognosis with those used in commerce and industry, in law courts, and in choice of policies by governments. Relevant also are mentalities indicated by philosophical and social programmes and responses in relation to their social, economic and sometimes military context. So too are the intellectual and social responses of society at large to making man an object of scientific inquiry and treatment. Likewise what external pressures and internal dispositions have operated in the intellectual and practical responses of one culture to another, of Islam to Greek thought, of medieval Western Christendom to Islam and to farther Asia, of early modern Europe to China and Japan and India and the New World, of Japan in its early history to China and in the sixteenth and nineteenth centuries to the West, of China throughout its history to any other culture, of the so-called developing countries now to the industrially developed? The essence of effective scientific thinking has been the advancement of knowledge through the identification of soluble problems. What have been the

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sources of new intellectual perceptions? How have the intellectual commitments or dispositions or habits or the technical potentialities of an individual or a group or period either promoted or discouraged creative discovery and technical invention? How have these interacted with the conditions for intellectual change or conservation in the philosophical, technical, social and materal ambience of science? To what extent has the internal logic of science taken over from features of this ambience, accidental analogies, or suggestions for new hypotheses or styles of thinking? What has been the part played in the initiation of progress by breaches of conceptual frontiers leading to asking new questions, seeing new problems, accepting new criteria of valid demonstration and cogent, satisfactory explanation? Scientific thinking has commonly progressed through periods of critical analysis bringing novel forms of speculation about the discoverable in nature in anticipation of technical inquiry. Obvious examples are the critique of the Aristotelian doctrine of qualities and causation preceding the new science of motion established from Galileo to Newton, the atomic speculations preceding the quantitative atomic theory promoted by John Dalton, and the evolutionary speculations preceding the scientific organization of the evidence and theory finally achieved by Charles Darwin. The older conceptions were discarded and the new first entertained by rethinking; but the new ideas became established as scientific knowledge only by technical scientific research. Only after that were their speculative precursors given a retrospective scientific significance. Of the essence of the Western scientific tradition, and of the evidence for its history, have been the self-conscious assessments of its presuppositions, performance and prospects that have continued through many changes of context from Archytas and Aristotle down to the latest disputes among scientists, philosophers and historians. The critical historiography of science has been an integral part of the scientific movement itself. Such assessments both of current science and of the history of science have had various purposes. Those made in medieval and early modern Europe aimed usually to monitor the identity and intellectual orientation of the contemporary scientific movement and to define its methods and criteria of acceptability of questions and answers. They were made during a long period when increasing scientific experience, historical scholarship, and awareness of other contemporary cultures enabled Europeans to measure their own scientific orientations and potentialities against those of diverse earlier and contemporary societies. The range of modern assessments points to the range of sources for an interpretation. The radical variations in contemporary assessments and their changes with time and context and individual disposition provide unique and indispensable primary evidence in historically taking the measure of the intellectual and technical and moral equipment available in any scientific situation. An habitual search during this period at once for the best form of

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science, and for its best ancient model, projected the earlier into the contemporary tradition but with extended power. Through the variations of the scientific movement there has run a consistency of development in conceptions of explanation and method. The growth of particular scientific knowledge has carried in its wake a growth of general understanding of scientific thinking and its varieties. This consistency clarifies the historical variety of accepted explanations and methods diversified by intellectual commitments and subject-matters. Both in the perception and solution of problems within the theoretical and technical possibilities available, and in the justification of the enterprise whether intellectual or practical or moral, the history of science has been the history of argument. Scientific argument forms the substance of the scientific movement, a discourse using experiment and observation, instruments and apparatus, mathematical reasoning and calculation, but with significance always in relation to the argument. The scientific movement brought together in its common restriction to answerable questions a variety of scientific methods, or styles of scientific inquiry and demonstration, diversified by their subject-matters, by general conceptions of nature, by presuppositions about scientific validity, and by scientific experience of the interaction of programmes with realizations. Throughout, methods of yielding accurately reproducible results were required equally by the practical commitment of technology and the arts to the control of materials, and by the theoretical commitment of science to establishing regularities or causal connections within a common form of demonstration. An historian needs to ask both what theories of scientific method contributed to science, and what methods were used by scientists. We may distinguish in the classical scientific movement six styles of scientific thinking, or methods of scientific inquiry and demonstration. Three styles or methods were developed in the investigation of individual regularities, and three in the investigation of the regularities of populations ordered in space and in time. Each arose in a context in which an assembly of cognate subject-matters was united under a common form of argument. Thus (i) the simple method of postulation exemplified by the Greek mathematical sciences originated within the common Greek search for the rational principles alike of the perceptible world and of human reasoning. This was the primary ancient model, uniting all the mathematical sciences and dependent arts, from optics and music to mechanics, astronomy and cartography, (ii) The deployment of experiment, both to control postulation and to explore by observation and measurement, was required by the scientific search for principles in the observable relations of more complex subject-matters. Starting with the Greeks, the strategy of experimental argument was elaborated in medieval and early modern Europe as a form of reasoning by analysis

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and synthesis in which the point at which experiment was brought into the argument, either for control or for exploration, was precisely defined. Moves towards quantification in all sciences may be traced to the general European growth both of mathematics and of the habits of measurement and recording and calculation arising from need in some special sciences, as in astronomy, and in the practical and commercial arts, where new systems of weights and measures and of arithmetical calculation were first developed. The scientific experimental method derived from the union of these practical habits with the logic of controls, with further quantification through new techniques of instrumentation and mathematical calculation. The rational experimenter was the rational artist of scientific) inquiry, (iii) Hypothetical modelling was developed in a sophisticated form first in application to early modern perspective painting and to engineering, and was then transposed from art into science as likewise a method of analysis and synthesis by the construction of analogies. The recognition that/in the constructive arts theoretical design must precede material realization anticipated the scientific hypothetical model. Each proceeding to a different end, artist and scientist shared a common style. The imitation of nature by art then became an art of inquisition; rational design for construction became rational modelling for inquisitorial trial, (iv) Taxonomy emerged first in Greek thought as a logical method of ordering variety in any subject-matter by comparison and difference. The elaboration of taxonomic methods and of their theoretical foundations may be attributed to the need to accommodate the vast expansion of known varieties of plants and animals and diseases following European exploration overseas, with attempts to relate diagnostic signs and symptoms to their causes and to discover the natural system that would express real affinities, (v) The statistical and probabilistic analysis of expectation and choice developed in early modern Europe again took the same forms whether in estimating the outcome of a disease, of a legal process, of a commercial enterprise, or natural selection, or the reasonableness of assent to a scientific theory. The subject-matter of probability and statistics came to be recognized through attempts to accommodate within the context of ancient and medieval logic situations of contingent expectation and uncertain choice, followed by the early modern discovery of the phenomenon of statistical regularities in adequately numerous populations of economic and medical and other events. Thus uncertainty was mastered by reason and stabilized in a calculus of probability, (vi) The method of historical derivation, or the analysis and synthesis of genetic development, was developed originally by the Greeks and then in early modern Europe first in application to languages and more generally to human cultures, and afterwards to geological history and to the evolution of living organisms. The subject-matter of historical derivation was defined by the diagnosis, from the

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common characteristics of diverse existing things, of a common source earlier in time, followed by the postulation of causes to account for the diversification from that source. Clearly all this scientific diversity can be understood only within the diversity and the changes of thought in the whole historical context. The history of science is the history of argument: an argument initiated in the West by ancient Greek philosophers, mathematicians and physicians in their search for principles at once of nature and of argument itself. Of its essence have been its genuine continuity, even after long breaks, based on the study by any generation of texts written by its predecessors, its progress equally in scientific knowledge and in the analysis of scientific argument, and its recurrent critique of its moral justification. A subtle question is what continued and what changed through different historical contexts, in the scientific argument and in the cultural vision through which experience is mediated, when education and experience itself could furnish options for a different future. Styles of thinking and making decisions, established with the commitments with which they began, habitually endure as long as these remain. Hence the structural differences between different civilizations and societies and the persistence in each despite change of a specific identity. Hence the need for historical analysis in the scientific movement of both continuity and change. These like most human behaviour begin in the mind, and we its historians who belong at the same time to its history must look in a true intellectual anthropology at once with and into the eye of its beholder.

REFERENCES 1. This paper is based on the historiographical introduction to my book, Styles of scientific thinking in the European tradition (Gerald Duckworth, London, 1994), which contains full documentation and bibliography; cf. also A. C. Crombie, "Science and the arts in the Renaissance: The search for truth and certainty, old and new", History of science, xviii (1980), 233-46; idem, "Historical commitments of European science", Annali del' Istituto e Museo di Storia della Scienza di Firenze, vii, part 2 (1982), 29-51; idem, "What is the history of science?", History of European ideas, vii (1986), 21-31; idem, "Experimental science and the rational artist in early modern Europe", Daedalus, cxv (1986), 49-74; idem, "Contingent expectation and uncertain choice: Historical contexts of arguments from probabilities" in The rational arts of living, ed. by A. C. Crombie and N. G. Siraisi (Northampton, Mass.: Smith College studies in history, 1987): the first three of these papers are included in A. C. Crombie, Science, optics and music in medieval and early modern thought (Hambledon Press, London, 1990). 2. Michael Faraday, Experimental researches in electricity, i (London, 1839), 515; cf. pp. 195 ff. 3. John Tyndall, Faraday as a discoverer (London, 1868), 53-55.

2

The Western Experience of Scientific Objectivity * At a depressing period of the Pelopennesian War, Thucydides included in his famous account of the moral disintegration of society in revolution two points of immediate relevance to a discussion of the European experience of scientific objectivity. Revolution had brought many and terrible sufferings upon the Greek cities. Unscrupulous mendacity and opportunist treachery masqueraded as superior cleverness, the sweeter if a rival trusting a pledge of reconciliation were taken off his guard. Anyone who excelled in evil and anyone who «prompted to evil someone who had never thought of it were alike commended*. Conspirators used fair words for guilty ends with cynical confidence that others would hypocritically welcome them as cover for their own moral cowardice or indifference. United only through complicity in crime, greed and envy against the moderate and the honest, «neither had any regard for true piety, yet those who could carry through an odious deed under the cloak of a specious phrase received the higher praise». 1 Among all this violence against both truth and person he noted interestingly : «Words had to change their ordinary meaning in relation to things and to take that which men thought fit*. And, he argued, these calamities of behaviour «have occurred and always will occur as long as the nature of mankind remains the same». For «human nature, always rebelling against the law and now its master, gladly showed itself ungoverned in passion», setting gain above justice and revenge above religion : «For surely no man would put revenge above religion, and gain before innocence of wrong, had not envy swayed him with her blighting power» 2 . It was the same in the plague of Athens. Strong and weak were swept indifferently away, victims with unquench* 'H (ivaxotvoxjis aveYV<J>a6y) UTT& TOU xaOvj^ToO ERWIN SCUEUCU, 8i6n 6 et
1. Peloponnesian War, iii.82. 2. Ibid, iii.84.

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able thirst drank much or little with common failure of relief, physicians could find no remedy and perished themselves, prayers and other measures all proved equally futile and were given up, and men thus bereft of fear of any law divine or human «now coolly ventured on what they had formerly done in a corner*1. Yet from those who had suffered and recovered from the plague, the sick and dying received help and compassion. Influenced by medical thought, Thucydides looked for the causes of social as of individual disorders in a theory of human nature, expressing in stable language the dependability of natural law. He offered a commitment to reasoned beliefs and actions against which to measure the motivation of behaviour. This may suitably introduce the subject of my brief contribution to this discussion of objectivity and culture, which is the interaction of reason, belief and motive in the history of science, medicine and technology. I shall argue that in order to understand our culture, we are not only advised but obliged to study the intellecutal attitudes and achievements of societies that have formed its history remote in time and seemingly remote in character from the immediate present. Yesterday's events can be the least relevant to educated understanding. In the spirit of a symposium evidently based on the belief that one main reason for studying history is to throw light upon ourselves, a belief which I fully share, there are various ways of doing this in the history of science, medicine and technology. It hardly now needs saying that in this field, as mutatis mutandis in all intellectual and social history whether of philosophy, law, theology or whatever, the particular thinking found in any period can be properly understood by us only by relating it to the categories in which nature, and man as a participant in and student of nature, were understood in the societies and by the individuals with which we are concerned. We can study the history of science as a kind of intellectual anthropology. We can make a natural history of intellectual and moral behaviour in situations presenting questions for decision. The enlightenment that we may derive from this kind of historical experience is like that we get from foreign travel, especially outside the areas of Western culture. We expose ourselves to the surprise of discovering that thinkers so effective in solving problems which we seem to be able to recognize should be able to do so within the context of such a variety of aims, categories and presuppositions, mostly very different from our own. We encounter also societies and individuals who find 1. Ibid, ii.54.

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15

intellectual satisfaction in categories of thought and explanation not aimed at solving scientific or technical problems at all but expressing some quite different purpose. Yet in looking for a comparative history or anthropology of approaches to nature, putting ourselves into the minds of those we are studying and trying to understand their questions, we need to control relativity by the contrasting light of the objective continuity of cultural tradition. Science has developed in the characteristically rational Western tradition as an approach to nature effectively competent to solve problems. Before the general direction towards scientific knowledge had been decided, either in antiquity or in early modern times, two essential general questions remained open. It was an open question what kind of world men found themselves inhabiting, and so it was also an open question what methods they should use to explore, explain and control it. The characteristically Western tradition of rational science and philosophy can be dated from the ancient Greek commitment to the decision of questions by argument and evidence, as distinct from custom, edict, authority, revelation, or some other source. The Greek philosophers and mathematicians at the same time committed the Western tradition to the belief that among many possible worlds, the world that exists is a world of exclusively self-consistent and discoverable rationality. In this way they introduced the fundamental conception of a scientific system, separately for each category of nature and collectively for every category. Pride in self-reliant intelligence, in skill of mind and hand which gave man mastery of earth and sea, of other living creatures, and of such difficult arts and sciences as writing, mathematics, astronomy and medicine, appears with the first Greek achievements in these fields in the fifth century B.C., notably in the Prometheus of Aeschylus. In the grasp and technical development of the logic of proof and decision by the ancient Greek philosophers, mathematicians and medics we may see the origins of our scientific tradition. They introduced decision into speculations about nature. The one world that actually exists did so in one discoverable way, which excluded others. Scientific thinking has proceeded and scientific knowledge has progressed ever since by such a logic of either — or, by decisions both about the general nature of the world and about particular questions each of which has committed the future towards one line of theory and away from others. Science has been recognized since Aristotle and Archimedes as a cumulative progress of knowledge, even through periods of the darkest gloom about the

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moral regress of mankind. 1 These rational commitments applied moreover as much to decisions about moral values and principles showing what ought or ought not to be done, as to the decisions of science about what was or was not the case. Aristotle meant his ethics to be derived as systematically from a theory of human nature as his physics was from a theory of matter and causation. To understand any historical culture we must then study its intellectual orientation and re-orientations through long tradition. The recovery of our own scientific culture after periods of external disaster or internal confusion has been the recovery of rational decision. In such a process we may see the origins of modern science in the rediscovery, exegesis and elaboration of the Greek model by medieval and early modern Europe. The rediscovery was made by a new society, with a different view of man and his place in nature and his destiny, a different theology and a different economy, but it was seen first, in the twelfth century, as a continuation of the ancient scientific movement. «Nothing is difficult unless you despair...», wrote the Englishman ADELARD OF BATH, translator into Latin of Euclid's Elements of Geometry and author of two works presenting his vision of natural philosophy early in that century; «Therefore hope and you will find the capability. For I shall be the more able to shed light on the matter, from the assumption of the constancy and certainty of principle*.2 Looking forward from the shoulders of giant predecessors,3 ADELARD and his contemporaries saw unlimited potentialities for the elaboration of scientific knowledge long before these were actually discovered in application to any of the numerous and diverse new problems and subject matters which we can now look back on. ADELARD'S countryman ROGER 1. Cf. E. R. DODDS, The Ancient Concept of Progress (Oxford, 1973) 1 sqq.; A. G. GROMBIE, «Some attitudes to scientific progress : ancient, medieval and early modern», History of Science, xiii (1975) 213 sqq., and also for the argument above Scientific Change, Introduction (London, 1963) 1 sqq., «Historical commitments of biology», The Britsh Journal for the History of Science, iii (1966) 97 sqq. 2. ADELARDUS VON BATH Quaestiones naturales, ed. M. MULLER (Beitrage zur Geschichte der Philosophic des Mittelalters, xxxi.2; Minister, 1934) 58; cf. T. STIEFEL, «The heresy of science : a twelfth-century conceptual revolution*, Isis , ixviii (1977) 347 sqq. 3. Cf. CROMBIE, «Some attitudes...» (1975) 220, «Historians and the scientific revolution*, Physis, xi (1969), and also «The relevance of the middle ages to the scientific movement)) in Perspectives in Medieval History, ed. K.F. DREW and F. S. LEAR (Chicago, 1963) 35 sqq.; citing myself here and elsewhere for ease of reference and further bibliography.

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BACON in the next century likewise looked to the recovery of a greater past as the first step towards a happier future, and this remained the common outlook of Christendom until some four hundred years later when modern scientific discovery had got confidently under way. Programmes for intellectual reform such as those of ROGER BACON and FRANCIS BACON, DESCARTES and others before and many since throw a special light on an essential characteristic of the Western scientific tradition : its persistent attention to the definition of norms of rational thought, applying to every kind of subject-matter and every aspect of life. The light may be as special as the reforming vision and historians are well advised to combine it with that of established contemporary practices. Together they illuminate the beliefs and motives arising from the whole intellectual and social ambience, as well as the scientific experience, which have given diversity to definitions of the rational, the possible, the desirable and the acceptable. ROGER BACON'S vision of rational human happiness and dignity foresaw the restoration of one true wisdom founded on the Scriptures equally with rational science as he conceived it. * Visions of happiness, of science and of BACON himself have all since changed selectively with human expectations. Discussions of the discoverable and the discovered as well as of the reputations of predecessors show how the commitments at a particular time of an individual or a society to general beliefs about nature, man and science can make certain kinds of question appear cogent and give certain kinds of explanation their power to convince, and exclude others, because they establish, in anticipation of any particular research, the kind of world that is supposed to exist. They give satisfaction because the supposedly discoverable has been discoverer and they point to what to do in research. The comparative historical study of the intellectual and social commitments that may make certain kinds of scientific understanding, discovery or practical application intellectually and socially possible in one society, but difficult or impossible in another, has an immediate relevance for the diverse cultures brought into contact with the science of our contemporary world. Its matching relevance to our understanding of ourselves may be illustrated by trying to identify some very general characteristics of our continuing rational tradition. After the medieval West had received its first intellectual impetus from antiquity with the recovery of Euclidean geometry and of Ari1. Gf. CROMBIE, «Some attitudes...» (1975) 221-2.

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stotelian logic and later of natural philosophy in the twelfth and thirteenth centuries, the philosophical community of the universities may be credited with two major achievements : the grasp and elaboration of the construction of a deductive explanatory system, whether in logic, mathematics, cosmology or physiology; and the grasp and elaboration of logical precision in the use of evidence in deciding an argument, including decision by experiment. Characteristic of this intellectual inheritance, at least as it was received, was a geometrical or mathematical rationalism which is evident, for example, in Euclid's two fundamental treatises on optics and on music. * Each demonstrated a stable relation between perceiver and perceived by postulating in the one linear rays of vision and in the other motions propagated from a sounding body, from whose specified angles or speeds were demonstrated what specific sizes and shapes must be seen or pitches and intervals heard. Reaching the West first mainly through Boethius and then through Arabic compendia (Euclid's texts became known only in the sixteenth century), these theories were made in the twelfth century part of philosophical programmes for the sciences which included also : «The science of engines (scientia ingeniis)... «which taught «the ways of contriving and finding out how natural bodies may be fitted together by some artifice according to number, so that the use we are looking for may come from them». 2 A programme is not an achievement but we are looking for mental attitudes, and it seems to me that we find already expressed in such words that urge towards rational analysis and ingenious contrivance for the mastery of nature, which was to be expressed in action by the artists, engineer-architects and musicians who from the fourteenth century were to give such an impressive practical demonstration of their theoretical control of visual space, material construction and instrumented sound. These groups introduced a new style of rationality into Western culture, adding to the logical control of argument and

1. Cf. CROMBIE, «The mechanistic hypothesis and the scientific study of vision*, Proceedings of the Royal Microscopical Society, ii (1967) 3 sqq., Mathematics, music and medical science*, Actes du XHe Congres international d'histoire des sciences 1968, i.B (Paris, 1971) 295 sqq., and for full discussion Styles of Scientific Thinking in the European Tradition (Gerald Duckworth, London, 1994). 2. DOMINICUS GUNDISSALINUS, De divisione philosophiae, ed. L. BA.UR (Beitrage. .., iv. 2-3; Miinster, 1903) 122; cf. LYNN WHITE j r., «Medieval engineering and the sociology of knowledge*, Pacific Historical Review, xliv (1975) 1 sqq.

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calculation achieved by the academic philosophers and mathematicians a matching control of materials. All these arts and sciences, LEONARDO DE VINCI insisted were «born of experience, mother of all certainty*,1 designed in the mind and issued through the hands. Typically of his period, he saw the art of design and the science of nature both as expressions of the rational necessary laws laid down by the art of Deus naturae artifex.* There is a parallel artistic rationalism in his philosophical contemporary MARSILIO FICINO'S vision of man acting like nature from rational principles within but freely and inventively, coming through his intellectual and material constructions to know by imitation God's creations, and becoming no longer nature's slave but rival. The goals of the arts should not be confused with those of philosophy and the sciences, but it does not seem difficult to recognize both the early modern arts and the early modern sciences as typical products of the same society. In both, experience of nature was mediated through the style and interests of a tradition. They were linked through their common foundation on rational and quantitative theory and also on knowledge of instruments and machines. Some historians8 have suggested that a Western disposition to base not only these, but activities of many different kinds, on a common foundation of reason and calculation may offer a possible explanation of the unique development of modern science in the West. Other examples are the rational quantification of time in the calendar and the abstract units of the mechanical clock; the introduction of mathematical cartography related to astronomical navigation; and the methods of book-keeping, commerce and fiscal administration, beginning in thirteenth-century Italy, operated by the calculation of exchanges and obligations in increasingly standardized abstract units. Can it be supposed that the habits of reason and calculation growing up through Western society in all these diverse activities provided an efficacious condition for the rise of mathematical and experimental science, that for example the habit of weighing, measuring and accounting in each of these activities encouraged the 1. Treatise on Painting : Codex Urbinas Latinus 1270, i.19, transl. A. P. McMahon, i (Princeton, 1956) 11; cf. CROMBIE, .Styles... 2. MARSILIUS FICINUS, Theologica Platonica, xiii.3 (Opera, Basileae, 1576) 295-7; Crombie, ibid. 3. Gf. especially MAX WEBER'S famous Introduction (1920) to The Protestant Ethic, transl. T. PARSONS (New York, 1958); also CROMBIE, «Quantification in medieval physics*, Isis, Hi (1961) 143 sqq.

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same habit in the others. The possible connection between methods of numerical recording in commerce and in theoretical and practical sciences is just one specific question for research. Does this all indicate a mental and social disposition, a dedication of will as much as of intelligence towards enlightenment and power, that provided a uniquely favourable set of circumstances enabling the West to exploit the intellectual opportunities offered by the recovery of Greek science, with an energy and purpose found in no other society. However these large questions of intellectual sociology are to be answered, dedication to quantity and logic did eventually lead to decisions on the fundamental question of identity both of science and of nature. During the sixteenth century the kind of physical world men thought themselves to inhabit, what they should ask about it, the appropriate methods of investigating it, what constituted a satisfactory explanation of it, and what could be known about it for certain, still remained in varying degrees open questions for the philosophical and scientific community at large. Dissatisfaction with the Aristotelianism established in the universities as the common basis for all education was encouraged by the arrival of other philosophies in credibly systematic form. The debates touched on natural philosophy sometimes at length, but within the consideration of general problems of knowledge and existence. They promoted not so much the accumulation of the technical content of science from one generation to the next, as the specificity of their intellectual outlook, commitment and expectation. As much part of this specificity, as of that of any intellectual reorientation, and at least as much its engine as the achievement of objectively successful scientific progress, was the style and method of opposition, of disagreement as well as agreement, of dealing with tension over the whole range of culture. The style of intellectual and moral behaviour in natural philosophy, in the individual and social processes by which discoveries and inventions have been made and have come to be accepted, may be illuminated as much by that in religion, law or art as by the natural philosophy itself. This evident, for example, in the styles of the thirteenth-century attempts to combine the newly translated Aristotelian philosophy with the theology of an omnipotent and providential creator, of the challenges made by the new Platonism of the fifteenth century and by the new scepticism of the sixteenth, and of GALILEO'S quantitative science as simply the latest in a succession of old and new philosophies. In some areas of natural philosophy as well as of religious, legal and

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artistic theory and practice, old and new remained in uncertain competition long after GALILEO was dead. It was nevertheless the generations of GALILEO and DESCARTES who finally clarified and defined science as a mode of rational thinking in the modern world and who gave it a recognizable and enduring identity in relation to other fields of inquiry and decision. The first half of the seventeenth century is then a genuine turning-point in the potentialities of Western culture, throwing light on what came both before and after. From that time a scientific community has come into existence with conditions of education and communication providing for both agreement and disagreement by a specific kind of rationality, and now globally providing standards which even if not always realized are a normal requirement for objective scientific success. Of immediate relevance for us all is the relation of this specific rationality to beliefs about man's moral nature and true end. This side of paradise, moral tension sacred or profane must accompany any framework of thought or society that gives meaning to existence. An obvious characteristic of the Western scientific tradition is that it has been from the beginning a moral enterprise as much as a means of solving physical problems. One form of this was the view established in different ways by Plato, Aristotle, the Stoics and other ancient philosophers of nature as at once a deductive system and a moral order, a view that has profoundly affected both the specifib intellectual character and the political role of science in Western culture. Plato's vision of knowledge producing virtue, and of the rational progress of human knowledge through mathematical abstraction to the eternal truths expressing the morally as well as intellectually normative economy and harmony of the real world, has deeply influenced the whole history of scientific explanation and education. It was used to justify the systematic introduction of mathematics into modern university teaching in the sixteenth and seventeenth centuries.1 The conception of the world as a work of divine art, whether in its Platonic, Aristotelian, Stoic or Christian versions highly charged with moral values of economy, proportion and fitness, has provided an enduring model and sufficient reason for physical behaviour : from the perfect circles of ancient cosmology and the perfect ancient consonant ratios between low numbers, to KEPLER'S planetary intervals, the eighteenth-century principle of least action and practically the whole theory of biological adaptation 1. GROMBIE, Styles. . .

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Science, Art and Nature in Medieval and Modern Thought

before CHARLES DARWIN. Matching this in Christian thinking was the conception of a benevolent Creator inviting man to use his gifts of reason and the senses to uncover the designs in nature towards his providential end and to teach and use his knowledge for the good of all mankind. The tensions generated by morally charged cosmology have come from its encounters with other sources of belief or with original thought. The moral charge quickly becomes a political charge. Some historians have seen the deepest consequences for the potentialities of scientific thinking in Western culture in encounters at the level of theology, most dramatically in that brought about in the thirteenth century by the introduction into the Latin West of the Aristotelian theory of the world as a necessary and eternal emanation from the First Cause. This carried with it the powerful belief that men could discover not only how the world was constructed, but also the necessary reasons in the First Cause why it must be so, was best so and could not be otherwise; a belief which Christian theologians and philosophers quickly rejected in defence of the freedom and responsibility of both God and men. It has been argued that by maintaining the fundamental revelation of God's creative freedom, they maintained also the liberty of man's inquiring mind; for man was then free to explore hypothetically the possible worlds which God might have created had he chosen.1 Whatever the historical cogency of this particular argument, the rejection then or later of any form of rigid historical determinism is by definition an essential condition for belief in free inquiry. Moreover even so qualified a secularization of the world must surely have been a liberation for both theology and natural science, a liberation to be extended when such divine attributes as economy were converted into variational principles of nature or regulative principles of science. But when one remembers some aspects of the extended cosmological debate, continuing through GALILEO'S Copernican controversies, the concern for the providential government of the world raised by geology and then by Darwinian evolution, and the agonies over man's alleged devaluation in our own century, one must admit that the meaning of this separation of categories is not one which our society has hastily sought. It may be argued that it was above all GALILEO who showed how to disembarrass nature of its moral charge, and who through his in1. Cf. especially PIERRE DUHEM, Etudes sur Leonard de Vinci ii (Paris, 1909) 411 sqq.; also CROMBIE, «The relevance . . . » (1963) 40 sqq.

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dividual thinking, public controversies and personal tragedy focussed the Western scientific tradition as a moral enterprise of freedom for the inquiring mind. GALILEO'S assumption of the right to intellectual freedom and truth represents perhaps the greatest moral contribution of science to the humane conception of a responsible, rational man. In defining the identity of natural science within contemporary intellectual culture, he distinguished both nature and science objectively from human wishes. In nature man was not the measure of all things. Engineers who attempted the impossible «as if with their engines they could cheat nature* and her ((inviolable laws» x cheated only themselves and their employers. For «Nature, deaf and inexorable to our entreaties, will not alter or change the course of her effects ».2 Nature could not be exploited in the spirit of magic or commerce, interrogated in the style of a legal hearing, or made the subject of mere academic disputation or literary search for philosophical or theological concordance. He himself, «being used to study in the book of nature, where things are written in only one way, would not be able to dispute any problem ad utranque partem or to maintain any conclusion not first believed or known to be true.»3 To all attributions of moral design in nature he replied : «We must not ask nature to accommodate herself to what might seem to us the best disposition and order, but we must adapt our intellect to what she has made, certain that such is the best and not something else.»4 He begged theologians, in his argument for the true moral agreement between the true cosmology and theology but in categories which logically did not meet, that they would consider with all care the difference that there is between opinable and demonstrative doctrines; so that, having clearly in front of their minds with what force necessary inferences bind, they might the better ascertain themselves that it is not in the power of professors of demonstrative sciences to change opinions at their wish, applying themselves now on one side and now on the other; and that there is a great difference between commanding a mathematician or a philosopher and directing a merchant or a lawyer; and that the demonstrated conclusions about the things of nature and of the heavens cannot be changed with the same ease as 1. GALILEO, Le mecaniche (c. 1593; Le opere, ed. naz.., ii, Firenze, 1968) 155; GROMBIE AND CARUGO , Styles . . . 2. GALILEO, «Terza Lettera delle macchie del Sole* (1612; Le opere, v) 218; GROMBIE, ibid. 3. GALILEO in 1612 (Le opere, iv) 248; GROMBIE, ibid. 4. GALILEO in 1612 (Le opere, xi) 344; GROMBIE, ibid.

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opinions about what is lawful or not in a contract, rent or exchange.1 The issues over which GALILEO felt obliged to make his stand, paralleled before and since whenever reason has seemed to challenge other sources giving meaning to existence, have made him from his own lifetime an historical symbol of the conflict of loyalties that can take place both within the minds of individuals, and externally in the relation of free inquiry to the habits of society and its institutions. GALILEO asserted the right to the truth as a moral norm for all men, the unavoidable objective truth. He claimed freedom to find and state the truth as an established right with precedence in all policy, and in the long run essential for all good policy. He knew the price of his political failure, writing to a friend in 1635 from his perpetual house-arrest at Arcetri: «I do not hope for any relief, because I have not committed any crime. I could hope for and obtain mercy and pardon if I had erred, for faults are matters upon which a prince can exert mercies and dispensations, whereas upon someone who has been innocently condemned it is convenient to be rigorous, so that it seems that it has been done according to the law.»2 But, he continued, his conscience was clear, and his hope for the acceptance of truth remained undiminished as he went on to produce what became his most distinguished contribution to science. Some private notes he wrote during that last Copernican campaign have an obvious application to many later situations : In the matter of introducing novelties. Who doubts that the novelty just introduced, of wanting minds created free by God to become slaves to the will of others, is going to give birth to very grave scandals? And that to want other people to deny their own senses and to prefer to them the judgement of others, and to allow people utterly ignorant of a science or an art to become judges over intelligent men and to have power to turn them round at their will by virtue of the authority granted to them-these are the novelties with power to ruin republics and overthrow states... Be careful, theologians, that, if you want to make the propositions concerning the movement and the rest of the Sun and of the Earth a matter of faith, you will expose yourselves to the risk of being in need of condemning perhaps in the long run as heretical those who asserted that the Earth stays at rest and the Sun moves from one 1. GALILEO, Lettera a Madama Cristina di Lorena (1615; Le opere, v) 326; CROMBIE, ibid., and «Sources of Galileo's early natural philosophy;* in Reason, Experiment, and Mysticism in the Scientific Revolution, ed. M.L. RIGHINI Bonelli and W.R. Shea (New York, 1975) 157 sqq. 2. GALILEO, Le opere, xvi., 215; CROMBIE, Styles. . .

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place to another : I say in the long run, when it has been demonstrated by the senses or by necessity that the Earth moves and the Sun stays fixed... Your doctrines are the new ones that harm, as you want... to force the mind and the senses not to understand and not to see... With novelties you cause great ruins in religion.1 The generations of GALILEO and DESCARTES established the specific rationality of modern science and gave confidence to its methods of research and criteria of acceptability by defining it as the art of the soluble. The act of definition required first a restriction, the delimitation of the questions as well as of the answers to be admitted. The questions had to be answerable by acceptable means, eventually if not immediately. These generations came to see experimental science as a deliberate union of the theoretical search for reduction to common forms of explanation and logical mastery of argument achieved by philosophy, with the practical demand for accurately reproduceable results required by technology. Later came an expansion of the initial restriction to exclusively answerable questions in all realms of experience and thought, with a development and diversification of methods along with that of subject-matter and theory. Modern science has developed its power to solve problems by its selectivity and by its programme of reduction of more and more classes of phenomena to increasingly general theories. From this it has eliminated all values except truth and the aesthetic economy of theories which must also pass the test of truth, and all questions of motive and of the meaning of existence. To all other values and to all such questions its clear logic has made it explicitly neutral. Yet natural science has emerged as the rational norm in the Western search for universally and exclusively true principles in all regions of thougth and action. This has made it a notable source first of conflicting certitudes and then of disquiet in Western societies, and a notable solvent of the confidence of other cultures to which the West has brought not simply its science, medicine and technology but its questioning of the meaning men give to existence as a whole and to human life, decision and disease within it. The paradoxical culmination of reasoned decision in our time has been an increasing magnification of means with a matching neutralization of ends. The paradox lies in a contradiction between the powerful logic of science and the notion of a responsible individual, the notion that created science, if man's moral nature it held to be confined within that 1. GALILEO, Le opere, vii, 540 541, 544; CROMBIE, ibid.

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logic. In trying to understand human nature itself, by its programme of selection and reduction science inevitably eliminates all data irrelevant to its current problems and theories, but these may be the most relevant to existence and experience outside a particular scientific scheme. There are many examples of this in the study of perception.1 The scientific understanding of human nature built up from biological, neuropsychological and psychiatric theory inevitably falls into the pattern of any general system, which must logically eliminate from consideration each individual's unique consciousness of attention, intention, thinking, anticipation, logical and moral choice, decision, purpose, responsibility. These are irreducible, yet they belong to our experience. Some people seem to have found in our scientific culture a need to use the discovered regularities of human psychology and social behaviour to deny individual responsibility, to treat all human acts as caused, all sins as sickness,2 all social injustices and all crimes as products of the system. But this does not follow from evident experience, it lacks the commonsense of proportion supplied by humour, and it contradicts the possibility of reasoned science on which it is presumably based. If the logic of science must eliminate meaning from the individual who yet remains paradoxically responsible for it, the organization of modern industrial society is likewise neutral to all values except its own logic and yet imposes what we have learnt to call its own quality of life. It is as if our whole society were in the grip of a vast theory, a reflection of the specific rationality of science, obliged by necessity to gear its programme of selection and reduction to one end alone, the mindless competitive acquisition of material advantage and power. It is no accident that rational science and rational power have arisen together in the experience of nature. But must we accept the committal of our society whatever the political system, Western or Communist, developed or developing, towards this single goal? The specific rationality of science, mirrored in industrial society, has indeed obliged us now to recover and retain for the quality of life the responsible decisions from which the individual is eliminated by faceless organization, and by obsession with power and achievement which is only one expression of science. Thus science which as the truest available account of nature can yet offer us no moral values, yet also obliges us if we 1. Gf. R. L. GREGORY, Eye and Brain, (London, 1966) 122 sqq. 2. Gf. P. LAIN ENTRALGO, Mind and Body (London, 1955)

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are to remain civilized to seek reasons for restraint. Science can show us as individuals and as societies the consequences our actions may have for our well-being or our survival. The greatest gift of scientific reason to the practical arts of civilization has surely been to provide mankind with both a true guide for our actions and the material capability of choice. Through our scientific tradition, we have liberated ourselves both from ignorance and from a purely biological regime of existence. Science has given us responsible information and practical power for making the difficult decisions between combinations of good with bad in medical practice, in legal pleading of diminished responsibility (in a society concerned for its own welfare a persistent disposition or intention to lie must presamably disqualify from responsibility whether psychiatric, criminal or political in motivation), in the use of the environment and of natural resources, or in military need. But what reasons can be offered to restrain the powerful from doing whatever they have power to do for their own selfish advantage, against nature, against rivals, or against the weak? Why should those with the power not feel entitled to exploit all opportunities? It is a question as bleak for us as it was for Thucydides, in which the weak are restrained more than the strong only by their weakness. One answer of course would be to find agreement on the true moral nature and end of man. That belongs to paradise, to some extent perhaps to a paradise lost. The Christian view of cosmological and human history, inherited from Hebrew theology, was elaborated by St. Augustine as the fulfilling through an extended time of the providential purpose of the creation. This conception of the benevolent destiny provided for responsible man had already by the thirteenth century, for example in ROGER BACON, x given that evangelical flavour, that desire to discover and spread true knowledge, which has characterised the Western sense of mission in science as in religion. The geologists, biologists and mechanistic philosophers, both social and natural, whose thinking notably from the eighteenth century dismissed design from time and history, inevitably gave the mission of science a rather different flavour. If the order of nature and of society were simply sequences through time of states of statistical equilibrium, if time and history were merely a meaningless, open-ended, interminable succession, and if something like that was the whole truth about existence, 1. Cf. CROMBIE, «Some attitudes...» (1975) 222, and Styles. . .

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it could be argued that moral values could be regarded only with profound frivolity or profound despair. 1 Yet if the paradise of providence has been lost, Western scientific culture retains its sense of mission if only because, in a plural human society, it offers pragmatic agreement on specific limited ends. It offers also something deeper. Reasoned truth from which these gifts have come is hard to find and hard for fallen man to keep. It is hardest of all when truth is made ambiguous policy. The authors of an analysis published thirty years ago of the Soviet genetical disputes of that period distinguished among the modes of argument used what they felicitously called «alogical discourse», which intermixed with logical argument appeals to authority, heresy, practical utility and attributed motives. In the last especially it seems that the Marxist geneticists were following a procedure much favoured by LENIN. 2 The procedure has been well illustrated by C.S. LEWIS through the fictitious character of EZEKIALBULVER, who should perhaps be better known and who used to attribute his formula for political power to a dispute between his parents overheard at the age of three. His father was routed in an attempt to prove to his mother that the sum of the internal angles of a triangle is two right angles by her finally defeating reply, that he said that only because he was a man. Hence our word bulverism. The suggestio falsi intended in this procedure may take various forms. Bulver learnt from his mother that it was much more effective in dispute not to meet the reasoning of your opponent, but rather to fix him in a category of motivation from which all his reasoning and behaviour was made to follow. Whether the category was false or irrelevant did not matter. Another common version has the logical form of the vulgar : Why doesn't he stop beating his wife? I once had the pleasure of seeing Senator JOSEPH MCCARTHY routed by a witness who with clear head simply unpacked the innuendos loaded into the questions put to him. The procedure is of course political, its goal not truth but advantage, and its motives, to quote locally from another context, needed to «have very little to do with the arguments in which they were expressed». Whatever its form or context, in result : ((Technically it was a smear; but it was also a myth, and, 1. Gf. GROMBIE, «Some attitudes...)) (1975) 225; also Lettres incites de John Stuart Mill a Auguste Comte, publics avec les rgponses de Comte, ed. L. LEVY-BRUHL (Paris, 1899), especially Mill to Comte on 3 April 1844. 2. P.S. HUDSON and R.H. RICHENS, The New Genetics of the Soviet Union (Imperial Bureau of Plant Breeding and Genetics, Cambridge, 1946) 23 sqq.

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like all powerful myths, it retained its potency even when its credibility had gone*.1 To meet reasons with attributions of motive, to make words mean what you choose, may be thought an insult to human intelligence. To promote in the open innuendos started in malicious corners, in corners of universities as of wider worlds, may be thought an insult at least to common sense. Such forms of violence against both truth and person have become too obviously part of the disreputable procedure for political advantage in our time. Mean spirited, naively cynical and usually transparent, its impudent mendacity is calculated on the assumption that enough even of our ostensibly honest fellow men prefer almost any formula for self-delusion, hypocrisy or sanctimonious betrayal to facing an uncomfortable truth or an indisputable lie. Paradoxically, an attempt to persuade by means of something less than the truth need not be criminal. It is essential to legal defence when justice assumes innocence until guilt is proven. And in the following appraisal by a military correspondent there is a disturbingly inverted kinship with pastoral care for virtue : «In the communist world the truth or falsehood of a statement is much less important than its effect. The aim is not primarily to convey information but to induce a response*.2 Those who accept persuasion from the devil need a long spoon and when dealing with smaller monsters at least to cease to be naive. But nature cannot be cheated. Nor need men. Effective science demands standards of truth beyond treachery, and even of the treacherous. Its criteria offer a political warning, and a moral therapy. I have tried then to sketch how the intellectual and moral history of science, medicine and technology, looking back with unavoidable impressionism to the orientations of our culture, can illuminate the continuity as well as the mutations of the Western tradition of scientific objectivity which has now, whether in welcome or reluctance, become the property of most of the world. As intellectual history indeed, as scientific thinking studied through the reconstruction of its cultural ambience, this subject has been developed during two decades and more in my own university of Oxford, with enough momentum now to continue in that style, linked equally and necessarily with the sciences, the various other histories and philosophy. This does not of course 1. The Spectator (London, 15 March 1975) 306. 2. The Times (London, 10 September 1975) 14.

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preclude other lines of study, even those most peripheral to the central subject of scientific thought. A wish to impose a narrow view must surely reflect an immature conception of history, indeed an immature character, just as a pretence that history has been other than it has may reflect some more disreputable calculation.

3

Historical Perceptions of Medieval Science

Quanta juniores, tanto perspicaciores. William of Conches in his gloss on this phrase of Priscian epitomised the earliest perception of medieval science by those bright generations of secular scholars who effectively launched the modern scientific movement in the first half of the twelfth century. Their outlook was at once dependent and optimistic. For if 'the moderns are able to see better than the ancients', this was because 'the ancients had only the writings which they composed themselves, but we have all their writings and all those as well which were composed from the beginning up to our time. Hence we see more, but we do not know more'. He repeated the famous image of Bernard of Chartres: 'We are like a dwarf put on the shoulder of a giant. He sees farther than the giant not from his own size but from the size of his support'.1 So placed they saw a way to independence. They had witnessed, together with an intellectual revival, also the beginnings of a modest but pregnant technological revolution. They possessed, as a fundamentally essential assumption of all rational thinking, a strong belief in the dignity and intelligibility of man and nature and of the relations of God with his creation. 'The human mind was made', runs another phrase attributed to William of Conches, 'With the capacity to know all things . . . This is its greatest worth'.2 Likewise Adelard of Bath: Those who are now called authorities gained their first credence among those less adept only because they followed reason'. He demanded reason independent of authority, even if only to exchange authorities, for: 'Nothing is difficult unless you despair. Therefore hope, and you will find the capability'.3 The way to knowledge of nature was through training in the mathematical quadrivium, as Thierry of Chartres insisted in offering from Plato's Timaeus a rational exegesis of the cosmogony of Genesis. 1 E. Jeauneau, ' "Nani gigantum humeris insidentes": essai d'interpretation de Bernard de Chartres', Vivarium, v (1967) 79-99, see p. 84; cf. for a full treatment of the subject of this paper A.C. Crombie, Styles of Scientific Thinking in the European Tradition (London, 1994), and also Science, Optics and Music in Medieval and Early Modern Thought (London, 1990). 2 C. Ottaviano, Un brano inedito delta 'Philosophia' di Guglielmo di Conches (Naples, 1935) 19; cf. R.W. Southern, Medieval Humanism and Other Studies (Oxford, 1970) 39 sqq. 3 Adelard of Bath, Quaestiones naturales, hrg. von M. Miiller (Beitrdge zur Geschichte der Philosophic des Mittelalters, iv.l; Minister, 1923), 12, 58.

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Thierry, according to his epitaph, could see through all the perplexities of the seven liberal arts, and 'he made quite clear to everyone what was hidden in obscurity for Plato and Socrates'.4 This he could seem to do by a perspective of superior science, enriched by the new translations into Latin such as Adelard's version of Euclid's Elements from the Arabic. The history of science is the history of vision explored and controlled by argument: a vision and an argument initiated in the West by the ancient Greek philosophers, mathematicians and physicians in their search for principles at once of nature and of argument itself. Argument has been deployed in different styles, in different periods and contexts and in different subjectmatters, to justify a vision of the nature of things able to solve specific problems. Of the essence of the scientific movement have been its genuine continuity, even after long breaks, based on the study by any generation of texts written by its predecessors; its progress equally in scientific knowledge and in the analysis of scientific argument; and its recurrent critique, varying considerably in different historical contexts, of its presuppositions about nature, about scientific cogency and validity, and about the intellectual, practical and moral justification of the whole enterprise. A subtle question is what continued and what changed through different historical circumstances, in scientific argument and its criteria of cogency and validity, and in the cultural vision through which experience is mediated, when education and practice could furnish options for a different future. Styles of thinking and making both intellectual and practical decisions, established with the intellectual and moral commitments with which they began, are maintained by habit and education as long as these remain. From such commitments come the specific identities of cultures and the structural differences between different cultures and societies whose enduring persistence have become in our present world daily more evident. Vectorial treatment is of the essence of historiography, yet there can be therapy in viewing the still life of a present moment unrelated to past or future. We, then, the historians of the scientific movement, who belong at the same time to its history, must look in a true intellectual anthropology at once with and into the eye of its beholder. Historical perceptions of the scientific movement in the middle ages have from the start been mediated through interpretations of the past and present motivated by expectations of a desirable future, interpretations that have varied with visions of the nature of human existence and with degrees of historical knowledge, prejudice or ignorance. In the twelfth and thirteenth centuries the texts translated from the Greek and the Arabic, and the new compositions written in their light, were of two different kinds: those concerned primarily with general questions of knowledge and existence, and those concerned with specific problems in the mathematical and natural

4

A. Vernet, 'Une epitaphe inedite de Thierry de Chartres' in Recueil de travaux offert a C. Brunei, ii (Paris, 1955) 670; cf. Southern, Medieval Humanism.

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sciences. There could of course be mixtures of the two. In a philosophical community sharing a common education in all these subjects, both were seen to belong to an integrated intellectual whole. The first provided a general programme for investigating the nature of things, the second provided specific advances of knowledge. The interactions of programmes with realisations, and within those of episteme with techne, scientia with ars, have been central to the whole subsequent dynamics of the scientific movement. Medieval perceptions of the history of science (as distinct from perceptions of scientific problems as such) focused primarily on the programme of man's relation to God and to nature as his creation. The context of human existence was defined by the scheme of providential history presented by Augustine. Thus Hugh of St Victor, the most systematically historical of the early twelfthcentury scholars, in an universal history written on Augustinian lines, traced the restoration of the divine likeness in fallen man by the development of the arts and sciences. The arts and sciences, invented under the spur of practical necessity and reduced to rule by reason, had been brought to perfection before Christ. It was their fulfilment in the return of man to God's grace that was promised for the future. For this 'entire sensible world is like a sort of book written by the finger of God';5 and in the contemporary image of Bernard Silvestris: There, marked down by the finger of the Supreme Scribe, can be read the text of time, the fated march of events, the disposition made of the ages'.6 Roger Bacon with much greater knowledge a century and a half later likewise looked first to the recovery of a wiser past as an essential step towards a happier future. Again from Augustine, he remodelled the historical belief that God had revealed to the Hebrew patriarchs and prophets, long before the Greek philosophers, the plenitude of wisdom entirely adequate for human needs and the source of all the arts and sciences and of untold powers over nature. This had been lost in ages of sin and foolishness and revived by virtue, and it could be recovered again in man's long return from divine alienation only by keeping to true belief and moral law. Hence, in his analysis of the 'causes of error'7 and of scientific stagnation in contemporary Christendom, the moral emphasis on the habits of prejudice and vanity as well as ignorance making obstacles to truth, for it was the paramount duty of Christians to grasp the truth and spread it to all the world. When Bacon sketched his programme for the restoration of experimental and mathematical science, with the invention of flying machines and submarines and so forth, he was describing 5

Hugh of St Victor, Didascalicon, de studio legendi vii.4, ed. J.P. Migne, Patrologia Latino, clxxvi (Paris, 1854) 814; cf. ed. C.J. Buttimer (Washington, D.C., 1939), transl. J. Taylor (New York, 1961). 6 Bernard Silvestris, De mundi universitate, hrg. C.S. Barach und J. Wrobel (Innsbruck, 1986) 13; cf. M.D. Chenu, La theologie au douzieme siecle (Paris, 1957, 1976) 170. 7 Roger Bacon, Opus maius i.l sqq., 14, ii.9, iii.i, ed. J.H. Bridges, i (Oxford, 1897), iii (London, 1900).

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what he believed had been known already to the ancients. He cited with approval Seneca's respect alike for ancient wisdom and for intellectual progress of the elite who alone among foolish mankind would not misuse it, and he insisted that 'the study of wisdom can always increase in this life, because nothing is perfect in human discoveries. Hence we of a later age should supply what the ancients lacked, because we have entered into their labours, by which, unless we are asses, we can be aroused to better things; since it is wretched to be always using and never making discoveries. Christians should . . . complete the paths of the unbelieving philosophers, not only because we are of a later age and should add to their works, but also in order that we may bend their labours to our own ends'.8 He saw the recent and future progress of scientific knowledge as the product as much of the recovery of ancient texts, and the discovery by the learned elite of their true hidden meaning, as of the direct investigation of nature. Hence his vision of the reform of education and knowledge within a theological scheme of man's providential destiny in the fulfilment of time to the end of the world. Such theological interpretations of the history of the arts and sciences persisted in various forms and contexts for several centuries after Bacon, but a different style of historical orientation came to be offered by the humanist scholars and philosophers who from the fourteenth century established so much of the basic methods and conceptions of modern historiography. The pedagogic function of history, the effectiveness of interpretations of the past that carried with them formulae for present action, was well understood in antiquity. The Italian scholars who introduced the threefold division of European history into ancient, medieval and modern gave to these periods an evaluation beyond mere chronology. It seems to have been Petrarch who first used the term medius tempus with the sense of a dark age lasting for a thousand years until his own time, when Latin poetry was revived and Italian vernacular poetry reborn (renatum).9 He was offering a programme. The image of medieval darkness was repeated at the end of the fourteenth century by the Florentine historian Filippo Villani, who described certain events as happening 'in ancient, medieval and modern times (priscis, mediis, modernisque temporibusy. When Dante revived the art of poetry he 'recalled it as from an abyss of shadows into the light', just as painting was raised again to life in modern times first by Cimabue, who 'began to recall it to the imitation of nature', and then by Giotto, 'who not only can be compared with the illustrious

8

Ibid, ii.15, vol. iii. Cf. T. Mommsen, 'Petrarch's Conception of the Dark Ages', Speculum, xvii (1942) 226-42; W.K. Ferguson, The Renaissance in Historical Perspective (Boston, Mass., 1948); D. Hay, 'Historians and the Renaissance During the Last 25 Years' in The Renaissance (London, 1982) 132; M.L. McLaughlin, 'Humanist Concepts of Renaissance and Middle Ages in the Tre- and Quattrocento', Renaissance Studies, ii (1988) 131-42 with further references. 9

Historical Perceptions of Medieval Science

35

painters of antiquity, but surpassed them all in skill and genius'.10 (It is a pity that he was unaware of the lively and accurate naturalistic illustrations of Frederick IPs Art of Falconry and of many others made in Italy, France, the Netherlands and England during the thirteenth and fourteenth centuries.) That the modern arts had come to revive (rinascere) and to surpass ancient models, and the historical term media tempestas,11 became commonplaces in the fifteenth century. Some scholars maintained that philosophy had flourished without interruption through the scholastic period and needed no revival.12 But in general the humanists gave to the medieval term a sense of total darkness, in order to promote the enlightenment they saw coming from ancient models of all kinds, whether in politics, Latin style or painting and sculpture. On similar lines philosophical historians like Machiavelli and Jean Bodin, looking for the causes of the progress or regress of civilisation in different periods, could project their historical analyses into programmes for present advantage or reform and future advance, or perhaps into diagnoses of decline. They studied history in order to manage or at least to anticipate its course. Hence the search for the best ancient models, and the successive proposals for true methods, whether for philosophy or science or art or theology or government, which were so evident in Western intellectual culture from the age of Roger Bacon to that of Francis Bacon and Descartes. Hence also the recurrent claims to novelty: to have discovered like the sixteenth-century Neoplatonist Francesco Patrizi the 'new, true, complete philosophy of the universe', ambitiously so 'proved with divine oracles, geometrical necessities, philosophical reasons and the clearest experiments'13 or other fashionably convincing criteria; or more realistically the claims to be practising like William Gilbert a 'new sort of philosophising',14 or to have invented like Francis Bacon a novum organum or like Galileo 'new sciences'.15 Reforming visions may show us the intellectual tradition of European science in varied and peculiar lights, as necessary for a true historical anthropology as the solving of problems and related contemporary practices. They show us the historical diversity of conceptions of the rational, the possible, the desirable and the acceptable. These may change with changing

10 Filippo Villani, Liber de civitatis Florentinae famosis civibus, ii.2, 7, iii.7, ed. G.C. Galletti (Florence, 1847). 11 Cf. Hay, 'Historians and the Renaissance'; McLaughlin, 'Humanist Concepts'; P. Lehmann, Vom Mittelalter und von der Lateinischen Philologie des Mittelalters (Quellen und Untersuchungen zur Lateinischen Philologie des Mittelalters, v.l; Munich, 1914). 12 E.g. Alamanno Rinuccini, Lettere ed orazione, a cura di V.R. Giustiniani (Florence, 1953) 106-7; cf. McLaughlin, 'Historians and the Renaissance'. 13 Francesco Patrizi, Nova de universis philosophia, 'Panurgia' i (Ferrara, 1591) f.l r . 14 William Gilbert, De magnete, Praefatio (London, 1600). 15 Galileo Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Leiden, 1638).

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human expectations, or they may persist as definitions of norms of rational thought for every kind of subject-matter and every aspect of life, or as a specified intellectual competence to solve problems, or as a deep moral commitment to discover and spread true and useful knowledge. The critical question is whether the vision casting its objects in this reforming light can stand the light of historical evidence. To the historiography of a political and literary and artistic renaissance centred in fourteenth- and fifteenth-century Italy, Erasmus added a further European element with his conception of close causal connection between the decline or revival of learning and those of religion. The renaissance of religion then came to be identified in Protestant historiography with the fortunes of the Protestant reformation. Science was brought into the historiography of a renaissance at this time first by such philosophical reformers as Peter Ramus16 and Francis Bacon, using the warning of past stagnation to promote their new optimism for mathematical and experimental methods, and later when in the dispute of the Ancients and Moderns the recent scientific triumphs replaced antiquity with progress as a guiding vision. An exemplary linking of the revival of classical learning, the Protestant reformation and the rise of the new philosophy as stages in the liberation of the inquiring mind was set out in the Dictionnaire historique (1697) by Pierre Bayle.17 Put together over two centuries through a series of disparate issues in politics, religion, literature, art, science and technology, this scheme has had its full influence on that large part of the historiography of science developed since the sixteenth century in which it has been assumed, in Walter Ralegh's phrase, that is was 'the end and scope of all historic, to teach by example of times past, such wisdome as may guide our desires and actions'.18 Historiography of science was an evaluation entailing a programme. Whatever wisdom history may teach us, the obvious disadvantage of a periodisation in evaluative terms like dark ages or renaissance, or like reformation or scientific revolution or enlightenment, as also the obvious disadvantage of simply assuming a linkage of apparently separate issues whether in the pursuit of some view of the human condition or even of truth or liberty, or in some causal series, is that these can cloud factual investigations. They tell us more about the periods in which they were invented than about those to which they referred. It is a curious fact that in the course of the successive controversies over the arts, religion and science the period of medieval darkness was moved forward to the sixteenth and early seventeenth centuries. Such terms distract attention from the apprehension of an intellectual culture in its historical context and in its own terms. They obstruct the analysis of connections of reason and motive both manifest and hidden, and the interaction of internal

16 17 18

Petrus Ramus, Scholarum mathematicarum . . . (Basel, 1569). Vol. ii (Rotterdam, 1697) 1123. Ralegh, History of the World, Preface and ii.21.6 (London, 1614) 537.

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37

intellectual needs with external social pressures evident in complex societies. Antecedent assumptions in historical as in scientific investigations may indeed direct our attention to questions otherwise overlooked, as likewise away from other questions indicated by other assumptions. Human historiography, like natural science, must proceed by means of a body of theory. Suitably distanced by time and experience, we can recognise fairly easily the theoretical assumptions generated in early modern historiography by the diverse disputes in which the innovating parties needed to define their position in relation to their immediate predecessors and current opponents.19 They used history in an exercise of persuasion to influence present attitudes and actions. This has been done by no means only on one side, nor despite its obvious dangers does it necessarily produce bad scholarship. European interest in medieval history, powerfully stimulated by Romanticism, led on the Continent during the nineteenth century to the methodical study of medieval thought and to some exemplary, especially German, technical studies of medieval philosophy and science. A little later that great man Pierre Duhem, under the pressure of opposition from French academic positivists, embarked on his magisterial exposition of medieval scientific thinkers and their relation to their early modern successors. Duhem was explicitly making a point with more than medieval historical relevance, and he has been justly criticised for certain historical distortions that have come from it. Yet all subsequent historians of medieval science, however much we may criticise and object, are to some extent his disciples. It was he beyond all others whose heroic vision of medieval natural philosophy and cosmology projected bright shafts of understanding through the cloudy darkness of academic prejudice. He gave fresh excitement to medieval science, and in consequence this gave academic careers to generations of young scholars. Yet on many details and perhaps on much of the whole vision we must criticise and differ. When we read a text in the history of science we need to identify the questions to which the text was directed and to which it offered answers. The questions may be explicit or they may be implied by the answers given. Aristotle, the first historian of science, assumed that his predecessors had been asking the same questions as himself but had not answered them so well. Our historical perceptions now make it clear that the questions, whether explicit or implied, can change so much as to be scarcely the same questions at all. The most fundamental changes, often obscured by the inertia of language and terminology, are those brought about by changes in the conceptions of nature 19 Ample evidence of the continuing interest in medieval natural philosophy during the sixteenth and early seventeenth centuries is provided by the printed editions recorded e.g. by G. Sarton, Introduction to the History of Science, 3 vol. (Baltimore, Md., 1927-47); cf. also A.C. Crombie, Robert Grosseteste and the Origins of Experimental Science (Oxford, 1953,1971) 278-9; A. Pacchi, Convenzione e ipotesi nella formazione della filosofia naturale di Thomas Hobbes (Florence, 1965), 'Ruggero Bacone e Roberto Grossatesta in un inedito hobbesiano del 1634', Rivista critica di storia della filosofia, xx (1965) 499-502.

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and of science presupposed by the questions being posed. Such changes can alter both the way in which particular scientific problems are formulated and the criteria for an acceptable scientific explanation. It is clear that the questions put or presupposed in the answers given by medieval natural philosophers were not identical with those put or presupposed in the seventeenth century. Structural changes in scientific thinking such as occurred over this period make the whole subject of predecessors extremely tricky, and it is tricky not only for the medieval predecessors dear to Duhem, but likewise for those of Darwin in the theory of evolution and equally throughout the history of science. We need to examine continuity and change at all the levels involved, from those of factual discovery and mathematical formulation to those of scientific demonstration and causal explanation. In the famous case of inertial motion, for example, the seventeenth-century concept was basically different from that formulated in the fourteenth century on the Aristotelian principle that, since every effect requires a cause, every motion requires a mover. Again, the analysis of the rainbow by Descartes starting from a general quantitative law was structurally different from that of Theodoric of Freiberg, whose sophisticated experiments with models were designed to discover the particular causal conditions for particular phenomenon. Yet again, Kepler came to make a structural break from his own first approach to the analysis of optical physiology, based on the assumption inherited from the Greeks that the process by which vision is effected through the living eye must yield an immediate explanation of visual perception. This had been accepted by Alhazen in his brilliant geometrical model of the eye and by all his successors. It led to insoluble problems like that of the inversion and reversal of the image. Kepler generalised the subject by treating the eye as a physical optical instrument like any other, as in fact a camera obscura, and thus he could separate its optical operation for analysis independently of the problem of perception. The question changed because the presuppositions generating them changed. Valuable light can be thrown on all this by the study of scientific and philosophical terminology, but here also there are dangers. Language can misrepresent or lag behind practice. It takes great care to interpret such important terms as lex naturae, resolutiva et compositiva, ratio, machina, experimentum and scientia experimental. So then: quanta juniores, tanto perspicaciores, sed caveat emptor.

4

Robert Grossteste (c. 1168-1253)

Grosseteste was the central figure in England in the intellectual movement of the first half of the thirteenth century, yet the only evidence for his life before he became bishop of Lincoln in 1235 is to be found in fragmentary references by Matthew Paris and other chroniclers, by Roger Bacon, and occasionally in charters, deeds and other records.1 His birth has been variously dated between 1168 and 1175, but since he is described as 'Magister Robertus Grosteste' (the first appearance of his name) in a charter of Hugh, bishop of Lincoln, of probably 1186-1190, the earlier date is the more likely. Tradition places his birth in Suffolk, of humble parentage. He may have been educated first at Lincoln, then at Oxford, and was in the household of William de Vere, bishop of Hereford, by 1198, when a reference by Gerald of Wales suggests that he may have had some knowledge of both law and medicine. After that it seems likely that he taught at Oxford in the arts school until the dispersion of masters and scholars during 1209-1214. He must have taken his mastership in theology, probably at Paris, during this period, some time before his appointment as chancellor of the University of Oxford, although with the title magisterscholarum, probably about 1214-1221, when he must have lectured on theology. Grosseteste was given a number of ecclesiastical preferments and sinecures, including the arch-deaconry of Leicester in 1229; but in 1232 he resigned them all except for a prebend at Lincoln, writing to his sister, a nun: 'If I am poorer by my own choice, I am made richer in virtues.'2 From 1229 or 1230 until 1235 he was first lecturer in theology to the Franciscans, who had come to Oxford in 1224. His influence there was profound and continued after he left Oxford in 1235 for the see of Lincoln, within the jurisdiction of which Oxford and its schools came. He contributed largely to directing the interests of the English Franciscans toward the study of the Bible, languages, and mathematics and natural science. Indispensable sources for this later period of his life are his own letters and those of his Franciscan friend Adam Marsh.

1 2

See D.A. Callus, ed., Robert Grosseteste. Epistolae, H.R. Luard, ed., p. 44.

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Science, Art and Nature in Medieval and Modern Thought

Grosseteste's career thus falls into two main parts, the first that of a university scholar and teacher and the second that of a bishop and ecclesiastical statesman. His writings fall roughly into the same periods: to the former belong his commentaries on Aristotle and on the Bible and the bulk of a number of independent treatises, and to the latter his translations from the Greek. Living at a time when the intellectual horizons of Latin Christendom were being greatly extended by the translations into that language of Greek and Arabic philosophical and scientific writings, he took a leading part in introducing this new learning into university teaching. His commentary on Aristotle's Posterior Analytics was one of the first and most influential of the medieval commentaries on this fundamental work. Other important writings belonging to the first period are his commentary on Aristotle's Physics, likewise one of the first; independent treatises on astronomy and cosmology, the calendar (with intelligent proposals for the reform of the inaccurate calendar then in use), sound, comets, heat, optics (including lenses and the rainbow), and other scientific subjects; and his scriptural commentaries, especially the Moralitates in evangelica, De cessatione legalium, Hexaemeron and commentaries on the Pauline epistles and the psalms. Having begun to study Greek in 1230-1231, he used his learning fruitfully during the period of his episcopate by making Latin translations of Aristotle's Nicomachean Ethics and De caelo (with Simplicius' commentary), of the Defide orthodoxe of John of Damascus, of Pseudo-Dionysius and of other theological writings. For this work he brought to Lincoln assistants who knew Greek; he also arranged for a translation of the psalms to be made from the Hebrew and seems to have learned something of this language. Although in content a somewhat eclectic blend of Aristotelian and Neoplatonic ideas, Grosseteste's philosophical thinking shows a strong intellect curious about natural things and searching for a consistently rational scheme of things both natural and divine. His search for rational explanations was conducted within the framework of the Aristotelian distinction between 'the fact' (quid) and 'the reason for the fact' (propter quid). Essential for the latter in natural philosophy was mathematics, to which Grosseteste gave a role based specifically on his theory, expounded in De luce seu de inchoatione formarum and De motu corporali et luce, that the fundamental corporeal substance was light (lux). He held that light was the first form to be created in prime matter, propagating itself from an original point into a sphere and thus giving rise to spatial dimensions and all else according to immanent laws. Hence his conception of optics as the basis for natural science. Lux was a instrument by which God produced the macrocosm of the universe and also the instrument mediating the interaction between soul and body and the bodily senses in the microcosm of man.3 Grosseteste's rational scheme included

3

E.G., Hexaemeron, British Museum MS Royal 6.E.V (14 cent.), fols 147v-150v; L. Baur, 'Das Licht in der Naturphilosophie des Robert Grosseteste' in Abhandlungen aus dem Gebiete

Robert Grosseteste

41

revelation as well as reason, and he was one of the first medieval thinkers to attempt to deal with the conflict between the Scriptures and the new Aristotle. Especially interesting are his discussions of the problems of the eternity or creation of the world, of the relation of will to intellect, of angelology, of divine knowledge of particulars, and of the use of allegorical interpretations of Scripture. Grosseteste's public life as bishop of Lincoln was informed by both his outlook on the universe as a scholar and his conception of his duties as a prelate dedicated to the salvation of souls. Analogous to corporeal illumination was the divine illumination of the soul with truth. He extended the luminous analogy to illustrate the relationship between the persons of the Trinity, the operation of divine grace through free will like light shining through a coloured glass,4 and the relation of pope to prelates and of bishops to clergy: as a mirror reflects light into dark places, he said in asserting his episcopal rights against the cathedral chapter of Lincoln, so a bishop reflects power to the clergy.5 In practice Grosseteste was governed by three principles: a belief in the supreme importance of the cure of souls; a highly centralised and hierarchical conception of the church, in which the papacy, under God, was the centre and source of spiritual life and energy; and a belief in the superiority of the church over the state because its function, the salvation of souls, was more vital. Such views were widely accepted, but Grosseteste was unique in the ruthlessness and thoroughness with which he applied them, for example, in opposing the widespread use of ecclesiastical benefices to endow officials in the service of the crown or the papacy. As a bishop he had attended the First Council of Lyons in 1245, and in a memorandum presented to the pope there in 1250 he expounded his views on the unsuitability of such appointments while accepting the papal right to dispose of all benefices. Likewise, his opposition to the obstruction of the disciplinary work of the church by any ecclesiastical corporation or secular authority brought him into conflict both with his own Lincoln chapter and with the crown over royal writs of prohibition when secular law clashed with church law and when churchmen were employed as judges or in other secular offices. Grosseteste was a close friend of Simon de Montfort and took charge of the education of his sons, but the degree to which he shared in or influenced Montfort's political ideals has probably been exaggerated. Above all he was a bishop with an ideal, an outstanding example of the new type of ecclesiastic trained in the universities.

der Philosophic und ihrer Geschichte. Eine Festgabe zum 70. Geburtstag Georg Freiherrn von Herding (Freiburg im Breisgau, 1913), pp. 41-55. 4 De libero arbitrio, caps. 8 and 10, in L. Baur, Die philosophischen Werke des Robert Grosseteste, pp. 179, 202. 5 Epistolae, pp. 360, 364, 389.

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Scientific Thought Some of Grosseteste's scientific writings can be dated with reasonable certainty, and most of the others can be related to these in an order based on internal references and on the assumption that the more elaborated version of a common topic is the later.6 From the evidence for his method of making notes on his reading and thoughts to be worked up into finished essays and commentaries,7 and from these writing themselves, it may be assumed that many of them arose out of his teaching in the schools. Gerald of Wales's description of Grosseteste at Hereford as a young clerk with a manifold learning 'built upon the sure foundation of the liberal arts and an abundant knowledge of literature'8 is borne out by what is probably his earliest work, De artibus liberalibus. In this attractive introduction he described how the seven liberal arts at once acted as apurgatio erroris and gave direction to the gaze and inclination of the mind (mentis aspectus et affectus). Of particular interest is hi treatment of music, of which his love became proverbial, and of astronomy. As for Boethius, music for him comprised the proportion and harmony not only of sounds produced by the human voice and by instruments but also of the movements and times of the celestial bodies and of the composition of bodies made of the four terrestrial elements - hence the power of music to mould human conduct and restore health by restoring the harmony between soul and body and between the bodily elements, and the related power of astronomy through its indication of the appropriate times for such operations and for the transmutation of metals. Related to this essay was his phonetical treatise De generatione sonorum, which he introduced with an account of sound as a vibratory motion propagated from the sounding body through the air to the ear, from the motion of which arose a sensation in the soul. Grosseteste developed his mature natural philosophy through a logic of science based on Aristotle and through his fundamental theory of light. In their present form most of the works concerned were almost certainly written between about 1220 and 1235. De luce and De motu corporali et luce, with his cosmogony and cosmology of light, seem to date from early in this period. The structure of the universe generated by the original point of lux was determined, first, by the supposition that there was a constant proportion between the diffusion or 'multiplication' of lux, corresponding to the infinite series of natural numbers, and the quantity of matter given cubic dimensions, corresponding to some finite part of that series. Second, the intensity of this 6 For the basic works on this question, see Baur, Die philosophischen Werke; and S.H. Thomson, The Writings of Robert Grosseteste - with the revisions by Callus, The Oxford Career of Robert Grosseteste' in Robert Grosseteste; A.C. Crombie, Robert Grosseteste and the Origins of Experimental Science (1953, 1971); and R.C. Dales, 'Robert Grosseteste's Scientific Works,' Commentarius in viii libros. 7 From William of Alnwick, as first noticed by A. Pelzer. See Callus, The Oxford Career of Robert Grosseteste,' pp. 45-47. 8 Giraldus Cambrensis, Opera, J.S. Brewer, ed., I (London, 1861), 249.

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activity of lux varied directly with distance from the primordial source. The result was a sphere denser and more opaque toward the centre. Then from the outermost boundary of the sphere lumen emanated inward to produce another sphere inside it, then another, and so on, until all the celestial and elementary spheres of Aristotelian cosmology were complete. Another seemingly early work in this series, De generatione stellarum, shows Grosseteste dependent on Aristotle in many things but not in all, for he argued that the stars were composed of the four terrestrial elements. Later, in his commentary on the Physics, he contrasted the imprecise and arbitrary way man must measure spaces and times with God's absolute measures through aggregates of infinities. In all these writings Grosseteste made it clear that by lux and lumen he meant not simply the visible light which was one of its manifestations, but a fundamental power (virtus, species) varying in its manifestation according to the source from which it was propagated or multiplied and in its effect according to its recipient. Thus he showed in De impressionibus elementorum how solar radiation effected the transformation of one of the four terrestrial elements into another and later, in De natura locorum, how it caused differences in climate. An explanation of the tides begun in De accessione et recessione maris or De fluxu et refluxu maris (if this work is by him)9 was completed in De natura locorum, in which he argued that the rays of the rising moon released vapours from the depth of the sea which pushed up the tide until the moon's strength increased so much that it drew the vapours through the water, at which time the tide fell again. The second, smaller monthly tide was caused by the weaker lunar rays reflected back to the opposite side of the earth from the stellar sphere. In De cometis et causis ipsarum Grosseteste gave a good example of his method of falsification in arguing that comets were 'sublimated fire' separated from their terrestrial nature by celestial power descending from the stars or planets and drawing up the 'fire' as a magnet drew iron. Later, in De calore solis (c. 1230-1235), he produced perhaps his most elegant exercise in analysis by reduction to conclusions falsified either by observation or by disagreement with accepted theory, finally leaving a verified explanation. He concluded that all hot bodies generated heat by the scattering of their matter and that the sun generated heat on the earth in direct proportion to the amount of matter incorporated from the transparent medium (air) into its rays. Grosseteste set out and exemplified the formal structure of his mature scientific method in his Commentaria in libros posteriorum Aristotelis, his Commentarius in viii libros physicorum Aristotelis,10 and four related essays

9 See R.C. Dales, The Authorship of the Questio de fluxu et refluxu maris Attributed to Robert Grosseteste,' in Speculum, 37 (1962), 582-588. 10 See the ed. by Dales. Grosseteste wrote probably about 1230 a summary of Aristotle's views in his Summa super octo libros physicorum Aristotelis.

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giving a geometrical analysis of the natural propagation of power and light. It seems likely that he began the commentary on the Posterior Analytics when he was still a master of arts, that is, before 1209, and completed it over a long period, finishing after 1220 and probably nearer the end of the decade. The commentary on the Physics was written later, likewise certainly over a period of years, probably around 1230. It has striking parallels with some of the scientific topics of the Hexaemeron but shows less than even the limited knowledge of Greek found in this work, suggesting that it just precedes it. For Grosseteste, as for Aristotle, a scientific inquiry began with an experienced fact (quid), usually a composite phenomenon. The aim of the inquiry was to discover the reason for the fact (propter quid), the proximate cause or natural agent from which the phenomenon could be demonstrated: Every thing that is to be produced is already described and formed in some way in the agent, whence nature as an agent has the natural things that are to be produced in some way described and formed within itself, so that this description and form itself, in the very nature of things to be produced before they are produced, is called knowledge of nature.11

His method of discovering the causal agent was to make first a resolutio, or analysis of the complex phenomenon into its principles, and then a compositio, or reconstruction and deduction of the phenomenon from hypotheses derived from the discovered principles. He verified or falsified these hypotheses by observation or by theory already verified by observation. Besides this double method, Grosseteste used in the analysis of the causal agent as the starting-point of demonstration another Aristotelian procedure, that of the subordination of some sciences to others, for example, of astronomy and optics to geometry and of music to arithmetic, in the sense that 'the superior science provides the propter quid for that thing of which the inferior science provides the quia.'12 But mathematics provided only the formal cause; the material and efficient causes were provided by the physical sciences. Thus 'the cause of the equality of the two angles made on a mirror by the incident ray and the reflected ray is not a middle term taken from geometry, but is the nature of the radiation generating itself in a straight path . . . '13 The echo belonged formally to the same genus as the reflection of light, but the material and efficient cause of the propagation of sound had to be sought in its fundamental substance: 'the substance of sound is lux incorporated in the most subtle air . . . '14 This introduced a fundamental addition to

11 12 13 14

Commentarius in viiiphysicorum Aristotelis, lib. I, Dales, ed. pp. 3-4. Commentaria in libros posteriorum Aristotelis, I, 12 (1494), fols. llr-12r. Ibid., I, 8, fol. 8r. 7Wd.,II,4,fol. 29v.

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the very similar discussion of the propagation of sound in De artibus liberalibus and De generatione sonorum. Grosseteste developed his geometrical analysis of the powers propagated from natural agents in the four related essays written most probably in the period 1231-1235. He said in the first, De lineis, angulis et figuris seu fractionibus et reflexionibus radiorum: 'All causes of natural effects have to be expressed by means of lines, angles and figures, for otherwise it would be impossible to have knowledge propter quid concerning them.'15 The same power produced a physical effect in an inanimate body and a sensation in a animate one. He established rules for the operation of powers: for example, the power was greater the shorter and straighter the line, the smaller the incident angle, the shorter the three-dimensional pyramid or cone; every agent multiplied its power spherically. Grosseteste discussed the laws of reflection and refraction (evidently taken from Ptolemy) and their causes, and went on in De natura locorum to use Ptolemy's rules and construction with plane surfaces to explain refraction by a spherical burning glass. 'Hence,' he resumed, 'these rules and principles and fundamentals having been given by the power of geometry, the careful observer of natural things can give the causes of all natural effects by this method.' This was clear 'first in natural action upon matter and later upon the senses. . . . '16 An example of the analysis of a power producing sensation is provided by Grosseteste's De colore. The resolutio identified the constituent principles: colour was light incorporated by a transparent medium; transparent media varied in degree of purity from earthy matter; light varied in brightness and in the multitude of its rays. In the compositio he asserted that the sixteen colours ranging from white (bright light, multitudinous rays, in a pure medium) to black were produced by the 'intension and remission' of these three variable principles. 'That the essence of colour and a multitude of the same behaves in the said way,' he concluded, 'is manifest not only by reason but also by experiment, to those who know the principles of natural science and of optics deeply and inwardly. . . . They can show every kind of colour they wish to visibly, by art [per artificium].'11 The last of these four essays, De iride seu de iride et speculo, is the most complete example of Grosseteste's method and his most important contribution to optics. The resolutio proceeds through a summary of the principle of subordination and its relation to demonstration propter quid into a discussion of the division of optics into the science of direct visual rays, of reflected rays, and of refracted rays, in order to decide to which part the study of the rainbow belonged. It was subordinate to the third part, 'untouched and unknown

15 16 17

De lineis angulis et figuris, in Baur, Die philosophischen Werke, pp. 59-60. De natura locorum, ibid., pp. 65-66. De colore, ibid., pp. 78-79.

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among us until the present time';18 and it is his treatment of refraction that has the greatest interest. This part of optics [perspectiva], when well understood, shows us how we may make things a very long distance off appear to be placed very close, and large near things appear very small, and how we may make small things placed at a distance appear as large as we want, so that it is possible for us to read the smallest letters at an incredible distance, or to count sand, or grain, or seeds, or any sort of minute objects.19

The reason, as he had learned from Euclid and Ptolemy, was 'that the size, position and arrangement according to which a thing is seen depends on the size of the angle through which it is seen and the position and arrangement of the rays, and that a thing is made invisible not by great distance, except by accident, but by the smallness of the angle of vision.' Hence 'it is perfectly clear from geometrical reasons how, by means of a transparent medium of known size and shape placed at a known distance from the eye, a thing of known distance and known size and position will appear according to place, size and position.'20 Grosseteste followed this account of magnification and diminution by refracting media with an apparently original law of refraction, according to which the refracted ray, on entering a denser medium, bisected the angle between the projection of the incident ray and the perpendicular to the interface. 'That the size of the angle in the refraction of a ray may be determined in this way,' he concluded, 'is shown us by experiments similar to those by which we discovered that the reflection of a ray upon a mirror takes place at the angle equal to the angle of incidence.'21 It was also evident from the principle that nature always acts in the best and shortest way. Grosseteste went on to use a construction of Ptolemy's to show how to locate the refracted image, claiming again that this 'is made clear to us by the same experiment and similar reasonings'22 as those used in a similar construction for locating the reflected image. The first of these references to experimental verification, since it would have been so inaccurate, may throw doubt on all such references by Grosseteste. As was true for a great many medieval natural philosophers, most of these references came from books or from everyday experiences. Clearly his interest was directed primarily towards theory. Yet he advocated and was guided by the principle of experiment and developed its logic. Besides these works related to optics, Grosseteste wrote important treatises on astronomical subjects. In De sphaera, of uncertain date between perhaps 18

De irlde, ibid., p. 73. See L. Baur, Die Philosophic des Robert Grosseteste, pp. 117-118; Crombie, Robert Grosseteste (1971), pp. 117-124. 19 De iride, in Baur, Die philosophischen Werke, p. 74. 20 Ibid., p. 75. 21 Ibid., pp. 74-75. 22 Ibid., p. 75.

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1215 and 1230, and De motu supercaelestium, possibly after 1230, he expounded elements of both Aristotelian and Ptolemaic theoretical astronomy. In a later work, De impressionibus aeris seu deprognosticatione, dating apparently from 1249, he discussed astrological influences and, again, his mature explanation of the tides. More original were Grosseteste's four separate treatises on the calendar: Canon in kalendarium and Compotus; correcting these, Compotus correctorius, probably between 1215 and 1219; and Compotus minor, with further corrections in 1244. He showed that with the system long in use, according to which nineteen solar years were considered equal to 235 lunar months, in every 304 years the moon would be one day, six minutes and forty seconds older than the calendar indicated. He pointed out in the Compotus correctorius (cap. 10) that by his time the moon was never full when the calendar said it should be and that this was especially obvious during an eclipse. The error in the reckoning of Easter came from the inaccuracy both of the year of 365.25 days and of the nineteen-year lunar cycle. Grosseteste's plan for reforming the calendar was threefold. First, he said that an accurate measure must be made of the length of the solar year. He knew of three estimates of this: that of Hipparchus and Ptolemy, accepted by the Latin computists; that of al-Battani; and that of Thabit ibn Qurra. He discussed in detail the systems of adjustments that would have to be made in each case to make the solstice and equinox occur in the calendar at the times they were observed. Al-Battani's estimate, he said in the Compotus correctorius (cap. 1), 'agrees best with what we find by observation on the advance of the solstice in our time.' The next stage of the reform was to calculate the relation between this and the mean lunar month. For the new-moon tables of the Kalendarium, Grosseteste had used a multiple nineteen-year cycle of seventy-six years. In the Compotus correctorius he calculated the error this involved and proposed the novel idea of using a much more accurate cycle of thirty Arab lunar years, each of twelve equal months, the whole occupying 10,631 days. This was the shortest time in which the cycle of whole lunations came back to the start. Grosseteste gave a method of combining this Arab cycle with the Christian solar calendar and of calculating true lunations. The third stage of the reform was to use these results for an accurate reckoning of Easter. In the Compotus correctorius (cap. 10), he said that, even without an accurate measure of the length of the solar year, the spring equinox, on which the date of Easter depended, could be discovered 'by observation with instruments or from verified astronomical tables.'23 And with Grosseteste's optics, it was Roger Bacon who first took up his work on the calendar; and Albertus Magnus first made serious use of his commentary on the Posterior Analytics, as did John Duns Scotus of that on the Physics. These attentions marked the beginning of a European reputation that

23

Compotus, R. Steele, ed., pp. 215, 259.

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Science, Art and Nature in Medieval and Modern Thought

continued into the early printing of his writings at Venice, the collecting of his scientific manuscripts by John Dee, and interest in them by Thomas Hobbes.24

BIBLIOGRAPHY i. ORIGINAL WORKS. The earliest dated printed ed. of a work by Grosseteste is Commentaria in librosposteriorum Aristotelis (Venice, 1494; 8th ed., 1552). It was followed by his Summa super octo librosphysicorum Aristotelis (Venice, 1498; 9th ed., 1637); Libellus dephisicis lineis angulis etfigurisper quas omnes actiones naturales complentur (Nuremburg, 1503); De sphaera, pub. as Sphaeraecompendium (Venice, 1508; 5th ed., 1531); and Compotus correctorius (Venice, 1518). His Opuscula (Venice, 1514; London, 1690) includes De artibus liberalibus, De generatione sonorum, De calore solis, De generatione stellarum, De colore, De impressionibus elementorum, De motu corporali, De finitate motus et temporis (appearing first as the concluding section of his commentary on the Physics), De lineis, angulis etfiguris, De natura locorum, De luce, De motu supercaelestium, and De differentiis localibus. All these essays, with De sphaera and the hitherto unprinted De cometis, De impressionibus aeris and De iride, were published by L. Baur in Die philosophischen Werke des Robert Grosseteste (see below). For further modern texts see Canon in Kalendarium, ed. by A. Lindhagen as 'Die Neumondtafel des Robertus Lincolniensis,' in Archiv for matematik, astronomi och fysik (Uppsala)., 11 no. 2 (1916); Compotus, factus and correctionem communis kalendarii nostri, R. Steele, ed., in Roger Bacon, Opera hactenus inedita, VI (Oxford, 1926), 212 ff.; S.H. Thomson, The Text of Grosseteste's De cometis,' in Isis, 19 (1933), 19-25; and "Grosseteste's Questio de calore, de cometis and De operacionibussolis,' in Medievalia ethumanistica, 11 (1957), 34-43; Commentarius in viii libros physicorum Aristotelis . . . , R.C. Dales, ed. (Boulder, Colo., 1963); and R.C. Dales, The Text of Robert Grosseteste's Questio defluxu de refluxu maris with an English Translation,' in Isis, 57 (1966), 455-474. See also Roberti Grosseteste episcopi quondam Lincolniensis epistolae. H.R. Luard, ed. (London, 1861). II. SECONDARY LITERATURE. For the fundamental work of identifying and listing Grosseteste's writing see L. Baur, Die philosophischen Werke des Robert Grosseteste, Bishop von Lincoln, vol. IX of Beitrdge zur Geschichte der Philosophic des Mittelalters (Miinster, 1912); and S.H. Thomson, The Writings of Robert Grosseteste Bishop of Lincoln 1235-1253 (Cambridge, 1940). For further discussions of his scientific writings with reference to additional items, see D.A. Callus, The Oxford Career of Robert Grosseteste,'

24 See Crombie, Robert Grosseteste (1971); A. Pacchi, 'Ruggero Bacone e Roberto Grossetesta in un inedito hobbesiano del. 1634,' in Rivista critica distoria dellafilosofia 20 (1965), 499-502; and Convenzione e Ipotesi nella formazione dellafilosofia naturale di Thomas Hobbes (Florence, 1965).

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in Oxoniensia, 10 (1945), 42-72; D.A. Callus, ed., Robert Grosseteste, Scholar and Bishop (Oxford, 1955); A.C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700 (Oxford, 1953; 3rd ed., 1971) and the comprehensive bibliography therein; and R.C. Dales, 'Robert Grosseteste's Scientific Works,' in Isis, 52 (1961), 381-402. The first modern biography was F.S. Stevenson, Robert Grosseteste, Bishop of Lincoln (London, 1899), while Callus, Robert Grosseteste, judiciously sums up more recent scholarship. The pioneering account of his scientific thought is L. Baur, Die Philosophic des Robert Grosseteste, Bischofs von Lincoln, XVIII, nos. 4-6 of Beitrdge zur Geschichte der Philosophic des Mittelalters (Miinster, 1917).

Further References See A.C. Crombie, Science, Optics and Music. . ., ch. 6 (1990) 137; J.D. North, Stars, Minds and Fate (London, 1989) 119-33; R. W. Southern, Robert Grosseteste, 2nd ed. (Oxford, 1992), the basic biography; with Robert Grosseteste, Hexaemeron, ed. R.C. Dales and S. Gieben (London, 1982); Metafisica delta luce: Opuscolifilosofici e scientific!, introduzione, traduzione e note di Pietro Rossi (Milano, 1986).

All science requires mathematices. . . . But only in mathematics . . . are what are known to us and what are known in nature, or known simply, the same. (Roger Bacon, Opus maius iv. 1.3)

5

Roger Bacon (c. 1219-1292) [with J.D. North] Apart from some brief references in various chronicles, the only materials for Robert Bacon's biography are his own writings. The date 1214 for his birth was calculated by Charles, followed by Little, from his statements in the Opus tertium (1267) that it was forty years since he had learned the alphabet and that for all but two of these he had been 'in studio.'1 Taking this to refer to the years since he entered the university - the usual age was then about thirteen - they concluded that in 1267 Bacon was fifty-three and thus was born in 1214. But Crowley has argued that his statements more probably refer to his earliest education, beginning about the age of seven or eight, which would place his birth about 1219 or 1220. Of his family the only good evidence comes again from Bacon himself. He wrote in the Opus tertium that they had been impoverished as a result of their support of Henry III against the baronial party, and therefore could not respond to his appeal for funds for his work in 1266.2 After early instruction in Latin classics, among which the works of Seneca and Cicero left a deep impression, Bacon seems to have acquired an interest in natural philosophy and mathematics at Oxford, where lectures were given from the first decade of the thirteenth century on the 'new' logic (especially Sophistici Elenchi and Posterior Analytics) and libri naturales of Aristotle as well as on the mathematical quadrivium. He took his M. A. either at Oxford or at Paris, probably about 1240. Probably between 1241 and 1246 he lectured in the Faculty of Arts at Paris on various parts of the Aristotelian corpus, including the Physics and Metaphysics, and the pseudo-Aristotelian De vegetabilibus (or Deplantis) and the De causis, coincident with the Aristotelian revival there. In arguing later in his Compendium studii philosophic for the necessity of knowledge of languages,3 he was to use an incident in which his Spanish students laughed at him for mistaking a Spanish word for an Arabic word while he was lecturing on De vegetabilibus. He was in Paris at the same

1 2 3

Opus tertium, Brewer ed., p. 65. Ibid., p. 16. Compendium studii philosophic, Brewer ed., pp. 467-468.

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time as Albertus Magnus, Alexander of Hales (d. 1245)4 and William of Auvergne (d. 1249).5 The radical intellectual change following Bacon's introduction to Robert Grosseteste (c. 1168-1253) and his friend Adam Marsh on his return to Oxford about 1247 is indicated by a famous passage in the Opus tertium: For, during the twenty years in which I have laboured specially in the study of wisdom, after disregarding the common way of thinking [neglecto sensu vulgi], I have put down more than two thousand pounds for secret books and various experiments [experientie], and languages and instruments and tables and other things; as well as for searching out the friendships of the wise, and for instructing assistants in languages, in figures, in numbers, and tables and instruments and many other things. Grosseteste's influence is evident in Bacon's particular borrowings, especially in his optical writings, but above all in the devotion of the rest of his life to the promotion of languages and of mathematics, optics (perspectiva), and scientia experimentalis as the essential sciences. He was in Paris again in 1251, where he says in the Opus maius1 that he saw the leader of the Pastoreaux rebels. This story and some later works place him there for long periods as a Franciscan. He entered the Franciscan order about 1257 and, soon afterwards, he also entered a period of distrust and suspicion probably arising from the decree of the chapter of Narbonne, presided over by Bonaventura as master general in 1260, which prohibited the publication of works outside the order without prior approval. Bonaventura had no time for studies not directly related to theology, and on two important questions, astrology and alchemy, he was diametrically opposed to Bacon. He held that only things dependent solely on the motions of the heavenly bodies, such as eclipses of the sun and moon and sometimes the weather, could be foretold with certainty. Bacon agreed with the accepted view that predictions of human affairs could establish neither certainty nor necessity over the free actions of individuals, but he held that nevertheless astrology could throw light on the future by discovering general tendencies in the influence of the stars, acting through the body, on human dispositions, as well as on nature at large. In alchemy Bonaventura was also sceptical about converting base metals into gold and silver, which Bacon thought possible. Whatever the particular reasons for Bacon's troubles within the order, he felt it necessary to make certain proposals to a clerk attached to Cardinal Guy de Foulques; as a result, the cardinal, soon to be elected Pope Clement IV (February 1265), asked him for a copy of his philosophical writings. The 4 Opus minus, Brewer ed., p. 325; Opus tertium, Brewer ed., p. 30; Compendium studii philosophic, p. 425. 5 Opus tertium, Brewer ed. pp. 74-75. 6 Ibid., p. 59. 7 Opus maius (1266-1267), Bridges ed., I, 401.

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request was repeated in the form of a papal mandate of 22 June 1266.8 Bacon eventually replied with his three famous works, Opus maius, Opus minus, and Opus tertium, the last two prefaced with explanatory epistole in which he set out his proposals for the reform of learning and the welfare of the Church. It is reasonable to suppose that after twenty years of preparation he composed these scripture preambule to an unwritten Scriptum principale between the receipt of the papal mandate and the end of 1267. In that year he sent to the pope, by his pupil John, the Opus maius with some supplements, including De speciebus et virtutibus agentium in two versions9 and De scientiaperspectiva,10 followed (before the pope died in November 1268) by the Opus minus and Opus tertium as resumes, corrections, and additions to it. The pope left no recorded opinion of Bacon's proposals. Perhaps at this time Bacon wrote his Communia naturalium and Communia mathematica^ mature expressions of many of his theories. These were followed in 1271 or 1272 by the Compendium studii philosophic, of which only the first part on languages remains and in which he abused all classes of society, and particularly the Franciscan and Dominican orders for their educational practices. Sometime between 1277 and 1279 he was condemned and imprisoned in Paris by his order for an undetermined period and for obscure reasons possibly related to the censure, which included heretical Averroist propositions, by the bishop of Paris, Stephen Tempier, in 1277. The last known date in his troubled life is 1292, when he wrote the Compendium studii theologii.11

Scientific Thought The Opus maius and accompanying works sent to the pope by Bacon as a persuasio contain the essence of his conception of natural philosophy and consequential proposals for educational reform. He identified four chief obstacles to the grasping of truth: frail and unsuitable authority, long custom, uninstructed popular opinion, and the concealment of one's own ignorance in a display of apparent wisdom. There was only one wisdom, given to us by the authority of the Holy Scriptures; but this, as he explained in an interesting history of philosophy, had to be developed by reason, and reason on its part was insecure if not confirmed by experience. There were two kinds of experience, one obtained through interior mystical inspiration and the other through the exterior senses, aided by instruments and made precise by

8 9 10 11

Brewer, p. 1. Cf. Opus maius, Bridges ed., pt IV, dist. ii-iv; and De multiplicatione specierum, Bridges ed. Cf. Opus maius, pt. V. Rashdall, pp. 3, 34.

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mathematics.12 Natural science would lead through knowledge of the nature and properties of things to knowledge of their Creator, the whole of knowledge forming a unity in the service and under the guidance of theology. The necessary sciences for this programme were languages, mathematics, optics, scientia experimentalis and alchemy, followed by metaphysics and mortal philosophy. Bacon leaves no doubt that he regarded himself as having struck a highly personal attitude to most of the intellectual matters with which he dealt, but his writings are not as unusual as the legends growing about him might suggest. They have, on the whole, the virtues rather than the vices of Scholasticism, which at its best involved the sifting of evidence and the balancing of authority against authority. Bacon was conscious of the dangers of reliance on authority: Rashdall draws attention to the irony of his argument against authority consisting chiefly of a series of citations. Most of the content of his writings was derived from Latin translations of Greek and Arabic authors. He insisted on the need for accurate translations. When it was that he learned Greek himself is not certain, but his Greek grammar may be placed after 1267, since in it he corrected a philological mistake in the Opus tertium. He also wrote a Hebrew grammar to help in the understanding of Scripture. One of the most interesting and attractive aspects of Bacon is he awareness of the small place of Christendom in a world largely occupied by unbelievers, 'and there is no one to show them the truth.'13 He recommended that Christians study and distinguish different beliefs and try to discover common ground in monotheism with Judaism and Islam, and he insisted that the truth must be shown not by force but by argument and example. The resistance of conquered people to forcible conversion, such as practised by the Teutonic knights, was 'against violation, not to the arguments of a better sect.'14 Hence the need to understand philosophy not only in itself but 'considering how it is useful to the Church of God and is useful and necessary for directing the republic of the faithful, and how far it is effective for the conversion of infidels; and how those who cannot be converted may be kept in check no less by the works of wisdom than the labour of war.'15 Science would strengthen the defences of Christendom both against the external threat of Islam and the Tartars and against the methods of 'fascination' that he believed had been used in the Children's Crusade and the revolt of the Pastoreaux, and would be used by the Antichrist. Bacon's mathematics included, on the one hand, astronomy and astrology (discussed later) and, on the other, a geometrical theory of physical causation related to his optics. His assertions that 'in the things of the world, as regards

12 13 14 15

Opus maius, VI, 1. Ibid., Bridges ed., Ill, 122. Ibid., II, 377. Opus tertium, Brewer ed., pp. 3-4.

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their efficient and generating causes, nothing can be known without the power of geometry' and that 'it is necessary to verify the matter of the world by demonstration set forth in geometrical lines'16 came straight from Grosseteste's theory of multiplicatio specierum, or propagation of power (of which light and heat were examples), and his account of the 'common corporeity' that gave form and dimensions to all material substances. 'Every multiplication is either according to lines, or angles, of figures.'17 This theory provided the efficient cause of every occurrence in the universe, in the celestial and terrestrial regions, in matter and the senses, and in animate and inanimate things. In thus trying to reduce different phenomena to the same terms, Grosseteste and Bacon showed a sound physical insight even though their technical performance remained for the most part weak. These conceptions made optics the fundamental physical science, and it is in his treatment of this subject that Bacon appears most effective. Besides Grosseteste his main optical sources were Euclid, Ptolemy, al-Kindi, and Ibn al-Haytham (Alhazen). He followed Grosseteste in emphasising the use of lenses not only for burning but for magnification, to aid natural vision. He seems to have made an original advance by giving constructions, based on those of Ptolemy for plane surfaces and of Ibn al-Haytham for convex refracting surfaces, providing eight rules (canones) classifying the properties of convex and concave spherical surfaces with the eye in various relationships to the refracting media. He wrote: If a man looks at letters and other minute objects through the medium of a crystal or of glass or of some other transparent body placed upon the letters, and this is the smaller part of a sphere whose convexity is towards the eye, and the eye is in the air, he will see the letters much better and they will appear larger to him. For in accordance with the truth of the fifth rule [Fig. 1] about a spherical medium beneath which is the object or on this side of its centre, and whose convexity is towards the eye, everything agrees towards magnification [ad magnitudinem], because the angle is large under which it is seen, and the image is larger, and the position of the image is nearer, because the object is between the eye and the centre. And therefore this instrument is useful for the aged and for those with weak eyes. For they can see a letter, no matter how small, at sufficient magnitude.18 According to the fifth rule,19 if the rays leaving the object, AB, and refracted at the convex surface of the lens meet at the eye, E, placed at their focus, a magnified image, MN, will be seen at the intersections of the diameters passing from the centre of curvature, C, through AB to this surface and the projections of the rays entering the eye. As he did not seem to envisage the use of 16

Opus mains, Bridges ed., I, 143-144. Ibid., p. 112. 18 Ibid., V.iii.ii.4 (Bridges ed., II, 157). 19 Figure I is redrawn and relettered from Opus maius, V.iii.ii.3, British Museum MS Royal V.f.viii, 13th cent., f. 93r. 17

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Fig. 1 combinations of lenses, Bacon got no further than Grosseteste in speculating about magnifications such that 'from an incredible distance we may read the minutest letters and may number the particles of dust and sand, because of the magnitude of the angle under which we may see them.'20 But he did make an important contribution to the history of physiological optics in the West by his exposition of Ibn al-Haytham's account of the eye as an image-forming device, basing his ocular anatomy on Hunayn ibn Ishaq and Ibn Sma. In doing so, he seems to have introduced a new concept of laws of nature (a term found in Lucretius and numerous other authors more widely read, such as St Basil) by his reference to the 'laws of reflection and refraction' as leges communes nature.21 His meaning is clarified by his discussion elsewhere of a lex nature universalis22 requiring the continuity of bodies and thus giving a positive explanation, in place of the negative horror vacui, which he rejected, of such phenomena as water remaining in a clepsydra so long as its upper opening remained closed - an explanation comparable to one found in Adelard of Bath's Natural Questions. Universal nature constituted from these common laws, including those de multiplication specierum, was superimposed on the system of particular natures making up the Aristotelian universe - not yet the seventeenth-century concept but perhaps a step toward it. 'Having laid down the roots of wisdom of the Latins as regards languages and mathematics and perspective,' Bacon began Part VI of the Opus maius, 'I wish now to unfold the roots on the part of scientia experimental, because without experience [experientia] nothing can be known sufficiently.23 This science, 'wholly unknown to the general run of students,' had 'three great

20

Ibid., Bridges ed., II, 165. Opus tertium, Duhem ed., pp. 78, 90; Opus maius, Bridges ed., II, 49. 22 Ibid., 1,151; De multiplicationespecierum, ibid., II, 453; Communia naturalium, Steele ed., fasc. 3, pp. 220, 224. 23 Opus maius, Bridges ed., II, 167. 21

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prerogatives with respect to the other sciences.'24 The first was to certify the conclusions of deductive reasoning in existing speculative sciences, including mathematics. As an example he gave an investigation of the shape and colours of the rainbow involving both theoretical reasoning and the collection of instances of related phenomena in order to discover their common cause. The second prerogative was to add to existing sciences new knowledge that they could not discover by deduction. Examples were the discovery of the properties of the magnet, the prolonging of human life by observing what plants produced this effect naturally in animals, and the purification of gold beyond the present achievements of alchemy. The third prerogative was to investigate the secrets of nature outside the bounds of existing sciences, opening up knowledge of the past and future and the possibility of marvelous inventions, such as ever-burning lamps and explosive powders. It is clear that Bacon's scientia experimentalis was not exactly what this term might now suggest, but belonged equally to 'natural magic' aimed at producing astonishing as well as practically useful effects by harnessing the hidden powers of nature. His approach had been profoundly influenced by the pseudoAristotelian Secretum secretorum, of which he had produced an annotated edition variously dated between 1243 and sometime before 1257, but he also insisted that his new science would expose the frauds of magicians by revealing the natural causes of effects. The 'dominus experimentorum' of the Opus tertium25 who may have been Pierre de Maricourt, the pioneer investigator of magnetism, is praised for understanding all these essential characteristics. In the Opus minus,26 Bacon described possibly original experiments of his own with a lodestone held above and below a floating magnet, and argued that it was not the Nautical (Pole) Star that caused its orientation, or simply the north part of the heavens, but all four parts equally. It was in this work, and in the Opus tertium27 that he inserted his main discussion of alchemy, including the conversion of base metals into gold and silver. There is a further discussion in the Communia naturalium,28 together with sketches of the sciences of medicine and agriculture. In the Communia mathematical and the Epistola de secretis operibus artis et naturae et de nullitate magiae,30 he described more wonderful machines for flying, lifting weights, and driving carriages, ships and submarines, and so on, which he believed had been made in antiquity and could be made again. Despite his occasional references to them, Bacon in his accredited writings deals with neither instruments nor mathematical tables in any but a superficial 24 25 26 27 28 29 30

Ibid., p. 172. Brewer ed., pp. 46-47. Ibid., pp. 383-384. Little ed., pp. 80-89. Steeleed.,fasc. 2, pp. 6-8. Steele ed., fasc, 16, pp. 42-44. Brewer ed., p. 533.

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way. For this reason it is hard to measure his stature by comparison with that of his contemporaries whom we should call astronomers and mathematicians. We are not encouraged to set great store by the stories that while in Paris he constructed astronomical tables and supplied the new masters with geometrical problems that none of their audiences could solve.31 His mathematics and astronomy were in fact almost wholly derivative, and he was not always a good judge of competence, preferring, for instance, al-Bitruji to Ptolemy. Bacon is often held to have achieved a deep and novel insight in regard to the role of mathematics in science, an insight that to the modern mind is almost platitudinous. In this connection it is easy to forget the large numbers of astronomers of antiquity and the middle ages for whom mathematics was an essential part of the science, and the smaller numbers of natural philosophers who had made use of simpler mathematical techniques than those of astronomy. It is more to the point to notice that Bacon argues for the usefulness of mathematics in almost every realm of academic activity. Part IV of the Opus maius is devoted to the usefulness of mathematics (1) in human affairs (this section was published separately as the Specula mathematica); (2) in divine affairs, such as chronology, the fixing of feasts, natural phenomena, arithmetic and music; (3) in ecclesiastical affairs, such as the certification of faith and the emendation of the calendar; and (4) in affairs of state, under which heading are included geography and astrology. When Bacon sang the praises of mathematics, 'the first of the sciences,' 'the door and key of the sciences,' 'the alphabet of philosophy,' it has to be remembered that he used the word in an unusually wide sense. Bacon seemed to fear that mathematics would be dismissed as one of the blacker arts, as when arithmetic was applied to geomancy. He sought 'per vias mathematics verificare omnia que in naturalibus scientias sunt necessaria', and yet in the last resort, experience was still necessary, and in a sense supreme.32 So loud and long were Bacon's praises of the mathematics that it is hard to avoid the conclusion that his love of the subject was unrequited. He could compose his De communibus mathematice and mention, in geometry, nothing beyond definitions, axioms, and methods. Apart from mathematically trivial results in such practical contexts as engineering, optics, astronomy and the like, his works apparently contain not a single proof, not a single theorem; and we must take on trust the story of the difficult problem he devised for the young Paris masters. As for his analytical skills and his views on the citation of authority, rather than try to resolve the geometrical paradox of the doctrine of atomism - that it can make the hypotenuse and side of a square commensurable - he preferred simply to dismiss it as being contrary to Euclid. The standard discussion of ratios in Euclid, Book V, did not include a numerical treatment of the subject, for which the standard medieval authority

31 32

Opus tertium, Brewer ed., pp. 7, 36, 38. See, e.g., Opus maius, Bridges ed., II, 172-173.

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was the Arithmetica of Boethius. There the different species of ratio are tediously listed and subdivided, and the absence of a similar logical division of ratio in Euclid was complained of by Bacon in Communia mathematical3 He was not to carry out the programme at which he might seem to have hinted, and not until Bradwardine's Geometria speculativa did the Schoolmen make any progress toward a numerical description of irrational ratios, except perhaps in some halting attempts to elucidate Proposition III of Archimedes' De mensura circuit. As for the relation of logic to mathematics, Bacon inverted, in a sense, the logistic thesis of our own century: without mathematics, for instance, the categories were unintelligible.34 Mathematics alone gave absolute certainty. Bacon was unusual in that he generally named his sources, citing such authors as Theodosius, Euclid, Ptolemy, al-Farabi, and - among modern writers Jordanus de Nemore (De triangulis and Arithmetica} and Adelard. Despite his criticism of Jordanus, by any reckoning a better mathematician than Bacon, he had praise for 'the only two perfect mathematicians' (of his time), John of London and Pierre de Maricourt. He also condescended to praise Campanus of Novara and a 'Master Nicholas,' teacher of Amauri, son of Simon de Montfort. In the last analysis, almost everything Bacon wrote under the title of mathematics is best regarded as being at a metaphysical level. His view that in mathematics we have perfect demonstration reinforced his theory of natural action. His philosophy of science, however, was inherently empiricist: rational argument may cause us to dismiss a question, but it neither gives us proof nor removes doubt. It was held in the Opus maius that a more accurate knowledge of the latitudes and longitudes of placed was needed for (1) knowledge of mankind and the natural world; (2) facilitation of the spiritual government of the world - missionaries, for example, would be saved from danger and from much wasted labour; (3) knowledge of the whereabouts of the ten tribes and even of the Antichrist. His geography was nevertheless a compilation of works on descriptive geography (in which he gave, as it were, an extended verbal map of the world) by such writers as Ptolemy and al-Farghani, supplemented by the reports of Franciscan travellers, especially to the East. In the Opus maius35 he stated the possibility of voyaging from Spain to India. The passage was inserted, without reference to its source, in the Imago mundi36 of Cardinal Pierre d'Ailly (d. 1420). Humboldt argued that this passage, quoted by Columbus in a letter of 1498 to Ferdinand and Isabella, was more important in the discovery of America than the Toscanelli letters. Thorndike suggests that Columbus probably did not read the vital work until

33 34 35 36

Steeleed.,fasc. 16, p. 80. Opus maius, Bridges ed., I, 102; cf. Communia mathematica, Steele ed., fasc. 16, p. 16. Bridges ed., I, 290 ff. Imago mundi was first published at Louvain in 1480 or 1487.

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his return from the first voyage of 1492.37 It is immaterial, as Thorndike points out, whether Bacon was merely optimistically citing Aristotle, Seneca, Nero, and Pliny on the distance of Spain from India. In fact Bacon argued as cogently from such longitudes and latitudes as were available in the Toledan tables as he did from classical authors. For the radius of the earth Bacon took a figure of 3,245 miles (al-Farghani). He stated that the earth's surface was less than three-quarters water. In both cases he selected good figures from a great many authoritative but bad ones. It is clear, nevertheless, from his repetition of the method of determining the size of the earth - a method he took from al-Farghani - that he had no appreciation whatsoever of the practical difficulties it involved. Bacon appears to have sent a map to the pope with his Opus mains. Although it is now lost, from the description he gave it appears to have included the better known towns of the world plotted by their latitudes and longitudes as found in many contemporaneous lists.38 We have no knowledge of the projection adopted, but the description is compatible with the use of a rectangular co-ordinate system. Bacon used the words 'astronomia' and 'astrologia' in a typically ambiguous manner, but there is no doubt that he believed in the reasonableness of what we would call astrology. In the Opus tertium he spoke of astrology as the most important part of mathematics, dividing it into a speculative, or theoretical, part, presumably of the sort included in Sacrobosco's Sphere, and a practical part, 'que dicitur astronomia,'39 concerned with the design of instruments and tables.40 A remark in the Opus maius,41 written in 1267, confirms a similar remark made four years later by Robertus Anglicus,42 to the effect that conscious efforts were being made to drive what amounts to a clock (in Bacon's example the spherical astrolabe was to be driven) at a constant rate. This seems to confirm approximately the terminus ante quern non previously determined for the mechanical clock. On many occasions Bacon emphasised at length that the two sorts of 'astrology' were essential if man was to learn of the celestial influences on which terrestrial happenings depended. By reference to Ptolemy, Haly Ibn Sina, Abu Ma'shar, Messahala, and others, he showed that the best astrologers had not held that the influence of the stars subjugated the human will, and that the Fathers who objected to astrology on these grounds had

37

A History of Magic and Experimental Science, II, 645. Bridges ed., I, 300. 39 Cf. Communia mathematica, Steele ed., fasc. 16, p. 49. 40 Brewer ed., p. 106. Since in ch. XII of the same work he seems to have used the word 'tables' to refer primarily to almanacs, i.e., ephemerides, and to have spoken of instruments only as a means of verifying tables, it is probable that here he meant to refer only to the astrolabe and the equatorium. 41 Bridges ed., II, 202-203. 42 See L. Thorndike, The Sphere ofSacrobosco and Its Commentators (Chicago, 1949), p. 72. 38

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never denied that astrology could throw light on future events. It was possible to predict human behaviour statistically but not with certainty in individual cases. Astrology might strengthen faith in the stability of the Church and foretell the fall of Islam and the coming of the Antichrist; and all these things 'ut auctores docent et experiencia certificat.'43 On occasion he likened astrological influence to the influence of a magnet over iron. In his main works Bacon did not discuss the technicalities of astronomy or astrology, but in both of the works ascribed to him with the title De diebus creticis44 the standard medical astrology of the time is rehearsed. These works are not merely compilations of older authorities. Although technically they are in no sense new, they have a rational cast and even include the testimony of medical men of the time. The first of these two works is interesting because it incorporates the whole of the De impressione aeris attributed to Grosseteste and printed among his works by Baur. Little45 suggests that Grosseteste (d. 1253) collaborated with Bacon. Internal evidence suggests a date of composition of about 1249. Some planetary positions quoted for that year are sufficiently inaccurate to suggest that the work was written before 1249 rather than after, and that the author was by no means as skilled as the best astronomers of the time. The Speculum astronomic, of doubtful authorship (see below), is inconsistent with certain of Bacon's accredited writings. It is essentially a criticism of Stephen Tempier's decree of 1277 attacking 219 errors, several involving a belief in astrology. As already seen, Bacon's prison sentence was probably related to the bishop's decrees. Bacon's astronomical influence was slight in all respects, although through Paul of Middleburg he is said to have influenced Copernicus.46 His writings on the calendar were frequently cited.47 Theologians treated the calendar with a respect it did not deserve, regarding it as a product of astronomy, while astronomers would have treated it with more disdain had they been detached enough to perceive it in a historical context. Here Bacon's scepticism was useful, and whatever the depth of his astronomical knowledge, he wrote on calendar reform with as much insight as anyone before Regiomontanus Nicholas of Cusa notwithstanding. In discussing the errors of the Julian calendar, he asserted that the length of the Julian year (365 1A days) was in excess of the truth by about one day in 130 years, later changing this to one day in 125 years. The length of the (tropical) year implied was better than

43

Opus maius, I, 385. Steele ed., fasc. p, appendices ii and iii, ed. Little. 45 Little, ibid., p. xxx. 46 Bridges ed., I, xxxiii, 292. 47 See bibliography. Note that the same passage occurs, word for word, in Opus tertium, Brewer ed., pp. 271-292; and in Opus maius, Bridges ed., I, 281. Notice, however, that the Computus, written 1263-1265, does not contain any passage from either of these works, and that it acknowledges Arabic, rather than paying lip service to Hebrew, sources. 44

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Ptolemy's, and indeed better than that accepted in the Alphonsine tables compiled a few years after the Opus maius. (The correct figure for Bacon's time was one day in a little over 129 years.) The Alphonsine tables imply that the Julian error is one day in about 134 years. There is no reason whatsoever to suppose, as many have done following Augustus De Morgan, that Bacon's data were his own. Thabit ibn Qurra made the length of the year shorter than the Julian year by almost exactly one day in 130 years, and according to a curious passage in the Communia naturalium Thabit was 'maximus Christianorum astronomus.' In the Computus, however, Thabit is grouped with alBattanl and others who are said to have argued for one day in 106 years, while Asophus ('Abd al-Rahman ibn 'Umar al-Sufi) appears to have been the most probable source of influence, with his one day in 131 years.48 As a means of reforming the calendar, Bacon seems finally to have recommended the removal of one day in 125 years (cf. the Gregorian method of ignoring three leap years in four centuries), and in connection with Easter, since the nineteen-year cycle is in error, the astronomical calculation of the feast; otherwise a lunisolar year like that of the eastern nations should be adopted. (Grosseteste had previously made this proposal.) He tempered this rash suggestion with the pious qualification that if an astronomical calculation of Easter was to be adopted, Hebrew astronomical tables should be used. His proposals may be compared with the much less radical ones of Nicholas of Cusa, who in his Reparatio calendarii (pre-1437?) merely suggested a temporary patching up of the calendar, eliminating a number of days to alter the equinox suitably (Gregorian reform, supervised by Clavius, took the same superfluous step) and changing the 'golden number' so as to make the ecclesiastical moon correspond for a time with reality. These solutions were inferior to Bacon's, including fewer safeguards against a future state of affairs in which Church usage and the ordinances of the Fathers might differ appreciably. It is worth noting that Stoffler proposed to omit one day in 134 years (an obviously Alphonsine parameter), while Pierre d'Ailly followed Bacon explicitly in advocating a lunisolar cycle. Again, in connection with a proposal for calendar reform in England, we find that in 1582 John Dee commended Bacon to Queen Elizabeth as one who had 'instructed and admonished' the 'Romane Bishopp,' who was now 'contented to follow so neare the footsteps of veritye.'49 Judging by the speed of English legislation in the matter of calendar reform, it seems that Bacon was a little less than five centuries ahead of most of his countrymen. Little wrote in 1914, The extant manuscripts of Bacon's works show that the "Doctor mirabilis never wanted admirers,"'50 and cited as evidence the

48 49 50

Steele ed., fasc. 6, pp. 12-18. Corpus Christi College, Oxford, MS C. 254, f. 161r. Pp. 30-31.

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existence of twenty-seven manuscripts of the Perspective?1 alone, dating from the thirteenth to the seventeenth centuries. Apart from his proposals for the calendar it was on Bacon's optics that most scientific value was placed, by his contemporary Witelo as well as by Francesco Maurolico, John Dee, Leonard Digges, Hobbes, and the first editors of his works. At the same time his accounts of alchemy and natural magic gave him more dubious fame, varying from the sixteenth to the nineteenth centuries with current popular prejudices.

BIBLIOGRAPHY i. ORIGINAL WORKS. A number of Baconian problems must remain unsolved until there is a complete critical edition of his works: see the bibliography by Little in Roger Bacon: Essays (Oxford, 1914), pp. 375-426; compare G. Sarton, Introduction to the History of Science, II (Baltimore, 1931), 963-967; and L. Thorndike and P. Kibre, A Catalogue oflncipits of Mediaeval Scientific Writings in Latin (2nd ed., Cambridge, Mass. 1963. The earliest of Bacon's authentic works to be printed was the Epistola de secretis operibus artis et naturae (De mirabili potestate artis et naturae) (Paris, 1542; Basel, 1593); in the Opera, J. Dee, ed. (Hamburg, 1618); in French (Lyons, 1557; Paris, 1612,1629); in English (London, 1597,1659); in German (Eisleben, 1608); and other eds. After this appeared the De retardandis senectutis accidentibus et de sensibus conservandis (Oxford, 1590; in English, London, 1683); and Specula mathematica (part of Opus maius IV); in qua De specierum multiplication earumdemque in inferioribus virtute agitur and Perspectiva (Opus maius V), both ed. J. Combach (Frankfurt, 1614). There were other early eds. of the doubtful Speculum alchemiae (Nuremburg, 1541; in French, 1557; English, 1597; German, 1608; with later reissues) and the collection De arte chymiae scripta (Frankfurt, 1603, 1620). The 1st ed. of the Opus maius was by S. Jebb (London, 1733), followed by an improved ed. (Venice, 1750), both including only pts. I-VI. Pr. VII was included in the new ed. by J.H. Bridges, 2 vols. (Oxford, 1897), with a supp. vol. (Ill) of revisions and additional notes (London, 1900). This ed. was trans, into English by R.B. Burke (Philadelphia, 1928). Pt. VII of the actual MS sent to the pope has been ed. by E. Massa, Rogeri Baconi Moralis philosophia (Zurich, 1953). The eds. of Jebb and Bridges (Vols. II and III, pp. 183-185) both include De multiplication specierum, a separate treatise forming part of a larger work; a further section of this has been ed. with a discussion of its date and associations by F.M. Delorme, 'Le prologue de Roger Bacon a son traite De influentiis agentium,' in Antionianum, 18 (1943), 81-90. The 1st eds. of the Opus minus and the Opus tertium, together with the Compendium studii philosophic and a new ed. of the Epistola de secretis 51

Opus maius, pt. v.

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operibus, were by J.S. Brewer in Fr. Rogeri Bacon Opera quaedam hactenus inedita (London, 1859). Further sections of the first two works have been ed. by F. A. Gasquet, 'An Unpublished Fragment of Roger Bacon,' in The English Historical Review, 12 (1897), 494-517, a prefatory letter and other parts of Opus minus; P. Duhem. Un fragment inedit de I'Opus tertium de Roger Bacon (Quaracchi, 1909), on optics, astronomy, and alchemy; and A.G. Little, Part of the Opus tertium of Roger Bacon, British Society of Franciscan Studies, IV (Aberdeen, 1912). The last two items include Bacon's De enigmatibus alkimie. For further parts of the Opus minus, including discussions of alchemy, still unpublished, see A. Pelzer, 'Une source inconnue de Roger Bacon, Alfred de Sareshel, commentateur des Meteorologiques d'Aristote,' in Archivium Frandscanum historicum, 12 (1919), 44-67. Other works have been ed. by E. Nolan and S.A. Hirsch, The Greek Grammar of Roger Bacon, and a Fragment of His Hebrew Grammar (Cambridge, 1902); H. Rashdall, Fratris Rogeri Baconi Compendium studii theologii, British Society of Franciscan Studies, III (Aberdeen, 1911); S.H. Thomson, 'An Unnoticed Treatise of Roger Bacon on Time and Motion,' in Isis, 27 (1937), 219-224; and in Opera hactenus inedita Rogeri Baconi, R. Steele, ed. (unless otherwise stated), 16 fasc. (Oxford, 1905-1940): (1) Metaphysical De viciis contractis in studio theologie (1905); (2-4) Communia naturalium (1905-1913); (5) Secretum secretorum cum glossis et notulis (1920); (6) Computus (1926); (7) Questiones supra undecimum prime philosophic Aristotelis (Metaphysica, XII) (1926); (8) Questiones supra libros quatuor physicorum Aristotelis, F.M. Delorme, ed. (1928); (9) De retardatione accidentium senectutis cum aliis opusculis de rebus medicinalibus, A.G. Little and E. Withington, eds. (1928); (10) Questiones supra libros prime philosophic Aristotelis (Metaphysica, I, II, V-X) (1930); (11) Questiones altere supra libros prime philosophic Aristotelis (Metaphysica, I-IV), Questiones supra de plantis (1932); (12) Questiones supra librum de causis (1935); (13) Questiones supra libros octo physicorum Aristotelis, F.M. Delorme, ed. (1935); (14) Liber de sensu et sensato, Summa de sophismatibus et distinctionibus (1937); (15) Summa grammatica, Sumule dialectices (1940); and (16) Communia mathematica (1940). The Chronica XXIV generalium ordinis minorum (ca. 1370) was pub. inAnalecta Franciscana, 3 (1897). II. SECONDARY LITERATURE. The best critical study of Bacon's life is T. Crowley, Roger Bacon: The Problem of the Soul in His Philosophical Commentaries (Louvain-Dublin, 1950). The pioneering study by E. Charles, Roger Bacon: Sa vie, ses ouvrages, ses doctrines d'apres des textes inedits (Paris, 1861), is now mostly of historical interest. Essential studies are A.G. Little, ed., Roger Bacon: Essays Contributed by Various Writers (Oxford, 1914), especially contributions by Little (life and works), L. Baur (Grosseteste's influence), Hirsch (philology), E. Wiedemann, S. Vogl, and E. Wiirschmidt (optics), Duhem (vacuum), M.M.P. Muir (alchemy), E. Withington (medicine)' and I.E. Sandys (English literature); Little, Franciscan Letters, Papers and Documents (Manchester, 1943); L. Thorndike, A History of Magic and

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Experimental Science, II (New York, 1929), 616-691; S.C. Easton, Roger Bacon and His Search for a Universal Science (Oxford, 1952), with bibliography; and F. Alessio, Mito e scienza in Ruggero Bacone (Milan, 1957). Studies of particular aspects are E. Schlund, Tetrus Peregrinus von Maricourt: Sein Leben unsd seine Schriften,' in Archivum Fransiscanum historicum, 4 (1911), 445-449, 636-643; L. Baur, 'Die philosophischen Werke des Robert Grosseteste,' in Beitrage zur Geschichte der Philosophic des Mittelalters, 9 (1912), 52-63 and 'Die Philosophic des Robert Grosseteste,' ibid., 18 (1917), 92-120; P. Duhem, Le systeme du monde (Paris, 1916-1958), III, 260-277, 411-442, V, 375-411, VIII, 121-168; A. Birkenmajer, '£tudes sur Witelo, i-iv,' in Bulletin international de I'Academie polanaise des sciences et des lettres, Classe d'histoire et de philosophis (1920), 354-360 and 'Robert Grosseteste and Richard Fournival,' in Mediaevalia et humanistica, 5 (1948), 36-41; R. Carton, L'experience physique chez Roger Bacon, L'experience mystique de I 'illumination interieure chez Roger Bacon, La synthese doctrinale de Roger Bacon, nos. 2, 3, 5 in the series Etudes de philosophic medievale (Paris, 1924); C.B. Vandewalle, Roger Bacon dans I'histoire de la philologie (Paris, 1929); G. Meyer, 'En quel sens peut-on parler de "methode scientifique" de Roger Bacon,' in Bulletin de litterature ecclesiastique (Toulouse), 53 (1952), 3-25, 77-98; A.C. Crombie, Roger Grosseteste and the Origins of Experimental Science 1100-1700, 3rd imp. (Oxford, 1971), pp. 41, 139-162, 204-207,213-218,278-281, with bibliography and The Mechanistic Hypothesis and the Scientific Study of Vision,' in Proceedings of the Royal Microscopical Society, 2 (1967), 20-30, 43-45; M. Schramm, 'Aristotelianism: Basis and Obstacle to Scientific Progress in the Middle Ages,' in History of Science, 2 (1963), 104-108; and A. Pacchi, 'Ruggero Bacone e Roberto Grossatesta in un inedito hobbesiano del 1634,' in Rivista critica di storia filosofia, 20 (1965), 499-502.

Further References See A.C. Crombie, Science, Optics and Music . . . (1990) 258, 284, Styles of Scientific Thinking . . . (1994); J.N.G. Hackett, The Meaning of Experimental Science (Scientia experimentalis) in the Philosophy of Roger Bacon (University of Toronto doctoral thesis, 1983), Roger Bacon: An annotated bibliography (New York, forthcoming); D.C. Lindberg, Theories of Vision from AlKindi to Kepler (Chicago, 1976), Studies in the History of Medieval Optics (London, 1983); with Roger Bacon, Philosophy of Nature, a critical ed. with English trans!., introd. and notes of De multiplication specierum and De speculis comburentibus by D.C. Lindberg (Oxford, 1983).

The most customary course of all this nature has certain natural laws of its own according to which both the spirit of life, which is in a creature, has in some way certain settled desires of its own, which even malevolence cannot overcome, and the elements of this corporeal world have their settled power and quality, what any one of them may or may not effect and what may or may not come from what. (St. Augustine, De Genesi ad litteram ix. 17)

6

Infinite Power and the Laws of Nature: A Medieval Speculation A fundamental problem for any system of thought is the validation of its first principles. This was the problem to which the earliest Greek mathematicians and philosophers had to address themselves in their search for principles which established the characteristically Western style of abstract thinking. They assumed that they were dealing with a stable world, both of thought and of existence, of which the principles had to be found. But what if an even more fundamental principle was postulated on which that Stability depended, a principle of unlimited or infinite power capable of changing the principles of the world? What, further, if this principle was essentially inscrutable? That was the question to which Western philosophers had to address themselves when dealing with the confrontation, during the 13th and 14th centuries, of Greek cosmology and metaphysics (especially of Aristotle) with the accepted Christian doctrine that the world had been created by an omnipotent and utterly undeterminable agent. I want to consider briefly the consequences for natural philosophy of that doctrine. We are familiar with the effects on physical science of fundamental conceptual changes, such as those brought about by using statistical instead of mechanical postulates and by the postulates of relativity. We may look at the effects of this Hebrew-Christian postulate of creation on Greek physics and metaphysics in a similar way, remembering of course that this was not a scientific postulate but one believed to have been handed down to mankind by revelation from the First Principle itself. The postulate of creation obliged medieval natural philosophers to rethink some basic assumptions of the Greek physics and metaphysics, with which they became familiar through the texts and Latin translations made available in Western Europe during the 12th and 13th centuries. They had to rethink the question of natural necessity involved in the regularities of nature, and the conception of causality both as existing in nature and as knowable by man. Out of these considerations came a new conception of laws of nature, in the form to become a scientific commonplace in the writings of Descartes, Boyle and Newton. So let us look briefly at the history of conceptions of natural necessity, law-like regularities and eventually laws of nature, as they appeared with diverse meanings depending on the context of assumptions about the nature of things. Essentially they were of two kinds: (1) as conceived

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by Plato, Aristotle, the Greek atomists and the Stoics, intrinsic in the existing world; (2) as conceived in Hebrew and Christian thought, laid down by the external creator of the world. Both involved a comparison between moral laws of mankind and physical laws of nature, a comparison requiring clarification in the course of scientific history. I will first say something briefly about the history of these questions, and then come finally to the effect of the postulate of the infinite power of the creator of nature upon the conception of laws of nature as established by the 17th century. The notion that nature followed inescapable laws or regularities was a fundamental conception introduced by the earliest Greek philosophers in contrast with earlier beliefs. The Babylonian astronomers for example had developed highly sophisticated arithmetical methods of calculating and predicting the movements of the heavenly bodies, within a system of beliefs in which those movements (and indeed everything that happened in the world) were carried out by the arbitrary wills of supernatural beings. The order of things was then a kind of legal or sociological order of arrangements between these beings. By contrast, the Greeks introduced two fundamental and related concepts: that of causality, which allowed for no freedom of action outside an exclusive causal order of things (I pass over the questions of chance and uncertainty which they also discussed); and that of proof from established or assumed first principles. These were related: effects followed from postulated causes just as consequences followed from postulated premises. Related also were the decision of questions by argument and evidence, as distinct from edict, custom, revelation etc., and the introduction of models embodying mathematical necessity and physical causality, such as Eudoxus's cosmological model postulating the celestial spheres. The order of nature so postulated was at once mathematical and physical, and also moral, and this combination was to characterize conceptions of nature (in different ways according to varying contexts of general beliefs) down through the 19th century, and in some respects residually does so still. For Homer and Hesiod nature (physis) was at once a physical and a moral order, in the sense that what was allotted by destiny (tnoira) happened both necessarily and also rightly in the physical world and in human affairs alike. A notion of law as distinct from custom or usage appeared in the meaning given to nomos as the dispensation of Zeus. Nomos then came to signify, beyond the normal processes and habitual behaviour of nature and mankind, the regular and rightful functions that ought to be exercised within the allotted limits of necessity 0). The changing significance of nature, necessity, law and related terms in Greek, Latin and later languages marked the changing contexts and contents of European natural philosophy. When the divine craftsman of the Timaeus

0) Cf. F. M. Cornford, From Religion to Philosophy, Cambridge 1912; Idem, The Laws of Motion in the Ancient World, Cambridge 1931; P. Brunei and A. Mieli, Histoire des sciences: Antiquite, Paris 1935; F. Heinimann, Nomos und Physis, Basel 1935; H. and H. A. Frankfort, J. A. Wilson and T. fakobsen, The Intellectual Adventure of Ancient Man, Chicago 1946; B. Snell, The Discovery of the Mind, trans. T. G. Rosenmeyer, Oxford 1953; G. Neugebauer, The Exact Sciences in Antiquity, Providence, R. I. 19572; W. K. C. Guthrie, A History of Greek Philosophy, 6 vols., Cambridge 1962-81. This paper s based on my discussion of the subject in my: Styles of Scientific Thinking in the European Tradition, London 1994, > with full documentation and bibliography.

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fashioned the world by imposing his moral design upon the materials given in «the nature of the universe» by «the laws of destiny (TKXV-CO? qnicnv v6[xou$ TOU<; eifiapfjievou<;)» (4IE), the consequence «was a mixed results of the combination of necessity and reason. Reason overcame necessity by persuading her to guide the greatest part of the things that become towards what is best» (48A). The demiurge could in this way fashion the world, but he did not create it, as did the omnipotent Jehovah in contemporary Hebrew doctrine, out of nothing, with an existence entirely external to and dependent upon himself. In the Latinized and Christianized Plato, this distinction was to be confused, as was the Platonic conception of law as a necessity rather arising from the materials given than laid down by divine decree. Thus Calcidius in the fourth or fifth century A.D. translated Timaeus (4IE) as «[...] universae rei naturam spectare iussit kgesque immutabilis decreti docuit ostendens» (2). Ficino translated this a millemum later as «monstravit universi naturam, at leges fatales edixit», and another phrase «contrary to the established use of nature (rcapa TOU? -afc (puae
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to bear, by which all diverse things may be created* (I, 817-29). But in nature «not by design did the first-beginnings of things place themselves each in their order with keen intelligence*, but rather, «by trying every kind of motion and union, at length they fall into such dispositions as those of which this created sum of things consists* (I, 1021-2, 1026-8). Thus the bodies of the first-beginnings in the ages past moved with the same motion as now, and hereafter will be borne on forever in the same way; such things as have been wont to come to being will be brought to birth under the same conditions [II, 297-301]. In this endless process neither can the motions of destruction prevail for ever, and bury life in an eternal tomb, nor yet can the motions of creation and increase for ever bring things to birth and preserve them. So war waged from time everlasting is carried on by balanced strife of the first-beginnings. Now here, now there, the vital forces of things conquer and are conquered alike [II, 569-76]. Just as the common letters of the alphabet gave rise to many different words and meanings, so the «first-beginnings common to many things* could «make up wholes different from one another* (II, 695-8). But just as in living things «all are born of fixed seeds and a fixed parent and can as they grow preserve their kind», so always what happened «must come about in a fixed way (certa fieri ratione)». It was not only living things in their generation that were «bound by these laws (teneri legibus hisce), but the same condition (ratio) sets a limit to all things* (II, 707-10, 718-9). We should not then assume purpose in asking «by what law (foedus) all things are created, and how they must of necessity abide by it, nor can they break through the firm ordinances of everlasting time (aevi [...] leges)» (V, 56-58). By the same laws of nature arose everything attributed to the gods. The world was too imperfect to be of divine origin, «so great are the faults with which it stands beset* (199). Thus «each of these things comes forth after its own manner, and all preserve their separate marks by a fixed law of nature (foedere naturae certo)» (923-4). One should look for such laws in everything, as in the generation of living things, or as one asked «by what law of nature it comes about that iron can be attracted by the stone which the Greeks call the magnet, from the name of its native place* (VI, 906-8). Or again one must look similarly for the law that gave rise to language, by which man got «the first power to know and see in his mind what he wanted to do* (V, 1049). The first systematic confrontation of Greek thought with the Hebrew theology of creation came in the 1st century B.C. with Philo Judaeus of Alexandria (5). The last great thinker of a line of Hellenized Jews in Alexandria who set out to reformulate Greek philosophy in terms of that theology, Philo in turn came both directly

(') Philo ludaeus, Opera, Geneva 1613; with English translation by F. H. Colson and G. H. Whitaker, 10 vols. with 2 supplements trans. R. Marcus, London 1929-62; Lei oeuvres, ed. by R. Arnaldez, J. Pouilloux, C. Mondesert, 16 vols., Paris 1961-67; cf. H. A. Wolfson, Pbilo, 2 vols., Cambridge, MA 1947; R. Arnaldez et Al, Philon d'Alexandrie, Paris 1967.

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and through Augustine and other routes to affect profoundly the formulation of later Christian, Moslem and Jewish thinking about the relation of God to the world and to mankind. Philo accepted the Greek conception of immutable causality which determined the order of the world, but he was at pains to identify the true source of that order. He made use of the Stoic terms logos and logos spermatikos, seminal principle or reason (6), but gave them a different meaning. He argued with the support of Scripture that God did not act as Aristotle had maintained as an essentially passive first cause coeternal with the world emanating by necessity from the divine reason, that God did not make the world out of preexisting matter as in the Timaeus, that God was neither material nor within the world as supposed by the Stoics, and that God was in no way necessitated, but that he had acted with entirely free omnipotence in creating ex nihilo a world separate from himself. Philo used the term logos for principles that entered into this process first as the rational pattern on which God modelled his creation like a «city which was fashioned beforehand within the mind of the architect* (De opificio mundi, 5,20) so that the world discerned only by the intellect is nothing else than the reason (logos) of God when he is engaged in the act of creation. For (to revert to our illustration) the city discernible by the intellect alone is nothing else than the reasoning faculty of the architect in the act of planning to found the city [6,24, cf. 4,16-7,29].

Finally the logos was the system of principles introduced in the act of creation into the world as its immutable laws, God's power existing within the world itself. These were found in «the natures of the heavenly bodies and the movements of the stars» and «numberless other operations of nature*, often obscure to us, for all things are not within the ken of mortals, yet working together for the permanence of the whole; operations which are invariably carried out under ordinances and laws (Oeo(ioT( xoti v6|xoi() which God laid down in his universe as unalterable [19,61].

The «cause for the sake of which this universe was created* (5,21) was as Plato had written God's desire to share his goodness, by an act not necessitated by his perfection but of wholly free providence not propotional to his acutal powers, «for these are without end or limit, but in proportion to the capacities of the recipients* (6,23). The logos existing in nature provided thus for its harmony and for the perpetuation of species by means of the «seminal essences (spermatikai ousiai)» within which «hidden and imperceptible are the logoi of all things* (13,43, cf. 44). But if God had so chosen, he could have created a different world, so that «if the existent One had willed to employ his skill, by which he made amphibious creatures, in making a new kind of creature living in all the elements* (Quod detenus potion insidiari solet) (42,154) (7), he could have changed the existing natural order. God was absolute lord of the universe: «For this world is the great city, and it has a single polity and a single law (nomos), and this is the reason (logos) of nature, commanding what should be done and forbidding what should not be done* (De (6) Cf. Diogenes Laertius, VII, 134, 136, 147. (7) Cf. Lucretius, op. cit., Ill, 784-787; V, 128-131.

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Josepho, 6,29); and as absolute lord he could overrule that law and order as in the miracles well attested by Scripture. Philo saw in Scripture both literal and underlying meanings, from which he could apply the concept of law to God as an analogy (8), but it was no more than an analogy. For God's nature was so unlike created natures as to be unknowable by human reason, a conclusion that was to take a central place in subsequent Christian, Moslem and Jewish philosophy. The survival and revival in the West of Platonic and atomist thought, as of the equally influential Greek scepticism and Stoicism, depended in the first place on the survival of the Greek texts and the making of Latin versions. Their survival and revival depended at the same time on the ideas presented. Platonism, atomism especially in its Epicurean form, and Stoicism each offered at once an account of the origin and nature of things and a morality for the human condition appropriate to that account. Sceptical criticism forced each alike to defend its principles and in turn was forced into defence against counterattack. These philosophies diversified the intellectual context of scientific thinking in antiquity, and again in medieval and early modern Europe, by relating the sciences of nature to more general problems of knowledge and existence. They promoted in the culture of each society or period a certain specificity of commitment and expectation. Platonic thought, with a deceptive similarity to Christianity which at first captivated Augustine, was promoted by him through the essential mediation of Plotinus with the firm proviso that, in its fundamental doctrines of God, the creation and the soul, it was very different. Augustine was much influenced, in his use of the scriptural theology of creation as a cardinal principle of his natural philosophy, by Philo Judaeus. He established a Platonized Latin Christian philosophy with the historically pregnant conception of the world as the work of an eternal omnipotent, omniscient, providential and wholly distinct creator. Augustine offered with his theological insight into the inexorable objectivity of the laws of nature, indifferent to human wishes even if alterable by their creator, an encouragement to rational knowledge of them, and a scientific conception of methods of acquiring and exercising such knowledge. God the creator of all things knew beforehand, without any beginning, all things to come in time. [...] And with respect to all his creatures, both spiritual and corporeal, it is not because they are that he knows them, but because he knows them they are. For he was not ignorant of what he was to create; hence he created because he knew, he did not know because he created [De Trinitate XV, 13.22] (»).

(8) De Josepho, 6, 28; Quaestiones in Genesim IV, 90, 151, 184, 205; Quaestiones in Exodum II, 19, 59. (9) Aurelius Augustinus Hipponensis Ep., Opera, 20 vols., Venice 1584; Opera omnia, ed. J. P. Migne, 16 vols., Paris 1861; with individual works in Corpus Scriptorum Ecclesiasticorum Latinomm, XXV..., Prague, Vienna & Leipzig 1891-..., and in Corpus Christianum, Turnhout, 1954-...; also Oeuvres, vol. V, 2 (De quantitate animae), ed. P. de Labriolle, Bruges 1939; De civ. Dei, trans. H. Bettenson, Harmondsworth, Middlesex 1972; cf. A. Schubert, Augustins lex-aetema-Lehre nacb Inhalt und Quellen, «Beitrage zur Geschichte der Philosophic des Mittelalters», XXIV, 2, Miinster 1924; J. F. Callahan, Four Views of Time in Ancient Philosophy, Cambridge, MA 1948; R. M. Grant, Miracle and Natural Law in Graeco-Roman and Early Christian Thought, Amsterdam 1952; E. Portalie, A Guide to the Thought of Saint Augustine, trans. R. J. Bastian, London 1960; A. C. Crombie, Some Attitudes to Scientific Progress: Ancient, Medieval and Early Modem, in «History of Science» XIII (1975), pp. 213-30.

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So God created nothing in ignorance; which cannot be truly said of any human artificer. Then if God created all things knowingly, he created things which he already knew. This appears surprising but yet as something true: that this world could not be known to us if it did not already exist, but it could not have existed if it had not been known to God [De civ. Dei XI, 10.3].

As for men: Some people, in order to discover God, read a book. But there is a great book: the very appearance of created things. Look above and below, note, read. God, whom you want to discover, did not make the letters with ink; he put in front of your eyes the very things that he made (10). The laws of nature were the laws of numbers, exemplified to the senses in time and space in the rational proportions of sounds and of the growth of plants and general order of the visible universe. All things appearing in the universe have in fact originally and primarily already been created in a kind of web of the elements; but they make their appearance only when they get the opportunity. For just as mothers are pregnant with their young, so the world itself is pregnant with things that are to come into being, things that are not created in it except from that highest essence where nothing either springs up or dies, nothing has a beginning or an end. But when appropriate conditions arose, then those things which are contained and hidden in the secret bosom of nature may break out and be outwardly created in some way by the unfolding of their proper measures and numbers and weights, which they have received from him who has ordered all things in measure and number and weight [De Trin. Ill, 9, 16, quoting Wisdom 11, 21]. Just as in music, the provindential unfolding of the history both of nature and of mankind required time for its rational pattern to appear, and that rational pattern was in all cases embodied in the unchanging laws of nature that generated the process through time. Thus: The most customary course of all this nature has certain natural laws (naturales leges) of its own according to which both the spirit of life, which is in a creature, has in some way certain settled desires of its own, which even malevolence cannot overcome, and the elements of this corporeal world have their settled power and quality, what any one of them may or may not effect and what may or may not come from what. From these, as it were, origins (primordia) of things, all things which come to be, whatever they are and of whatever genus, take their beginnings and progresses, their departures and ends. So it is that a bean is not born from a grain of wheat, nor wheat from a bean, nor a man from a beast, nor a beast from a man. Above this natural motion and course of things the power of the Creator (10) Sanctus Augustinus, Novos ex codicibus vaticanis Sermones, Nova patrum bibliotheca, Sermo CXXVI, 6, ed. A. Mai, vol. I, Rome 1852, p. 292; cf. E. R. Curtius, European Literature and the Latin Middle Ages, trans. W. R. Trask, New York 1953.

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If the certainty of belief in the rational and providential creation of nature and destiny of mankind encouraged a disposition towards scientific inquiry (ll), Augustine's further insights into the conception of natural laws offered a context for the exercise of scientific knowledge. To acquire knowledge we could argue from natural signs or from general laws. Thus we argued from smoke to fire, from track to animal, from facial expression to emotion. We could also use conventional signs to convey information, as we did through language and as both we and the animals did through voice and gesture (12). We could prognosticate either legitimately or illegitimately: For it is one thing to say: If you drink the juice of this herb, your stomach will not hurt, and quite another to say: If you hang this herb round your neck, your stomach will not hurt. The first course is recommended as a healthful remedy; the second is to be condemned as a superstituous sign.

But more effective were arguments from general laws and starting conditions as in astronomy. For: It contains beyond a demonstration of present circumstances an element akin to historical narration, since on the basis of the present position and motion of the stars it is possible to trace their past courses according to rule. It also includes predictions concerning the future made according to rule which are not superstituous and portentous but certain and fixed by calculation. We do not seek to learn from these any application to our deeds and fates in the manner of the ravings of the astrologers but only information that pertains to the stars themselves. For just as he who computes the phases of the Moon, when he has observed its condition today, can determine its condition at a given period of years in the past or in the future, so in the same way those who are competent can make assertions about any of the other stars [De doctrina christiana II, 29].

Likewise in the arts whether of construction or of medicine, agriculture and navigation or of dancing and wrestling: «In all of these arts experience with the past makes possible inferences concerning the future, for no artificer in any of them performs operations except in so far as he bases his expectations of the future on past experience* (II, 30). Such predictions were made from the unchangeable laws of numbers instituted by God in nature, and discovered by men as the measure of the past and future: ( u ) Cf. De civ. Dei, XXII, 24; cf. A. C. Crombie, Some Attitudes..., cit. (12) De doctrina christiana, II, 2-3, trans. D. W. Robertson, Indianapolis & New York 1958; cf. R. A. Markus, St. Augustine on Signs, in «Phronesis» II (1957), pp. 60-83.

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It is perfectly clear to the most stupid persons that the science of numbers was not instituted by men, but rather investigated and discovered. Virgil did not wish to have the first syllable of Italia short, as the ancients pronounced it, and it was made long. But no one could in this fashion because of his personal desire arrange matters so that three threes are not nine, or do not geometrically produce a square figure, or are not the triple of the ternary, or are not one and a half times six, or are evenly divisible by two when odd numbers cannot be so divided. Whether they are considered in themselves or applied to the laws of figures, or of sound, or of some other motion, numbers have immutable rules not instituted by men but discovered through the sagacity of the more ingenious [II, 38]. By whatever mysterious means it may be that the future is foreseen, it is possible to see only something that exists; and whatever exists is not future but present. So when we speak of foreseeing the future, we do not see things that are not yet in being, that is, things that are future, but it may be that we see their causes or signs, which are already in being. In this way they are not future but present to the eye of the beholder, and by means of them the mind can form a concept of things that are still future and thus is able to predict them. These concepts already exist, and by seeing them present in their minds people are able to foretell the actual facts which they represent. [...] Suppose that I am watching the break of day. I predict that the Sun is about to rise. What I see is present, but what I foretell is future. I do not mean that the Sun is future, for it already exists, but that its rise is future, because it has not yet happened. But I could not foretell the sunrise unless I had a picture of it in my mind, just as I have at this moment while I am speaking about it. Yet the dawn, which I see in the sky, is not the sunrise, although it precedes it; nor is the picture which I have in my mind the sunrise. But both the dawn and my mental picture are seen in the present, and it is from them that I am able to predict the sunrise, which is future. The future then is not yet; it is not at all; and if it is not at all, it cannot possibly be seen. But it can be foretold from things that are present, because they exist now and can therefore be seen [Confessions XI, 18] ( ). Roger Bacon moved towards a new conception of nature by making the particular regularities which he called the laws of reflection and refraction examples of the common laws of nature. Likewise it was a lex nature universalis requiring the continuity of bodies that prevented the water from running out of a clepsydra, a vessel with a hole at the top and a perforated bottom, so long as the upper opening remained closed. This provided a positive cause for a positive phenomenon instead of the negative horror vacui .which Bacon rejected as contrary to the whole doctrine of adequate causation. The real cause he wrote in an early discussion of the question was «the orderly regulation of the bodies of the universe and the congruence of the machine of the world (ordinatio corporum universi et mundi machine congruentia)» (14). This he developed by explaining that «the particular nature of water remains in position upwards not by itself but by the power (virtus) of universal (1}) Trans. R. S. Pine-Coffin, Harmondsworth, Middlesex 1961, with changes. (M) Roger Bacon, Quaestiones supra libros quattuor Physicorum Aristotelis, ed. F. Delorme in Opera hactenus inedita, vol. VIII, Oxford 1928, pp. 200-1; cf. A. C. Crombie, The Significance of Medieval Discussions of Scientific Method for the Scientific Revolution, in Critical Problems in the History of Science, ed. M. Clagett, Madison, WI 1959, pp. 66-101; Idem, The Relevance of the Middle Ages to the Scientific Movement, in Perspectives in Medieval History, ed. K. F. Drew and F. S. Lear, Chicago 1963, pp. 35-57; A. C. Crombie and J. D. North, Bacon, Roger (c. 1219-c. 1292), in Dictionary of Scientific Biography, I, New York 1970, pp. 377-85; M. Schramm, Aristotelianism: Basis and Obstacle to Scientific Progress in the Middle Ages, in «History of Science* II (1963), pp. 91-113.

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nature», for it was held up «by a law of universal nature (ex lege nature universalis)» (15). This natura universalis acted as both efficient and final cause. Universal nature constituted from its common laws thus subordinated to itself the system of particular natures with their natural tendencies making up the Aristotelian universe. Its laws were necessary and general. The idea seems to have been suggested by Avicenna to whom Bacon referred in explaining in De multiplicatio specierum (I, 6) how «although by a law of particular nature (ex lege nature particularis) there is aptitude* for certain actions on the part of certain substances, nevertheless by divine ordination and a law of universal nature, about which Avicenna makes mention in Metaphysics VI, the capability is cut off and the act excluded* (16). The «common laws of natural multiplication (leges communes multiplicationum naturalium)» were shared by the propagation of light and other forms of energy, but these again could be dispensed for the benefit of natural order by «the capability of the power of the soul» in completing the act of vision (Opus maius V, 1,7). This occurred at the ultimate seat of sensory perception in the brain. Alhazen had argued that all that was required for true visual perception was that the image formed in the eye should preserve the proper arrangement of its parts corresponding to those of the object seen. To explain how this image was transmitted through the hollow optic nerves for presentation in the brain it was not then required that it should follow in these sentient organs the rectilinear propagation followed in non-sentient transparent media. Bacon brought this into his system as a further regular mode of propagation: After I have shown the power of mathematics, I have come to the position of optics (perspectiva) [...]. Next I show the origin and composition of the eyes, because without this we cannot know how vision is effected. Therefore I disclose how the evidently concave optic nerves in which is the visual power arise from parts of the brain, and how they are composed of a threefold membrane and intersect like a cross in the surface of the brain, in which intersection and not in the eye is the principle organ of seeing. [...] After this I show that the image (species) of a thing is sent forth to sight [...] because images come to every part of the pupil from the separate parts of the thing. [...] Next because vision would be ruined unless there were a refraction of the image between the pupil and the common nerve where there is the common section of the nerves of which I spoke above, and right would be seen left and vice versa, therefore I demonstrate this by the law of refraction (per legem refractionutn), set out geometrically, so that vision is thus saved. Yet it is necessary nevertheless that the image of the thing seen should propagate itself by a new kind of propagation, so that it should not transgress the laws which nature keeps in the bodies of the world. For the image at its place of refraction advances according to the tortuosity of the visual nerve, and does not keep to a straight path, which is wonderful, but nevertheless necessary for the completion of the operation. So that the power of the soul makes the image relinquish the common laws of nature (leges communes nature) and advance in a way that suits its operations [...] (17). That the laws of reflection and refraction are indeed common to all natural actions I have shown in the treatise on geometry [...] but principal(l3) Roger Bacon, Liber primus Communia naturalium, ed. R. Steele in Opera hactenus inedita, cit., vol. Ill, Oxford 1911, pp. 220, 224. (16) Idem, De multiplicatione specierum, ed. D. Lindberg in Roger Bacon's Philosophy of Nature, Oxford17 1983, pp. 84-5. ( ) Roger Bacon, Un fragment inedit de I'Opus tertium, Quarracchi 1909, pp. 75-8.

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ly in a separate work where I have explained the whole generation and multiplication and action and corruption of power (species) in all the bodies of the world (18).

It was the moral law of God that Thomas Aquinas looked for in nature. «A11 the moral precepts of law come from the law of nature (lex naturae)» (Summa tbeologiae, I, q. 60, art. 5) he wrote; and «the law of God is the natural inclination imprinted in any creature to act in a way suited to it according to nature*. Then came the question whether God can do anything outside the established order of nature. Aquinas answered with an exemplary account of the omnipotent freedom of the Hebrew and Christian God as the creator of the world, by contrast with the rational necessity of the Aristotelian God as its first cause. It might seem that God could not do anything outside the order of nature which he established, for if he did he would be acting against the order of justice which he had established likewise and moreover he would seem to be changeable. Aquinas distinguished the total freedom of God as the first cause from the necessity of secondary causes to follow the higher causes to which they were subject. We could suppose that God as the first cause would not «act against his foreknowledge, or his will, or his goodness*, but he is not subject to the order of secondary causes. On the contrary this order is subject to him, since it proceeds from him not by natural necessity but by the choice of his own will; for he could have created another order of things. Therefore God can do something outside this order created by him when he chooses: for example by producing effects of secondary causes without them, or by producing certain effects to which secondary causes do not extend. So Augustine says: God acts against the wonted course of nature, but by no means does he act against the supreme law, because he does not act against himself.

Then «since the order of nature is given to things by God, if he does anything outside this order, it is not against nature. Hence Augustine says: That is natural to each thing which is caused by him from whom is all limit, number and order in nature* (I, q. 105, art. 6) (19). The problem for the philosophers was at once epistemological and theological. The epistemological problem of defining what could be known about different subjectmatters and with what degrees of certainty was subordinated to the theological principle that the entire created world was contingent upon the inscrutable omnipotence of the Creator. William of Ockham in developing his theory of evidence under this principle limited the knowledge of the creation available to us to our immediate experience of the regularities found in particular objects. Empirically established connections were validated universally by the assumed principle that «all individuals of the same kind (ratio) are so made as to have effects of the same kind in a subject of the same kind disposed in the same way» (Super Quattuor libros SententiaC8 Ibidem, p. 90, referring to Comm. nat. and De mult, spec.: cf. ed. D. Lindberg in Roger Bacon's Philosophy..., cit., pp. 365-6. (19) Quoting Augustine, Contra Faustum XXVI, 3 (Opera omnia, ed. J. P. Migne, cit., vol. XLII, p. 480), and De utilitate credendi XVI (ibidem, p. 90).

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rum, Prol. q. 2, K) (20). Hence «there is between cause and effect indeed an essential order and dependence* (Prol. q. 9, F), but effect and cause were separate things and knowledge of one thing did not contain knowledge of another. For «I say that although God acts through the mediation of secondary causes*, such «action is voluntary, not necessary*. This did not «make secondary causes superfluous, because God does not act in any action with his whole power*. But from the omnipresence of divine power it follows that it is not possible to demonstrate that some effect is produced by a secondary cause: because although combustion always follows the bringing of fire near combustible material, it could still stand that fire is not its cause. Because God could have ordained that always when fire is present the nearby subject itself alone causes combustion, just as he has ordained with the Church that when certain words are brought forth grace is caused in the soul. Hence it is not possibile to prove by an effect that someone is a man, especially by an effect that appears in us, because everything we see in a man can be done by an embodied angel, as eating, drinking etc. That is evident from the angel of Tobias* [II, q. 4-5, R] (21).

He argued in a subtle analysis that the «intuitive notion (notitia intuitiva)» gained through sensory perception of something that existed was naturally infallible in providing «evident knowledge* of this fact «to which we gave assent*. But «God can cause a creditive act by which I believe that a thing that is absent is present* (Quodlibeta, V, 5). For «whatever God produces with secondary causes mediating he can produce and conserve immediately without them*. Then «God can make us see without a created object on which vision depends only as on a secondary cause* (VI, 6) (22). This doctrine placed natural philosophy and with it the relation (M) William of Ockham, Super Quattuor libros Sententiarum annotations..., Lyons 1495; Scriptum in lib. I Sentent. Prologus, ed. G. Gal and S. Brown, in Opera philosophica et theolagica, vol. I, St. Bonaventura, N.Y. 1967, pp. 91, 241; cf. R. Guelluy, Philosophic et theologie chez Guillaume d'Ockham, Louvain & Paris 1947; A. C. Crombie, Robert Grosseteste, Oxford 1953, 2nd cd. with corrections 1971; Idem, Augustine to Galileo, London & Cambridge, MA 1959, 3rd ed. reprinted 1979; L. Baudry, Lexique philosophique de Guillaume d'Occam, Paris 1958; F. Oakley, Christian Theology and the Newtonian Science: the Rise of the Concept of Laws of Nature, in «Church History* XXX (1961), pp. 433-57; Idem, Medieval Theories of Natural Law: William of Ockham and the Significance of the Voluntarist Tradition, in «Natural Law Forum* VI (1961), pp. 65-83; M.A. Pernoud, Innovation in William of Ockham's References to the Potentia Dei, in «Antonianum» XLV (1970), pp. 65-97; Idem, The Theory of the Potentia Dei according to Aquinas, Scotus and Ockham, ibid. XLVII (1972), pp. 69-95; W. J. Courtenay, Nominalism and Late Medieval Religion, in The Pursuit of Holiness in Late Medieval and Renaissance Religion, ed. C. Trinkaus and H. A. Oberman, Leiden 1974; A. Maurer, Ockham and the Possibility of a Better World, in «Medieval Studies* XXXVIII (1976), pp. 291-312; D. W. Clark, Voluntarism and Rationalism in the Ethics of Ockham, in «Franciscan Studies* XXXI (1971), pp. 72-87; Idem, Ockham on Human and Divine freedom, ibid. XXXVIII (1978), pp. 122-60; F. Oakley, Omnipotence, Covenant, and Order, Ithaca, N.Y. 1984, incorporating earlier papers and further discussion. (21) Ed. 1495, Quaestiones in lib. II Sent., q. 3-4, ed. G. Gal and R. Wood, in Opera philosophica, cit., vol. V, 1981, pp. 72-3; cf. Tobias 12, 19. (22) Quodlibeta septem, first complete ed., Strasbourg 1491, ed. J. C. Wey, in Opera philosophica, cit., vol. IX, 1980; cf. P. Boehner, The notitia intuitiva of Non-existents according to William of Ockham, in «Traditio» I (1943), pp. 223-75; A. C. Pegis, Concerning William of Ockham, ibid. II (1944), pp. 465-80; M. M. Adams, Intuitive Cognition, Certainty, and the Scepticism of William of Ockham, ibid. XXVI (1970), pp. 389-98; J. F. Boler, Intuitive and Abstractive Cognition, in The Cambridge History of Later Medieval Philosophy, ed. N. Kretzmann, A. J. Kenny and J. Pinborg, Cambridge 1982, pp. 460-78; K. H. Tachau, The Problem of species in medio at Oxford in the Generation after Ockham, in «Medieval Studies* XLIV (1982), pp. 394-443.

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of perceiver to perceived in a wholly new context. The order of nature as known to us as an order of observable facts depended on God not being a deceiver. The dominance of Christian thinking by the theology of divine omnipotence had specific consequences for natural philosophy in the 13th and 14th centuries through the distinction drawn between God's absolute and his ordained power (potentia Dei absolute et ordinate) (2i). The recovery and incorporation into the educational system of the entire body of Aristotle's writings in the 13th century restructured treatment of the relation of philosophy to theology and of reason to faith, and provided a new apprehension of the relation of God to the world and to mankind and hence of nature as the object of scientific inquiry. Discussion focused on the nature of God and the opennes of divine to human knowledge. The Platonic God as the good whose reason generated the world in accordance with the eternal ideas and the Aristotelian God as the rational first cause from which everything eternally emanated were alike necessitated by their rational perfection to produce the best of all possible worlds. Human reason moreover could know that divine reason in such a way as to discover not only the true constitution of the world but also why it must necessarily be so constituted and not otherwise, both morally and physically. The God of Abraham and of Christian theology by contrast, in his act of creating a world utterly distinct from himself, was absolutely free and inscrutable to man except in so far as he chose to reveal his providential plan through the patriarchs and prophets and through Christ and his Church. This was the historical world of Christian belief and expectation, a world of which the creation by God's providential will established the beginning and sequence of time in which under divine rule man was free to fulfil his ordained destiny. The contrast offered by the Aristotelian God as reason, of whose discovered essence and perfection the world was an eternally necessary consequence without beginning or end, was the sharper because Aristotelian metaphysics entered the Latin West accompanied by Arabic paraphrases and commentaries which stressed its determinism. Muslim as Christian theologians had had to defend God's omnipotent freedom against the same Aristotelian determinism, but when the philosophers Avicenna, Alfarabi and especially Averroes introduced the idea of creation into their interpretations of Aristotelian metaphysics they appeared in doing so to deny alike free providence to God and free responsibility to man (24). The Christian response was to examine the nature of God's power and its relation to his other attributes of will, reason, goodness and foreknowledge. Out of this examination came the distinction developed notably by Albertus Magnus and Aquinas between God's power considered absolutely in itself (potentia absolute), without regard to the order of the creation which he had established, and his ordained power (potentia ordinata) by which he acted in his

(") See on this subject especially F. Oakley, Omnipotence, Covenant..., cit., by which I have been guided in what follows. (24) Cf. F. Van Steenberghen, Aristote en Occident, Louvain 1946; Idem, Introduction a I'histoire de la philosophic medievale, Louvain 1974; L. Gardet and M. M. Anawati, Introduction a la theologie musulmane, Paris 1948; Majid Fakhey, Islamic Occasionalism and its Critiques by Averroes and Aquinas, London 1958; W. J. Courtenay, The Critique of Natural Causality in the Mutakallimun and Nominalism, in ^Harvard Theological Review* LXVI (1973), pp. 77-94; H. A. Wolfson, The Philosophy of Kalam, Cambridge, MA 1976.

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creative plan in accord with his providence and goodness (25). Absolutely then God could do as he liked, but in dealing with his creation he voluntarily restrained that absolute power within the providential order which he had created, except only when he chose to transcend it with a miracle. From each side of this distinction came specific consequences for natural philosophy. When Bishop Etienne Tempier of Paris in 1277 condemned a collection of philosophical theses his main purpose was to defend God's absolute power against any attempt to limit it by current Aristotelian philosophy (26). Thus a number of propositions asserted explicitly what God could not do: he could not make more than one world (34), make a man without the agency of a human father (35), move the world in such a way as to produce a vacuum (49), move anything differently from the way it moved (50), make an accident exist without a subject or more than three dimensions (141), or perform the absolutely impossibile (147). Tempier also condemned the proposition that there was no question disputable by reason which a philosopher ought not to dispute and decide by argument (145). Despite this last, the effect of the theological affirmation of God's absolute power seems to have been to have liberated the more enterprising natural philosophers from such Aristotelian limitations so that they could explore in speculation a variety of possible worlds which God might have created had he so chosen, possibilities involving the void, infinity and a plurality of universes. The condemned propositions were cited in the 14th century among others by Thomas Bradwardine, Jean Buridan, Nicole Oresme and Albert of Saxony and as late as the 17th century in defence of Galileo's cosmological arguments by Tommaso Campanella (27). The doctrine of the absolute and inscrutable power of God was to have a long reach in expanding the domain of the supernaturally and speculatively possible at the expense of accepted certainties of experience and demonstrations of philosophy. It was God's voluntary restraint of his absolute by his ordained power that preserved the established order of nature as a possible and proper object of human inquiry. That order was identified by Ockham as the order of laws that God had ordained and established: for «I say that God can do one thing by ordained power (23) Cf. Thomas Aquinas, Summa tbeologiae I, q. 25, art. 5 and Augustine (sec note 19); M. A. Permoud, The Theory of the Potentia Dei..., cit.; W. J. Courtenay, Nominalism and Late..., cit.,; B. Hamm, Promissio, Pactum, Ordinatio, Tubingen 1977, and especially F. Oakley, Omnipotence, Covenant..., cit. (26) Chartularium Univenitatis Parisiensis, ed. H. Denifle, A. Chatelain, vol. I, Paris 1889, pp. 54355, of which the numbering is followed here; cf. E. Grant (ed.), A Source Book in Medieval Science, Cambridge, MA 1974, pp. 45 ff. (") Cf. P. Duhem, Etudes sur Leonard de Vinci, vol. II, Paris 1909, pp. 41-4; Idem, Le systeme du monde, vols. VI, VIII, Paris 1954, 1958; A. Maier, Die Vorlaufer Galileis im 14. Jabrbundert, Rome 1949, pp. 155-215 (2nd ed. 1966); Idem, Metapbysische Hintergriinde Spatscholastischen Naturphilosophie, Rome 1955, pp. 381; A. C. Crombie, The Significance of Medieval..., cit.; J. E. Murdoch in The Cultural Context of Medieval Learning, ed. J. E. Murdoch and E. D. Sylla, Dordrecht & Boston, MA 1975, pp. 271-348; Idem, Infinity and Continuity, in The Cambridge History of Late Medieval Philosophy, cit., pp. 566-9; J. F. Wippel, The Condemnations of 1270 and 1277 at Paris, in «Journal of Medieval and Renaissance Studies* VII (1977), pp. 169-201; E. Grant, The Condemnation of 1277, God's Absolute Power, and Physical Thought in the Late Middle Ages, in «Viator» X (1979), pp. 211-44; Tommaso Campanella, Apologia pro Galileo, Frankfurt 1622, p. 24, English trans, by G. McColley («Smith College Studies in History» XXII, 3-4, Northampton, MA 1937); Italian trans, by L. Firpo, Torino 1969; R. Hissette, Enquete sur les 219 articles condamnes a Paris le 7 man 1277, Louvain 1977; L. Bianchi, L'errore di Aristotele: La polemica contra I'etemita del mondo nel XIII secolo, Firenze 1984.

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and another by absolute power». These were of course a single power in God, who did nothing that was not ordained. In this way we should understand that he can do something, whenever this is taken according to the laws ordained and established by God (secundum leges ordinatas et institutes a Deo) and that means what God can do by ordained power. In the other way, to be able to do something is taken for being able to do everything that does not involve a contradiction, whether God ordained this to be done or not, because God can do many things which he does not want to do [...]; and that means what God can do by absolute power. Thus the Pope cannot do something according to the law (jus) established by him which however he can do absolutely speaking.

Again in the scheme of salvation ordained by Christ to replace the Old Law (lex defuncta), «what was then possible according to the laws then established is no longer possible according to the law now established, although absolutely speaking it is possible* (28). Ockham in effect applied to the created world in general, alike to the moral order governing human behaviour and to the natural order governing the behaviour of irrational beings, the metaphor of laws decreed by a ruler, here the inscrutable God the Father Almighty, Maker of Heaven and Earth, of the Christian creed. With God's reasons no longer in any degree transparent to human reason as they still had been for Aquinas, mankind had no option but to accept the order of things as it was given in experience 0).

It was the «necessitee condicionel» of Chaucer's Nun's Priest's Tale, by which God granted free choice despite his foreknowledge, by contrast with the «symple necessitee» by which something had to be done (11. 4433-41) (}1). (») William of Ockham, Quodlibeta VI, 1, ed. J. C. Wey, cit., pp. 585-86; cf. F. Oakley, Christian Theology..., cit.; Idem, Medieval Theories..., cit.; Idem, Omnipotence, Covenant..., cit. (w) William of Ockham, Quaest. in lib. II Sent., q. 15, ed. G. Gal et R. Wood, cit., p. 352, cf. q. 3-4, pp. 58-60; F. Oakley ibid, with further references. C0) Quoted with changes from H. A. Oberman, The Harvest of Medieval Theology, Cambridge, MA 1963, p. 168 n.; Idem, Forerunners of the Reformation, New York 1966, p. 149; cf. W. Kolmel, Von Ockham zu Gabriel Biel: zur Naturrecbtslehre des 14. und 15. Jahrhunderto, in «Franziskanische Studien* XXXVII (1955), pp. 228-59. (3l) Cited with Holcot from F. Oakley, Omnipotence, Covenant..., cit., p. 64.

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The attribution of the natural order entirely to laws of nature imposed from without by God's ordained will, and the elimination from the concept of nature of any intrinsic principle of rationality such as Aristotle had postulated, assimilated nature to a product of art. It was the product of a divine art not transparent like that of the Timaeus to human reason, but utterly impenetrable, its order discoverable only so far as it was directly observable or divinely revealed. Hence the evident empiricism of 14th-century natural philosophy and its focus not on any ultimate purpose which the natural order might have in the divine economy, but rather on the regularities of nature visible to man and on explanations postulated to account for them in a creation separated from its Creator. Thus Buridan in applying the dynamics of impetus to the celestial spheres: One could say in fact that God, when he created the universe, set each of the celestial spheres in motion as it pleased him, impressing on each of them an impetus which has moved it ever since. God has therefore no longer to move these spheres, except in exerting a general influence similar to that by which he gives his concurrence to all phenomena. Thus he could rest on the seventh day from the work he had achieved, confiding to created things their mutual causes and effects (32).

Hence likewise the new relevance of analogies between the contrivance of the divine artificer, whose reasons man could not penetrate, and the contrivances which man could understand because he made them himself. The gravitational clock, propelled first by water and then mechanically by weights, had become gradually part of daily life by about the middle of the 14th century in many Western towns, where clocks had been set up in public places over the previous hundred years. Some appear to have been planetaria or astronomical clocks paralleling the motions of the celestial bodies, others to have been designed to measure the terrestrial hours. Elaborate astronomical clocks were devised and constructed by the Oxford mathematician Richard of Wallingford and in Italy by Giovanni de' Dondi. Perhaps the most famous terrestrial clock was that erected by Henri de Vick in Paris on the Palais Royal (now the Palais de Justice) in 1370, when Charles V of France ordered all churches in the city to ring the hours and quarters according to the equal divisions of the day incorporated in this instrument. Clocks came to interest philosophers as programmed mechanisms capable of self-regulation. Seven years after de Vick had installed his clock, Nicole Oresme completed his Le livre du del et du monde, commissioned by Charles V within his plan for translating into French the whole of Aristotle with commentaries. In this he wrote that it could be supposed that when God created the heavens, he put in them motive qualities and powers just as he put weight in terrestrial beings, and he put in them resistances against these motive powers. [...] And these powers are so adjusted, tempered and harmonized to the resistances that the movements are made without violence; and except for violence it is doubtless like a man making a clock and letting it go and be moved by itself. Thus God left the heavens to be moved continually according to the propor()2) Johannes Buridanus, Subtilissime Questiones supra octo Pbisicorum libros Amtotelu, VIII, q. 12, Paris 1509; cf. A. Maicr, Die Impetustheorie (1940) revised in Zwei Grundprobleme der Scbolastischen Naturpbiloiopbie, Rome 1951, p. 212; Idem, Metaphysische Hintergriinde..., cit.; A. C. Crombie, Augustine to Galileo, cit., vol. II, p. 82.

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tions which the motive powers have to the resistances and according to the established order [II, 2].

That order God respected even when extraordinarily he performed a miracle, for as Oresme argued in explaining that he could have lengthened the day for Joshua far more economically by stopping a rotating Earth than the whole rotating heavens: «When God performs a miracle, it must be supposed and held that he does this without disturbing the common course of nature more than the least that is necessary» (II, 25) (»). These ideas were all to have a long reach. Thus the Jesuit Francisco Sudrez in his Tractatus de legibus ac Deo legislator (1612) distinguished among the meanings of the term lex naturalis not only «that law which is in mankind» but also «that which fits all things, in accordance with the inclination imparted to them by the Author of nature*. But this latter acceptation of law is metaphorical, since things lacking reason are not properly speaking capable of law, just as they are not capable of obedience. Hence the efficacy of divine power and the natural necessity resulting therefrom in these things are called law metaphorically [I, 1].

God's free acts in so far as they operated externally might be said to relate to art, and in so acting he observed a law which God as artist (artifex) has imposed upon himself, so that he may carry out his works in accordance with it. For although God could have made and ruled the world in various ways, he has decided to constitute and govern it according t'o a certain definite law

applying to both the physical and the moral order. Hence it is said that God cannot do certain things according to ordinary law, namely which he has imposed upon himself, or that he cannot according to his ordained power (secundum potentiam ordinatam), that is reduced to such order by the same law. [...] Thus the free works of God are ruled by a law established by himself [II, 2] (M).

Similarly Descartes was to insist that even «the mathematical truths, which you call eternal, have been established by God and depend on him entirely as well (") Nicole Oresme, Le livre du del et du monde, ed. A. D. Menut and A. J. Denomy, trans. A. D. Menut, Madison, WI 1968; cf. for clockwork E. Zinner, Aus der Friikzeit der Raderuhr, in «Deutsches Museum: Abhandhungen und Berichtc* XXII (1954), 3, pp. 1-64; H. A. Lloyd, Mechanical Timekeepers, in A History of Technology, ed. C. J. Singer et AL, vol. Ill, Oxford 1957, pp. 648-75; D. J. de S. Price, On the Origins of Clockwork, Perpetual Motion Devices and the Compass, in ^Smithsonian Institution Bulletin* CCXVIII (1959), pp. 81-112; S. A. Bedini and F. R. Maddison, Mechanical Universe: The Astrarium of Giovanni de Dondi, ^Transactions of the American Philosophical Society* N.S. LVI, 5, Philadelphia, PA 1966; J. D. North, Richard of Wallingford, Oxford 1976; J. Le Goff, Pour un autre moyen age: Temps, travail et culture en Occident, Paris 1977; D. S. Landes, Revolution in Time, Cambridge, MA 1983; also A. C. Crombie, Augustine to Galileo, cit. ()4) Francis Suarez, S. ]., Tractatus de legibus..., Coimbra 1612, pp. 7-8, in Selections from Three Works, with introduction by J. B. Scott, vol. I, Oxford 1944, pp. 103-104; cf. F. Oakley, Omnipotence, Covenant..., cit.

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as do all other creatures*. For «it is God who has established these laws in nature, just as a king establishes laws in his kingdom*, and likewise «he could change them just as a king does his laws. [...] But I comprehend them as eternal and immutable. [...] But his will is free [...] yet his power is incomprehensible* (35). If it were asked «what has necessitated God to create these truths [...] I say that he has been as free to make it untrue, that all the lines drawn from the centre to the circumference were equal, as not to create the world* (36). We could not comprehend that divine power, by which again God could make it untrue that twice four was eight (37). Robert Boyle likewise was to be in no doubt that «if we suppose God to be omnipotent, (that is, to be able to do whatever involves no contradiction, that it should be done)*, the possibility of human science depended entirely upon his freely chosen constancy. For if we consider God as the author of the universe, and the free establisher of the laws of motion, whose general concourse is necessary to the conservation and efficacy of every particular physical agent, we cannot but acknowledge, that, by withholding his concourse, or changing these laws of motion, which depend perfectly upon his will, he may invalidate most, if not all the axioms and theorems of natural philosophy: these supposing the course of nature, and especially the established laws of motion among the parts of the universal matter, as those upon which all the phaenomena depend (}8).

As these were established, he thought that God's agency in the world [...] is like a rare clock, such as may be that at Strasburgh, where all things are so skilfully contrived, that the engine being once set a moving, all things proceed, according to the artificer's first design.

As for the term law, although for brevity and by custom he spoke of «the laws of motion and rest* as «the laws of nature*, this like Suarez he regarded as «but an improper and figurative expression*. For «to speak properly, a law being but a notional rule of acting according to the declared will of a superior, it is plain, that nothing but an intellectual being can be properly capable of receiving and acting by a law*. God as «the supreme and absolute Lord, [...] when he made the world, and established the laws of motion, gave them to matter, not to himself*. What he created he also disposed, and though I think it probable, that, in the conduct of that far greatest part of the universe which is merely corporeal, the wise Author of it does seldom manifestly ()3) R. Descartes to Marin Mersenne 15, IV, 1630, in Oeuvres, ed. by Ch. Adam and P. Tannery, vol. I, Paris 1897, pp. 145-6; cf. A. Funkenstein, Descartes, Eternal Truths, and Divine Omnipotence, in «Studies in History and Philosophy of Science* VI (1975), pp. 185-99; H. Frankfurt, Descartes and the Creation of the Eternal Truths, in «Philosophical Review* LXXXVI (1976), pp. 36-57. (J6) R. Descartes, letter of 27, V, 1630, in Oeuvres, cit., pp. 151-2. (") Idem, Meditationes prima philosophia, Responsio ad sextes objectiones (1641); Oeuvres, vol. VII, (1904), p. 436; cf. Pliny, Nat. hist., II, 5, 27 and 27, 97 (note 4 above). (38) R. Boyle, Some Considerations about the Reconcilableness of Reason and Religion, sects. 2, 3 (1675), ed. T. Birch, Works, vol. Ill, London 1744, pp. 515, 516; cf. J. A. H. Murray et Al., A New English Dictionary, VI, 1, ed. H. Bradley, Oxford 1903: Law; E. M. Klaaren, Religious Origins of Modem Science: Belief in Creation in Seventeenth-Century Thought, Grand Rapids, MI 1977; F. Oakley, Omnipotence, Covenant..., cit.

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procure a recession from the settled course of the universe, and especially from the most catholic laws of motion

yet where men were concerned I think it becomes a Christian philosopher to admit, in general, that God doth sometimes, in a peculiar though hidden way, interpose in the ordinary phenomena and events of crisis's; but yet that this is done so seldom, at least in a way that we can certainly discern, that we are not hastily to have recourse to an extraordinary providence, and much less to the strange care and skill of that questioned being called nature, in this or that particular case, though perhaps unexpected, if it may be probably accounted for by mechanical laws, and the ordinary course of things. For

the omniscient and almight author of things having once framed the world, and established in it the laws of motion, which he constantly maintains, there can no irregularity, or anomaly, happen, [...] that he did not from the beginning foresee and think fit to permit, since they are but genuine consequences of that order of things, that, at the beginning, he most wisely instituted.

Only «on some special occasions, this instituted order, either seemingly or really, has been violated* (}9). Against the deist use of the argument against God's special providence, that «after the first formation of the universe, all things are brought to pass by the settled laws of nature», Boyle insisted that God's special providence was evident above all in «the first formation of things*. For «the laws of motion, without which the present state and course of things could not be maintained, did not necesarily spring from the nature of matter, but depended upon the will of the divine author of things*. Besides, he repeated, I look upon a law as a moral, not a physical cause, as being indeed but a notional thing, according to which, an intelligent and free agent is bound to regulate its actions. But inanimate bodies are utterly incapable of understanding what a law is, or what it enjoins, or when they act conformably or unconformalby to it; and therefore the actions of inanimate bodies, which cannot incite or moderate their own actions, are produced by real power, not by laws; though the agents, if intelligent, may regulate the exertions of their power by settled rules ( °).

Boyle's attempt to restrict the term law to its proper human and moral context did not succeed, but the long tradition behind his insistence on the utter dependence of human science upon God's omnipotent will received an interesting extension by Isaac Newton. For God who created the world, who «governs all things [...] as Lord over all*, and who «knows all things that are and can be done* (41), could as easily if he so chose «vary the laws of nature, and make worlds of several sorts in several parts of the universe* (42). (39) R. Boyle, A Free Inquiry into the Vulgarly Received Notion of Nature, sects. 1, 2, 5, 6, 7 (1666-82); in Works, cit., vol. IV, (1744), pp. 362, 367, 385, 398, 403. («°) Idem, The Christian Virtuoso (1690); in Works, cit., vol. V, (1744), p. 46. (41) I. Newton, Philosophiae naturalis Principia mathematica, vol. Ill, Scholium generale, Londini 1687. («) Idem, Opticks, 4th ed. query 31, London 1730, pp. 379-80.

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Within this intellectual context the essentially theological concept of laws implanted by God in the creation of nature came to offer an invitation to man to discover and draw out these laws of nature by scientific observation and analysis. The theological concept of ordained law became transformed into the scientific concept of natural laws, not as moral imperatives sanctioned by right reason but as physical principles, albeit of a nature still with moral attributes. By the time of Newton the term laws of nature had come to designate the object of all scientific inquiry: the principles or axioms to be discovered by experimental and theoretical exploration, or postulated for experimental control. By itself the concept of laws of nature could scarcely have been a guide to how to conduct such an inquiry. What made it scientifically effective was its amalgamation with two matching concepts. First the analogy of natural with human art offered an invitation to simulate natural effects with artifacts made by and therefore understood by man: by discovering how to control hypothetical models of his own contrivance man could thus gain insight into the laws controlling nature itself. Secondly the concept of laws of nature became quantified by association with that of mathematical functions expressing the quantitative dependence of effect on cause in concomitant degrees (43). Thus changes in an effect (as the dependent variable) expressed as an algebraic function of the conditions necessary and sufficient to produce it (as the independent variables) could be precisely calculated from those conditions. It may be argued that the concept of functions can be found implicitly but effectively in antiquity: in tabulated correspondences of celestial motions in Babylonian and Greek astronomy, in the linkage made by musical theorists, from Archytas of Tarentum and Plato to Boethius, of different sensations of pitch with variations in the speeds of the motions producing sound, in Ptolemy's systematic correlation of the degrees of refraction of light with increasing angles of incidence, and so on. The concept may seem to be implied also by the Aristotelian principle that a cause must be adequate to produce an effect, and therefore that there must be a quantitative proportion between a cause and its effect. Yet it was evidently not until the 13th or 14th centuries that the implied notion of functional dependence between variable quantities was explicitly recognized in the West. Then it was developed first only in principle, without the systematic practice of measurement that was necessary to incorporate it effectively into experimental science. That practice was to develop first in the technical arts. It was not until the 17th century that systematic measurement was (43) Cf. my Styles of Scientific Thinking..., cit.,ptiv: Hypothetical Modelling, and for the concept of functions 'cns.~ 3, 5, 7, 9 with E- Cassirer, Das Erkenntnisproblem in der Philosophic und Wissenschaft der neueren Zeit, vol. m, Berlin 1923; J. L. Coolidge, The Origins of Analytical Geometry, in «Osiris» I (1936), p. 231-50; Idem, History of Geometrical Methods, Oxford 1940; C. B. Boyer, The Concepts of the Calculus, New York 1939; Idem, History of Analytical Geometry, New York 1956; A. Maier, Der Funktionsbegriff in der Physik des 14. Jahrhunderts, in «Divus Thomas» XIX (1946), pp. 147-66; On the Threshold of Exact Sciences, ed. and trans, by S. D. Sargent, Philadelphia, PA 1982; A. C. Crombie, Robert Grosseteste, cit.; Idem, Quantification in Medieval Physics, in «Isis» LII (1961), pp. 145-60; A. P. Youschkevitch, Geschichte der Mathematik in Mittelalter, Leipzig 1964; Idem, The Concept of Function up to the Middle of the Nineteenth Century, in «Archive for History of Exact Sciences» XVI (1976), pp. 37-85; M. Schramm, Steps towards the Idea of Function, in «History of Science* IV (1965), pp. 70-102; E. Grant, A Source Book..., cit.; O. Pedersen, Logistics and the Theory of Functions, in «Archives internationales d'histoire des sciences* XXIV (1974), pp. 29-50; Oberwolfach Mathematisches Forschungs — Institut, Proceedings of a Conference on the Development of the Concept of Function, Basel 1975.

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to be made essential to all physical research. It was combined then with a rational theory of quantity expressed in linear scales, replacing the inhibiting Greek conception that the properties of substances were present and had to be expressed as pairs of opposites, and with the analytical formulation of functional dependence by means of increasingly precise and powerful mathematical symbolism. By this time the mathematically defined general laws of nature had come to be seen to offer possibilities not given by the Aristotelian specific natures or forms or causes as the object of scientific inquiry. It was the mathematicization alike of the form and the content of scientific argument that brought about an essential change in natural science from the syllogistic logic of subject and predicate, within which the causal conditions for specific phenomena were defined, to the mathematical logic of linear demonstration, defining general relations of dependence within which the specific phenomena were included. All this can obviously not be seen as a consequence simply of a theological concept of infinite power. What can be seen as its consequence are expectations about the possibility of certain scientific knowledge. These appeared most dramatically in the cross-purposes that bedevilled Galileo's controversies with theologians. When Galileo in his first letter about the sunspots (1612) announced his hope to discover «the true constitution of the universe; for such a constitution exists, and exists in only one, true, real way, that could not possibly be otherwise* (Opere, V, 102) (44), he used the language Aristotle used for a completed and closed system of scientific knowledge. That was the constitution of the universe that must follow from true and certain knowledge of the First Principle. To achieve his goal Galileo in fact relied on the open-ended criterion of range of confirmation, by his telescopic observations and dynamical arguments, but theologians thought that by asserting that the discovered constitution of the universe could not be otherwise, he was imposing limitations on divine omnipotence. Neither side grasped clearly the difference that mathematical thinking made to the possibilities of apodeictic proof as envisaged traditionally in Aristotelian logic. But that is another story discussed elsewhere (43).

(") Le Opere di Galileo Galilei, ed. A. Favaro, 20 vols., Florence 1890-1909. (45) Cf. A. C. Crombie, Sources of Galileo's Early Natural Philosophy, in Reason, Experiment and Mysticism in the Scientific Revolution, ed. M. L. Righini Bonelli and W. R. Shea, New York 1975, pp. 157-75, 303-5; A. Carugo and A. C. Crombie, The Jesuits and Galileo's Ideas of Science and of Nature, in «Annali dell'Istituto e Museo di Storia della Scienza di Firenze» VIII, 2 (1983), pp. 3-68; Crombie and Carugo, Galileo's Natural Philosophy (forthcoming).

Galileo Galilei, from II Saggiatore (1623): frontispiece. The brilliantly witty rhetoric of his argument in this work delighted the newly elected Pope Urban VIII but infuriated the Jesuit object of his irony, the mathematician and architect Orazio Grassi.

7

Experimental Science and the Rational Artist in Early Modern Europe

T

HE ESSENTIAL TERM IS THE ITALIAN VIRTU, which Leon Battista Albert! used in the fifteenth century for "those excelling gifts which God gave to the soul of man, greatest and preeminent above all other earthly animals."1 A man of virtu in Renaissance Italian, coming from the Latin virtus meaning power or

^on Battista Alberti, I libri della famiglia, ed. Cecil Grayson (Opere volgari, vol. i, Ban, Italy: Laterza, 1960), p. 133; cf. for full documentation of this paper with bibliography Alistair C. Crombie, Styles of Scientific Thinking in the European Tradition (London: Duckworth and Co., 1994); also "Science and the Arts in Renaissance: The Search for Truth and Certainty, Old and New," History of Science 18 (1980), pp. 133-46, and in Science and the Arts in the Renaissance, ed. John W. Shirley and F. David Hoeniger (Washington, DC: The Folger Shakespeare Library, 1985), pp. 15-16, "Philosophical Presuppositions and Shifting Interpretations of Galileo" in Theory Change, Ancient Axiomatics and Galileo's Methodology: Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science, vol. i, ed. Jaakko Hintikka, David Gruender, and Evandro F. Agazzi (Dordrecht, Holland: D. Reidel, 1981), pp. 171—186, "Historical Commitments of European Science," Annali dell'Istituto e Museo di Storia della Scienza di Firenze, 7 (i) (1981), pp. 19-51: these and other papers are included in A.C. Crombie, Science, Optics and Music in Medieval and Early Modern Thought (London: Hambledon Press, 1990). A shorter version of this present paper was given at Williams College, MA, while Visiting Bernhard Professor, at the conference organized there by Professor Samuel Y. Edgerton, Jr. in October 1984 on "Art and Science in Related Revolutions." For the relations between the arts and the sciences in this period there are Rafaello Caverni, Storia del metodo sperimentale in Italia, 6 vol. (Florence: 1891-1900); Leonardo Olschki, Geschichte der neusprachlichen wissenschaftlichen Literatur, vol. i (Heidelberg: 1919), vol. ^ (Leipzig: 1911), vol. 3 (Halle an der Salle: 1917); Hedley Rhys, ed., Seventeenth Century Science and the Arts (Princeton, NJ: Princeton University Press, 1961); Erwin Panofsky, "Artist, Scientist, Genius: Notes on the 'Renaissance-Dammerung'" in The Renaissance: Six Essays by Wallace K. Ferguson et al. (New York: Harper Torchbooks, 1961), pp. 111-81; William P.D. Wightman, Science in a Renaissance Society (London: 1971); and Shirley and Hoeniger, eds., Science and the Arts in the Renaissance; and for most of the persons named the Dictionary of Scientific Biography, ed. Charles C. Gillispie, 16 vol. (New York: Charles Scribner and Sons, 1970-80).

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capability, was a man with active intellectual power to command any situation, to do as he intended, like an architect producing a building according to his design; by contrast with someone at the mercy of fortuna, of chance or luck, of the accidents of fortuitous circumstance, unforeseen and hence out of control. The conception of the man of virtu, the virtuoso aiming at reasoned and examined control alike of his own thoughts, intentions, and actions and also of his surroundings, points to the essence of the moral and intellectual commitments by which the Western scientific movement was generated. The conception of virtu embodied a program for relating man to the world as perceiver and knower and agent in the context of his integral moral, social, and cosmological existence. The program presupposed the stability of nature and mankind and of their relations; it entailed a commitment to an examined life of reasoned consistency in intellectual, practical, and moral life alike and it generated a common style in the mastery of self, or nature and of mankind alike by the rational anticipation of effects. To understand that common style we must take a long view reaching back to the Greek philosophers, mathematicians, medical men, historians, and dramatists who provided the models equally for the medieval and early modern scientific movement, as for the contemporary visual, musical, and literary arts. It was surely no accident that the same culture produced sciences and arts based alike on stable expectations, whether physical or moral: a mathematically and causally structured science of nature, a morally structured drama, and painting and music each structured mathematically to make their aesthetic or dramatic effects. The virtuoso was then the rational artist in all things, designing his intentions first by antecedent analysis in the mind, before executing them through the hands, whether he was aiming at mathematical or experimental investigation, at artistic composition, at the cultivation of private or public good by habit guided by right reason, or as an expedient politician at calculating from the regularities of human experience the most effective form of machination. We could take the virtuoso in this sense as diagnostic of Western civilization, as distinct from other civilizations of comparable or greater age and magnitude. Also diagnostic is a particularly rational form of being blinded by reason, which we could call the blind idiot syndrome. This refers to a computer programmed to make translations. It was asked to translate from English into Russian, and then back again into

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English, the phrase: "Out of sight, out of mind." The phrase came back from the Russian: "Blind idiot." Problems of this kind have arisen from perceptions that oversimplify or in other ways fail to comprehend what exists, in this case what existed in the English language. In every culture at any time men have experienced their world through the mediation of a particular vision of existence and of knowledge. This defines their cultural style. Failures of European vision to comprehend what existed, because it was unexpected, appeared in abundance in the intellectual and pictorial records of European expansion overseas, whether into various parts of Asia, or the Americas, or the South Pacific.2 Failures of scientific comprehension have regularly accompanied the revelations of such new scientific instruments as the microscope and telescope.3 The history of scientific thought is strewn with examples of even the most original scientific minds failing to comprehend or even to acknowledge certain phenomena, which could not exist within their powerful theoretical vision. Technical frontiers may leave phenomena out of sight; conceptual frontiers put them out of mind. The style common to the Western sciences and arts may be illustrated by a collage of examples, through which will become evident the pattern in which in a diversity of contexts virtu imposed structure eventually even upon fortuna itself. Thus wrote Plato: an architect used technical theory, providing antecedent analysis and design, as a "directive science" (Statesman 2,60 A—B) to control the construction of a building by means of measurement and calculation. For "all arts and forms of thought and all sciences employ ... number and calculation" (Republic, vii, 52,2 C). Any artist or craftsman in making something "has before his 2

Cf. Bernard Smith, European Vision and the South Pacific: A Study in the History of Art and Ideas (Oxford: Oxford University Press, 1960); Barbara M. Stafford, Voyage into Substance: Art, Science, Nature, and the Illustrated Travel Account, 1760-1840 (Cambridge, MA: MIT Press, 1984). 3 Cf. Gerard L'E Turner, "The Microscope as a Technical Frontier in Science" in Proceedings on the Royal Microscopical Society 2 (1967), pp. 175-197; Bernard Cohen, "The Influence of Theoretical Perspective on the Interpretation of Sense Data: Tycho Brahe and the New Star of 1572, and Galileo and the Mountains on the Moon," Annali dell'Istituto e Museo di Storia delta Scienza di Firenze 5 (i) (1980), pp. 3-13; Ian Hacking, "Do We See Through a Microscope?" Pacific Philosophical Quarterly 62 (1981), pp. 305-22; Samuel Y. Edgerton Jr., "Galileo, Florentine 'disegno,' and the 'Strange Spottedness' of the Moon," Art Journal (Fall 1984), pp. 225-32, and "The Renaissance Development of Scientific Illustration" in Science and the Arts, ed. Shirley and Hoeniger, pp. 168-97.

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mind the form or idea" (x, 596 B) of what he was to make. This was his model, just as the divine maker modelled the world from the eternal forms (Timaeus 2,8A-3oC, 466-480, 536). Sometimes in our perceptions "we are satisifed with the judgement of our senses" (Republic, vii, 52.36), but sometimes the senses alone could not resolve the apparent contradictions or illusions produced by nature or by art, as when apparent size varied with distance or when a straight stick partly in water looked bent, or in "many tricks of illusion, like scene-painting and conjuring. But such illusions can be dispelled by measuring, counting and weighing. We are no longer at the mercy of the senses; reason takes control" (x, 602.0-36). Art then lay across the boundary between true representation and deceit. On one side was "the making of likenesses, as in creating a copy that conforms to the proportions of the original in all three dimensions with every part properly coloured": this was fairly called a likeness [eikon]. But when for example the true proportions of a large sculpture were distorted to make them appear correct when seen from below, this only "seems to be a likeness" but is in fact merely "a semblance [phantasma]" produced by art (Sophist 2.25D-6C). Visual art then was like sophistry, which imposed upon its listeners "by means of words that cheat the ear, exhibiting images [eidola] of all things in a shadow-play of discourse so as to make them believe that they are hearing the truth" (2346). The sophistries of rhetoric were aimed not at truth but only at persuasion; but a master of persuasion might share common methods of argument with a true scientist seeking a different goal. Plato likened the methods of rhetoric to those of medicine. Each, in order to reach its goal, had to discover the true nature of its object. Rhetoric had to grasp the nature of the soul in order to see how it was persuasible; medicine had to grasp the nature of the body in order to see how it was healthy or curable: "In both cases you must analyze a nature... if you are to proceed scientifically, not merely by practice and routine, to impart health and strength to the body by prescribing remedies and diet, or by proper discourses and training to give to the soul the desired belief and virtue." At the end of his analysis the scientific rhetorician "will classify the types of discourse and the types of soul, and the various ways in which souls are affected, explaining the reasons in each case: suggesting the types of speech appropriate to each type of soul, and what kind of speech can be relied upon to create belief in one soul and disbelief in another, and why." For "a certain type of hearer will be easy to persuade, by a certain type of

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speech, to take such and such action, for such and such reason; while another type will be hard to persuade. All this the orator must fully grasp, and next he must watch it actually taking place in men's conduct." When the student of rhetoric, having grasped the theory, could place any individual person in this classification of characters, and could know how to seize the occasion for the appropriate tricks, "then and not till then he has well and truly achieved the art." There was "absolutely no need for the budding orator to concern himself with the truth about what is just or good conduct" or "who are just and good men In the law courts nobody cares about the truth in these matters, but only about persuasion, and that is concerned with what seems most likely" for the purpose. The would-be master of persuasion must then suppress or substitute facts according to need and say "goodbye to the truth forever." Then he will be "equipped with the art complete" (Phaedrus 269D-73A). Plato delineated very clearly in this account the goal of rational power over its subject matter that was to define the whole Western rational tradition, whether in seeking to find the truth or to persuade to belief or action. He set out systematically for the first time in his various writings the historic fact that mastery of rational scientific understanding brought with it power to manipulate matter and mind alike. Physical engineering and social engineering had the same form, and persuasion of the scientific (as of the artistic) acceptability of whatever was proposed or done became as much part of the scientific tradition as demonstrative proof. According to Aristotle, everything constituted by nature "has within itself a principle of motion and of stationariness" (Physics, ii. i, i92,b 14-15). Art by contrast imposed an external principle of change, but "art imitates nature" and hence was part of natural science (ii. 2,1943 22-23). For "if a house had been made by nature, it would have been made just as it is now by art; and if things made by nature were made also by art, they would be made in just the same way ...; in general art partly imitates nature, and partly completes what nature cannot complete." Thus "if the ship-building art were in the wood, it would produce the same results by nature" (ii. 8, 1993 12-17, b28). Art, entailing the ability to invent by rational deliberation and choice and to learn, distinguished man from other animals. Man alone "lives by art and reasonings." Hence man alone could progress. Aristotle distinguished "mere experience" of particular sensory perceptions from "connected experience" where memory of particulars

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led to knowledge of general regularities. In the latter sense "experience seems pretty much like science and art, but really science and art come to men through experience." For "knowledge and understanding belong rather to art than to mere experience, and artists are wiser than men of mere experience...; because the former know the cause, but the latter do not" (Metaphysics, i. i, 980025-981328). The "with things made the principle is in the maker; it is either reason or art or some faculty" (vi. i, iO25b22-3), and "all makings proceed either from art or from a faculty or from thought ...; from art proceed the things of which the form is in the soul of the artist" (vii. 7, 1032,32,5^1). Thus, whether in the practical, productive, or theoretical arts and sciences, two things were essential: "One is the choice of the right end or aim, the other is the discovery of the actions that will bring it about In all the arts and sciences both the end and the means should be within our control" (Politics, vii. 13, i33ib 25-37). Likewise in his moral behaviour man alone could choose and initiate his actions, and could, through practice guided by right reason, cultivate skill in virtue or vice as in any other art. Hence "choice is either desiderative reason or ratiocinative desire, and such an origin of action is a man" (Nicomachean Ethics, vi. 2, i i39b4~5). For "art is identical with a state of capacity to make, involving a true course of reasoning. All art is concerned with coming into being, that is, with contriving or considering how something may come into being which is capable of either being or not being, and whose origin is in the maker and not in the thing made"; it was in nature not in art that things existed "by necessity" (vi. 4,11403 1-16). By art then, by practice guided by reason, men acquired skill to control every aspect of their lives, whether in making material artifacts, or in managing the plants and animals and their own bodies or their fellow men, or in cultivating moral virtue or vice. The fulfillment of human intelligence in the arts and sciences was made possible by the fact that "of all animals man alone stands erect, in accordance with his godlike nature and essence" (De partibus animalium, iv. 10, 686a 27-29), for this raised up with his head the most exact senses of vision and hearing, and liberated his hands as an instrument for making both artificial things and other instruments. Thus by mind, eye, and hand man was the animal alone equipped for technical advance. There was an analogy between the rational art of nature and the rational art of man: "Our wonder is excited first by phenomena which occur in accordance with nature but of which we do not know

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the cause, and secondly by those which are produced by art despite nature for the benefit of mankind. Nature often operates contrary to human expediency; ... when therefore we have to do something contrary to nature, the difficulty of it perplexes us and we must call art to our aid." Then by "mechanical skill...: Mastered by nature, we overcome by art" (Mechanica, c. i, 8473 lo-b 16). One could say of anyone who had grasped the revolutions of the heavens that "his soul is like that of whoever fashioned them in the heavens. For when Archimedes fastened on to a [metal] sphere the movements of the moon, the sun, and the five planets, he did the same as the god of Plato who built the world in the Timaeus; he made one revolution of the sphere control several movements utterly unlike in slowness and speed. Now, if in this world this cannot be done without a god, neither could Archimedes have been able to imitate those same movements upon a sphere without divine genius" (Cicero, Tusculanae quaestiones, i. 25. 61-3). To investigate all the diverse subject matters of art and science upon which Aristotle imposed a similar rational form, he employed a likewise similar method of argument by analysis and synthesis. Thus he applied to politics as to physics "the method that has hitherto guided us. As in other departments of science, so in politics, the compound should always be resolved into the simple elements or least parts of the whole" (Politics, i. i, 12523 19-24). As with physical phenomena, so with the state and human society, the complex whole must first be analyzed into its elementary constituents, so that it could be reconstructed from those elements and so scientifically understood (Physics, i. i, 18439^1). Apart from the Timaeus, Plato's main works became known to the Latin West only with Marsilio Ficino's Latin translations made towards the end of the fifteenth century, followed by editions of the Greek. By contrast, practically all of Aristotle was known by the middle of the thirteenth century, mostly through the translations made during the previous hundred years. Hence philosophical conceptions of the relation of natural science to art, and of the structure of scientific argument, whether leading to scientific understanding or beyond that to artistic construction or engineering, were in early modern Europe at first predominantly Aristotelian. Later during the sixteenth century came the influence of Plato and with that of Greek mathematicians, especially Archimedes, in addition to Euclid, who had provided a model of scientific argument since the twelfth century. The original insight by which the Greek mathematicians had

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discovered an abstract order behind the chaos of immediate experience was into a realm of simple relations, as in the mathematical sciences of astronomy, optics, mechanics, and acoustics, which they had developed most successfully. Their inquiry into the explanation of a phenomenon became a search for the simplest and fewest principles that would produce it. Then, when the principles were postulated, the phenomenon must follow. Thus they exploited the speculative power of geometry by imposing upon phenomena at once its deductive logical structure and an appropriate model delineating for each its form in space. Euclid had established the classical postulational style first by developing in the Elements a rational theory of geometrical space. From this he developed in the Optics a geometrical theory of what must be seen in specified situations, accepting his postulates, which took the eye as the point of origin of straight lines of vision. Similarly, in the Sectio canonis, he developed a theory of acoustical perception from the postulate that sounds were produced by motions standing in a numerical ratio to each other in which pitch was determined by frequency. Euclid and other Greek mathematicians aimed ideally to develop their research into the phenomena purely theoretically within their geometrical or arithmetical model. Later they came to realize, as did Ptolemy in his Optics, that in exploring complex phenomena postulation must be controlled by observation and experiment, in order to decide whether a possible theoretical model yielded the consequences found in the actual world. The style of scientific argument in optics came thus especially through Ptolemy, and likewise later through Alhazen, to be seen in the thirteenth-century West as one of experimentally controlled postulation. This was to be the style of Renaissance art. It was already in the twelfth century envisaged as a program by Domingo Gundisalvo, following the tenth-century Arabic philosopher al-Farabl: "The artist" he wrote "is the natural philosopher who, proceeding rationally from the causes of things to the effects, and from effects to causes, searches for principles." Thus for "what appears in vision," whether true or illusory, optics "assigns the causes by which these things are brought about, and this by necessary demonstrations." Likewise for music, and for engineering: "The science of engines is the science for contriving how one can make all those things..., of which the measures are expressed and demonstrated in mathematical theory, agree ... in natural bodies. ... The sciences of engines therefore

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teach the ways of contriving and finding out how natural bodies may be fitted together by some artifice according to number, so that the use we are looking for may come from them."4 Again, Robert Grosseteste wrote in the thirteenth century: "All causes of natural efforts have to be given by means of lines, angles and figures, for otherwise it is impossible to have knowledge of the reason [propter quid] concerning them."5 Hence the need for mathematics in all natural philosophical investigations. Likewise, according to the French architect Villard de Honnecourt a generation later, in building and making machines, in design and portraiture alike "the art of geometry commands and teaches"; and "in order to work easily," it must be kept in high regard by anyone "who wants to know how each must work."6 Without going into the questions of precisely what these general programmatic utterances meant in particular practice, and of what mathematics meant in different contexts and periods, we may see in them a style of rational justification to be repeated again and again. No one was to argue more insistently than Roger Bacon for "the power of mathematics in the sciences and in the affairs and occupations of this world. ... Of these sciences the gate and key is mathematics" (Opus maius, iv. i. i). That effective natural philosophy required also practical experimental art was eloquently stated by Bacon's contemporary Pierre de Maricourt in his letter of 1269, De magnete. For he wrote "while the investigator of this subject must understand nature . . . he must also diligently use his own hands." Then "he will be able in a short time to correct an error which he could not do in eternity by natural philosophy and mathematics alone, if he lacked care with his hands. For in hidden operations we greatly need manual industry, without which we can usually accomplish nothing perfectly. Yet there are many things subject to the rule of reason which we 4

Dominicus Gundissalinus, De divisione philosophae, ed. L. Baur (Beitrage zur Geschichte der Philosophic des Mittelalters, 4 (1-3) Miinster: 1903), pp. 10,17, iiz, 122; cf. Alpharabius, De ortu scientiarum, ed. C. Baeumker (ibid., 19 (3) Miinster: 1916). 5 Robert Grosseteste, De lineis, angulis et figuris in Die philosophischen Werke, ed. L. Baur (Beitrage zur Geschichte der Philosophic des Mittelalters, 9 Miinster: 1912), p. 60; cf, A.C. Crombie, Robert Grosseteste and the Origins of Experimental Science 1100-1700 (Oxford: Oxford University Press, 1953, 1971). 6 Villard de Honnecourt, Kritische Gesamtausgabe des Bauhuttenbuches ms. fr. 19093 der Pariser Nationalbibliothek ed. H. R. Handloser (Vienna: 1935), folios iv, i8v, i9v.

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cannot investigate completely with the hand."7 Matching this rather with practical art than with natural philosophy in view, a contemporary asked of Alberti "in what class of learned men" to put him. He answered: "Among the natural scientists [physici].... Certainly ... he was born only to investigate the secrets of nature. And what kind of mathematics does he not know? Geometer, arithmetician, astronomer, musician, he wrote marvellously better than anyone for many centuries on perspective. ... He wrote on painting, he wrote on sculpture ... and he not only wrote but also made with his own hands."8 Alberti himself explained in 1435: "In writing about painting ... we will, to make our discourse clearer, first take from mathematicians those things which seem relevant to the subject. When we have learned these, we will go on, to the best of our ability, to explain the art of painting from the basic principles of nature. ... We will now go on to instruct the painter how he can represent with his hand what he has conceived with his mind."9 Alberti exemplified in his account of the painter the active self-conscious man of virtu, the rational artist who made himself effective by means of knowledge, technique, and continual practice. Governing all his thinking was his perception of analogy within diversity. He searched in all his work for an economy of explanation and of practice reached by thinking out the general principle behind each subject, whether in perspective painting, in the anatomical variations of the human body as in De sculptura, in architecture as in De re aedificatoria, in surveying as in the Descriptio urbis Romae and Ludi rerum mathematicarum, in the relation of Italian vernacular to classical Latin as in the Regule lingue florentine, in the art of ciphering as in De componendis cifris, or in his theory of moral life. He looked everywhere also for the issue of theory in practice and thereby its confirmation by observation. Thus moral like scientific virtu was to be cultivated by reasoned analysis of personal and contemporary experience, and by discourse with other men both present and past who recorded the experience and reflections of mankind. The ultimate aim of man in his natural life on this Earth 7

Petrus Peregrinus Maricurtensis, De magnete book i, ch. 2., ed. G. Hellman (Kara magnetica; Neudriicke von Schriften und Karten iiber Meteorologie und Erdmagnetismus 10 Berlin: 1898). 8 Cristpforo Landino, Commento... spora la Comedia di Danthe Algheri (Florence: 1491), folio iv1. 9 Alberti, De pictura book i, sections i and Z4, ed. Grayson in On Painting and On Sculpture (London: Phaedon Press, i97z), p. 36, 58.

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was to cultivate himself by reason, technique, and letters as a wellcomposed and controlled work of art. This was an Aristotelian humanist ideal viewed perhaps with skepticism by some contemporaries engaged more roughly with the real world, but its principle of reasoned control in an examined life had long been made part of traditional Christian moral theory. For Alberti it was the basis of both the personal and the social responsibility that all human activities and works entailed. Hence the necessity both for education and for that continual effort of practice in virtu, which alone could restrain the hazards of "unjust and malevolent fortuna" (I libri delta famiglia, prologue, p. 3). God had endowed man with an inborn virtu, and this it was our duty to cultivate both for our own sakes and by our work "so that times past and those present will be of service to those that have not yet come" (Profugiorum ab aerumna i, pp. 122-3). "Our first and proper use is to exert the power of our soul towards virtu," for: "To man alone among mortals is it given to investigate the causes of things, to examine how true are his thoughts and how good are his actions" (De iciarhia i, pp. 198, 212). At the same time he must live responsibly for the benefit of others, above all for "justice and truth" (ii, p. 286).10 All the practical arts proceeded then from a rational analysis of the subject matter and objectives of the art to their achievement in an appropriate representation or manipulation or use of the products of the analysis. Practical art like natural science became at once both highly intellectualized and precisely controlled. This was the intellectual bond uniting Alberti with his contemporaries, Nicolaus of Cusa, Paolo dal Pozzo Toscanelli, Georg Peurbach, and Piero della Francesca, in their common search for a quantified geometrical space and techniques for its measurement in astronomy and cartography, optics and painting alike; and again later uniting Leonardo da Vinci and Albrecht Diirer, and likewise the musicians Franchino Gaffurio, Lodovico Fogliano, and their successors in their search for an arithmetically quantified music that accommodated the requirements of the human ear. When Diirer wrote that "a good painter is inwardly full of figures," which pour forth "from the inner ideas of which Plato writes,"11 he was presenting the aesthetic theory of an artist with both philosophical education and technical knowledge of 10

Alberti, Opere volgari, ed. Grayson, vol. i (1960) and vol. 2 (1966). E. Panofsky, The Life and Art of Albrecht Diirer, 4th ed. (Princeton, NJ: Princeton University Press, 1955), p. 280.

n

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practical mathematics. The program became a commonplace. Thus Giorgio Valla: "the artist reasons when he wants something for himself, fashions and forms it inwardly, and accordingly makes an image for himself of everything that is to be portrayed."12 Marsilio Ficino: "What is a work of art? The mind of the artist in matter separate from it. What is a work of nature? The mind of nature in matter united with it. ... And what is remarkable, human arts construct by themselves whatever nature herself constructs, as if we were not slaves of nature but rivals." But "not just anybody can discern by what principle and in what way the work of a clever artist, artistically constructed, is put together, but only he who has the same power of artistic genius [artis ingenium].... And he who discerns on account of similarity of genius could certainly construct the same things when he had recognized them, provided materials were not lacking." Since therefore man had seen and measured the order of the heavens, "who will deny that he has a genius (so to speak) almost the same as that of the Creator of the heavens and that he could in a certain way make the heavens if he obtained the instruments and celestial matter; since he makes them now, though of other matter, yet very similar in arrangement."13 Leonardo da Vinci: "Astronomy and the other sciences proceed by means of manual operations, but first they are mental as is painting, which is first in the mind of him who theorizes on it, but painting cannot achieve its perfection without manual operation."14 But "although nature starts from the reason and finishes at experience, for us it is necessary to proceed the other way round, that is starting... from experience and with that to investigate the reason."15 "There is no effect in nature without reason: understand the reason and you do not need experiment."16 "Oh speculator on things, I do not praise you for knowing the things that nature through her order naturally brings about ordinarily by herself; but, I say, rejoice in knowing the end of those things which 12

Giorgius Valla, De expetendius et fugiendis rebus opus, book i, ch. 3, (Venetiis: 1501). 13 Marsilius Ficinus, Theologica Platonica, book 4, ch. i, book 13, ch. 3 (Opera, Basilae: 1576), pp. 1x3, 2.95-7. 14 Leonardo da Vinci, Treatise on Painting, Codex Urbinas Latinus 1270, book i, chs. 19, 35 trans. A.P. McMahon (Princeton, NJ: Princeton University Press, 1956): a posthumous compilation. 15 Leonardo da Vinci, Les manuscrits ... de la Bibliotheque de I'Institut, Codex E., ed. Charles Ravaisson-Mollien, folio 55r (Paris: Institut de France, 1888). 16 Leonardo da Vinci, // Codico Atlantico nella Biblioteca Ambrosiana di Milano, transcribed by G. Piumati, folio i47v (Milan: 1894-1904).

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are designed by your own mind."17 Four ancient works that were to propel in this same direction conceptions developed in the sixteenth century of the relations between the arts and sciences were the Aristotelian Mechanica, Hero of Alexandria's Automata, Proclus's neoplatonic commentary on the first book of Euclid's Elements, and Vitruvius's De architectura. Thus Vitruvius on the architect: "His works are born from both construction and reasoning" (i. i. i). Men learned to devise the machines [machinae] and instruments [organi] necessary for improving the material arts by imitating the "devised nature [natura machinata] " (x. i, 4) exemplified in the celestial revolutions. An exegesis of these terms given in the philological commentary on the earliest Italian translation (in 152.1) made the essential point: "Machinatio ... may be derived from I cunningly contrive,... I deliberate, I think out,... stratagem, ... whence undertaking, thinking, machine and ... mechanic or mechanical operator."18 "Machina Mechanics... is commendable whether for its basic imitative resemblance to the divine work of the construction of the world, or for the great and memorable usefulness reached. ... And that furthermore ... has been put into practice through a burning desire to produce in sensible works with their own hands that which they have thought out with the mind."19 Daniele Barbaro in the principal sixteenth-century Italian commentary on Vitruvius wrote of Michelangelo that "the artist works first in the intellect and conceives in the mind, and then signs the external matter with the internal habit."20 But "the intellect of man is imperfect and not equal to the divine intellect, and matter so to speak is deaf, and the hand does not respond to the intention of art." Hence "the architect must think very well and, in order to make more certain of the success of the works, will proceed first with the design and the model...; and ... he will imitate nature, which does not do anything against its maker. Yet he will not search for 17

Leonardo da Vinci, Les manuscrits Codex G., ed. Ravaisson-Mollien, folio 47' (Paris: 1890). 18 Marcus Lucius Vitruvius Pollio, De architectura libri dece, traducti de latino in. vulgare, affigurati, commentati, book i, ch. 3 (Como: 1521) folio 18: begun by Cesare Cesariano and completed by Benedetto Giovio and Bono Mauro; see Paolo Galluzzi, "A proposito di un errore dei traduttori di Vitruvio nel '500,' " Annali dell'Istituto e Museo di Storia della Scienza di Firenze i (z) (1976), pp. 78-80. 19 Vitruvius, ibid., book 10, ch. i commentary folio i6zv. 20 See the preface of Daniele Barbaro, I died libri dell' Architettura di M. Vitruvio, tradutti e commentati (Venice: 1556), p. 9.

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impossible things, either as to the matter or as to the form, which neither he nor others can accomplish."21 The limits of the possible in nature were brought into sharp focus by these rational artists whose essential purpose was to succeed in the practical execution of their projects. Thus Giuseppe Ceredi, engineer and scholar of Greek mathematics, insisted that "I am accustomed to practice both with the mind and with works"; for "I remembered, as was well said by Aristotle and Galen, that no science or art aimed at action can be perfectly possessed by anyone who may know its precepts but does not then confirm them with a variety of experiments [esperienze] many times and finally succeeding." There was a powerful precedent for "putting into execution so many beautiful mathematical and physical reasons, seeing that nature herself, as if become mechanical [quasi divenuta mecanica] in the construction of the world and of all forms of things, seems to be striving designedly to produce every hour more ingenious instruments [artificiosi organi]." Theory had been opened up for Ceredi by his being sold some manuscripts of Hero of Alexandria, Archimedes, Pappus, and other Greek mathematicians from the collection made at Milan by Giorgio Valla. Putting theory into practice, he offered as a method of antecedent analysis in any undertaking the construction of "small and large models [modelli], adding, changing, and removing many things according to whether the condition of the material, or the coming together of many far and near causes, or the variety of means, or the degree of the proportions, or the force of motions, or many other impediments that one can encounter, required it." Thus he could conveniently bring together the "numerous observations" that had to be made and kept "in the mind in order to achieve some new and important effect." For in order "to bring them properly together and to direct them firmly to the prescribed work," errors had to be recognized "from experience and so corrected by reason that at last one comes to the perfection of art and to the stable production of the effect that is expected."22 Again Guidobaldo del Monte pointed out that "art with wonderful skill overcomes nature through nature herself, by so arranging things as nature herself would do if she

21

Ibid., i (3), p. z6. Giuseppe Ceredi, Tre discorsi sopra il modo d'alzar acque da' luoghi bassi, book i (Parma: 1567).

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decided that such effects should be produced by herself."23 Art then could not cheat nature, but by discovering, obeying, and manipulating natural laws, with increasing quantification and measurement, art was seen to deprive nature of her mysteries and to achieve its mastery by reasoned foresight, whether in the representation of a visual scene, the design and control of a machine, the composition of music, the navigation of a ship across the ocean, or optimistically the diagnosis, prognosis, and control of a disease or even of the affairs of state. Galileo was defining the identity at once of nature and of natural science when he commented on engineers who "would apply their engines to works of their own nature impossible: in the success of which both they themselves have been deceived, and others also defrauded of the hopes they had conceiv'd upon their promeses ...; as if, with their engines they could cosen nature" and her "inviolable laws." For "this is according to the necessary constitution of nature Nay if it were otherwise, it were not only absurd, but impossible And... all wonder ceases in us of that effect which goes not a poynt out of the bounds of nature's constitution."24 Galileo's last pupil and first biographer Vincenzo Viviani wrote significantly that for him "the book of nature" was "always open to those who enjoyed reading and studying it with the eyes of the intellect." He said that the letters in which it was written were the propositions, figures, and conclusions of geometry, by means of which alone was it possible to penetrate any of the infinite mysteries of nature. If the intellect did the reading, the "main doors" through which it entered in order to do so were "observations and experiments, which could be opened by the noblest and most inquisitive intellects by means of the keys of the senses." Viviani drew attention to Galileo's training both in music (through his father Vincenzo Galilei), showing in the First Day of the Discorsi e dimostrazioni matematiche intorno a due nuove scienze (1638) "a marvellous understanding of" the theory of music," and in perspective drawing (at the Florentine Accademia del Disegno), delighting in painting, sculpture, architecture, "and all the arts subordinate to

23

Guidobaldus e Marchio Montis, In duos Archimidis Aequeponderantiutn libros paraphrasis scholiis illustrate, Preface (Pesauri: 1588), p. z.

24

Galileo Galilei, Le mecaniche, national edition, ed. Antonio Favaro (Le Opere z Florence: G. Barbara, 1968), p. 155, trans. Robert Payne (1636): transcribed from the British Museum MS Harley 6796, f. 317', by Adriano Carugo.

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design."25 Living from Michelangelo's death to Newton's birth, Galileo marks the transition between two great European intellectual movements each in its own way dominated by mathematical rationality: the transition from the world of the rational constructive artist to that of the rational experimental scientist. The common element in these intellectual movements and the channel of their mutual influence seems to have been their common form of argument: their common use of postulation controlled by practical experience and experiment. That is what emerges from our collage of examples stretching from Plato to Galileo. It extended much more widely than those examples, to the whole conduct of life by the man of virtu, who knew how to proceed with rational intent in the control at once of argument and of a variety of materials and activities. This was the style also of the right reason of Aristotelian ethics, exemplified by the moral and political philosophy of Thomas More and more ambiguously of Machiavelli. But we should not confuse Machiavelli's moral intentions with his analysis of the technique that would enable the political virtuoso to succeed as a blackguard if he so chose. In the same style the rational artist achieved a common mastery of his materials, whether in the mechanical, plastic, visual, or musical arts or in the experimental sciences, by an antecedent analysis providing a rational anticipation of effects. Thus Galileo wrote of his law of falling bodies: "I argue ex suppositione, imagining a motion"26 that might be possible, following the example of Archimedes. This then led him to the experiments by which he decided whether that possible motion was realized in the actual world. The experimental philosopher as rational artist might make his antecedent analysis by means of theory alone, quantified as the subject matter allowed, or by modelling a theory with an artifact

25

Vicenzo Viviani, "Racconto istorica della vita di Galileo" (1654; Le Opere 19), pp. 625, 627; cf. A.C. Crombie, "The Primary Properties and Secondary Qualities in Galileo Galilei's Natural Philosophy" in Saggi su Galilei (Florence: G. Barbera, preprint 1969), Styles of Scientific Thinking, Chs. 9-11; A. Carugo and Crombie, "The Jesuits and Galileo's Ideas of Science and of Nature," Annali dell'Istituto e Museo di Storia della Scienza di Firenze 8 (2) (1983), pp. 1-68,

26

Galileo to Pierre de Carcavy, June 5,1637, Le Opere 17, pp. 90-1; cf. to Giovanni Battista Baliani, January 7, 1639, ibid., 18, pp. 11-13.

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analytically imitating and extending the natural original. Galileo was behaving in a way just like his exact contemporary Shakespeare, when he offered an analysis of human character in his imaginary world which we recognize at once as true of our real experience. Scientist and artist alike were creating possible worlds that would in some way explain the real world of experience. They were both in different ways creating theoretical models, and it is through the model in its various forms that the interpenetration of art and science can be seen at its most telling. Painters from the time of Alberti used scientific optics to carry out an analysis of visual clues, by means of which they could construct a painting by simulating those clues: that is as a perceptual model imitating the natural clues in true perspective. To make then they had first to know. At the same time their perceptual models affected the way people looked at the natural world and what they saw in it. Conversely, in explaining the technique of perspective painting, they also provided models for the physiological operation of the eye. Kepler solved the problem of the formation of the retinal image by first isolating the geometrical optics of the eye from the questions of causation and perception, inherited within the package of ancient and medieval theories of vision, which inhibited a purely geometrical physical analysis. He treated the eye as a camera obscura containing a lens.27 To know then we might say that physiologists, at least when they tackled some problems, had first to learn how to make. The invasion of science by art through the method of hypothetical modelling went very deep during the seventeenth century. For some natural philosophers indeed art seemed to have taken over the epistemology of natural science altogether. Thus wrote Marin Mersenne: "One is constrained to acknowledge that man is not capable of knowing the reason for anything other than that which he can make, nor other sciences than those of which he makes the principles himself, as one can demonstrate in considering mathematics."28 Again in examining physical things "we must not be surprised if we cannot find the true reasons for the way they 27

A.C. Crombie, "The Mechanistic Hypothesis and the Scientific Study of Vision," Proceedings of the Royal Microscopical Society ^ (1967), pp. 3-111, republished in Science, Optics and Music.

28

Marin Mersenne, Les questions theologiques, physiques, morales, et mathematiques, question 22 (Paris: 1634) in; cf. Robert Lenoble, Marin Mersenne, ou la naissance du mecanisme (Paris: J. Vrin,e 1943); Crombie, "Mathematics, Music and Medical Science," Actes du XII Congres International d'Histoire des Sciences, Paris 1968 (Paris: A. Blanchard, 1971), pp. 195-310.

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act or are acted upon, because we know the true reasons only for things that we can make with the hand or with the mind; and because, of all the things that God has made, we cannot make a single one, whatever subtlety or effort we bring to it; besides which God could have made them in some other way."29 The experimental natural philosophers and the rational artists were creating possible worlds for themselves and each other and for a wider public in more ways than one. The analysis of visual clues carried out for the purposes of perspective painting showed what must be seen when these were present. At the same time it generated expectations in those familiar with it of what they should be seeing to produce a given set of clues received. Thus Galileo with training in perspective and chiaroscuro saw and drew through his telescope in 1609 mountains and valleys on the moon, just as they could be seen and touched on an indented stone ball; Thomas Harriot with no such training saw through a comparable instrument in the same year only strange spots.30 Likewise the exact measurement and true scaling required by linear perspective completely transformed the communication of information in the sciences and technical arts through pictorial illustrations. The immediate effects were apparent in the views and in the sixteenth-century plans drawn of cities, in cartography, and in the depiction of the external and internal structures of animals, plants, minerals, and of machines. Depiction became an instrument of scientific research. It seems that the engineers Mariano di Jacopo, called Taccola, and Francesco di Giorgio Martini, to name only two, designed their machinery by inventive drawing before construction;31 and that Descartes expected to find in the animal body a kind of mechanism analogous to mechanisms made familiar in printed illustrations.32

29

Marin Mersenne, Harmonic universelle, vol. 2, "Nouvelles observations physiques et mathematiques" (Paris: 1637), p. 8. 30 Edgerton, "Galileo, Florentine 'disegno,' and the 'Strange Spottedness' of the Moon," pp. 125—32. 31 Edgerton, "The Renaissance Development of Scientific Illustration," pp. 168-97;

also Joan Gadol, Leon Battista Alberti: Universal Man of the Early Renaissance (Chicago, IL: Chicago University Press, 1969). Eg. Salomon de Caus, Les raisons des forces mouvantes avec diverses machines tant utiles que plaisantes, aus quelles sont adoints plusieurs desseigns de grottes et fontaines (Frankfurt, Germany: 1615); cf, Willem van Hoorn, As Images Unwind: Ancient and Modern Theories of Visual Perception (Amsterdam: University of Amsterdam Press, 1972).

32

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10 7

Matching perspective painting within the mathematical and experimental arts and sciences, which established a unique style of thought and action in early modern Europe, was music. The science of music, like that of perspective, was concerned primarily with the identification and quantitative analysis of clues to sensations: the acoustical quantities expressible in numbers which stimulated the diversities of auditory perception. It was Mersenne who finally developed the science of music as a systematic exploration of a whole subject matter. Again he aimed to show how through scientific analysis to achieve rational control: of musical perception and its effects on the emotions, of composition through a calculus of permutations and combinations of notes, and of information communicated through sound leading to a theory of language. "Music is a part of mathematics" he opened his first musical essay, the Traite de I'harmonic universelle (1627), "and consequently a science that shows the causes, effects and properties of sounds, tunes, concerts, and of everything that belongs to them." The science of music depended then on arithmetic and geometry "but also on physics from which it borrows knowledge of sound and of its causes, which are the movements, the air, and the other bodies that produce sound."33 He developed his science of music as a program of systematic measurement of the acoustical quantities effecting hearing, combined with an analysis on one side of the physics of sound producing these external quantities, and on the other of the internal processes mediating sensation and its effects on the soul. As in painting, all attempts to establish a scientifically rational control over musical composition foundered on the pecularities of auditory as of visual perception in providing aesthetic pleasure through art. The judgements of the ear could often differ from the expectations of mathematical theory. The 33

Mersenne, Traite de I'harmonie universelle, book i, theorem i (Paris: 1617), pp. 2, 9-, cf. for music Claude V. Palisca, "Empiricism and Musical Thought" in Seventeenth Century Science, ed. Rhys, pp. 91-137, "The Science of Sound and Musical Practice" in Science and the Arts, ed. Shirley and Hoeniger, pp. 59-73; D. Perkin Walker, Studies in Musical Science in the Renaissance (London: Warburg Institute, 1978); Crombie, "Mathematics, Music and Medical Science," pp. 295-310, "Marin Mersenne (1588-1648) and the Seventeenth-Century Problem of Scientific Acceptability," Physis 17 (1975), pp. 186-204, Styles of Scientific Thinking, ch. 3, section 4, Marin Mersenne and the Science of Music (forthcoming); Jamie C. Kassler, "Music as a Model in Early Science," History of Science zo (1982), pp. 103-39; H. Floris Cohen, Quantifying Music: The Science of Music in the First Stage of the Scientific Revolution, 1580-1650 (Dordrecht: D. Reidel, 1984).

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science of music, developed during the sixteenth and seventeenth centuries, clarified this important question, notably in exploring the relation of aesthetic pleasure to mathematical proportions and physical motions in consonance and dissonance, and the effects of cultural habits, familiarity, the expectations of the ear, and their changes. Aesthetic judgements thus differed essentially from those of science, even though there might be general agreement among knowledgeable persons within any particular period or culture.34 Mersenne recognized this, but he exemplifies once more the rational artist in his aim to stabilize all auditory experience by scientific theory covering sounds and sensations, their aesthetic effects, and their functions in human and animal communication. Through his systematic conception and practice of acoustical "experiences bien reglees et bien faites"35 Mersenne became a major architect of the modern experimental argument. He based his experimental analysis on the logic of agreement, difference, and concomitant variations with an explicit use of experimental controls. Thus to investigate the acoustical phenomena of vibrating strings (fundamental in musical theory since Pythagoras) he stretched two strings on a monochord. One was the control. In the other he kept all the relevant quantities (length, tension, specific weight) constant except one, and adjusted the remaining variable quantity in this string until it sounded in unison with, and hence vibrated with the same frequency as, the control. In this way he completed the work 'of Giambattista Benedetti, Vincenzo Galilei, Isaac Beeckman, and others in establishing the relations of frequency (hence pitch) to these quantities. Beyond that, by measuring the actual frequencies (as distinct from their ratios) producing different pitches and intervals he demonstrated experimentally for the first time that the musical intervals were determined by frequencies of vibrations of the air, whatever their source. He went on to explore, distinguish, and measure further acoustical quantities: the upper and lower limits of audible frequency and pitch and their variation in different individuals, the speed and loudness of sound, and the relation of loudness to distance, the

34

Cf. Palisca, "Scientific Empiricism and Musical Thought"; Walker, Studies in Musical Science in the Renaissance; Cohen, Quantifying Music; Crombie, Styles of Scientific Thinking. 35 Mersenne, Harmonie universelle vol. i, "Traitez de la nature des sons, et des mouvemens de toutes sortes de corps," Book 3, proposition v (Paris: 1636), p. 167.

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phenomena of resonance, consonance, dissonance, temperament, harmonics, and so on.36 Mersenne's style as a rational artist is well illustrated by two examples concerning in two different ways the control of information. By treating the ratios of the frequency of strings to the quantities determining it as in effect an acoustical function, he showed how a "deaf man could put them at any consonance he wished," without hearing anything, by adjusting these quantities in accordance with the "general rules" embodied in this function. For the benefit of the deaf he drew up a table showing the quantities that would produce the different notes of an octave.37 Thus he could generalize experimental information beyond its receipt by a particular sense. Even more generally, his conception of human and animal language as both biological and social phenomena, his attempt to account for the reception and communication of information in men and animals firmly by empirical and experimental investigations, and his rethinking of the physiological coordination of behavior, led him to look for the common elements in all human languages and beyond these in all forms of communication whether by human beings, animals, or machines. In this analysis he saw a possible means of inventing a new universal language for communication among all mankind. This would redeem the scandal of Babel, and would reunite mankind whose common understanding of meaning through a common reason had been disintegrated by the diversification of languages following the diverse and separate historical experiences of different peoples. Again Mersenne's model was music. Basing his linguistic experiments on a calculus of permutations and combinations of a given set of elements that he had already developed for musical composition, he proposed to devise a system of notations that could be expressed symbolically in music.38 Increasing European awareness of the diversity of the cultures of the world and of the relativity of human values and expectations directed attention in the seventeenth 36

See for these investigations Crombie, "Mathematics, Music and Medical Science," and "Mersenne, Marin (1588-1648)" in the Dictionary of Scientific Biography 9 (1974), pp. 316-22. 37 Mersenne, Harmonic universelle vol. z, "Traitez des instrumens," vol. 3, prop, vii (1637), pp. 123-6, cf. prop, xvii, pp. 140-6, vol. i, props, xvi-xx, pp. 42-52. 38 Ibid., vol. i, "Traitez de la voix ...," book i, especially props, xii, xlvii-1, pp. 12-13, 65-77, "Traitez ... des sons ...," book i, props, xxii, xxiv, pp. 39-41, 43, vol. 2, "De Putilite de Pharmonie," prop, ix, also La verite des sciences, book 3, ch. 10 (Paris: 1625), pp. 548, 544-80, Les questions theologiques, physiques,

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century to the diversity of the perceptual worlds inhabited by different peoples, and also by animals.39 Deaf mutes likewise raised the question of the mental world of persons deprived of a sense. Following his analysis of music and the voice he proposed a method (already used in Spain by Pedro Ponce of Leon) of teaching the deaf to speak by showing them how to form the tongue and lips in appropriate positions and then associating these with written words and with the things they signified.40 Thus the science of music, including in it all the phenomena of sound, could restore personal dignity and bring about the unity of mankind within the rational and stable harmonic universelle that God had chosen to exhibit, both in the structure of his physical creation and in the information about it that men were able to discover and communicate. Antecedent theoretical analysis could direct the experimental argument in different ways. Theoretical expectations could open inquiry in certain directions and close it in others. Within a general and conventional agreement that trial by experiment was the ultimate test, a diversity of theories of what existed or could exist in nature, both in general and in particular, created expectations of what could or what could not be found by experimental inquiry. The boundaries of rationality either of nature or of scientific knowledge, however clearly defined by some leading scientific virtuosi in the seventeenth

morales, et mathematiques question 34 (Paris: 1634), pp. 158-65 (expurgated edition); cf. Lenoble, Marin Mersenne, ou la naissance du mecanisme; Crombie, "Mathematics, Music and Medical Science," "Marin Mersenne (1588—1648) and the Seventeenth-Century of Scientific Acceptability," and Styles of Scientific Thinking, ch. 3, section 4, ch. 7, section i; Mersenne, Les questions theologiques, physiques, morales, et mathematiques, and Traite de I'harmonie universelle; Arno Borst, Der Turmbau von Babel: Geschichte der Meinung iiber Ursprung und Vielfalt der Sprachen und Volker, 4 vol. (Stuttgart: 1957-63); Hans Aarsleff, From Locke to Saussure: Essays on the Study of Language and Intellectual History (Minneapolis, MN: 1982); Mary Slaughter, Universal Languages and Scientific Taxonomy in the Seventeenth Century (Cambridge, England: Cambridge University Press, 1982). 39 Mersenne, Les preludes de I'harmonie universelle, question 6 (Paris: 1634), pp. 150-7, Questions harmoniques, questions 1—3 (Paris: 1634), Harmonie universelle, "Traitez de la voix ...," book i prop, lii, pp. 79-81, cf. props, v-xiv, xxxviii-xli. pp. 7-15, 47-55; Thomas Willis, De anima brutorem (Oxford: 1672). 40 Mersenne, "Traitez de la voix ...," book i props, x-xi, li, pp. 11-12, 77-9; cf. David Wright, Deafness (London: Allen Lane, 1969); Crombie, "Mathematics, Music and Medical Science"; Harlan Lane, When the Mind Hears: A History of the Deaf (New York: Random House, 1984), The Deaf Experience (Cambridge, MA: Harvard University Press, 1984).

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century, were never accepted within all the diverse intellectual and social contexts concerned. Thus experiment and mathematics could have different meanings within inquiries directed by different preconceptions of what was discoverable in nature, and their results could give different satisfactions according to whether what was supposed to be discoverable could be interpreted as having been discovered. Kepler, for example, looked with neoplatonic vision for harmony in nature expressed in simple mathematical proportions supported by sound metaphysical reasons, and he insisted throughout that the proportions postulated must agree with observation. His quarrel with Robert Fludd, who shared something of the same vision, was that Fludd would not agree to acceptable experimental criteria for believing rather in one kind of world than in another, so that when Fludd cited measurements made with his weather glass (a kind of thermometer), they could not agree even on what was being measured. Between the absolutely different mental worlds they inhabited, the one as a scientific rational artist and the other as a Hermetic magician, there could be evidently no communication.41 Theory well supported by experimental argument could also blind even the most rational natural philosophers to unexpected experimental novelties. William Gilbert's theoretical expectations obstructed for a generation recognition that the declination of the magnetic needle from true north varied in the course of time, even though the evidence was available.42 William Harvey refused to accept that the lacteal vessels and thoracic duct discovered by Gasparo Aselli and the receptaculum chyli discovered by Jean Pequet had any function in the transport of nourishment from the intestines to the body: he objected theoretically on the grounds that these vessels were not found in all animals whereas the necessity for such transport was universal, that the mesenteric veins were sufficient, and that "nature never does anything thoughtlessly."43 Harvey was well aware of the analogy between the rational artist, who formed in his mind a conception of what he would represent in

41

Cf. Wolfgang Pauli, "The Influence of Archetypal Ideas on the Scientific Theories of Kepler" in Carl G. Jung and Pauli, The Interpretation of Nature and the Psyche (London: Routledge and Kegan Paul, 1955). 42 Cf. Eva G.R. Taylor, The Mathematical Practitioners of Tudor and Stuart England (Cambridge, England: Cambridge University Press, 1955). 43 William Harvey to Robert Morrison, April 28, 1652 in The Circulation of the Blood, trans. Kenneth J. Franklin (Oxford: Oxford University Press, 1957), p. 86.

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his painting and how he would do so, and the rational experimental scientist who proceeded likewise by an antecedent theoretical and quantitative analysis of his subject matter. For "art itself is nothing but the reason of work, implanted in the artists minde. And in the same way by which we gaine in art, by the very same we attain any kinde of science or knowledge whatever: for as art is a habit whose object is something to be done, so science is a habit, whose object is something to be known; and as the former proceedeth from the imitation of exemplars; so this latter, from the knowledge of things naturall. The source of both is from sense and experience" (with the Aristotelian meanings respectively of particular sensory perceptions and connected experience of their regularities), "since it is impossible that art should rightly be purchased by the one, or science by the other, without a direction from ideas."44 Experimental scientist and rational artist were then both alike exemplary men of virtu, achieving their objectives by a similar intellectual behavior, mastering their subject matters by an analytical anticipation of effects, and committed to an examined life of reasoned consistency in all things. In this context the rapid extension in the seventeenth century of scientific experience of the exploration of nature generated its own critical response. This was twofold, scientific and epistemological. The response in scientific method was a dramatic increase in the «power, precision, and range of techniques of logical, mathematical, and instrumental analysis. The response in epistemology was a stricter and stricter examination of what scientific investigation could be accepted as having established. Within the ambience of a certain general philosophical skepticism, the contrast between the acknowledged successes of the mathematical and technical sciences and arts in solving specific and clearly defined problems, and the disputed claims of metaphysicians to true and certain knowledge of the whole essence of existence, led to the conclusion that scientific art alone could yield the only certainly true science of nature available to us. Scientific thinking has nearly always been guided or stimulated by ideas or beliefs coming from outside the strict boundaries of scientific demonstration. Through the seventeenth century, scientific experience itself brought about a recognition, within an increasingly professional scientific community, that positive reasons must be required for ^Harvey, Exercitationes de generatione animalium, Preface (London, 1651), translated as Anatomical Exercitations Concerning the Generation of Living Animals (London: 1653).

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accepting such beliefs as valid or relevant within a scientific argument. The scientific movement, propelled by a deliberate combination of a theoretical search for common forms of explanation with a practical demand for accurately reproducible results, came then to base the acceptability of scientific explanations on a criterion of art: the range of experimental confirmation on an open frontier, capable of yielding not certainty but only probability to a degree increasing with its range. The triumphal march of rational virtu towards control of scientific ideas of all kinds received at this point a check, indicated by Mersenne, from experienced scientific skepticism supported by theology: the doctrine of the omnipotent Creator which reduced the world from the human point of view to contingent regularities of fact.45 What then about the realm of fortuna that virtu aimed to master, the realm of untidy accidents and unfathomable motivations, of contingent expectation and uncertain choice? One aspect of that realm was mastered by reason through the calculus of probability, developed first in the context of commercial insurance and partnerships from the fourteenth century in Italy, and reduced by Pascal and Christiaan Huygens to an exactly calculated expectation at any point of time. Thus as Pascal wrote "what was rebellious to experience has not escaped the dominion of reason. Indeed we have reduced it by geometry with so much security to an exact art, that it participates in its certainty and now boldly progresses. And so, joining mathematical demonstrations with the uncertainty of chance, and reconciling what seemed contraries, taking its name from both, it justly arrogates to itself this stupendous title: the geometry of chance [aleae geometria]."46 Scientifically that may be said to have removed some aspects of the game of life from the long accepted realm of irrational fortune and personal luck into that of impersonal calculation. But what about those other seemingly irrational aspects of

45

Cf. A.C. Crombie, "Infinite Power and the Laws of Nature: A Medieval Speculation" in L'infinito nella scienza (Rome: Istituto della Enciclopedia Italiana, 1986), republished in Crombie, Historical Studies in Scientific Thinking. 46 Blaise Pascal, "Adresse a 1'Academic Parisienne" (1644), ed. Louis Lafuma (Oeuvres completes, Paris: Editions du Seuil, 1963), pp. 101-3; cf. A.C. Crombie, "Contingent Expectation and Uncertain Choice: Historical Contexts of Arguments from Probabilities" in The Rational Arts of Living, ed. A.C. Crombie and Nancy G. Siraisi (Northampton, MA: Smith College Studies in History, 1987); cf. Styles of Scientific Thinking, ch. 18.

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human motivation that have always been recurrently part of our culture: the temptations of magic or demonology for example, or the apparently deliberate cultivation of evil or the desire to destroy or deconstruct from whatever motive but for no evidently positive end? Out of sight in ages of reason, the dramatic irrationalism of our time has sensitized our minds to its counterparts in earlier periods. It has reverberated through our century like a Wagnerian opera: too loud, too long. How should a historian of virtu treat it? Certainly not like a blind idiot. Rather he can use his rational judgement as a kind of comparative historical anthropologist, getting to the viewpoint of its motivations, commitments, and expectations, in the past as in the present, in the minds of its historians as of their subjects, however irrelevant it may seem to the history of the problems solved by science or art.

8 Mathematics and Platonism in the Sixteenth-Century Italian Universities and in Jesuit Educational Policy1

Chairs or lectureships for different parts of the Arts 'quadrivium' seem to have existed from the end of the fourteenth century in Bologna (arithmetic 1384-5, astrology with the duty to teach Euclid and algorithm 1405, arithmetic and geometry 1443)2 and perhaps elsewhere in Italy. Domenico Maria Novara (1454-1504) of Ferrara held a lectureship in Bologna in astronomy from 1483 to 1504, Luca Pacioli one in mathematics in 1501-2, and Girolamo Cardano (1501-76) worked there on mathematics while holding a lectureship in medicine from 1562 to 1570.3 At the reform of the University of Rome by Leo X in 1514 two professors of mathematics were appointed, one being Pacioli; other major chairs were in philosophy, astronomy and medicine.4 The Roman philosophers according to the historian of the university5 were predominantly 1

This paper is based on A.C. Crombie and A. Carguo, Galileo's Natural Philosophy (forthcoming). The use by the original publisher of inverted commas instead of italics in the titles of books and journals has been left unchanged. Information has been supplied by Dr. Carugo for nn. 6 and 95. 2 Bortolotti, 'La storia delle matematiche nell' Universita di Bologna' (1947) 22, 8, 24. What follows is based on published sources: there is a great need to pursue these questions in university archives. For mathematics in 16th-century Italy cf. Tiraboschi, 'Storia della letteratura Italiana', vii (1791) 107 sqq.; Libri, 'Histoire des sciences mathematiques', iii (1840) 101 sqq; Bortolotti, 'Studi e ricerche sulla storia della matematica in Italia . . . ' (1928), 'La matematica in Italia . . . ' (1933); dTrsay, 'Histoire des universites', i (1933) 240, ii (1935) 2-3. 3 Bortolotti, 'La storia . . . ' (1947) 20, 24-33, 74-6; cf. Olschki, 'Geschichte' . . . i, 151 sqq. 4 Renazzi, 'Storia dell' Universita . . . di Roma', ii (1804) 24-30, 44-51, esp. 50-1, 61-6. For the name Sapienza revived for the university by Gregory XIII in 1568 see pp. 165-7; and for Cardano at Rome during 1571-76 see pp. 219-20. 5 Renazzi, ibid.,'ii, 173-4: 'Seguica la filosofia di Aristotele a dominar nelle Scuole della Romana Universita, ne ancor sorto era alcuno a contrastarle 1'antico suo impero. Que' raggi di vivo splendore, che cominciavano altrove a lampeggiare sul vasto campo delle filosofiche discipline, non erano ancor giunti a penetrare nelle Scuole Romane. Aveva, egli e vero, il Vives al principio del secolo XVI, su cui noi qul c'aggiriamo, nel suo eccellente libro 'De corruptis disciplinis', segnato le dritte vie, che batter conveniva per rettamente filosofare. Gia secondo il consiglio di Platone, allo studio della filosofia i piu accorti e saggi facevano agl'iniziandi premettere quello degli elementi dell'algebra, e della geometria. Imperciocche si era da quelli capita, che i difetti degli studj sin'allora usitati, nascevano specialmente dal non accopiarvi lo studio delle matematiche. Gio mosse nel secole XVI parecchi profondi ingegni a coltivarle, e illustrarle con

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medical and Aristotelian; mathematics on the contrary was cultivated on Plato's advice as the best introduction to philosophy. Giambattista Raimondi (c. 1536-1614),6 appointed to the mathematical chair in 1576 and also an oriental linguist, is said to have led the way through his lectures in toppling Aristotle from the philosophical throne and replacing him by Plato. Galileo's friend Luca Valeric (1552-1618), who taught mathematics at Rome about 1600, likewise had Platonic affiliations.7 From the middle of the sixteenth century an effort was made to foster the mathematical sciences by establishing chairs or lectureships in other Italian universities. Pisa had a mathematical chair in 1484.8 With the renovation of the

impegno maggior; e per tal'opportunissimo fine circa la meta di quello 1'intermessa lettura di matematiche ricomparve nella Romana Universita. In fatti la giustezza di pensare, la precisione dell'idee, 1'esattezza del metodo, che in seguito s'introdussero a poco a poco in tutte le scienze, fu il sostanzioso e utilissimo frutto, che il dilatamento, e i progress! dello studio delle matematiche felicemente produssero. Lo spirito geometrico nato da tale studio e di maggior importanza e giovamento, che le astratte verita, le quali dalla geometria propongonsi, e si dimostrano. Ma tra noi i filosofi troppo altamente erano prevenuti per le dottrine peripatetiche, e oltre modo imbevuti delle scolastiche sottigliezze. Chi si maravigliera percio, se persistessero tenacemente attaccati ai vecchi loro pregiudizi, e se nel tempo di cui qui trattiamo, continuassero a spiegar, e sostenere dalle cattedre Aristotele con indefessa fatica, e con ardente entusiamo? La maggior parte dei Romani Maestri erano medici di professione come andremo divisando nel produrne qui ora il catalago; poiche allora congiungevansi quasi sempre gli studi prattici di medicina cogli astratti della fiosofia'; cf. pp. 174-7. 6 Ibid. 177: 'Un'altra cosa pure del Raimondi deesi qui accennare, che cioe fu esso un dei primi ad alzar nei suoi discorsi bandiera contro Aristotele e a preparar in Roma la letteraria rivoluzione di rovesciarlo dal filosofico trono, e rimettervi il gia abbandonato Platone, di che diremo a suo luogo': cf. G.O. xx 515. Raimondi was in great favour with Pope Clement VIII (Ippolito Aldobrandini) and especially with his nephew Cinzio Aldobrandini. On G.B. Raimondi see Girolamo Lunadoro, 'Relatione della corte di Roma e de 'riti da osservarsi in essa e de'suoi Magistrati et Officii, con la loro distinta giurisdittione' (Venezia, 1635) 63-5, where he is remembered as having 'belli pensieri circa la doctrina di Platone, et di Aristotele, per essere versatissimo, in ambi due questi auttori', and for his dedication to mathematical sciences. Notable achievements were his Latin translations from Greek, such as of Euclid's 'Data', 'uno delli libri necessarii per la intelligenza della scienza resolutiva, che e nelle mathematiche', and from Arabic, such as of Apollonius's eight books 'De Conis' (!). Lunadoro adds that Raimondi 'ha commentato i cinque (!) libri di Pappo' (books 3-5 ?) and 'Ha scritto poi Comentari, e dotti, et esquisiti sopra tutti i libri di Archimede'. He also mentions his work on Arabic, Persian and Turkish dictionaries and his learning in theology. This passage from Lunadoro's book was excerpted by John Pell, in an autograph memorandum now in the Brit. Mus., MS Add. 4458, ff. 95-96. Raimondi left an unprinted commentary on Pappus, now in the Bibl. Naz. Cent, di Firenze, MS Magi. cl. XI, no. 107. Under his supervision, in the famous 'Stamperia medicea' attached to the Collegio Romano, were printed many important works in Arabic, including Avicenna's 'Canon' (1593) and Nasir addin's edition of Euclid (1594). 7 Renazzi, 'Storia . . . ', iii (1805) 36, 85. 8 Fabronius, 'Historia Academia Pisanae', i (1791) 326-7: 'Difficile est reperire quid de illius aetatis mathematicis dicas. Prorsus illi ignorabant quid Graeci omnis praeclarae artis inventores, ac praesertim Archimedes vir prope divinus contulissent ad amplificandos geometriae fines, adjungendumque illius usum ad physicas res; et qui hanc profitebantur scientiam, nullum aliud praeceptum artis esse putabant, quern quod ni Euclide continentur'.

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university begun in 1543 under Duke Cosimo I three mathematical appointments were made in the same year 1548: Juliano Ristoro, a Carmelite described as having already professed mathematics in Siena and Florence, to a chair in astronomy with a view to facilitating astrology,9 and two others to positions as 'mathesis praeceptores'.10 It was to one of these latter posts that Galileo was to be appointed in 1589 through the interest of Guidobaldo's younger brother Cardinal Francesco Maria del Monte, after he had failed in the previous year to get a similar position at Bologna.11 The mathematical chair at Padua, to which Galileo moved in 1592 with the help of Giovanni Vincenzo Pinelli12, had been initiated in 1520 by Federico Delfino, who at his death in 1547 was succeeded by an undistinguished logician, Pietro Catena,13 who held it until his death in 1576. During 1559-60 Catena was joined briefly by Francesco Barozzi.14 Catena's successor from 1577 to 1588, Gioseffe Moleto, was a man who showed some originality, for example in recognising that all bodies should fall with the same speed and dealing with the contradiction between this conclusion and Aristotelian physics.15 He and Galileo were in

9

Fabbruccio, 'De Pisano Gymnasio . . . ' (1960) 112-6; Fabronius, op. cit. ii (1792) 385-6 470; Baldi, 'Cronica' (1707) 122. 10 Fabronius, op. cit. ii 385-6; cf. Schmitt, The Faculty of Arts at Pisa at the time of Galileo' (1972). 11 Fabronius, op. cit., p. 392; Favaro, 'Galileo Galilei e lo Studio di Padova', i (1883) 30-2. 12 G.O. x 42, 47-60, xix 111-2 117-25; Favaro, ibid. pp. 48-53, 'Cronologica Galileiana' (1892), 'Scampoli Galileiani, ser. ix' (1894). 13 Favaro, 'Galileo Galilei e lo studio di Padova' i, 100-36, esp. 133-6; see also Favaro, 'Intorno alia vita . . . di Prosdrocini de'Beldomandi' (1879) 46-55; 'Le matematiche nello Studio di Padova' (1880), 'I lettori di matematiche nella Universita di Padova' (1922) 61-7; Baldi, 'Cronica' (1707) 112, 135-6, Affo 'Vita di . . . Baldi' (1783) 9; Tiraboschi, 'Storia . . . ' vii (1791) 657; Crapulli, 'Mathesis universalis' (1969) 42-62. Catena was much concerned with mathematical demonstration in Aristotle, writing in one of his books. 'Universa loca in logicam Aristotelis in mathematicis disciplinas hoc novum opus declarat' (1556) 4:' . . . etiam si exiguas (nam apprime novi quam sit mihi curta suppellex) expederem in eruendo Aristotele ex illo obscuro, id autem tarn comode apte fieri putabam, si mathematica exempla sua expressiora redderem, quibus in explicandis logicis usus fuit ipse presertim hoc tempore quo publicis lectionibus mathematicis in Paduano Gimnasio incumbebam . . . .' He went on in commenting on 'Post. Anal.' i.i, 71a 19-22 (= text 3) to make the contrast: ' . . . Neque id ostenditur per inductionem Topicam quae a particularibus ad universalem procedit, et contrariatur huic posterioristico processui, qui fit ab universali and particularia . . . ' (p. 25). He followed this with another work: Petrus Cathena, artium et theologiae doctor, professor publicus artium liberalium in Gymnasio Patevino, 'Super loca mathematica contenta in Topicis et Elenchis Aristotelis', nunc et non antea in lucem aedita (1561). 14 Boncompagni, 'Intorno alia vita ed ai lavori di Francesco Barozzi' (1884) 796-7. 15 Favaro, 'Galileo Galilei e lo Studio di Padova', i, 21-36, 135-6, 'Giuseppe Moletti' (1917).

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contact through correspondence during the year before he died in 1588.16 From both Padua and Florence, the greatest influence on mathematical teaching in Italian universities was eventually to be that of Galileo himself. His pupil and friend Benedetto Castelli (1578-1643) was to be appointed at Pisa in 1613, and to move from there to the mathematical chair at the Sapienza in Rome in 1626.17 Another pupil, Bonaventura Cavalieri (1598-1647), was to hold the chair at Bologna from 1629 until his death. One of Castelli's pupils in Rome, Evangelista Torricelli (1608-47), was to succeed Galileo as mathematician to the Tuscan court in 1642; another, Giovanni Alfonso Borelli (1608-79), was to be appointed about 1635 to a mathematical lectureship in Messina, whence he moved in 1656 to the chair at Pisa. In the same year Marcello Malpighi (1628-94) went from a lectureship in logic at Bologna to the chair of theoretical medicine at Pisa, finally returning by way of the main medical chair at Messina to that at Bologna in 1666.18 Borelli and Malpighi, both members of the Accademia del Cimento, and Borelli's pupil Lorenzo Bellini (1643-1704) who succeeded Malpighi in the chair of theoretical medicine at Pisa, were to be primarily responsible for carrying the Galilean mathematical programme into biology. It was however the Jesuits who made the teaching of mathematics most explicitly part of an educational policy. The Jesuit 'Constitutiones' (1556) laid down that 'the end of the Society and of its studies is to aid our fellow men to the knowledge and love of God and to the salvation of their souls'.19 The principal emphasis of Jesuit universities was to be placed upon theology as the most appropriate means to this end, but a full range of other humane and useful subjects was to be taught: literature and history, classical and oriental languages, and 'the arts or natural sciences' since they 'dispose the intellectual powers for theology, and are useful for the perfect understanding and use of it, and also by their own nature help towards the same ends'.20 From Ignatius Loyola himself came the injunction: 'Logic, physics, metaphysics and moral science should be treated and also mathematics in the measure suitable to the end proposed'21. Medicine and law, being more remote from this end, were not to be taught in Jesuit universities or at least not by members of the society. 16

G.O. i, 183-5; x, 21, 30, 42, 77; xix, 111, 606. Fabronius, op. cit. ii, 404-9; Renazzi, op. cit. iii, 86-8: Favaro, 'Benedetto Castelli' (1907-8): Zannini, 'La vita di Benedetto Castelli' (1961). 18 For these authors see the 'Dictionary of Scientific Biography' (1970). 19 'Constitutiones Soc. Jesu', iv. 12 ('Mon. hist. Soc. Jesu', 1936) 468; Ignatius of Loyola, The Constitutions . . .' iv. 12, transl. Ganss (1970) 50-4, 213-4; cf. 'Constitutiones', iv. 12 (1583) 15961; 'Mon. paed. Soc. lesu' i, ed. Lukacs (1965) 281-5. 20 'Constit. SJ.' iv. 12 (1936) 470, (1965) 482; cf. (1583) 160-1. 21 Ibid. For Jesuit education see Antoniano, 'Dell'educazione cristiana e politica dei figliuoli' (1926); Farrell, 'The Jesuit Code of Liberal Education' (1938); Dainville, 'Les Jesuites et 1'education . . . : La naissance de 1'humanisme moderne' (1940) (note p. 75, Ignatius to Diego de Mendoza, 1553; cf. above n. 46 eh), 'Les Jesuites . . . : La geographic des humanistes' (1940). A convenient summary of Jesuit hisotry is 'Synopsis hist. Soc. Jesu', preface by Groetstouwers (1950). 17

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In the central Jesuit university, the Collegio Romano founded by Ignatius in 1550, a chair of 'Mathesis (cum Geometria et Astronomia)'22 was established in 1553 with Balthassar Torres as the first professor. After him it was held more or less continuously by Christopher Clavius from 1565 until his death in 1612. Both were in touch with Francesco Maurolico (1494-1575) in Messina: Torres corresponded with him about Jesuit mathematical teaching; Clavius developed a closer relationship after visiting him in 1569 and became largely responsible for the appearance of his major posthumous mathematical and optical writings. He gave a number of his manuscripts to Clavius on a further visit from him in 1574.23 Clavius was joined at the Collegio Romano in 1595 by his pupil and eventual successor Christopher Grienberger (1561-1636), another of Galileo's future friends, who likewise taught mathematics there, with interruptions, over a long period, until 1633.24 In 1553-4 a Balthassar Torres also initiated the chair in metaphysics, whence he moved in 1554-5 to that in 'Physica (seu Philosophia Naturalis)'. These two chairs as well as that in logic were also held at different times between 1559 and 1567 by Benito Pereira, Francisco de Toledo and Achille Gagliardi (1537/8-1607).25 It was Clavius who by his defence of mathematics within the context of Jesuit educational goals, and by creating a mathematical school at the Collegio Romano where most of the society's scientists studied, was principally responsible for establishing Jesuit policy and eventual achievements in the mathematical sciences. His 'Modus quo disciplinae mathematicae in scholis Societatis possent promoveri' indicates the kind of doubts he had to overcome within the society and gives his arguments for mathematics on the grounds of both intellectual necessity and practical utility:26 The way in which the mathematical disciplines could be promoted in the schools of the Society. First a master must be chosen with uncommon erudition and authority; for if either of these is absent the pupils, as experience shows, seem unable to be attracted to the mathematical disciplines. Now in order that the master should 22

Villoslada, 'Storia del Collegio Romano' (1954) 59, 335. Scaduto, 'II matematico Francesco Maurolico e i Gesuiti' (1949) 132-4,137-41, cf. 'Le origini dell' Universita di Messina' (1948) 9; Rosen, 'Maurolico's attitude towards Copernicus' (1957) 179, 187-8; for Torres also 'Mon paed. Soc. Jesu . . . ' ed. Gomez Rodeles et al. (1901) 477-8. 24 Villoslada, op. cit. 187-99, 335; Sommervogel, 'Bibliotheque' . . . iii (1892) 1810-2. 25 Villoslada, op. cit. 51-2, 78-9, 326-7, 329, 331; for these professors see below nn. 44, 99; Sommervogel, op. cit. iii, 1095-9; cf. 'Mon. paed. Soc. Jesu' (1901) 150-62, 491-3, 500, 504, 515, 522, 571, 728. 26 'Mon. paed. Soc. Jesu' (1901) 471-3: autograph, 'Manu P. Christophori Clavii'; see Dainville, 'Les Jesuites . . . : La naissance de l'humanisme' (1940) 88 sqq., 139 sqq., 'L'enseignement des mathematiques dans les colleges jesuites . . . ' (1954) 7-8; Cosentino, 'L'insegnamento delle matematiche nei collegi Gesuitici nell'Italia settentrionale' (1971) 207 sqq.; cf. Phillips The correspondence of Father Christopher Clavius S.I. (1939) 205-20, with Possevino (1585), Baldi, Galileo and Guidobaldo del Monte (1588), and other mathematicians down to 1611. The debates about mathematics can be found in 'Mon. paed. Soc. Jesu' (1901) and 'Mon. paed. Soc. lesu', i (1965); cf. Farrell, 'The Jesuit Code of Liberal Education', pp. 153-362, esp. 338, 343, 370-1. 23

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have greater influence over his pupils, and the mathematical disciplines themselves be of greater value and the pupils understand their utility and necessity, the master must be invited to take part in formal acts in which doctors are created and public disputations held, in such a way that if he is capable he too may sometimes put forward arguments and help those who are arguing. For by this means it will easily come about that the pupils, seeing the professor of mathematics together with the other teacher taking part in such acts and sometimes also disputing, will be convinced that philosophy and the mathematical sciences are connected, as they truly are; especially because pupils up to now seem almost to have despised these sciences for the simple reason that they think that they are not considered of value and are even useless, since the person who teaches them is never summoned to public acts with the other professors. It also seems necessary that the teacher should have a certain inclination and propensity for lecturing on these sciences, and should not be taken up with many other occupations; otherwise he will scarcely be able to help his pupils. Now in order that the Society should have capable professors of those sciences, some men should be selected apt and capable for carrying out this task who may be instructed in a private school in various mathematical subjects; otherwise it does not seem possible that these studies should last long in the Society, let alone be promoted; although they are a great ornament to the Society and are very frequently the subject of discussion in colloquia and meetings of leading men, where they might understand27 that our members are not ignorant of mathematical matters. Whence it comes about28 that our members necessarily become speechless in such meetings, not without great shame and disgrace; as those to whom this very thing has happened have often reported. I do not mention the fact that natural philosophy without the mathematical disciplines is lame and incomplete, as we shall show a little later. So much for the master of mathematical disciplines; now let us add a few words about his students. Secondly then, it is necessary that the pupils should understand that these sciences are useful and necessary for rightly understanding the rest of philosophy, and that they are at the same time a great ornament to all other arts, so that one may acquire perfect erudition; indeed these sciences and natural philosophy have so close an affinity with one another that unless they give each other mutual aid they can in no way preserve their own worth. For this to happen, it will be necessary first that students of physics should at the same time study mathematical disciplines; a habit which has always been retained in the Society's schools hitherto. For if these sciences were taught at another time, students of philosophy would think, and understandably, that they were in no way necessary to physics, and so very few would want to understand them; though it is agreed among experts that physics cannot rightly be grasped without them, especially as regards that part which concerns the number and motion of the celestial circles ('orbes'), the multitude of intelligences, the effects of the stars which depend on the various conjunctions, oppositions and other distances between them, the division of continuous quantity into infinity, the ebb and flow of the sea, winds, comets, the rainbow, the halo and other meteorological things, the proportions of motions, qualities, actions, passions and reactions etc. concerning which 'calculators' write much. I do not mention the infinite examples in Aristotle, Plato and their more celebrated commentators, which can by no means be understood without a

27 28

Reading 'intelligant' for 'intelligunt' (p. 471). As the editor points out, the preceding does not lead immediately to what follows (p. 472).

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moderate understanding of the mathematical sciences; indeed, because of their ignorance of these, some professors of philosophy have very often committed many errors, and those most grave, and what is worse they have even committed them to writings some of which it would not be difficult to bring forward. By the same token teachers of philosophy should be skilled in mathematical disciplines, at least moderately, lest they run onto similar rocks, with great disgrace and loss of the reputation which the Society has in letters. I do not mention the fact that the professors would hereby gain great influence over their students, if they understood that they treated as they deserved the passages in Aristotle and other philosophers which concern the mathematical disciplines. Whence it will also come about that the pupils understand better the necessity for these sciences. It will also contribute much to this if the teachers of philosophy abstained from those questions which do not help in the understanding of natural things and very much detract from the authority of the mathematical disciplines in the eyes of the students, such as those in which they teach that the mathematical sciences are not sciences, do not have demonstrations, abstract from being and the good,29 etc.; for experience teaches that these questions are a great hindrance to pupils and of no service to them; especially since teachers can hardly teach them without bringing these sciences into ridicule (which I do not just know from hearsay). The influence of Clavius is evident in the first Jesuit 'Ratio Studiorum' of 1586 and in the definitive version of 1599. Both outlined a full programme of philosophical and mathematical studies.30 The course of natural philosophy set out in 1586 covered the whole range of Aristotelian subjects from the heavens and their motions and influences (to be treated by a philosopher when there was no professor of mathematics), through the elements, meteorology, generation and the soul. Aristotle was to be followed except where detracting from or repugnant to faith.31 Quoting Loyola's injunction from the 'Constitutiones'32 the section 'De mathematicis' went on:33 Constitutions, part 4, ch. 12, C: There will be treated, they say, logic, physics, metaphysics, moral science, and also mathematics but only in so far as it is conducive to the end proposed to us. Now it seems no little conducive, not only because without mathematics our academies would lack a great ornament, indeed they would even be mutilated, since there is almost no fairly celebrated academy in which the mathematical disciplines do not have their own, and indeed not the last, place; but much more because the other sciences also very much need their help, because, for poets they supply and expound the risings and settings of the heavenly bodies; for historians the shapes and distances of places; for the Analytics examples of solid 29

Cf. Plato, 'Republic' vii, 533-4. 'Ratio Studiorum', iii, 'De studio philosophiae' (1586) 171 sqq., iv, 'De mathematicis', pp. 198 sqq.; ed. Pachtler, 'Ratio Studiorum', ii (1887) 125 sqq. (1586), cf. 256, 348 (1599). 31 'Rat. Stud.', iii (1586) 193-7; ed. Pachtler, ii (1887) 138-41. 32 Above n. 21. 33 'Rat. Stud.', iv (1586) 198-9; ed. Pachtler, ii (1887) 141-2; cf. Barbera, 'La Ratio Studiorum . . . ' (1942) 126; Cosentino, 'Le matematiche nella 'Ratio Studiorum . . . ' (1970), and op. cit. (1971) 2078-11; Dainville, 'Les Jesuites . . . : La naissance de 1'humanisme' (1940) 71-88, op. cit. (1954) 7-8; Villoslada, op. cit. (1954) 96 sqq. 30

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demonstrations; for politicians admirable arts for good administration at home and in time of war; for physics the forms and differences of heavenly revolutions, light, discords, sounds; for metaphysics the number of spheres and intelligences; for theologians the main parts of the divine creation; for law and ecclesiastical custom the accurate computation of times; not to mention what advantages redound to the state from the work of mathematicians in the care of diseases, in navigations, and in the pursuit of agriculture. Therefore we must try to bring it about that, just like the other disciplines, so mathematics too may flourish in our schools, so that from this too our students may become more suited to serving the various interests of the Church, especially as, to our great disgrace, we lack professors who can give the teaching of mathematics that is needed for so many and excellent uses. At Rome too, if you except one or two, scarcely anyone will be left who is qualified either to profess these disciplines or to be at hand at the Apostolic Seat when there is discussion about ecclesiastical times.34

Two professors of mathematics were to be appointed. One should teach students of logic, who in their first year were 'preparing themselves for the Posterior Analytics, which can scarcely be understood without mathematical examples'. In their second year they would be studying physics, when 'the remaining part of the mathematical compendium which is to be completed by Father Clavius will be expounded'. The second professor in Rome, 'but only if he can be Father Clavius, is to provide a fuller knowledge of mathematical things over three years and is to teach privately about eight or ten of our students, who are at least moderately intelligent and not unmathematical and have studied philosophy, and who would be summoned from various provinces, if possible one from any one'.35 But Jesuit views on mathematics were by no means uniform even after these dates. For example Clavius had maintained in his commentary on Euclid (1574) that mathematics offered the most certain demonstrations but that these were not syllogistic. On the power of mathematical demonstrations he agreed with Francesco Barozzi.36 The philosopher Benito Pereira in his 'De communibus omnium rerum naturalium principiis' (1562,1576) had agreed on the contrary with Alessandro Piccolomini. He wrote: 'It is the opinion of many that the kind of most powerful demonstration ("demonstratio potissima"), which is treated in the Posterior Analytics i, is to be found either nowhere, or surely above all in the mathematical disciplines'. Among the reasons given were that this kind of demonstration was the goal of mathematical resolution, and that mathematical demonstrations did not suffer from the variety and disagreement of opinion found in those of physics and metaphysics. 'But although this opinion is very common and accepted by many, I however can in no way approve it: for I think that most powerful demonstration which is

34

I.e. the calendar. 'Rat. Stud.' iv (1586) 199-210; ed. Pachtler, ii (1887) 142-3. 36 Cf. Boncompagni (1884) appendix i: 'Lettera di Francesco Barozzi al P. Christoforo Clavio' (pp. 831-7). 35

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described by Aristotle in the Posterior Analytics i can in no way, or only with difficulty, be found in mathematical sciences'.37 'My opinion', he wrote, 'is that mathematical disciplines are not proper sciences . . . To have science ("scire") is to acquire knowledge of a thing through the cause on account of which the thing is; and science ("scientia") is the effect of demonstration: but demonstration (I speak of the most perfect kind of demonstration) must be established from those things that are "per se" and proper to that which is demonstrated, but the mathematician neither considers the essence of quantity, nor treats of its affections, as they flow from such essence, nor declares them by the proper causes on account of which they are in quantity, nor makes his demonstrations from proper and "per se" but from common and accidental predicates'. He confirmed this from Plato who had written in the 'Republic' vii that 'mathematicians dream about quantity, and in treating their demonstrations proceed not scientifically, but from certain suppositions. Therefore he does not want to call their doctrine intelligence ("intelligentia") or science, but only acquiring knowledge ("cognitio"); on which judgement Proclus wrote much in book i of his Commentaries on Euclid'.38 To illustrate the use by mathematicians of non-causal demonstrations Pereira cited from Proclus, as Piccolomini had done, Euclid's proof that the sum of the internal angles of a triangle equals two right angles. The proof depended on a construction projecting one side to make an external angle, but this did not make the property demonstrated of the internal angles: 'Who does not see that this middle term is not the cause of that effect which is

37

Pererius, 'De communibus', iii.4 (1576) 72. Pererius, 'De comm.', i 12, p. 24. Isaac Barrow in his 'Lectiones . . . in ... Acad. Cantab. An. Dom. MDCLXIV, v (1683) 89 quoted these 'Words of Pererius, who was no mean Peripatetic' ('Mathematical Lectures', transl. Kirkby, v, 'Containing answers to the objections which are usually brought against mathematical demonstration', 1734, p. 80) in discussing the same question. In these lectures given at Cambridge during 1664-6 Barrow continued the 16thcentury discussions of the relation of mathematical demonstrations to the theory of demonstration set out in the 'Posterior Analytics', and of the question whether mathematical entities have any existence outside {he mind, citing those 'who will have Mathematical Figures to have no other Existence in the Nature of Things than in the Mind alone. And it is wonderful to me that this Opinion should be embraced by Persons, who are otherwise most excellently skilled in the Mathematics: Among whom we may reckon Blancanus ('Libro de Natura Mathem.' p. 7), whose words are these: "Though Mathematical Beings have no real Existence, yet because their Ideas do exist both in the Divine and Human Mind, as the most exact Types of Things, therefore the Mathematician treats of those Ideas which of themselves are primarily intended, and are true Beings" ': Barrow, ibd., 1683, p. 85; 1734, p. 76; Blancanus, 'De mathematicarum natura' (1615) 7. Giuseppe Biancani was a Jesuit pupil of Clavius and professor of mathematics at Bologna; cf. his 'Aristotelis loca mathematica ex universis ipsius operibus collecta et explicata' (1615). Barrow in his second published series of 'Lectiones' (1684) also cited Clavius on Euclid (see Lect. vi, pp. 2767). Cf. the well known contrast between the axiomatic ideal of Greek geometry and the demonstrations possible in physics made by Huygens in the preface (1690) to his 'Traite" de la lumiere'; also Newton, 'Opticks', query 30 (1706). 38

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demonstrated'.39 This literal insistence on the identity of reasoning and causation in true science measures the gulf separating the logic of Aristotelian physics from that of the mathematicians. Again like Piccolomini, Pereira went on to argue: 'mathematical things are abstracted from motion, therefore from all kinds of cause';40 mathematics, as Proclus had said, gave several demonstrations of the same conclusion of which one was no better than another, except perhaps in brevity; mathematical demonstrations owed their certainty primarily to their subject-matter, abstract quantity. These views remained unchanged in later editions of his book. He concluded:41 Now they are called mathematical sciences, as a synonym for disciplines, not on account of the excellence of their demonstrations, but on account of the very great ease of learning them, and of the very beautiful order and wonderful connection of the demonstrations with each other. Now mathematical demonstrations are the most certain, most evident, and easiest, by reason of the subjectmatter, namely quantity; for quantity is the most sensed ('maxime sensata') since it is perceived by all the senses, and is the middle or principle of mathematical demonstrations. They can be expounded and declared in such a way that they lie open to the senses themselves, which cannot be done in natural or divine things. Moreover the principles of mathematics do not require long experience and diligent observation like the principles of physics or medicine. And Aristotle in the sixth book of the Ethics42 gives this as the reason why boys can become mathematicians but not physicists or wise. Lastly mathematical things afford very easy abstraction from matter, because quantity is not tied to and dependent on any fixed and determinate matter, as are other physical accidents, and therefore it can easily be abstracted and conceived by the intellect. Hence too it comes about that mathematical things are called by Aristotle beings from abstraction ('entia ex abstractione'), doubtless because of the ease of abstraction; and what is easily abstracted from matter is also easily understood. It remains then that for these reasons mathematical demonstrations are the most certain, most evident and easiest for us wherefore they are called by philosophers perfect or absolute demonstrations. We are speaking at present of purely mathematical disciplones, such as geometry and arithmetic, for in astronomy, perspective and others called middle or mixed, things are otherwise. But that is enough for the present question. Next we must see whether knowledge of all the causes which a thing has is necessary to the understanding of that thing . . . . These differences of opinion, as well as the scope of the Jesuit commitment to mathematics, are indicated in the 'Bibliotheca selecta qua agitur de ratione studiorum' (1593) by the Jesuit scholar and diplomatist Antonio Possevino (1533/4-1611), a friend of Clavius and one of the authors of Jesuit educational 39

Pererius, ibid. 24. Barrow, op. cit., vi (1683) 108 ('Of the causality of mathematical demonstrations' ed. 1734) again cited Pereira's comment on this theorem (Euclid, 'Elements', i. 32) in a discussion comparing geometrical and syllogistic demonstration. 40 Pererius, 'De comm.', iii, 3, pp. 69-70. 41 Pererius, 'De comm.', iii, 4, pp. 73-4. 42 Aristotle, 'Ethica Nicomachea', vi. 8, 1142a 12-19.

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policy.43 Possevino entered the society in 1559 with the three brothers Achille, Leonetto and Ludovico Gagliardi, who had been horrified by the suspect and atheistic tendencies of the Averroist philosophy they had heard at the University of Padua.44 Apostolic and diplomatic journeys in Savoy and France led to three years as first rector of the new Jesuit college in Avignon,45 at the end of which he published in his 'Coltura de gl'ingegni' (1568)46 an account of the aims, methods and content of education in Jesuit universities throughout Europe. This he introduced with a brief history of Christian philosophy. Two periods as Papal Nuncio to the King of Sweden (1568, 1577-80) involved further travels in Germany and Poland.47 Another mission took him in 1581-82 to Moscow, where Pope Gregory XIII sent him in response to a request from Czar Ivan IV, the Terrible, for negotiation of an end to the long war between himself and the King of Poland. Peace was concluded with both Poland and Sweden in 1582. Possevino's reports of this mission, with descriptions of political and religious conditions in Russia and neighbouring lands, and an account of a discussion of the Catholic religion held with Czar Ivan on 21 February 1582, were published in part in his 'Moscovia' (1586).48 Papal policy aimed to bring about an alliance of these Christian princes against the Turks, and religious unity on the basis of the Council of Florence. Possevino continued his diplomatic missions during 1583-7 in Poland and Hungary,49 according to his biographer well fitted for these tasks by 'un savoir eminent, une facilite prodigieuse a apprendre les langues' as well as by 'un zele apostolique, un courage a 1'epreuve des plus grandes difficultes, une dexterite a traiter les affaires les plus epineuses, des manieres tout a fait engageantes surtout avec les grands, une connoissance parfaite des cours du nord, des interets et des coutumes de toutes ces nations'.50 His intervention played an important part in the introduction of the reformed Gregorian calendar into

43

Antonii Possevini Societatis lesu 'Bibliotheca selecta', 2 partes (Romae, 1593); revised ed., 2 torn., Coloniae Agrippinae, 1607. For Possevino see Dorigny, 'La vie du Pere Antoine Possevin' (1712); Sommervogel, 'Bibliotheque' . . . vi (1895) 1061-93; Dainville, 'Les Jesuites . . . : La geographic des humanistes' (1940) 47; 'Mon. paed. Soc. lesu' (1965) 107, 127. 44 Dorigny, op. cit. 4, 13-18, 25-7; Castellani, 'La vocazione alia Compagnia di Gesu del P. Antonio Possevino' (1945) 102-4, 108, 114-5. For the Gagliardis see Sommervogel, op. cit. iii, 1095-9; and for the following discussion of the Jesuits in Padua, Cozzi, 'Galileo Galilei e la societa veneziana' (1968) 10-14. 45 Dorigny, op. cit. 27 sqq., 105-6, 115-6, 135-6. 46 Vicenza, 1568; a Latin version was published in his 'Bibl. sel.', lib. i (1593) i, 13-65. 47 Dorigny, op. cit. 166-252; Possevini 'Missio Moscovitica', ed. Pierling (1882) 109-20; see next note. 48 Vilnae 1586, republished Antverpiae 1587; further documents in the Vatican archives were published as Antonii Possevini 'Missio Moscovitica', curante Pierling (1882); see also Dorigny, op. cit. pp. 253-438; Pierling, 'Un nonce du Pape en Moscovie' (1884) 146,180 sqq., 'La Russie et la Sainte-Siege' (1896) 375 sqq.; 'Synopsis hist. Soc. Jesu' (1950) 86. 49 Dorigny, op. cit. 438-94. 50 Ibid. 259; cf. 496, 499.

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Poland.51 In 1587 he returned to Padua to teach at the Jesuit college, the 'Gymnasium Patavium Societatis Jesu'.52 He was one of G.V. Pinelli's Jesuit friends in a circle which included Robert Bellarmine, the Gagliardi brothers, and the Cardinals Cesare Baronio and Ippolito Aldobrandini (to become in 1592 Pope Clement VIII) as well as Gabriele Falloppio, Cardano, Sperone Speroni, Gioseffe Moleto, Guidobaldo del Monte, Mark Welser and Girolamo Fabrizio d'Acquapendente.53 In Padua during 1587-91 he wrote the 'Bibliotheca selecta'.54 This major work is an encyclopaedia and bibliography of current learning covering education, Scriptural history, theology, religious orders, schismatics and heretics, the Jews, the Mahometans, the beliefs of the peoples of India, Japan, China and the New World, the history of philosophy, jurisprudence, medicine and the mathematical sciences, the ancient and modern secular history of the world and its chronology since the creation, poetry, painting, and the art of writing letters. Book xiii on philosophy reflects current Italian preoccupations and controversies, with a massively eclectic, critical knowledge of ancient, medieval and modern authors. Possevino commended Francesco Bonamico for his adherence to the Greek text of Aristotle, reproval of Averroes, and use of Archimedes in dealing with heavy and light bodies.55 He warned frequently against the Arabic interpreters.56 He praised among Christian interpreters Aquinas, Albertus and other scholastics, Giovanni Pico della Mirandola (with caution)57 for drawing out true philosophy from Aristotelian shadows, and above all in recent times Chrisostomo Javelli, Caietanus, Domingo de Soto, Francisco de Toledo, Francisco Valles and

51

Ibid. 481-4; cf. 483 on Clavius. Ibid. 497-9; Favaro, 'Galileo Galilei e lo Studio di Padova', i (1883) 75-99. 53 Paolo Gualdo, 'Vita Joannis Vincentii Pinelli' (1607) 14-15,18-19,29, 38-40, 45,73,100,103, 117; Dorigny, op. cit. 512-4: cf. Tiraboschi, 'Storia', vii (1791) 243-5. Luca Pinelli was a Jesuit: Sommervogel, 'Bibliotheque . . . ', vi, 802. 54 Dorigny, op. cit. 499-502, 512-4. 55 Possevinus, 'Bibl. sel.' xiii, 'De philosophia' (1593) ii, 120-1: 'Franciscus Bonamicus Florentinus primarius Pisis Professor, qui decem libros De Motu emisit: quo sat magno volumine generalia naturalis philosophiae principia continentur. Sane vero ut viri eruditissimi, licet mihi de facie ignoti, testimonium catenus praebeam, quatenus qui eius labores non legerunt, avidius excipiant, haec possum dice re: modestus philosophus est, ac satis tutus, Graecis potius adhaeret; Simplicii, sensus explicat liquidius, quam plerique fecerint alii, uti et aliorum Graecorum; Graece enim novit, atque ad textum Graecum plura revocat; Averroem saepe, ac quidem merito reprobat; ubi agit de gravibus et levibus, multa ex Archimede desumens, apte explicat; misce pulchra problemata; sextum, et septimum Physicorum interpretatur copiose; idque agit, ut offendat, an recte concludat Aristoteles'. 56 Ibid. 99-101, 106-9 (107 on Averroism in the universities). 57 Ibid. 104: 'quae ad Aristotelem intelligendum, atque ad veram philosophiam e tenebris eruendam pertinent, in quo tamen unum id fortasse cavendum est, ne quoniam perspicasissimo fuit ingenio, Hebraeaque volumina, et Platonicam, Pythagoricamque philosophiam cupiditate omnia percipiendi avidissime versavit'; cf. 115, 206-7. 52

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'Benedictus Pererius noster'.58 But the religious end to which he saw philosophy leading gave him a preference for Plato, with a very definite caveat, as a guide to knowledge. Philosophy had arisen from man's natural desire to find God.59 Among a full range of recent Platonists he cited with general though qualified approval Marsilio Ficino60 and Giovanni Pico,61 with special praise Javelli62 and Fox Morcillo,63 and for specific points Francesco Patrizi64 and Jacopo Mazzoni.65 The main source of his view of the history of philosophy was Pereira.66 Many had received the light of philosophy from Plato, more from Aristotle;67 many had been against Plato, many for, so he would separate the correct use of him from the abuse.68 Plato's chief errors concerned the human soul (belief in its transmigration to and from the brute animals, existence from eternity or from the beginning of time, and presence not as the true form of an individual but like the pilot of a ship) and the origin of the world from a chaos of already existing elements. Those who vindicated him called him the wisest and holiest of philosophers and the Attic Moses, and these included not only Cicero and Plutarch, but Jerome, Augustine, Basil and Clement.69 It was agreed by Christian scholars that Pythagoras, from whom Socrates and Plato learnt so many doctrines, had been the disciple of a Nazarine Jew. Plato himself could have consorted with Jews when he was in Egypt.70 But Augustine both in The City of God' and in the 'Retractationes' confessed that he had been deceived by Plato and came to reject his doctrines: they were against both Catholic faith and natural reason.71 The gentile philosophers had to be read with caution.72 Possevino shared the 58 Ibid. 104, 106, 113-4, 120-1. For the conciliatory policy of the 16th-century Dominican Aristotelian, Javelli, who held Aristotle valid for the natural sciences but Plato better for morality and religion, see Garin, 'Storia . . . ' (1966) 586-7. By the time Possevino was writing reconciliation of Plato and Aristotle seems to have lost much of its charm in Padua: cf. Nardi, 'Saggi' (1958) 363. 59 Possevinus, ibid. lib. xiii. 1, p. 59; c.3, p. 62: 'Origo philosophiae, instrumentaque noscendarum rerum homini collata a Deo', caput iii. Naturale homini desiderium ad sciendum a Deo inditum est, quod omnes sentimus, philosophique ipsi sempte inculcarunt'. 60 Ibid. 87-8. 61 Ibid. 65, 68, 75-8, 104, 181. 62 Ibid. 79, 82, 86-8. 63 Ibid. 88: 'Sed et Sebastianus Foxius Morxillus magna cum laude Platonem interpretatus est'; cf. 112, 225. 64 Ibid. 88, 98, 109, 225. 65 Ibid. 117, 181, 200; cf. ibid. (1607) 28, 31-2, 50 where he cited also Mazzoni's 'De comparatione Platonis et Aristotelis' (1597); below nn. 74, 104. 66 Possevinus, 'Bibl. sel.' (1593) 72-4, 104, 113-4, cf. 69-72, 115-9; cf. Pererius, 'Comm. . . . in Genesim', i, praefatio (1601) -16; below nn. 127 seq., also 97. 67 Ibid. 59. 68 Ibid. 78. 69 Ibid. 78-9. 70 Ibid. 82-4. 71 Ibid. 79-80, 84. 72 Ibid. 88, cf. 100.

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contemporary belief in the concordance of all authorities in an essentially theological truth. Thus, he wrote, some had held that God was indifferent to nature, others that the natural world was all there was. The first was heretical, the second atheistic. Against both errors Plato, Aristotle and the Stoics agreed that God governed all, whether natural or supernatural, by reason and conducted it to its end.73 In Book xv on mathematics Possevino made it clear that mathematics and Platonism mutually reinforced each other in Jesuit educational policy. He had been helped in writing this book by Clavius. Mathematics was practically useful, necessary for physics, a parry to scepticism, and it also provided a means of exegesis of the abstract ideas of the Creator:74 Since this is so the necessity, worth and utility of the mathematical disciplines are shown by the fact that Plato and Aristotle have included them in the principles of contemplation and of action. So Plato, taking the whole mathematical genus, including arithmetic and geometry, away from the senses, in his own words calls them 'the drawer, the leader, the summoner, the energiser, the turner of mind, thought, vision, truth':75 that is, such that it draws, impells, excites, arouses and turns intelligence, reasoning, contemplation and truth. And by these words he means, not sophistical shadows, but the logical action of the mind, whereby the demonstration of truth is more purely and more accurately considered. And indeed the Timaeus of Plato and the Physics of Aristotle are very great proof of how much light mathematics itself sheds on philosophy.76 For in the Timaeus Plato makes God construct the soul of the world from arithmetical ratios and proportions and its body from geometrical shapes. Therefore Plato's physics, being made from numbers and lines, is arithmetical and geometrical; and it certainly cannot be understood by those ignorant of geometry. Hence it came about that there was fixed by Plato over the entrance to the Academy that saying: 'Let no-one ungeometrical enter';77 let nobody without geometry enter. In fact all that Aristotle says about motion and rest, about time and the heavens, and 73 Ibid. 117-8: 'Antequam ad Elenchum interpretum Physices accedam, pauca praemonenda sunt. Vidimus apud duo genera hominum, cum ab eorum magistris in haec studia inducerentur, sic in prolegomenis agi, ut alii inter Deum, et Naturam nihil interesse docerent: atque eodem tempore libellos obtruderent, qui specie pietatis fucati, mentes ab interiore, ac solida caussarum contemplatione avertebant. Alii vero dum una cum Plinio, et eiusmodi reliquis pergerent Mundum ita vocare Universum; ut videlicet ipso nihil praestantius, maius, melius esset, fecere, ut plerique ex philosophiae studiis felicitatem in eo constituerent, quem neque ortum fuisse, neque interiturum, sese demonstraturos pollicebantur. Prioris generis, haeretici quidam adhuc sunt, reliqui neque haeretici, neque catholici, sed potius ad atheismum vergentes'; cf. 90,99-105,130-5. 74 Ibid. lib. xv, 'De mathematicis', c. 1, 'Mathematica generatim', (1593) ii, 175-9; cf. also 1812; for Clavius's help 173, cf. 114; and for the history of mathematics 175 sqq. See Phillips, 'The correspondence of Father Christopher Clavius' (1939) 205 (with Possevino, 1585). In the 1607 ed. Possevino added a new c. 2, 'Disciplinarum mathematicarum certitudo quaenam' (torn, ii, 217-8) in which he cited Alessendro Piccolomini and Pereira in agreement on this question. 75 In Greek, followed by Latin translation. 76 The lines following come almost verbally from Ramus, 'Scholarum mathematicarum', ii (1569) 46-7; cf. Timaeus' 35A - 37C, 41D - 44B. 77 In Greek, followed by Latin translation: this remark occurs in Philoponus, 'Comm. in lib. De anima Aristotelis', i, comm. 45 (1535) sig. D iii, and in Franciscus Barocius, 'Opusculum' (1560) f. 39 r; cf. above n. 14.

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about the progression and history of animals, and the whole of his physical discussions abound, not only with examples but also with foundations drawn from geometry. For in the first book78 he brings forth the tetragon of Antiphon in order to refute it. In the second book he quotes examples concerning the two right angles in a triangle, besides what he did in the Posterior Analytics. In the third book he mentions certain points about the construction of gnomons. In the remainder he mentions the infinity of magnitude, motion and time; so that learned men have formed the opinion that a complete exposition of those books should be left out by most people, because they have not studied the mathematical disciplines deeply enough . . . . Archytas too and Eudoxus, so Plutarch says in his life of Marcellus,79 when they had transferred geometrical contemplations from the mind, and from things falling within the contemplation of thoughts alone, to examples of sensible and corporal things, they enriched geometry with a variety of demonstration not only logical but practical. Aristotle too taught mechanics, and by publishing it made it common knowledge. Nor indeed were these the only fruits seen to result from this: that Archytas80 gave flight to a wooden dove which he had suspended with weights in such a way that it was propelled by hidden wind of breath; or that Archimedes and Posidonius fashioned those spheres by attaching to which, so Cicero81 says, the motions of the Sun and Moon and the five planets, they brought about the same effect as that god who built the world in the Timaeus, namely that one revolution ruled motions very dissimilar in slowness and speed; or that the Nuremberger82 exhibited a fly and an eagle fitted with geometrical wings; or the new near-miracles of nature that Claudius83 seems to have performed in recent years in the gardens of Cardinal Atestinus84 by the Tiber, when he brought it about that by the soft and placid falling of water the motion, voice and song of a little bronze bird, opportunely pausing at the arrival of a night owl, and more opportunely being resumed on its departure, so closely imitated the truth, that anyone who has called it artificial deserved to be thought rash, rather than anyone judging it real deserved to be thought too credulous (he also added a water-organ from which a most sweet and harmonious sound was heard); and that (a thing that was indeed still more remarkable) at his will he so elegantly and truthfully projected a heavenly rainbow which the Latins call 'iris', that God was to be praised for having given such acumen to human brains, even in a matter of this kind . . . . And these things would certainly seem more than enough to excite minds ('ingenia') towards those disciplines, were it not that two other things add to their reputation: the one said by Plato, which (so Plutarch says) smacks of Plato's character , although it does not survive in his dialogues, namely that 'God above

78

I.e. of the Physics. The lines following come almost verbally from Ramus, 'Schol. math.', i (1569) 16-19; cf. i-iii, pp. 1-112. 80 Cf. Ramus above, citing Aulus Gellius, 'Noctes Atticae', x, 12.8. 81 Cicero, Tusculanae quaestiones', i, 25.63, 'De republica', i. 14. 22. 82 Cf. Baldi,'Discorso', in Herone Alessandrino'De gli automati', trad . . . Baldi(1589)ff. 5°6r. 83 Marg.: Claudius Galius. 84 I have not found the source of this story. 79

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all geometrises';85 the other having regard to their origins, for they have spread down from the most ancient patriarch Abraham86 to other men. Indeed He, by whose divine mind everything is providently administered, for the safety and presentation of all, has been said by Plato to govern and control this universe by geometrical proportion; seeing that every function of God is included in it, not only that which consists of contemplation but also that which comprises the building and administration of the world. And indeed Plutarch says that God, in the creation of the world, geometrised so much that he made up this geometrical problem: given two figures, to construct a third equal to the one and similar to the other. This, according to Plutarch, was that very celebrated problem upon the solution of which Pythagoras or Thales87 is said to have sacrificed; but there was 85 (p. 178); cf. Plutarch 'Quaest, conviv.', viii.2.1,718C-E, ed. and transl. Minar ('Moralia', ix, 1061) 118-21: 'Diogenianus, making a new start, said: If you please, let us on Plato's birthday take Plato himself as partner in the conversation, and since we have spoken about the gods, consider what he had in mind when he asserted that God is always doing geometry- if indeed this statement is to be attributed to Plato. I remarked that while this statement is not made explicitly in any of Plato's writings, it is well enough attested and is in harmony with his character, and Tyndares immediately took up the argument: Do you think, Diogenianus, that this saying conceals a reference to some recondite or difficult doctrine, and not merely to what he himself said and wrote many times, when he sang the praise of geometry for drawing us away from the world of sense to which we cling, and turning us toward the intelligible and eternal level of existence, the contemplation of which is the goal of philosophy, as being a viewer is the goal of a mystery-rite? For the nail of pleasure and pain, by which he represents the soul as fastened to the body, seems to have this as its greatest disadvantage, that is makes the objects of sense-perception clearer than those of intellectual knowledge, and forces the understanding to judge by emotion rather than by reason. Being habituated, through the experience of intense pain and pleasure, to paying heed to the shifting and changeable aspects of physical things, as though they were true being, the understanding is blinded to truth and loses that organ - that light within the mind, worth thousands of eyes [Plato, 'Republic', vii. 527E], by which alone the divine may be contemplated. Now in all of the so-called mathematical sciences, as in smooth and undistorted mirrors, there appear traces and ghost-images of the truth about objects of intellectual knowledge; but geometry especially, being, as Philolaos says, the source and mother-city of the rest, leads the understanding upward and turns it in a new direction, as it undergoes, so to speak, a complete purification and a gradual deliverance from sense-perception. It was for this reason that Plato himself reproached Eudoxus and Archytas and Menaechmus for setting out to remove the problem of doubling the cube into the realm of instruments and mechanical devices, as if they were trying to find two mean proportionals not by the use of reason but in whatever way would work. In this way, he thought, the advantage of geometry was dissipated and destroyed, since it slipped back into the realm of sense-perception instead of soaring upward and laying hold of the eternal and immaterial images in the presence of which God is always God'. 86 Cf. Pereira above n. 66, below nn. 97, 127 sqq. 87 Plutarch, ibid, viii.2.4, 720A - C, pp. 128-31: 'You will easily see the point, I replied, if you recall the threefold division, in the Timaeus, of the first principles from which the cosmos came to birth. One of them we call, by the most appropriate of names, God, one matter, and one form. Matter is the least ordered of substances, form the most beautiful of patterns, and God the best of causes. Now God's intention was, so far as possible, to leave nothing unused or unformed, but to reduce nature to a cosmos by the use of proportion and measure and number, making a unity out of all the materials which would have the quality of the form and the quantity of the matter. Therefore, having set himself this problem, these two being given, he created a third, and still creates and preserves throughout all time that which is equal to matter and similar to form, namely, the cosmos. Being continuously involved in becoming and shifting and all kinds of events, because of its congenital forced association with its body, the cosmos is assisted by the Father and

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also that other problem which is ascribed to Pythagoras by Proclus88 and by all the ancients, that is where in a right-angled triangle the square of the side opposite the right-angle is proved equal to the squares of the other two sides. In such a way then, God, in Plato's opinion, constructed the world. For that of which the first origin of the world consists Plato89 divides into three, God, matter and idea; that is, God as the most excellent of efficient causes, matter as the most unordered substance of all things, and idea as the fairest of all examples. Therefore if anyone mentally conceives God as wisest and as Geometrical Architect for all, for whom matter and idea are proposed as two dissimilar figures and who has to construct the world as a third figure from the two proposed, similar to the one, equal to the other, he will understand that the world has been joined together by God from all substances and from the whole of matter; but since he wished to leave nothing discordant and unordered, but to adorn it with ratio, measurement and number (for nothing was to be fairer than the world or more excellent than its maker), therefore the Craftsman of the world ('Opifex mundi') imitated the fairest and eternal exemplar. Therefore he formed the world in such a way that it should be a copy of that eternal exemplar and form which we call the Idea . . . .

In his discussion of the mathematical sciences, pure and mixed, Possevino essentially followed Geminus's division as reported by Proclus.90 The large range of authors cited points to Clavius's excellent guidance to the mathematicians and Possevino's own scholarship and eclectic concern with their relation to philosophical and theological issues. Thus on arithmetic he cited, for example, on the one hand Clavius himself, Cardano and Pacioli, and on the other hand Gianfrancesco Pico, Francesco Barozzi's work 'De numero Platonis' and Mazzoni's 'De triplici hominum vita'.91 On music he cited among many others Aristoxenus, Ptolemy, Gioseffe Zarlino, Giorgio Valla, Vincenzo Galilei, Francesco Giorgio ('sed qui sit expurgatus') and Mazzoni, and published a revision of Jean Pena's edition of Euclid's 'Musica' made from further Greek manuscripts.92 On geometry and the subordinate sciences of astronomy, geodesy, mechanics, optics, catoptrics, painting, sculpture and architecture he again cited Mazzoni and named Euclid, Archimedes and Ptolemy as preeminent. His authorities included Euclid's 'Elements' in Greek, Latin and Italian, Federico Commandino's editions of Apollonius and Archimedes, Proclus's Euclid, Michael Psellus's 'Compendium mathematicum', Ptolemy's 'Almagest' and 'Geographia', Copernicus's 'De revolutionibus', Clavius's commentary on Sacrobosco's 'Sphaera' (1593), 'Apologia pro Creator, who, by means of reason, and with reference to the pattern, gives limits to that which exists. Thus the aspect of measure in things is even more beautiful than their symmetry'; cf. Euclid, 'Elements', vi.25. 88 Proclus, 'In primum Eucl. Elem.' props.ii.47 (= ed. Friedlein, pp. 426 sqq.). 89 Plato, Timaeus' 27D - 34 B, 48E sqq. 90 Possevinus, ibid. 173,179,200. Possevino (pp. 179-81) also cited the divisions of mathematics made by Boethius and Hugh of St Victor. 91 Ibid. 181-2, 200, cf. 87-8, 176. 92 Ibid. 182-200; cf. Euclidis 'Rudimenta musices, eiusdem sectio regulae harmonicae', . . . loanne Pena Regio Mathematico interprete (Parisiis, 1557).

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Kalendario' and 'Euclid', Hero's 'Spiritalia', 'De machinis bellicis' and 'Automata', works of Ctesibus and Philo of Byzantium in the Vatican Library, Athenaeus's 'De machinis bellicis', Aristotle's 'Mechanica' in Niccolo Leonico's version, Allesandro Piccolomini's Taraphrasis', Niccolo Tartaglia's 'Nova scientia' and 'Quesiti', Guidobaldo del Monte's 'Mechanica' and 'Aequeponderantium', Giuseppe Ceredi's Tre discorsi sopra il modo d'alzar acque', Albrecht Diirer's 'Geometricae institutiones', 'Symmetria' etc., Euclid's 'Optica' and 'Catoptrica', Egnazio Danti's Trospettiva d'Euclide', Alhazen's and Vitelo's 'Opticae', Daniele Barbara's 'Perspectiva', Vitruvius's 'Architectura' in the editions of Philander and Daniele Barbaro, and Leon Battista Alberti's 'Architectura'.93 He went on to give a refutation of judicial astrology, finding support from Pereira's commentary on 'Genesis'.94 His account of the origins and parts of architecture was based on Vitruvius, Alberti, Palladio and Daniele Barbaro but included a discussion of the building of Solomon's Temple.95 Cosmography and geography he again based on Biblical, as well as ancient Greek and Latin and modern sources.96 Sympathy for Platonism such as that shown by Possevino and Pereira should not obscure the basically Thomist character of Jesuit philosophy. Pereira had made it plain in his preface to 'De communibus'97 that he was looking for a 93

Possevinus, ibid. 200-2. Ibid. 176, 202-7; cf. 104; above n. 66. 95 Ibid. 207-12. Cf. Villapando's massive commentary on the building of Solomon's temple, largely devoted to mathematical sciences and mechanics, which was published as vol. 3 of a large commentary on Ezechiel's prophesies: Hieronymi Pradi et loannis Baptistae Villelpandi e Societate lesu, 'In Ezechielem explanationes et Apparatus urbi et templi Hierosolymitani, commentariis et imaginibus illustratus', opus tribus tomis distinctum (Romae, 1596-1605). Juan Batiste Villalpando (1552-1608), a Spanish Jesuit, learned in mathematics and philosophy, had joined Jeronimo Prado, another Spanish Jesuit, in the ambitious task of preparing such a commentary and for this purpose they both moved to Rome, to work in the Collegio Romano. After Prado's death in 1595 Villalpando carried on the work, and managed to publish the first three volumes, the third being the 'Apparatus urbis et templi Hierosolymitani' (Romae, 1604), a large folio of 655 pp., containing a series of treatises of arithmetic, geometry, weights and measures, mechanics, etc. Its sources range from Girolamo Cardano to Giovanni Battista Benedetti and Clavius. Duhem, in 'Etudes sur Leonard de Vinci', i (1906) 511 sqq., maintains that Villalpando's discussion of the centre of gravity reproduces a treatise on local motion by Leonardo, now lost. Villalpando's discussion on the centre of gravity was set out again by Mersenne in the 'Mechanicorum libri' included in his 'Synopsis mathematica' (Paris, 1626). Excerpts from Villalpando's treatise 'De ponderibus et mensuris' ('Apparatus', pp. 249 sqq.) are to be found in Thomas Harriot's papers, Brit. Mus. MS Add. 6788, ff. 109-11, among other excerpts and notes on specific weights, written in 1604-1605. 96 Possevinus, ibid. 215-8. 97 Cf. Pererius, 'De comm.', iv 'De antiquis philosophis', c. 20 (1576) 164: 'De veterum igitur opinionibus, quae pertinent ad principia rerum naturalium (ut aliquis tandem huic libro terminus et finis imponatur) ita sit a nobis non (ut opinor) indiligenter, nee ineptem disputatum. De Platonis autem opinione mirum nemini videri debet, nihil a nobis hoc in libro dictum esse: nam cum de principiis rerum plurimae atque gravissimae quaestiones et controversiae sint inter Platonem et Aristotelem nequaquam satis adhuc explicatae, aliis quidem hos duos philosophos non rebus, sed verbis tantum dissidere affirmantibus, aliis autem contendentibus eos inter se omnino discrepare, non debuit tanta quaestionum moles in hunc libellum intrudi, et opinio Platonis simul cum aliorum 94

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concordance of Plato and Aristotle in truth as known by reason and revelation. Some unpublished lectures on 'De anima'98 given in Rome in 1566-67 show the same policy of reconciliation. Part of the attraction towards Platonism came from repulsion from Averro'ist interpretations of Aristotle. Pereira himself became regarded as unorthodox in the Collegio Romano. In 1567 he was moved from the chair in metaphysics first to that in scholastic theology and then in 1576 to that in scripture. A year or so later, another occupant of the theology chair, Achille Gagliardi, who was also prefect of studies, took the lead in opposing publication of Pereira's writings on the grounds that he was inclined to Averroi'sm." Gagliardi went from Rome to teach during 1579-80 at the Jesuit 'Gymnasium' in Padua, and after various other postings returned to the region in 1599 as superior of the Jesuit house in Venice. 10° By that time the Averroi'sm of the University of Padua had gained strength from the appointment in 1590 of Cesare Cremonini (1550-1631) from Ferrara to a chair in philosophy at Padua.101 Possevino's book no doubt reflects this hostility between the two institutions. The proposal made in 1602 by Gagliardi 'with some gentlemen' of Venice to found an 'Accademia della dottrina Platonica'102 indicates a general concern about the social consequences of the university's

philosophorum sententiis involui, et communi iudicio cognosci, sed satius fuit ea destinato in id libro aliquo, separatim explicari, et subtiliter ac proprie diiudicari'. Another effort at concordance is indicated by Possevino, 'Bibl. sel.' XIII (1593) ii, 87: 'Accedit ad haec perutile sane Seminarium Platonicae simul et Peripateticae philosophiae, quod collegit loannes Baptista Bernardus, vir, qui summis muneribus in Republica Veneta perfunctus, mirabili ordine, et labore universum philosophiam per locos, ordinemque collegit: rei nempe cuiusque, qua de agitur, propositiones, quae in earn in universum cadunt, turn divisiones, inde definitiones, deinceps causas, et ortus, atque ad extremum, si quid dilucidius agendum sit, liquidiorem lucem ex ipso Platone, et Platonicis afferens. Inter Platonicos autem, e quibus illud Seminarium confecit (licet Platonis dialogos non redegerit in eas classes, in quas supra redactae sunt) philosophos tamen, et alios auctores Christianos numeravit; qui sunt hi': a list follows beginning with 'Mercurii Trismegisti Pimander, Asclepius' and including at the end Patrizi, Fox Morcillo and Piccolomini; cf. 98; and 'Bibl. sel.' xii.12 (1607) ii, 31-2: 'Quinam conciliare Aristotelem cum Platone, vel attentarunt, vel polliciti sunt'; above nn. 66, 86, 74, below nn. 127 sqq. 98 Mendendez Pelayo, 'De las vicisitudes de la filosofia platonica en Espana' (1889/90), in 'Ensayos' (1948) 82; Villoslada, 'Storia del Collegio Romano' (1954) 78-9; Kristeller, 'Iter Italicum', i (1963) 287: 'Bened. Pererius, Lectiones super libros de anima (Rome, 1566-67)', Bibl. Ambrosiana, Milan, MS D 497 inf. (16 cent.). 99 Villoslada, op. cit. 79-80, 323-4, 327. On 16th-century Averrosim and its background cf. Nardi, 'Saggi sull' Aristotelisrno Padovano' (1958). 100 Castellani, 'La vocazione . . . del Possevino' (1954) 105 n. 101 Cremonini studied philosophy at the University of Ferrara with Federico Pendasio and became there a friend of Patrizi and of Torquato Tasso, and was called to the chair of philosophy in 1590. In the same year he was called to Padua, where he transferred in 1591: G.O. XX, 429-30; Garin, 'Storia . . . ' (1966) 558 sqq., 580. 102 Pirri, 'II P. Achille Gagliardi . . . ' (1945) 33; see Cozzi, 'Gesuiti e politica sul finire del Cinquecento' (1963), 'Galileo Galilei e la soceita veneziana' (1968) 12,15; cf. Favaro, 'Lo Studio di Padova e la Compagnia di Gesu sul finire del secolo decimosesto' (1878). The Jesuits were expelled from the Venetian Republic in 1606.

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philosophy, especially its anticlericalism. On its part the Pinelli circle, after Moleto's death in 1589, discussed Galileo in connection with the vacant mathematical chair and at the same time the possibility of introducing the study of Plato at the university. After Galileo had accepted the mathematical post at Pisa, Benedetto Zorzi, a Venetian patrician who was an admirer of both Plato and the Jesuits, wrote on 2 December 1589 to the Florentine Baccio Valori (1535-1606) :103 . . . . I heard about Galileo from Signer Pinelli, and I am pleased that the way has been opened to that man to show his learning publicly in a University. I am afraid that the chair will still be vacant this year, because there is a lack [i.e. of competent people] especially in this subject, the name of which Signer Contarini and I kept alive in the memory of those who govern the University; in which I should like on my part to see the study of Plato introduced, as I believe that His Highness is likely to bring it back in Pisa; and I would be glad if you would kindly let me know how this goes.

In 1588 the Grand Duke of Tuscany had in fact brought Mazzoni to teach Platonic philosophy at Pisa.104 When Galileo eventually did go to the Paduan mathematical chair in 1592 Pinelli's friendship drew him into his circle, as distinct from that of Cremonini.105 But the university introduced no chair in Platonic philosophy. Platonic philosophy seems to have been first officially recognised in university teaching at Pisa, when in 1576 the Grand Duke Francesco I authorised Francesco Vieri ('il Secondo Verino') to give extraordinary lectures on Plato in addition to his ordinary ones on Aristotle. Vieri had been active in the Florentine Academy, and from 1553 had taught first logic and then natural philosophy and medicine at Pisa.106 He was a friend of Baccio Valori107 and of Antonio Persio,108 and was opposed to the kind of Aristotelianism taught at 103

G.O. x, 42; see for Zorzi G.O. xx, 561, Cozzi, op. cit. (1968) 13n.; for Valori G.O. xx, 551. Cf. Serassi, 'La vita di Jacopo Mazzoni' (1790); Rossi, 'I. Mazzoni. . .' (1893); G.O. x, 446, xx, 479; Corsano, 'Per la storia . . . iv. 1: Mazzoni . . . ' (1959); Garin, 'Storia . . . ' (1966) 607-8, 614; Purnell, 'Jacopo Mazzoni. . .' (1972); Crescini, 'II problema metologica . . .' (1972) 365 sqq.; above n. 65, below nn. 133 sqq. 105 Cozzi, op. cit. (1968) 14; Gualdo, 'Vita . . . Pinelli' (1607) 29, 115. On Galileo and the Jesuits at Padua cf. Nelli, 'Vita . . . di Galileo', i (1793) 25,112; Favaro, 'Galileo Galilei e lo Studio di Padova', i (1883) 4, 72-99: Favaro (pp. 98-9) rejected Nelli's opinion that Jesuit hostility to Galileo began at Padua. 106 See Fabbruccio, 'De Pisano Gymnasio . . . ' (1760) 132-4; Fabronius, 'Historia Academia Pisanae', ii (1792) 96 sqq., 346 sqq., 469; and for a brief account of the introduction of Platonism into Italian universities, Kristeller, 'Studies . . . ' (1956) 291-3, esp. 292 n. for the date 1576. 107 See Fabbruccio, ibid. 134; Viviani, 'Vita ed opera di Andrea Cesalpino' (1922) 170-1; cf. Kristeller, ibid. 295, 323 n. and 290 n. for his correspondence with Patrizi; Bandini, 'Memorie per servire alia vita del senator Pier Vettori' (1756) for his acquaintance at Pisa with Cesalpino; Cochrane, The Florentine background . . .' in McMullin (ed.), 'Galileo' (1967) 126-7,136-7; and cf. Campanella on Valori, G.O. xvii, 352 (1638). 108 Cf. Gabrieli, 'Verbali. . . dalla prima Accademia Lincei (1603-1630)' (1927), 'Notizio . . . di Antonio Persio Linceo' (1933); G.O. iii, 366-8, xi, 298, 301-3. 104

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Pisa by Bonamico109 and Girolamo Borri.110 He manoeuvred in various ways to follow the tradition of concordance between Plato, Aristotle and orthodox Catholic theology initiated by Ficino. The essentially moral and religious aim of his Platonism is indicated by his definition of philosophy in the educational scheme set out in the 'Discorso' (1568): 'Speculative philosophy is a habit of the human spirit by which all those things become known which depend on God and on nature, and which guides us finally to knowledge of the intelligences and of God himself, in the contemplation of whom consists the supreme human happiness in this mortal and earthly life . . . . Again it can be defined with other words, as it is defined by the divine Plato, when he says that "philosophy is a knowledge of divine and human things through which man makes himself similar to God so far as is possible for him" '.m Of the three contemplative disciplines, he saw mathematics and natural science as essentially means by which the mind rose up to the science of the divine, so that in St Paul's words 'through visible creatures it ascends to the invisible God', their Creator.112 Within this scheme mathematics had a central place, for 'mathematics is a science of quantities considered without matter and substance (although always existing in some matter and substance) in order to give us knowledge in the factive things of the arts and of human activities governed by action, and in the natural and divine substances speculated about in natural and in divine science; all that, which in all these things concerns either continuous or discontinuous quantity, . . . proclaiming the usefulness to be got from this mathematical science'.113 It made known true demonstrations as illustrated by Euclid's geometry, and their rules as set out in Aristotle's 'Posterior Analytics'. Hence it served all the demonstrative sciences and the f active arts using machines, such as architecture and military art, teaching the theory ('ragione') and mode of construction of different instruments, military formations, camps and fortifications, measurements of heights of towers and so forth.114 'Mathematics', he wrote again, 'are useful, indeed necessary to the speculative sciences'.115 Among these, in subject-matter divine science came first in excellence and perfection, natural science concerned with natural corporal substances came next, and mathematics came last because it was concerned with accidents, those of'quantity. But in certainty and exactness of demonstration mathematics came first because it was more abstract than natural science, and more open to human reason than the divine obscurities

109

Fabbruccio, ibid. p. 133; Fabronius, ibid, ii, 341 sqq., 353 sqq. Fabbruccio and Fabronius, ibid. 111 Vieri, 'Discorso' (1568) 9; cf. his similar definition to Valori in 1590; Viviani, 'Andrea Cesalpino' (1922) 170; Cochrane, op. cit. 136-7, nn. 48, 52. 112 Vieri, ibid. 75, cf. 72-75. 113 Ibid. 73-4. 114 Ibid. 79-80; citing Plato, 'Rep.' vii and Polybius. 115 Vieri, ibid. 84 sqq.:'. . . le matematiche sono utili anzi necessarie alle scienze specolative'. 110

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made known to us only superhumanly. He accepted the Platonic argument that in education mathematics, being simply open to grasp by reason, should be taught first, then natural science, and lastly metaphysics.116 Vieri's view of the arts and sciences exemplifies the strength of the rational Florentine tradition specified by Leonardo da Vinci and Ficino. 'Art (to start from the first and lowest grade)', he wrote, 'is nothing other than a habit of our spirit which proceeds with a right reason concerning those things that we call factive and which are all those which serve the body. Its subject is all the factive things such, so to speak, that they depend on our operations which always terminate in the completion of something material outside ourselves'.117 Reason meant the mathematical sciences, embracing the arts and natural philosophy. Thus 'geometry is not only useful for knowing how to measure the Earth, to build buildings with rule and measure, and for other similar arts which use machines, but serves also for the understanding and contemplation of the whole universe and for skilful operation, and in sum serves for everything where in some way there is continuous quantity. Whence it can be defined from the subject and from the end in this way, by saying that it is a speculative science of continuous quantity, without being applied to anything natural and sensible, which can serve later for sensible things'.118 One subalternate of geometry to which he gave attention was astronomy and especially its derivative, judical astrology. His attitude was traditionally Catholic, based on Augustine and the councils, lastly that of Trent. He held that it was possible to predict general and simple effects such as rain, winds, snow and so on depending immediately on the heavens and their light, which could be calculated from observations with good instruments.119 But as for more composite effects, such as are those which can happen to man, the astrologer cannot prescribe as in those more simple and more general effects because, although man in many operations depends on the heavens nevertheless in voluntary and free acts he is not subjected to the heavens, or else very indirectly in so far as the intellect and will make use of the senses and corporeal power; and so in his free acts man is not necessitated or constrained, even though he may be influenced. Otherwise divine, natural and civil laws would be banished away, all of which command him to act well and forbid him to act badly, offering fit reward to whoever acts well and penalty to whoever does the contrary. Thus he

116

Ibid. 88-96. Ibid. 6. 118 Ibid. 96-7. 119 Ibid. 99; he wrote concerning the proposition that astrology 'predice le cose avvenire: la quale scienza quanto agl' effetti piu universali, e piu semplici, come pioggie, vend, nevi, e altri simili, i quali immediatamente dependono dal cielo, e dal lume suo, e certissima, e vera, di maniera che di cotali effetti si apporra sempre 6 il piu delle volte il buono astrologo ogni volta, purche oltre all'essere eccell. in cotal dotrina e'sia ancora diligente in calculare bene; usi buoni stormenti, pigli el pun to vero; e in somma, osservi tutto quello, che si richiede'. For his reference to Augustine and the Councils see p. 106. He made no reference to Copernicus. 117

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does the contrary. Thus he would not take council in his acts because everything would happen of necessity, and yet it is evident from experience that those who take council act much better than those who act by chance. Otherwise justice would be taken away . . . . Finally our most holy and true Christian religion, and the Catholic and Roman Church, master of all truth and unable to err, teach that man is free and that the heavens cannot constrain him.120

He made an interesting choice of topics, linking the arts and sciences through mathematics, in his brief discussion of optics and music. After stereometry, astronomy, cosmography, geography and chorography came another part of mathematics concerned with continuous quantity called perspective because it applies lines to seeing, considering them in so far as they go out from the eyes and come to things, speaking however in the manner of the perspectivists, who think that we see things because rays go out of our eyes and come as far as the things seen in the shape of a pyramid of which the apex would start from the eyes and the base terminate at the surface of the thing seen. But speaking in the manner of Aristotle and of the truth, these lines of sight are boundaries of the species ('specie') of the thing seen, which species or true image starts from the thing seen, terminating its apex in our eye. When we are so far away that the apex of the species or image of the thing does not arrive at our eyes, we cannot see; and according to whether we are more or less near the things, and the angle of the said apex opposite to the base and to the thing is larger or smaller, whence by the teaching of Euclid in the first book of the Elements the base which terminates at the thing seen will be larger if the angle is larger and smaller if the angle is smaller, so that the thing appears larger or smaller according to whether it is seen through a larger or smaller angle; and it is seen through a larger angle if it is nearer to us and through a smaller one if it is farther away. The perspectivist then considers that the line from our eye either goes out from it and comes to the thing, or comes from the thing to the eye; this for the present does not matter. Enough that perspective is a science which reasons from a line that goes out from the eye and comes from that, or that is the boundary of the image of the thing which starts from the thing itself and terminates in the eye, drawing together by virtue of the blackness of the eye, which colour has power to unite, or by virtue of the eye's round shape which shape also unifies it, as is seen in convex and round mirrors in which our face appears very small and foreshortened and by contrast in concave mirrors much larger. Perhaps the images of the thing unite with each other when they arrive at the eye for the one reason or the other.121

120 Ibid. 100,102. He illustrated his argument (p. 101) with the story of the Stoic Zeno's slave, who claimed that he had broken his master's vase by necessity, to which Zeno replied that he chastised him by necessity. 121 Ibid. 108-10; cf. Crombie The mechanistic hypothesis and . . . vision' (1967).

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Going on to discuss the three divisions of perspective, dealing respectively with direct, reflected and refracted visual lines, he drew attention to Aristotle's analogies between the reflection of images from a mirror, the bouncing of a ball from a wall, and the echoing of the voice from a cavern 'down to the last syllable'.122 Perspective explained illusions such as a stick appearing bent in water, problems of natural philosophy such as the shape and colours of the rainbow, and the foreshortening used by painters. Arithmetic like geometry was also both speculative and practical: 'the speculative is called by Plato in the Philebus the arithmetic of philosophers, and the other that of the common people', as used by merchants.123 So likewise was music. As with geometry and its subalternates, so with 'arithmetic, which is more certain than music, because arithmetic treats numbers which it does not apply to any sensible matter, and music treats the same numbers while applying them to sensible things, as are sounds, high-pitched and low-pitched'.124 Thus speculative music applied the science of discrete quantity to notes which together could produce harmony and consonance. Through these practical music played in various ways could excite the concupiscent or irascible appetites of the senses shared with the animals, or in man alone a third 'rational appetite for those things which help and delight the soul, such as the appetite and longing to know natural, mathematical and divine things, and to act in short virtuously according to moral and to speculative virtue'.125 This last was that understood by the divine Plotinus which led men to transcend 'the eye of the body' so that 'the intellect, which is divine, would rise to think that if man has been able to form notes of such proportion, with how much greater harmony had God, who in knowledge, will and power is so far ahead of men and every other creature, composed this universe and such marvellous orders of creatures, all directed to the services of man . . . '.126 A year after he had begun his lectures on Plato at Pisa, Vieri published another work aiming at concordance: 'Compendio della dottrina di Platone in quello che ella e conforme con la fede nostra' (1577). True 'virtuosi', he wrote in the preface, embellished the spirit in three ways: with knowledge above all of divine things, secondly of visible things, and thirdly of the teaching of Plato. Josephus had said that Plato imitated Moses: 'Numenius the Pythagorean, having read the books of Moses and of Plato, considered Plato to be another

122

Vieri, ibid. Ill; Aristotle, 'De anima', ii.8, 419b 25-35. For perspective Vieri (pp. 112-3) cited Euclid, Archimedes, Pecham and Witelo. 123 Vieri, ibid. 114-5; citing also the 'Republic' vii and the 'Laws'. 124 Vieri, ibid. 91-2. 125 Ibid. 115-6; see 113-20, esp. 117-8; the ancient Lydian and loniam modes excited the concupiscent and amorous appetite; the Phyrigian mode the irascible and warlike; and the Dorian the contemplative. 126 Ibid. 118-9, citing Plotinus and Aristotle's 'Polities', viii.7.

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Moses who spoke in the Attic tongue';127 Justin Martyr, Augustine and Ficino confirmed the conformity of Plato's doctrines with Christian theology. Cosimo de' Medici, through his encouragement of Gemistus surnamed Plato because he was 'almost a new Plato', of Ficino and the formation of a Platonic Academy, and thereby of Pico della Mirandola, had by the will of Divine Providence resurrected there in Tuscany the pious and divine philosophy of Plato: 'which had originated from Zoroaster with the Persians, succeeded among the Egyptians thanks to Mercurius Trismegistus and among the Thracians through the work of Orpheus and Aglaophemus, and grew with the Greeks and Italians under Pythagoras and with the Athenians through the care of Plato'.128 Vieri paid attention in this work to concordance over the whole range from moral teaching to accounts of the creation: 'God has produced the whole universe as is said by Moses in the beginning of Genesis and by Plato in the Timaeus', and also by Hermes Trismegistus in the 'Pimander'.129 His last effort at concordance appeared in his final year at Pisa: 'Vere conclusioni di Platone conformi alia dottrina Christiana et a quella d'Aristotile' (1590). This was a polemical reply to his Aristotelian colleague Borri's 'De peripatetica docendi atque addiscendi methodo' (1584). From Vieri's dedicatory preface to Baccio Valori it seems that he had been obstructed by the Aristotelians in giving his lectures and had been forced to abandon them.130 Meanwhile in Ferrara Patrizi is listed as lecturing on Plato's 'Republic' in 1578 and on Platonic philosophy in a number of subsequent years down to 1587. In that year he left, but Platonic courses seem to have continued in the university.131 Patrizi was an all-out Platonist, concerned about concordance with Christian theology but not with Aristotle. In the University of Rome the Platonic impetus given by the mathematical scholar Raimondi was strengthened by Patrizi's appointment to a new chair in Platonic philosophy there in 1592, through the Neoplatonic interests of Ippolito Aldrobrandini, who had in that year become Pope Clement VIII, and his family.132 A chair for the introduction of lectures on Plato in Bologna had been discussed in 1588 and Mazzoni proposed for it.133 But in that year he joined Vieri at Pisa, where he 127 Vieri, 'Compendio', dedicatory preface to Giovanna d'Austria, Gran Duchessa di Toscana (1577) sig. a4-2; cf. for Numenius Pythagoricus of Apamea in Syria (2nd cent, A.D.) Sarton, 'Introduction', i (1927) 298; for Josephus, 'Against Apion', ii, 15-17, cf. Dewish, 'Antiquities' i.2.3; and for his Hermetic Neoplatonic view of intellectual history, advocated in the 15th century by Georgius Gemistus Pletho, Kieszkowski, 'Studi . . . ' (1939) 113 sqq.; Kristeller, The Philosophy of Marsilio Ficino' (1943) 13 sqq., 'Studies . . . ' (1956) 36-7, 233; Saitta, 'II pensiero italiano', ii (1950) 75 sqq.; Garin, 'L'umanismo italiano' (1953) 108 sqq., 'Studi. . . ' (1958) 153 sqq., 216 sqq., 'Storia . . .' (1966) 358 sqq.; Yates, 'Giordano Bruno' (1964) 14 sqq.; Wind, 'Pagan Mysteries . . .' (1967) 241 sqq.; Walker, The Ancient Theology' (1972); cf. above nn. 66, 86,97. 128 Vieri, ibid. sig. a4+3; this Cosimo was 'Padre della Patria' (1389-1464); see for Algaophenus etc. Kristeller, Studies . . . (1956) 233. 129 Vieri, ibid, c.ll (1577) index, and pp. 85 sqq., citing these three ancient authors. 130 Cf. Fabronius, op. cit. ii (1792) 347, 469; Kristeller, Studies . . . (1956) 292; Garin, L'umanismo italiano (1952) 165, Storia . . . (1966) 587-8. 131 Solerti, 'Documenti riguardanti lo Studio di Ferrara' (1892) 32-48; Kristeller, Studies . . . (1956) 191-2. 132 Renazzi, Storia dell'Universita di Roma, iii (1805) 31-2, 224-5. 133 Costa, Ulisse Aldrovandi e lo Studio Bolognese (1907) 90; Kristeller, ibid. 292.

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remained until 1597 when he was brought by Clement VIII to succeed Patrizi in Rome.134 In Pisa Mazzoni was eventually succeeded in his chair by another of Galileo's academic colleagues, Fortunio Liceto (1577-1657), who held it from 1605 until he moved to Padua in 1609.135 In the sixteenth century Platonic philosophy seems to have been officially recognised only in Pisa, Ferrara and Rome, followed briefly at the beginning of the seventeenth century by Pavia.136

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C. Sommervogel, 'Bibliotheque de la Compagnie de Jesus', nouv. ed., i-ix (Bruxelles et Paris, 1890-1930), x-xi (Paris, 1909-32), xii (Toulouse, 1930). G. Tiraboschi, 'Storia della letteratura Italiana', 8 torn. (Modena, 1787-94). Francesco Vieri, 'Discorso di M. Francesco de Vieri, cognominato il Verino, del soggetto, del numero, dell'uso, et della dignita et ordine degl'habiti deH'animo, cioe dell'arti, dottrine morali, scienze specolative, e facolta stormentali' (Fiorenza, 1568). M. Francesco de Vieri cognominato il Secondo Verino, 'Compendio della dottrina di Platone in quello che e conforme con la fide nostra' (Fiorenza, 1577). R. Garcia Villoslada, 'Storia del Collegio Romano, dal suo inizio (1551) alia soppressione della Compagnia di Gesu (1773)', 'Analecta Gregoriana' Ixvi (Romae, 1954). U. Viviani, 'Vita ed opera di Andrea Cesalpino' (Arrezzo, 1922). D.P. Walker, 'The Ancient Theology: Studies in Christian Platonism from the Fifteenth to the Eighteenth Centuries' (London, 1972). E. Wind, 'Pagan Mysteries in the Renaissance', 2nd ed. (London, 1967). F.A. Yates, 'Giordano Bruno and the Hermetic Tradition (London, 1964). G. Zaccagnini, 'Bernardino Baldi nella vita e nelle opere', 2a ed. (Pistoia, 1908). G.L. Masetti Zannini, 'La vita di Benedetto Castelli' (Breschia, 1961).

Further References See A.C. Crombie, Styles of Scientific Thinking . . . (1994) 763 n. 131, 766 n. 267,1824,1826; U. Baldini, 'Christopher Clavius and the scientific scene in Rome' in Gregorian Reform of the Calendar, ed. G.V. Coyne et al. (Citta del Vaticano, 1983) 137-69, Legem impone subactis: Studi sufilosofia e scienza del Gesuiti in Italia 1540-1632 (Roma, 1992); G.P. Brizzi (a cura di), La 'ratio studiorum': Modelli culturali e pratiche educative del Gesuiti in Italia tra Cinque e Seicento (Roma, 1981); A. Carugo, 'Giuseppe Moleto' in Aristotelismo veneto e scienza moderna, a cura di L. Olivieri (Padova, 1983) 509-17; G. Codina Mir, Aux sources de la pedagogic des Jesuites: Le 'Modus Parisiensis' (Roma, 1968); N. Jardine, 'The forging of modern realism: Clavius and Kepler against the sceptics', Studies in History and Philosophy of Science, x (1979) 141-73; E. Knobloch, 'Christoph Clavius: ein Astronom zwichen Antike und Kopernikus' in Vortrage des erstens Symposiums in Bamberger Arbeitskreises Antike Naturwissenschaft und ihr Rezeption, hrg. K. Doring and G. Wohrle (Wiesbaden, 1990); J.M. Lattis, Ch. Clavius and the Sphere ofSacrobosco: The roots of Jesuit astronomy on the eve of the Copernican revolution (University of Wisconsin doctoral thesis, 1989); C. Naux, 'Le Pere Christophe Clavius, sa vie et son oeuvre', Revue des questions scientifiques, liv (1983) 55-68,181-94; with Christophe Clavius, Correspondenza, a cura di U. Baldini e P.D. Napolitani, 7 vol. in 14 (Pisa, 1992).

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'He exalted Plato to the skies for his truly golden eloquence, and for his method of writing and composing in dialogues; but above everyone else he praised Pythagoras for his way of philosophising, but in genius he said that Archimedes has surpassed all, and he called him his master'. The omission of Aristotle's name from this honours list by Galileo's second seventeenthcentury biographer, Niccolo Gherardini, is no surprise; nor is his preceding remark that, far from following current fashion in running Aristotle down, Galileo praised his marvellous writing on literature and ethics but found that 'this great man's way of philosophising did not satisfy him, and that there were in it fallacies and errors' (Galileo, Opere, xix, 645). Nevertheless, I shall respond to the invitation given to me to discuss briefly some 'wider issues' relating to Stillman Drake's very interesting paper, by taking up just one question on which I shall argue that Aristotle had a far more profound influence on Galileo's scientific thinking than remarks such as Gherardini's might suggest. Professor Drake make a point of stressing Galileo's alleged decision 'to limit the scope of his inquiries to separate and well-defined areas, and not to seek a general theory of the universe'. He seems to refer to the range of content or subjects Galileo was prepared to consider. But going on to say that this is 'an extremely important part of his scientific methodology', he cites the Dialogo and // Saggiatore for examples of Galileo's limit being place on the expectation of certainty rather than the range. Galileo's performance in scientific inquiry was undoubtedly guided by his policy of selecting acceptably answerable questions as much as by his criteria for acceptable answers. But whether Professor Drake means that Galileo limited the range or the certainty he expected science ultimately to achieve, I should argue that the opposite is true. First Galileo's very effective method of limiting problems in order to solve them was nearly always aimed in the end, whether through the science of motion and mechanics or through telescopy, precisely at establishing not only true methods of natural philosophy, but also the true general theory of nature. This was a theory comprising matter and its properties as discovered by both terrestrial and celestial inquiries, their bearing on cosmology, the relation of

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perceiver to perceived and of knower to known, and the bearing of all on theology. Secondly, throughout his scientific inquiries and debates, Galileo wrote continually of finding 'true and necessary demonstrations' (Opere, ii, 155; v. 330) of his conclusions, and on one famous occasion, in his First Letter about the Sunspots (1612), he looked forward not un-typically to solving 'the greatest and most admirable problem there is, the true constitution of the universe. For such a constitution exists, and exists in only one, true, real way, that could not possibly be otherwise' (Opere, v. 102). Strong words; in fact, the words of Aristotle's Posterior Analytics (i.2, 71b9-72a24; 6, 74b5-6; 10, 76a31-b31), well known in Galileo's day to every educated person. We have unqualified scientific knowledge of something, Aristotle had written, when 'we know the cause on which the fact depends, as the cause of that fact and no other and, further, that the fact could not be other than it is' (i.2, 71b9 = text. 7, Opera omnia, i, 1552, f.!30v); 'Demonstrated knowledge must rest on necessary first principles; for the object of scientific knowledge cannot be other than it is' (i.6, 74b5 = text. 44, f.!42v). I should argue that Galileo aimed in the end at total certainty, that is was Aristotle and no other who provided him with this ideal of truly scientific certain knowledge, and that he retained this ideal from his earliest to his latest writings, even as he rejected the methods and destroyed the content of Aristotle's physics, and even when he recognised that demonstration truly scientific by Aristotelian criteria eluded his grasp. We might say that by attempting to prove so much so powerfully Galileo got himself scientifically and personally into a lot of unnecessary trouble. But given his background and education in sixteenth-century Italy, to say nothing of his own quite specific intellectual vision, it was very natural for him to see beyond the solutions of particular problems to a general philosophical reform to which they would effectively contribute. In this he was certainly encouraged by early influences to make a characteristic response to the striking variety of current intellectual attitudes and aims, themselves the products of successive European responses to successive recoveries of ancient thought. Most relevant was the well-known difference between the philosophers on the one hand, and the mathematicians and artists on the other. Both sides had been exposed in different ways to a mathematical rationalism imposed on art and nature through mathematical theories of painting, music and machines, and on philosophy through Neoplatonic visions of a morally normative and therapeutic numerological harmony, and of mathematics as a stage in the education of the mind for theology. Mathematics became an antidote to the threat of scepticism. But the recovery of alternatives to the academic Christian Aristotle, and especially of this new Plato, made much sixteenth-century philosophy notably eclectic, tolerant of opposing systems, seeking concordance between authorities, circling in the habit of scholastic disputation, seeing mathematics as a means of moral education rather than of solving scientific problems. Jacopo Mazzoni (1548-98), friend of Galileo's father and professor of both Aristotelian and Platonic philosophy at Pisa from 1588 to 1597, was the

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most obvious and intelligent philosophical contemporary giving mainly this meaning to mathematics. By contrast the artists, engineers and mathematicians concerned with their problems were obliged by the practical crafts to make clear limited decisions. The Florentine ambience provided by Galileo's father, as an eminent practical as well as theoretical musician, and by his friends among artists and mathematicians, was strongly scientific in this sense and unsympathetic towards the more numerological and cosmic aspects of Platonism. Moreover, Vincenzo Galilei (c. 1520-91) in his experimental analysis of the mathematical basis of music looked beyond the Pythagorean proportions, like Aristotle, for some process of physical causation. We could say perhaps that Galileo Galilei tried to carry the decisiveness of the mathematical arts into natural philosophy through the discovery of true processes of physical causation, as distinct from those accepted by conservative contemporary Aristotelians. Out of this, above all under the guidance of Archimedes, came the distinction he made between what he called the mathematical 'definitions' (e.g. Discorsi on two new sciences, 1638; Opere, viii, 197 sqq.) and the physical causes which he never ceased to look for. He was to carry the consequent decisions of his natural philosophy into theology. His earliest surviving philosophical writings show however an influence on his intellectual formation that was neither mathematical, not artistic, nor Platonic but conservatively Aristotelian. To these I must now turn. During 1969 and 1971 my colleague Adriano Carugo, then working at Oxford and now at the University of Venice, and I solved the main problem of the sources of Galileo's early writings in his own hand, published by Favaro as Juvenilia (Opere, i). These comprise two incomplete treatises, each in two parts, on major Aristotelian themes: the Tractatio prima de mundo with the Tractatio de caelo concerned essentially with questions of cosmology and cosmogony raised for Christian theology by Aristotle's De caelo; and the fragmentary Tractatus de alteratione with the Tractatus de dementis concerned with the theory of elements and qualities put forward by Aristotle in the Physics and the De generatione et corruptione. We have also studied a third autograph treatise, again incomplete and in two parts, which Galileo left in manuscript but of which Favaro published only a small section, describing it as 'some scholastic exercises' (Opere, ix, 273). This is the Disputationes de praecognitionibus et de demonstratione (Biblioteca Nazionale Centrale di Firenze, MS Galileiano 27; Fig. 1), a commentary on Aristotle's Posterior Analytics with a detailed analysis of questions of the logic connecting cause with effect, of types of scientific demonstration, and of the relation between mental assent, as in a mathematical proof, and demonstration of actual existence. I shall summarise our conclusions about the sources, dates and nature of these three treatise, and then briefly discuss some of the philosophical views Galileo expressed in them and their relation to those he expressed in later life.

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Fig. 1 Beginning of Galileo's autograph Disputationes de praecognitionibus et de demonstratione (Biblioteca Nazionale Centrals di Firenze, MS Galilaiano 27, f. 4r).

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I myself began studying the Tractatus de alteratione et de elementis in 1964 when I was looking for the sources and earlier thinking behind the famous distinction which I discussed in my article, 'The Primary Properties and Secondary Qualities in Galileo Galilei's Natural Philosophy', for the Saggi su Galileo Galilei and in more detail in the unpublished volume Galileo's Natural Philosophy in which Adriano Carugo collaborated, both completed in 1968 (see the Bibliographical Note). By that date I had become interested in a further range of ancient, medieval and more recent sources cited in Galileo's treatise as well as in the Tractationes de mundo et de caelo and the Disputationes, of which I began to make a preliminary study and got a microfilm in the autumn of 1967. The next stage in this story was that in 1968 Adriano Carugo began to suspect and in 1969 showed conclusively that many of Galileo's citations of ancient and medieval sources in the Tractatus de alteratione et de elementis and the Tractatio prima de mundo came from the textbooks of two Jesuit professors of philosophers at the Collegio Romano, both Spaniards: Benito Pereira (c. 1535-1610) and Francisco de Toledo, or Toletus (1532-96), who became a Cardinal. These textbooks were Pereira's De communibus omnium rerum naturalium principiis et affectionibus libri quindecim (published at Rome, 1576; first edition with a different title 1562), and Toletus's commentaries on Aristotle's Physics (published at Paris, 1581) and Degeneratione et corruptione (published at Venice, 1579). Carugo showed that Galileo used Pereira's book as his main source of information for his discussion in De motu of the dynamical theories of Philoponus, Hipparchus, Avempace, Averroes, Julius Caesar Scaliger and other ancient, medieval and more recent authors. Then in June 19711 discovered that important parts of the Tractatio de caelo, including the earliest appearance in Galileo's hand of the name of Copernicus (Fig. 2), whose location of the Earth in an orbit round the Sun is there rejected, all came from a well-known textbook by another Jesuit professor at the Collegio Romano, In Sphaeram loannis de Sacro Bosco commentarius (published at Rome, 1581) by the German mathematician Christopher Clavius (1527-1612). So Galileo's basic sources were three prominent contemporary Jesuits of the Collegio Romano. These identifications required some luck as well as cunning, for although Galileo clearly indicated Pereira as a source, he named Clavius only once and Toletus not at all; but of course they were based essentially on considerable and sometimes tedious reading of sixteenth-century natural philosophy, made in order to explore and understand Galileo's intellectual background and its relevance to his own thought. Sometimes Galileo took from his sources whole passages verbatim, including lists of references, not always copied accurately. Sometimes he went through these to the ancient or medieval originals. But he did not simply copy, but organised and often rearranged the materials for his own sharply independent arguments. I have shown that he used another work by Pereira, a commentary on Genesis (first volume, published at Rome, 1589), in the same way for his discussion in his Lettera a Madama Cristina di Lorena (1615) of the exegetical rules for relating demonstrated science to the authority

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Fig. 2 Autograph page of Galileo's Tractatio de caelo with the earliest reference in his hand of Copernicus's great work: 'Nicol. Copn: in op. de revolutione orbinum caelestinum' (Biblioteca Nazionale Centrale di Firenze, MS Galileiano 46, f. 22r).

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of revealed Scripture. In the Disputationes he cited some two dozen ancient, medieval and more recent authors, but again he seems to have used intermediate sources, here mainly the Dominican philosopher Thomas de Vio Caietanus's In . . . libros Posteriorum Analyticorum Aristotelis castigatissima commentaria (published from 1505 in many editions, including one at Venice in 1565) and the sixteenth-century Averroi'st logician Girolamo Balduino's Quaestia aliquot. . . logica et naturalia (available in various editions including one published at Venice in 1563 with his commentary on the Posterior Analytics). We have a complete transcription made during 1970-71 by Adriano Carugo of the unique manuscript of the Disputationes (MS Galileiano 27), and we are publishing with an English translation the parts of this most relevant to scientific thought. All three treatise comprise closely reasoned arguments, scholastic in form, making often fine distinctions between opposing opinions. Apart from Aristotle, cited continuously, the highest rates of citation are scored by his commentator Averroes, followed by Aquinas and the Thomistae' (Opere, i, 76, 117-118, 144), chiefly Italian and Spanish. This is matched by agreement with Thomist opinions especially on cosmology, for example for the world created being the best possible, for the heavens being probably incorruptible but not necessarily so because no natural power could limit God's absolute freedom, and so on. If we look at Galileo's Jesuit sources themselves, we find an astringently rational view of nature, natural causation and natural philosophy very like so many later expressions of his own. Pereira, for example, argued that the disproof of alchemical gold came not from the theory that alchemists had no access to celestial fire, which he himself thought was the same as terrestrial fire, but from the fact that no one had ever produced if (De communibus, viii, 21, pp. 299-300). He was equally sceptical of magic and astrology. Clavius gave a brilliantly lucid exposition of the criteria for deciding whether or not the spheres and epicycles, postulated in astronomical theory to account for the observations, had any real physical existence (In Sphaeram, c.4, pp. 434-437). Galileo did not discuss this in the Tractatio de caelo, but we may see a kinship between his later position on Copernicus and Clavius's insistence that celestial like terrestrial science must argue from effects to their real physical causes, that it was only the syllogistic form that made the dialectical rule that truth can follow from falsehood seem plausible, that Copernicus himself had postulated his new arrangement of spheres and epicycles not as fictitious but real, and that while he himself was not convinced by Copernicus' arguments he would thank heartily anyone who could produce a better system than any so far produced. What are these writings? We have derived a possible order and dating from their content and from the paper used. The chronology in the Tractatio prima de mundo, deriving from a combination of Biblical and ancient Greek chronology total of 5,748 years from the creation, with 1584 years from the birth of Christ 'down to the present time' (Opere, i, 27; cf. Favaro's editorial comment on p. 12), might be thought to make this at least its earliest date of composition, even

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if it was all copied from another source. Since the Tractatio de caelo is written on the same kind of paper, watermarked with a faint CT or CL, they seem to belong to the same period. Should both be placed at the end of Galileo's period as a student at Pisa, before his return to Florence in 1585? But, as William Wallace has pointed out to me, Galileo corrected mistakes in writing down this total chronology (MS Galileiano 46, f.!0r) and when repeating it later wrote it as 6,748 years without correction (f.!5v; corrected in Opere, i, 36), so it seems to be fragile evidence. Moreover, in the Tractatio de caelo he quoted Clavius. He visited Clavius in Rome in 1587 and evidently discussed astronomy, for in a subsequent letter of 8 January 1588 (Opere, x, 22-23) he referred to the Jesuit's still unpublished defence of the new Gregorian calendar. In his letter of 15 November 1590 (Opere, x, 44-45) to his father from Pisa, a year after he had returned there as lecturer in mathematics, he awaits the arrival from him of 'la Sfera', which could have been Clavius's. So perhaps we should date the Tractationes de mundo et de caelo from his period either with his father at Florence (when in 1588 he wrote his cosmographical lectures on Dante's Inferno, on different paper however) or as a young lecturer at Pisa. The Disputationes is written on paper without watermark. Since here he does not mention Archimedes, explicitly the new enlightenment of his Theoremata circa centrum gravitatis solidorum (dated late 1587 or early 1588: see Carugo's edition of the Discorsi, 1958, pp. 840-847) and thereafter of the lectures on the Inferno, the dialogue and treatise De motu, and La bilancetta (dated 1586 by Favaro on Vincenzo Viviani's not always reliable testimony, but plausibly later on other evidence to be discussed in our forthcoming book), it seems that the Disputationes must probably precede these works. Of these La bilancetta, the Dialogus de motu and part of the Tractatus de motu were written on similar paper without watermark. He wrote the Tractatus de alteratione et de elementis on the kind of paper, watermarked with a device of a lamb and flag (Fig. 3), which he used also for the Inferno and for another part of the Tractatus de motu. It has been argued, mainly from the doctrines proposed, that he wrote both the dialogue and the treatise De motu after his return to Pisa in 1589. If the paper is a guide to the date of the Tractatus de elementis, this would connect the sudden appearance of citations of Galen in this work with the seven volumes of Galen which Galileo said in the same letter of 15 November 1590 that he was expecting from his father with the Sfera. Some years after giving up medicine, it was Galen the philosopher whom he cited. In this letter he told his father that he was 'studying and having lessons with Signer Mazzoni, who sends you greetings'. Must we then conclude that the Tractatus de alteratione et de elementis was a study of these questions of Aristotelian natural philosophy written by the young lecturer in mathematics under the influence of Mazzoni, side by side with the critique of Aristotle he was developing in De motu under the influence of Archimedes and Plato? The targets for criticism are also indicated by Mazzoni: Aristotle's lack of mathematics and his uncritical reliance on the senses. Galileo contrasted both with his own new mathematical method, but neither criticism is incompatible

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Fig. 3 The watermark showing a backward-looking lamb with flag enclosed in a circle: Briquet no 48 (Biblioteca Nazionale Centrale di Firenze, MS Galileiano 46, ff. 71, 74: the paper is folded and bound across the middle of the circle).

with his making at the same time a serious study of Aristotle's theory of the elements and qualities and its ancient rivals. In the unpublished volume I have already mentioned, I suggested that Galen's exposition of atomist doctrines in his De elementis secundum Hippocratem could have been a source of Galileo's later distinction between primary properties and secondary qualities which he had known from that time. This was also suggested by William Shea in his article 'Galileo's Atomic

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Hypothesis' (Ambix, xvii, 1970, p. 23). Moreover in De motu itself Galileo retained scholastic forms of argument alongside the mathematical form learnt from Archimedes, and continued not only citing philosophical commentaries but also using Pereira as an important source of information. Already in De motu Galileo used Archimedes and Plato to replace Aristotle's ideological structure of the universe with a structure that was the resultant, still providentially designed, of mechanical forces, and at the same time to begin replacing the whole Greek theory of pairs of contrary qualities with quantitative linear scales of weight, density, heat and so on. The full integration of his new mathematical method with a new theory of matter was something he brought about only much later, precisely through a further critique of Aristotle. We may then dismiss the hypothesis that Galileo's three earliest treatise were notes he took of philosophical lectures heard as a student at Pisa. The long-standing candidate for the lecturer, Francesco Bonamico, has in any case been shown by Eugenio Garin (Scienza e vita civile, 1965, pp. 124-127, 144145, 165-166) to be impossible, and this was confirmed in 1969 by Adriano Carugo's further comparisons of Bonamico's De motu (Florence, 1591) with the Juvenilia. Bonamico was no Thomist and he disagreed with Galileo too often. Galileo was to take him on years later in his Discorso (1612) on floating bodies, and interestingly was to cite from him the logical rule for discovering the cause of effects through presence or absence, which he used in experiments for that work (Opere, iv, 52; cf. 19, 22, 27). But that is another question. I do not think it possible to say what Galileo wrote these treatises for, or indeed exactly when he wrote them. Was he lecturing on these subjects and were they his own lectures? Were they simply for his own edification? For that matter why, and indeed over what years, did he write De motul Before we made the discoveries I have described no one known to us, no one we had been in touch with or whom we knew to be working on Galileo, had identified any of these sources. It seems that we looked back across nearly four and a half centuries to something known before perhaps only to Galileo himself. But someone was bound to identify them fairly soon, and in fact William Shea did independently discover Galileo's use of Clavius a couple of years after me. William Wallace noticed certain similarities with Pereira and Toletus, but saw them only among others through a glass darkly and failed to identify them as sources. Full details of our work will be published in our forthcoming book, but meanwhile we thought it might be useful to make authorised information available. It seems likely that Galileo used other secondary sources not yet identified. The sheer number of references, not just to ancient, medieval and modern philosophers and astronomers but also to points of theology in Scripture, patristic writings and the decisions of Councils of the Church, suggests some common source. Perhaps someone, not me, will look further. Nevertheless these early writings impress by their scholarship. They show Galileo then as indeed he appears in his later writings (despite his biographers) as the highly literate, well-read man of his time and ambience

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that he was, a match for anyone in learned dialectical debate, and a philosopher who in wanting to show forth the true system of the universe and of knowledge, wanted also the support of the truest ancient model. He famously asked to be entitled 'philosopher' as well as 'mathematician' to the Grand Duke on his return to Florence in 1610 (Opere, x, 353). The theory of the truly scientific demonstration expounded by Aristotle in the Posterior Analytics was a model on which everyone in Galileo's time had been educated and which was widely accepted as the ideal goal of knowledge. Galileo's Disputationes de praecognitionibus et de demonstratione was his account of that model. It is significant that he should have written it as one of his earliest philosophical essays. Let me conclude by looking briefly at its place in Galileo's thought. We are caused to have knowledge, Galileo wrote in De praecognitionibus, by the first principles we grasp (disputatio ii, quaestio, MS Gal. 27, f.5v). We may know these in various ways: the most universal only through knowledge of terms, as that the whole is greater than its part; others only through the senses, as that fire is hot; others through various forms of inductive or hypothetical argument; others through experience, as in medicine; others only through habit, as those of moral science which we cannot understand unless we practice them (ii.l, f.4r). But whereas in nature an effect must necessarily follow from its sufficient cause, man is free and cannot without his assent be made to have knowledge (iv.2, f.!2v). This leads to a discussion in the Tractatio de demonstratione (disputatio i, quaestio i, f.!3r) of Aristotle's criteria for the first principles of truly demonstrated knowledge: these must be true, primary and immediate in not being themselves demonstrated from any prior principles, and related to their conclusions as cause to effect (Post. Anal. i.2). Galileo argued that only true propositions can actually be known, because true knowledge of things is had through the causes by which they exist. Demonstrations of true conclusions from false premisses can only be per accidens, not per se, and we cannot actually know such things as the void and the infinite for they are nothing. The proper object of true knowledge in ens reale, real being, not just ens rationis (ii, 1, ff.!7v-18r). He went on to analyse at length Aristotle's criterion that truly scientific demonstrations must-proceed from true causes, though we have first to discover these from our more immediate knowledge, for example through the senses. The premisses of mathematics cause knowledge and are as immediately knowable to us as their conclusions, but mathematical entities do not exist (ii.6, f .22™). The sciences subordinate to mathematics (as astronomy, music etc) do not have truly scientific demonstrations because they must proceed ex suppositione from principles assumed from the superior science (ii.4, f.20v). We may give our certain assent with evidence as to knowledge through the senses, or without evidence as in our faith, but we come to rest most agreeably in knowing a conclusion because it follows from true premisses (ii.6, ff.22v-23r).

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He concluded with a discussion of the recognised kinds of demonstration: ostensiva, ad impossibile, quia, propter quid, potissima (iii.1-2, ff.29r-30r, cf. i.l, f.!3r). Here, as elsewhere, he seems to be using Proclus' commentary on Euclid, as well as Averroes and other authors whom he named, but he took an independent line. Demonstration ad impossibile is not truly scientific because it proceeds by raising questions from false premisses in order to find the true ones (f.29r). Truly scientific demonstration could be reduced to two kinds, demonstratio quia which demonstrates the existence of an effect and from that a posteriori its cause, the demonstratio propter quid which demonstrates both the cause and hence the existence of the effect (f.30rv). That demonstratio quia is truly scientific is proved on the authority of Aristotle and all commentators, and because like demonstratio propter quid it proceeds from true and necessary premisses to true and necessary conclusions, and so generates knowledge and not probable opinion (f.30r). That an attribute is connected with a subject we know from experience; that the connection is naturally necessary when it always occurs we know by the light of our intellect, for otherwise nature would have been improvident; it can be truly demonstrated by intrinsic, extrinsic or other kinds of cause (f.30r). This seems to be the origin of Galileo's later designation of demonstration both from observation and from theory as 'necessary demonstration'. The scientific argument, he went on, especially in the physical sciences where we began by not knowing the physical causes, alternated in a 'demonstrative regress' (iii.3, f.31rv) in both directions, from effect to cause and vice versa. In mathematics the regress is little needed because premisses are as immediately known as their conclusions. In any case it is not circular because, starting from an effect which one knows better than its reason, it demonstrates the reason for that effect. The complete true cause and the effect entail each other reciprocally and uniquely (f.31v). Parts of the Disputationes (despite its containing no precisely scientific illustrations of the logic) resonate with many of Galileo's well-known later practices and sentences. This is not the occasion to discuss the organisation of his experimental argument, for example in De motu and in the Discorso (1612) on the floating bodies, on the logic of la progressione demonstrativa, the methodo resolutiva, and the reductio ad impossibile or ad contradictionem (Opere, i, 260-265, 284-285, 318; iv, 19, 22, 27, 67). But it is relevant to note that he continued to carry on about 'true and necessary demonstrations' and 'the necessary constitution of nature' (as he put it in Le mecaniche, 1593; Opere, ii, 155, 189), and 'true demonstrations' from 'the true, intrinsic and total cause' (Discorso, 1612; opere, iv, 67), from his earliest writings and throughout the telescopic, mechanical and Copernican debates of 1610-16 and down to the Dialogo (1632). The great attraction for him of his argument, firs put forward in 1616, from the tides to the Earth's motions seems to have been that here he had a truly scientific demonstration by Aristotle's criteria: this cause must produce those effects, and those effects must entail this cause and no other (Opere, v 377-381, 393; vii, 443,470-472). Galileo hedged by claiming

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this as perhaps only the most probable cause advanced so far, but he exposed himself of course to a double accusation: that he was committing the logical fallacy of affirming the consequent, for phenomena could not uniquely determine their causes; and that he was claiming to demonstrate something necessary not just about the world that existed but also about its omnipotent Creator (cf. Antonio Rocco in 1633 on the Dialogo: Opere, vii, 628-629, 699-700). Galileo's necessity surely belonged to a conception inherited from Greek philosophy, that of the possibility of a completed and bounded knowledge of all that does and can exist. God's omnipotence made this existentially untenable, and this Galileo was to be careful to accept, by distinguishing his arguments about the world God had in fact created from any suggestion that God could be bound by any natural necessity (cf. Dialogo: Opere, vii, 128-131, 488-489; Lettera a Madama Cristina di Lorena: Opere v. 316-321). In his scientific practice, the open-ended character of mathematics and experiment and of the Archimedean argument ex suppositione (as in his letter of 7 January 1639 to Baliani: Opere, xviii, 12-13, aptly quoted by Stillman Drake), his appreciation of the complexity of natural causes themselves in such phenomena as light and heat, above all his use of range of confirmation as the test of a theory, notably of the new cosmology, effectively killed the scientific ideal of necessary truth imposed by Aristotle's logic. What are we to make then of Galileo's apparent blindness to this in expressions of continuing hope? Perhaps just words. But it seems to me that we have here in the slow general understanding of the difference that mathematical thinking made to traditional logic and to scientific explanation, found after all in sixteenth-century attempts to put Euclid into syllogisms, a phenomenon in European intellectual history, in European scientific methods mediated through cultural habits and inherited preconceptions, that greatly merits attention.

BIBLIOGRAPHICAL NOTE The subject of this paper (which has been checked by Adriano Carugo and is presented as a result of our joint researches) is discussed in detail in our forthcoming book to be published as: A.C. Crombie and Adriano Carugo, Galileo's Arguments and Disputes in Natural Philosophy. This work is a considerably revised version of our unpublished volume, Galileo's Natural Philosophy (1968), which was awarded the Galileo Prize and is deposited in the Domus Galilaeana, Pisa. All citations of Galileo's published writings refer to Le Opere di Galileo Galilei, A. Favaro, ed., 20 vols. (Florence, 1890-1909): cited in the text as Opere. References are made to the major Latin edition Aristotelis Stagiratae Omnia quae extant opera . . . Averrois Cordubensis In ea opera omnes qui ad

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nos pervenere commentarii . . ., 11 vols. (Venetiis apud luntas, 1550-52); Galileo seems to have used a reprint of 1573-76. Relevant secondary publications are C.M. Briquet, Les filigranes: Dictionnaire historique des marques du papier des leur apparition vers 1282 jusqu'en 1600, a facsimile of the 1907 edition with supplementary material, ed. A. Stevenson, 4 vols. (Amsterdam, 1968); A.C. Crombie, The Primary Properties and Secondary Qualities in Galileo Galilei's Natural Philosophy', Saggisu Galileo Galilei, a cura di C. Maccagni (preprint, Firenze, 1969; published 1972); Galileo Galilei, Discorsi e dimostrazione matematiche intorno a due nuove scienze, a cura di A. Carugo e L. Geymonat (Torino, 1958); E. Garin, Scienza e vita civile nel Rinascimento italiano (Bari, 1965); A Procissi, La collezione Galileiana della Biblioteca Nazionale di Firenze, i, 'Anteriori', 'Galileo', compilata da Angiolo Procissi (Roma, 1959); William R. Shea, Galileo's Intellectual Revolution (London, 1972); William A. Wallace, 'Galileo and the Thomists', in St Thomas Aquinas 1274-1974 Commemorative Studies (Pontifical Institute of Medieval Studies, Toronto, 1974) 293-330: an innacurate note on p. 330 about the discovery of Galileo's early sources is to be corrected. The study of the paper used by Galileo for these early autograph writings was begun by Adriano Carugo and extended with certain precisions by myself. All the paper is made with parallel wire lines 28-30 mm apart, at right angles to which are fainter parallel textural lines about 1 mm apart. The watermarks, always consistently related to the wire lines, appear on the folios at fairly regular intervals according to the foldings. By this criterion the writings may be grouped as follows: 1 On paper without watermark: Disputationes de praecognitionibus et de demonstration (Biblioteca Nazionale Centrale di Firenze, MSS Galileiani 27, ff. 3-31; Procissi p. 106; Galileo, Opere, ix, 279-282, 291-292); Plutarch, Opere morali (MSS Gal, 27, ff. 34-42; Procissi p. 106; Opere, ix, 285-290); Sonetti (MSS Gal, 27, f. 45; Procissi p. 107; G.O. ix, 289-290); La bilancetta and Tavola delleproporzioni delle gravita in specie del metalli e delle gioie pesate in aria ed in aqqua (MSS Gal. 45, ff.55, 60-62; Procissi p. 120; Opere, i, 215-20, 225-8); Fragment of Greek-Latin vocabulary (MSS Gal. 70, f.4; Procissi p. 148); Dialogus de motu (MSS Gal. 71, ff. 435; Procissi p. 151; Opere, i. 367-408)' Tractatus de motu (MSS Gal. 71, ff.43-60; Procissi p. 151; Opere, i, 344-366). 2 On paper showing a mark CT or CL (cf. Briquet no.9553): Tractationes de mundo etde caelo (MSS Gal. 46, ff. 1-54; Procissi p. 123; Opere, i, 14-111). 3 On paper with watermark showing a backward-looking lamb with a flag enclosed in a circle: Fig. 3 (Briquet no. 48): Due lezioni all'Accademia fiorentina circa lafigura, sito e grandezza dell'inferno di Dante (1588; Bibl. Naz. Cent, di Firenze, MSS Filza Rinuccini 21, insertion 19, ff. 1-29; Opere, ix, 31-57); Tractatus de alteratione etde elementis (MSS Gal. 46, ff. 57-100; Procissi p. 123; Opere, i. Ill-Ill, cf. 133); Tractatus de motu (MSS Gal. 71, ff. 115-124; Procissi p. 151; Opere, i, 326-340); Isocratis ad

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demonicum admonino (MSS Gal. 71, ff. 125-132; Procissi p. 151; Opere, ix, 283-284). 4 On paper with watermark showing a forward-looking lamb with flag enclosed in a circle with a cross above: Tractatus de motu (MSS Gal. 71, ff. 61-104, 133-134; Procissi p. 151; Opere, i. 251-312, 341-343). 5 On paper with watermark showing a swan on three semicircles (Briquet no. 12550): Tractatus de motu (MSS Gal. 71, ff. 105-114; Procissi p. 151; Opere, i, 312-326). This paper is whiter than that of the preceding and succeeding folios. There are linking marks H on ff. 104V and 105r and 7 on ff. 114V and 115r. Corrections and some repeated words throughout the Tractatus de motu suggest that Galileo was making a fair copy on different kinds of paper. In fact all the longer of these autograph writings show such mistakes. 6 On paper with watermark showing a ladder in a shield; Dialogus de motu (MSS Gal. 46, ff. 102-104: Procissi p. 123; Opere, i, 375-378, cf. 248); Memoranda de motu (MSS Gal. 46, ff. 102, 104-110; Procissi p. 123: Opere, i, 409-417); Italian-Latin vocabulary (MSS Gal. 46, f. 112; Procissi p. 123; Opere i, 246), MSS Gal. 46, f. 113 continuing the vocabulary has a watermark showing a star above the shield with the ladder (Briquet no. 5926), and this appears also on blank ff. 121-126.

Further References A. Carugo, 'Les J6suites et la philosophie naturelle de Galilee: Benedictus Pererius et le De motu gravium de Galilee' in Science: The renaissance of a history, ed. P. Redohdi (History and Technology, iv; London, 1987) 321-33; J.M. Lattis, Ch. Clavius and the Sphere ofSacrobosco in Further references to ch. 8. For an up-to-date discussion of the dating of Galileo's writings see below ch. 10, with Appendix (a).

Galileo Galilei, Dialogo (1632), Dialogo III: diagram of the Copernican system with the Sun in the centre, surrounded by the orbits of Mercury, Venus, the Earth with the Moon, Mars, Jupiter with its satellites, and Saturn.

10

The Jesuits and Galileo's Ideas of Science and of Nature with A. Carugo

1. Let us begin by saying first what is not the subject of this paper. We will not discuss the personal relations between Galileo and the Jesuits, because these have already been adequately discussed by the Jesuit Fathers Adolf Miiller (1909) and Bellino Carrara (1914)'. Nor are we concerned with any questions about the relation of the medieval

* This paper was presented in briefer form at the Novita Celesti e Crisi del Sapere: Convegno Internationale di Studi Galileiani Pisa-Venezia-Padova-Firenze 19-26 marzo 1983. Since it is too long for the Atti of the Convegno, it is published instead here in the Annali. 1 A. MULLER, Galileo Galilei und das Kopernikanische Weltsystem (Freiburg im Breisgau, 1909); B. CARRARA, La S. Scrittura, i SS. Padri e Galilei sopra il moto delta terra (Verona, 1914), I Gesuiti e Galileo (Verona, 1914).

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philosophical tradition to sixteenth and seventeenth century natural science. Our subject is the relation of the ideas developed by Galileo of science and of nature to the scholastic revival of Aristotelianism and Thomism, promoted by the Council of Trent and articulated in the late sixteenth and early seventeenth centuries by the Jesuits. It is one of the main subjects treated in our forthcoming book on Galileo's natural philosophy2. The policy of this scholastic revival was to defend a rational philosophy of science and of nature,; and with this to establish the possibility of rational knowledge for men both of God and of nature, against what were perceived as two current threats from within the Catholic world. One threat was seen to come from the conglomerate of Neoplatonism, Hermeticism and magic launched especially into Italian philosophy mainly by Marsilio Ficino and Giovanni Pico della Mirandola and sustained more recently in different ways by Francesco Patrizi and Giordano Bruno. Their aim was to bring about a truly Christian reform of education and religion through the knowledge and cultivation of occult harmonies believed to exist between the creation and the human soul. The whole of existence was a pattern of occult powers, and through these man could know God3. The other threat 2 A. C. CROMBIE and A. CARUGO, Galileo's Natural Philosophy (forthcoming), which contains full documentation and bibliography; see for various questions discussed therein CROMBIE, "The primary properties and secondary qualities in Galileo Galilei's natural philosophy", Saggi su Galileo Galilei (preprint, Firenze, 1969, wrongly dated 1967), "Sources of Galileo's early natural philosophy" in Reason, Experiment and Mysticism in the Scientific Revolution, ed. M. L. RIGHINI BONELLI and W. R. SHEA (New York, 1975a), "Mathematics and Platonism in the sixteenth century Italian universities and in Jesuit educational policy" in Prismata: Naturwissenschaftsgeschichtliche Studien: Festschrift fur Willy Hartner, hrg. Y. MAEYAMA und W, G. SALTZER (Wiesbaden, 1977), "Philosophical presuppositions and shifting interpretations of Galileo" in Theory Change, Ancient Axiomatic*, and Galileo's Methodology: Proceedings of the 1978 Pisa Conference on the History and Philosophy of .Science, ed. J. HINTIKKA,. D. GRUENDER and.E. AGAZZI, I (Dordrecht etc., 1981), "Galileo in Renaissance Europe" in Firenze e la Toscana dei Medici nell'Europa del Cinquecento, a cura di P. GALLUZZI (Firenze, 1983); and CARUGO, "Giuseppe Moleto: mathematics and the Aristotelian theory of science at Padua in the second half of the sixteenth century" in Aristotelismo Veneto e scienza moderna: Atti del 25° Anno Accademico del Centro per la storia della tradizione aristotelica nel Veneto, a cura di L. OLIVIERI, I (Padova, 1983), with also his extensive notes in Galileo Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze, a cura di A. CARUGO e L. GEYMONAT (Torino, 1958). The present paper is based on our independent researches, as will be specified in our book. Here we have brought together some of these researches into a coherent argument. We have presented the dating of Galileo's writings as a series of problems, and their problematic character is further emphasised by our not always agreeing on all the possible solutions suggested. 3 Cf. BENEDICTUS PERERIUS, Adversus fallaces et superstitiosas artes, id est, de magia, de observatione somniorum et de divinitione astrologica, libri tres (Ingolstadti, 1591); D. P. WALKER, Spiritual and Demonic Magic from Ficino to Campanella (London, 1958), The Ancient Theology: Studies in Christian Platonism (London, 1972); F. YATES,

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was seen to come from the revival especially in France of Greek scepticism promoted notably by Michel de Montaigne and Pierre Charron, which denied the possibility of any certain human knowledge, scientific or theological or otherwise4. The question of Galileo's relation to this neoscholastic philosophical policy arose from our discovery of the sources of Galileo's misnamed Juvenilia. We were concerned first with the short closely reasoned essays in Galileo's own hand on Aristotelian natural philosophy comprising two incomplete treatises, each in two parts: the Tractatio prima de mundo with the Tractatio de caelo concerned essentially with questions of cosmology and cosmography raised for Christian theology by Aristotle's De caelo; and the fragmentary Tractatus de alteratione with the Tractatus de elementis concerned with the theory of the elements and qualities put forward by Aristotle in the Physics and De generatione et corruptione (both in the Biblioteca Nazionale Centrale di Firenze, Ms. Galileiano 46) 5 . At the same time we were making a study of another autograph scholastic treatise left unpublished by Galileo, the logical Disputationes de praecognitionibus et de demonstrations to be discussed below, which Antonio Favaro did not include among the Juvenilia. We showed that the two autograph treatises on natural philosophy which he published as Juvenilia were based on textbooks, sometimes copied word for word, by three well-known Jesuit professors at the Collegio Romano. Since in this joint paper we need sometimes to distinguish its two authors, we do this henceforth simply if a little inelegantly by using the name of the author concerned. Carugo then established during 1968-69, while revising parts of the monograph on Galileo's natural philosophy for which we were awarded the Galileo Prize in 1969, that the Tractates Giordano Bruno and the Hermetic Tradition (London, 1964); CROMBIE (1975a) 165-6, above n. 2, below nn. 4, 35, 76. 4 Cf. ANTONIUS POSSEVINUS, Bibliotheca selecta qua 'agitur de ratione studiorum, XV: "De mathematics" (Romae, 1593); H. Bus SON, La pensee religieuse franqaise de Charron a Pascal (Paris, 1933), Le rationalisme dans la litterature franqaise de la renaissance (1533-1601) (Paris, 1957); R. LENOBLE, Mersenne ou la naissance du mecanisme (Paris, 1943); D. C. ALLEN, Doubts Boundless Sea: Skepticism and faith in the Renaissance (Baltimore, Md., 1964); R. H. POPKIN, "Scepticism, theology, and the scientific revolution in the seventeenth century" in Problems in the Philosophy of Science, ed I. LAKATOS and A. MUSGRAVE (Amsterdam, 1968) 1-39, and The History of Scepticism from Erasmus to Spinoza (Berkeley and Los Angeles, Calif., 1979); C. B. SCHMITT, "The recovery and assimilation of ancient scepticism in the renaissance", Rivista critica di storia della filosofia, XXVII (1972) 363-84; A. C. CROMBIE, "Marin Mersenne (1588-1648) and the seventeenth century problem of scientific acceptability", Physis, XVII (1975b) 186-204; and Clavius, Mazzoni etc. below nn. 29 sqq., 43-45, 76. 5 Cf. A. PROCISSI, La collezione Galileiana della Biblioteca Nazionale Centrale di Firenze, I (Roma, 1959); Le opere di Galileo Galilei, direttore A. FAVARO, 20 vol. (Firenze, 1890-1909), ristampa 1968: all references to Galileo's published writings are given simply by volume and page in this edition.

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de alteratione et de elementis and the Tractatio prima de mundo were based on Benito Pereira's De communibus omnium rerum naturalium principiis et afectionibus libri quindedm and Francisco de Toledo or Toletus's commentaries on Aristotle's Physics and De generatione et corruptione. Benito Pereira's book was published first with a different title in 1562 and as De communibus... in 1576. Toletus's commentary on the Physics was published first in 1581 and that on De generatione et corruptione in 1579. Crombie discovered Christopher Clavius as a third source in June 1971, showing that important parts of the Tractatio de caelo all came from his In Sphaeram loannis de Sacro Bosco commentarius. His commentary on Sacrobosco's Sphaera was published in 1581 in its second enlarged edition which includes the addition used by Galileo. All three sources were republished in several later editions 6. Crombie gave an authorized account of our discoveries, of their relation to the work of other scholars, and of the bearing of our studies on Galileo's attempt to construct a conception of scientific inquiry and scientific knowledge, in 1974 in his paper "Sources of Galileo's Early Natural Philosophy", published in 1975 7. Our identifications, to quote from that paper, have "solved the main problem of the sources of Galileo's early writings in his own hand" (p. 160). More than that, by showing that "Galileo's basic sources were three prominent contemporary Jesuits at the Collegio Romano" (p. 164), they have provided an entirely new and unexpected perspective both on Galileo's intellectual biography and on its context in the contemporary European scene. We had not then solved the problem of the sources of the unpublished logical Disputationes, essentially a commentary on Aristotle's Posterior Analytics. Like the other two scholastic treatises this is again incomplete and in two parts: De praecognitionibus and Tractatio de demonstration 8. It contains a detailed analysis of such topics as the model expounded by Aristotle and later commentators of truly scientific demonstration as that which makes us know, the various kinds of first principles and ways of knowing them, the different forms of scientific demonstration in physics and mathematics, the arguments for establishing the connection of cause with effect and the existence of causes postulated, and related questions. Carugo solved the major 6

Cf. below nn. 7, 11. See above n. 2; and for these Jesuits and their writings C. SOMMERVOGEL, Bibliotheque de la Compagnie de Jesus, I-IX (Bruxelles et Paris, 1890-1930), X-XI (Paris, 19091932), XII (Toulouse, 1930). 8 Section headings were published by FAVARO as "some scholastic exercises" in IX, 273, 279-82; cf. CROMBIE (1975a) above n. 2. 7

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problem of its sources in April 1975, when he established similar word-for-word direct copying by Galileo, in the first part of his treatise, of Ludovico Carbone's Additamenta ad F. Toleti Commentaria una cum Quaestionibus in Aristotelis Logicam, first published in 15979. A complete list of textual correspondences will be presented in our book, where we show how closely Galileo followed point by point some long and complex arguments developed by Carbone. Most of the particular questions discussed by Galileo in De praecognitionibus were not commonly included in books on logic at that time. In discussing them Carbone, and later the Jesuit Paolo Delia Valle (Latinized as Paulus Vallius) in his Logica (Lugduni, 1622), were exceptional. In the prefaces to both volumes of Delia Valle's book we read that he had lectured on logic at the Collegio Romano in 1587-88. No such lectures are extant. In the same prefaces he referred to publications on logic identifiable as Carbone's, with the accusation that in them their author had plagarized his lectures. He named the Additamenta in the second of these prefaces, but there is no evident correspondence between Delia Valle's much more diffuse text and that of Galileo. The following are some examples of correspondences between Galileo and Carbone in single passages: Galileo, Disputationes de praecognitionibus et praecognitis in particulari (Ms. Galileiano 27)

Ludovico Carbone, Additamenta ad commentaria D. Francisci Toleti in logicam Aristotelis, (Venetiis, apud Georgium Angelerium, 1597) "Tractatio de praecognitionibus et praecognitis"

scientias participates non solere praecognoscere talia principia, non quia illorum notitia non sit necessaria, sed quia per se nota supponuntur ab illis; adde accendetem ad scientias debere esse ita dispositum ut, cognitis principiis per se notis, illis assentiatur (f. 4v).

particulares scientiae, non ideo non cognoscunt ista principia, quod eorum notitia non sit aliquo modo necessaria, sed quia, cum sint per se nota, supponuntur tanquam vera. Quia is qui docendus accedit ad aliquam scientiam, debet esse dispositus ad assentiendum primis principiis (f. 42va).

propria scientiae demonstrativae principia actual!ter sunt praecognoscenda. Turn quia ita docet Aristoteles p. post tex. 5°, 16°, 2° post, cap.6 ultimo, 6° eticorum cap.6 3°, quibus locis docet Aristoteles non posse cognosci conclusionem aliquam nisi praecognitis illius

principia propria demonstrationis praecognoscenda sunt actu... Probatur ex Aristotele qui variis in locis (Lib. I. poster, t.5 et 15. Li.2.ca.ult.li.6 eth. c. 3) hoc docet, dum ait, nihil posse cognosci, nisi intelligantur propria principia eius quod cognoscitur. Secundo,

9

Carugo announced in April 1975 at a conference held at Santa Margherita that he had made this discovery.

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principiis. Turn quia ilia principia sunt causa efficiens scientiae; ergo non potest haberi cognitio scientiae actualis nisi praehabeatur ipsorum principorum (f. 5v).

horum principiorum notitia... est caussa efficiens proxima conclusionis: ergo non potest actu cognosci conclusio, nisi eius principia actu cognoscantur (f. 42va).

Dignitates quae ingrediuntur demonstrationem aliquam imperfectam, qualis est ilia quae ducit ad impossibile, actu praecognosci debent. Probatur ex Aristotele tex. 16°, Philopono in tex. 2°, Temistio passim cap.6 12°. Secundo, eadem ratione qua superiori; nam dignitates quae ingrediuntur aliquam demonstrationem sunt principia tanquam propria illius (f. 5v).

si prima principia et dignitates actu ingrediantur aliquam demonstrationem saltern imperfectam, ut est ilia quae ducit ad impossibile, praecognoscenda sunt actu. Primum patet haec positio ex doctrina Aristotelis, qui hoc aliquando docuit (I.Post. t.26): cui consentit Philoponus (I.Post. t.2), Themistius (cap. 11.12) et alii. Deinde confirmatur eadem ratione, qua probata fuit prima conclusio. Caeterum quando prima principia ingrediuntur demonstrationem, non habent propriam dignitatum rationem, sed potius quorundam principiorum particularium et propriorum illius conclusionis (f. 43ra).

ilia principia actu sunt praecognoscenda, a quibus intrinsece pendet conclusio; sed a dignitatibus conclusio non pendet intrinsece, cum illae neque actu neque virtute ingrediantur demonstrationem; ergo. Dices: si conclusio nullo modo pendet ex his dignitatibus, quare habitualiter sunt praecognoscenda? Respondeo, primo, quia licet conclusio non pendeat in esse ab illis, pendet tamen in cognosci aliquo modo. Secundo, ut possimus protervos convincere (f. 5v6r).

ilia (sell, principia) sunt cognoscenda actu, ante demonstrationem, a quibus conclusio proxime dependet; atqui ab hoc principorum genere (sett, a dignitatibus) non dependet proxime cognitio conclusionis... dicta principia non ingrediuntur actu demonstrationem, cum non sint propria; neque virtu te, cum res non pendeat intrinsece ab illis... ergo non est necesse, ut actu praecognoscantur. Sed dices, si ita est, quare necessario praecognoscenda sunt aliquo modo, ut est probatum? (ie. dignitates seu prima principia ante demonstrationem cognoscenda sunt saltern habitu). Respondeo, quia licet non sint caussae in essendo, sunt tamen caussae in cognoscendo... Adde etiam quod praecognoscenda sunt ad convincendos protervos (f. 42vb-43ra).

principia prima et immediata nullo modo posse probari, quia alias non essent prima, quia darentur priora illis per quae probarentur. Dices: Quid dicendum quando principia prima sunt ignota et non possunt ostendi a posteriori? Respondeo: pertinere ad scientiam subalternantem probare talia principia

prima principia... non possunt probari a priori... quoniam si possent demonstrari a priori non essent prima, quia haberent ilia priora ex quibus penderent... Quod si petas, quod si ilia (soil, prima principia) ignota fuerint et non possint probari a posteriori, quaenam scientia ilia demonstrabit?

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quoad propria, ad dialecticam quoad probabilia, ad Metaphisicam quoad communia (f. 6v).

Respondeo, probari debere a subalternante sive a superiore scientia: et a Dialectica ex probabilibus, a Metaphysica vero ex communibus (f. 44ra).

authores in hac quaestione in duobus convenire. Primo, in principle adquisitionis scientiae fuisse necessariam actualem existentiam rei; cuius ratio, est, quia, cum omnis nova cognitio ortum habeat ex sensu, qui versatur tantum circa existentiam, sequitur etc. Secundo, in progressu scientiae esse praecognoscendum de subiecto esse. Differre autem quid nomine huius esse secundi intelligendum sit, de quo loquitur Aristoteles (f. 7r).

Sunt autem duo in quibus omnes conveniunt. Primum, in acquisitione scientiae opus fuisse subiectum esse in rerum natura, quia nostra scientia habet ortum a sensu, qui solum versatur circa ea quae actu existunt. Secundum, in ipso etiam scientiae progressu praecognoscendum esse... subiectum esse. Sed dubium est, quid nomine esse intelligendum sit, et quid Aristoteles intelligat cum ait etc. (f. 46rb).

Tria esse quae quaestionem hanc perdifficilem reddunt. Primo, an de subiecto semper praecognoscendum sit esse existentiae actuale, quia multa sciuntur a nobis semper, quae tamen non semper existunt. Secundo, quare non sufficiat praecognoscere esse essentiae tantummodo de subiecto. Tertio, quare in aliquibus demonstrationibus non sit necessarium praecognosere an sit subiecti (f. 7r).

Tria sunt quae hie difficultatem faciunt. Primum, an de subiecto semper praecognoscendum sit esse existentiae.. cum videamus de multis esse scientiam quae non semper existunt. Secundum, cur de aliqua re non sufficiat tantum praecognoscere esse essentiae. Tertium, an aliqua possit esse demonstratio de subiecto, cuius nullum esse praesupponatur (f. 46vb).

Scientiae abstrahunt ab existentia; ergo non poterunt praecognoscere existentiam suorum subiectorum. Respondeo, si spectemus rationem formalem scientiarum, illas quidem abstrahere ab existentia subiectorum: cum enim considerent universalia, non possunt ilia ut existentia cognoscere; si autem attendamus conditionem sine qua non, nego illas abstrahere ab existentia (f. 7v).

Omnes scientiae abstrahunt ad existentia; igitur non praecognoscunt illam de suis subiectis. Respondeo, scientias abstrahere ab esse existentiae, si spectemus rationem formalem ipsarum; quia cum versentur circa universalia formaliter, non possunt considerare subiectum ut formaliter existit; sed si consideremus conditionem sine qua non ipsius subiecti, nego abstrahere ab existentia (f. 47vb-48ra).

Tria esse genera rerum, quae reperiuntur in scientiis. Quaedam sunt omnino notae, et haec non possunt demonstrari; nam demonstratio ad ignota tantum probanda exigitur; quae enim per se notae sunt, non egent probatione. Quaedam sunt ignotae, et haec, vel a priori vel a posteriori saltern probari possunt. Quaedam sunt quae partim notae sunt, partim ignotae, et haec, licet non possint

Tria sunt genera rerum quae in aliqua scientia reperiuntur; aut enim sunt res omnino notissimae, aut sunt omnino ignotae, aut... partim notae et partim ignotae. Si sint prioris generis nullo modo probari queunt, quia demonstratio est instituta ad probandum ignota. Si secundi, probari potest eas existere vel a priori vel saltern a posteriori. Si vero tertii, non possunt probari... genere aliquo demonstrationis, sed

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demonstrari aliquo genere demonstrationis, tamen vel inductione vel silogismo ipotetico ostendi possunt (f. 8v).

solum aliqua inductione vel syllogismo hypothetico (f. 48rb).

Carbone was not a Jesuit, but he had been educated in Jesuit colleges and had attended lectures at the Collegio Romano. The discovery that Galileo's source was the Additamenta published first in 1597, and reprinted several times thereafter as an appendix to Toletus's commentary, establishes 1597 as the earliest possible date for the Disputationes, when Galileo was at Padua as a mature man of thirtythree. A copy of an unspecified edition of Toletus's commentary was among the books owned by Galileo 10. Hence we are forced to make a radical reexamination of Galileo's intellectual biography, which we had not yet done when Crombie's article on "Sources..." was completed in 1974. This means that we must reexamine the traditional dating of Galileo's main undated writings. The available evidence comes mostly from such conceptual and material connections as can be found between these and the writings that are dated n. 10

A copy of Toletus's commentary on Aristotle's logic was entered as "Logica del Toleto. 4°" in the "Inventario di tutti i libri trovati serrati in uno scaffale del salotto terreno dell'abitazione della Sig.ra Sestilia Bocchineri Galilei il di 23 e 24 Genn. 1668 ab Inc." (Ms. Gal. 308, f. 168). Favaro, in his reconstruction of the list of books owned by Galileo, specified for no apparent reason the edition Toleti Francisci Commentaria una cum quaestionibus in universam Aristotelis logicam (Coloniae Agrippinae, 1596): see A. FAVARO, ' La libreria di Galileo Galilei' in Miscellanea galileiana inedita (Venezia 1887), entry no. 486, and Bullettino di bibliografia e di storia delle scienze naturali e fisiche, XIX 11(1886), entry no. 78. We announced our discoveries for the first time to anyone else in a letter written by Crombie on 31 March 1972 to William Wallace in response to a letter of 16 July 1971 from him with information about his own work and a typed copy of his paper on "Galileo and the Thomists". Crombie wrote: "You may not know that in a volume entitled Galileo's Natural Philosophy, written by myself with the collaboration of Adriano Carugo, we went into considerable detail in the study of Galileo's so-called Juvenilia as well as of his Disputationes de praecognitionibus et de demonstratione (Ms. Galileiano 27) into the sources he used. We have a complete transcription of the text of the latter work of which we are publishing a substantial section with English translation in our book. In 1969 this book was awarded the Galileo Prize [...] So far as the sources of the Juvenilia are concerned, we have shown that three main sources, sometimes copied word for word, are Clavius's commentary on Sacrobosco's Sphaera, Pereira's De communibus omnium rerum naturalium and Toletus's commentaries on the Physics and on De generations et corruptione. Certainly there is no evidence for, and there is negative evidence against, his using Bonamico. [...] We have in fact gone into the question of dating of most of Galileo's early writings in some detail, using watermarks as well as other evidence, and have proposed some revision of the accepted dates. [...] Besides the Juvenilia etc. we have a lot of new material on Galileo's Platonism and its background, cosmology of light, the sources of his distinction of primary and secondary qualities, his father's and his own contributions to scientific musical theory, and other matters."

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We need then to establish some fixed points in Galileo's intellectual biography, and first to relate this to his background. We know that especially during the years 1585-1589 when he was living with his father Vincenzo Galilei in Florence, between his two periods at Pisa, Galileo developed a strong interest in mathematics and the mathematical sciences and arts. His association with the Accademia Fiorentina del Disegno was the beginning of a life-long fascination with the techniques of perspective painting and sculpture12. His father's Francesco Bonamico had of course been proposed as Galileo's source by Favaro on the supposition that Galileo's essays were lecture notes taken as a student at Pisa. Before we informed William Wallace of our discoveries which focussed attention on the Collegio Romano, he had begun to look in the right direction. In his paper "Galileo and the Thomists", published in St. Thomas Aquinas 1274-1974 Commemorative Studies (Pontifical Institute of Medieval Studies, Toronto, 1974), he had noted some resemblances between parts of the Juvenilia and commentaries by various scholastics including Pereira and Toletus, but he failed to identify any specific sources. In his concluding discussion of different hypotheses about the sources of the Juvenilia, he wrote that "there is no evidence of direct copying from any of the Thomist authors mentioned in this study". He observed perspicaciously that if the source were a professor at Pisa, he "would appear to be sympathetic to the writings of two members of the newly-founded Society of Jesus, Pererius and Toletus" (p. 327). But he did not identify these two Jesuits as Galileo's sources, and he did not mention Clavius at all. The purpose of his letter enclosing his paper with these suggestive but "largely negative results" (p. 329) was in fact to ask for support for a proposal to the American National Science Foundation for a study of the natural philosophy of the Juvenilia and their background and the identification of their sources. Jesuit authors and the Collegio Romano were not mentioned in the copy of this proposal which he later sent us (noted as received by the National Science Foundation on 30 September 1971), which specified quite other directions of search for Galileo's sources, directions suggested very naturally by his own earlier work and the residue of accepted beliefs: cf. for the first part of his programme W. A. WALLACE, Galileo's Early Notebooks: The Physical Questions (Notre Dame, Ind., 1977). After Crombie's letter of 31 March 1972 and after Wallace had visited both him and Carugo later in that year, Crombie sent him at his request the relevant typed sections of our book setting out our evidence. Carugo gave him also for his private use a copy of his transcription of Galileo's logical Disputationes. In the following year he announced, without consulting us, and gave in the public domain of the Annual Conference of the American History of Science Society at San Francisco on 29 December 1973, a paper based on our discoveries and evidence with the title: "Christopher Clavius: a source of Galileo's early notebooks" (History of Science Society, Newsletter, II.3, 1973, p. 10). He agreed not to publish this; he proposed to send it with his report to the National Science Foundation. He added to the published version of his "Galileo and the Thomists" (1974) a misleading footnote about our discoveries, writing that our "work confirms the thesis only tentatively advanced in this study, namely that the Juvenilia were probably composed by Galileo himself, with little or no direct use of primary sources but with a recognisable dependence on the writings of Pererius and Toletus, and also with some borrowings from Christopher Clavius's commentary on the Sphaera of Sacrobosco" (p. 330, n. 133). This is contradicted by the paper itself, which contains no thesis about these Jesuits and no reference to Clavius. After promising to set the record straight at the earliest opportunity, he compounded the error yet further in a footnote to another paper: "Galileo and reasoning ex supposition: the methodology of the Two New Sciences", Boston Studies in the Pilosophy of Science, XXXII (1976) 100-1, n. 3a. Here he stated he had requested funds from the National

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unpublished manuscripts indicate that some of the acoustical experiments to be reported in the D iscorsi (1638) were carried out by Vincenzo during those years. Thus Galileo would have been introduced by his father through the art of music both to experimental science and also perhaps to a conception of natural philosophy. Vincenzo became strongly antipathetic to the more numerological and cosmic aspects of Platonism, and he insisted that an explanation of musical experience must reach beyond Pythagorean conceptions of musical harmony and proportion and look with Aristotle for some process of physical causation13. It is strictly relevant to Galileo's intellectual biography that Italian mathematicians and mathematical scholars in the

Science Foundation in 1971 to enable him to check the texts of these three Jesuit authors: their names do not appear in the copy of his proposal which he sent to us. Following the lines of research then going on independently, no doubt someone was bound to have identified these Jesuit sources, even in a sea of possibilities. William Shea did independently discover Galileo's use of Clavius about two years after us, without knowing of our work. We trust that these precisions will finally, in this small affair, set the record straight. More recently, Wallace has tried to show that Galileo used different Jesuit sources from those we have identified. He has made a study of manuscript reports or summaries of lectures given at the Collegio Romano during the last decades of the sixteenth century: see his Prelude to Galileo: Essays on medieval and sixteenth-century sources of Galileo's thought (Dordrecht etc., 1981). This has provided the useful and interesting information that Jesuit treatment of natural philosophy, in lectures as in books, followed a similar pattern with similar contents, and that books and manuscripts alike have a general resemblance to each other and to Galileo's scholastic writings. This has enriched our knowledge of sixteenth-century scholasticism, of Jesuit university teaching, and of the European intellectual scene. But it proves nothing about Galileo's sources. There are evidently no specific resemblances between Galileo's writings and any of these manuscripts, which cannot be found also, and more closely, in the printed books. This is not surprising, since it seems unlikely that Galileo would have spent time chasing up in obscure manuscripts what he had already found in well-known publications in print. We do not propose to discuss this line of speculation, because for Galileo there is nothing specific to discuss. 12 Cf. VIVIANI in XIX, 599-605, 627-8, cf. 36, 636-7, 645, II, 607-8; L. OLSCHKI, Geschichte der neusprachlichen wissenschaftlichen Literatur, I (Heidelberg, 1919), II (Leipzig, 1922), III (Halle a.S., 1927); E. PANOFSKY, Galileo as a Critic of the Arts (The Hague, 1954); A. C. CROMBIE, "Science and the arts in the Renaissance: the search for certainty and truth, old and new", History of Science, XVIII (1980) 233-46, and (1981) above13 n. 2. Cf. GALILEO, Discorsi, ed. with notes by CARUGO (1958) 702-14, above n. 2; C. V. PALISCA, "Scientific empiricism in musical thought" in Seventeenth Century Science and the Arts, ed. H. H. RHYS (Princeton, 1961); A. C. CROMBIE, "Mathematics, music and medical science", Actes du XIIe Congres International d'Histoire des Sciences Paris 1968 (Paris, 1971) 295-310, (1983) above n. 2, and the forthcoming Marin Mersenne: Science, Music and Language; S. DRAKE, "Renaissance music and experimental science", Journal of the History of Ideas, XXXI (1970) 483-500; D. P. WALKER, "Some aspects of the musical theory of Vincenzo Galilei and Galileo Galilei", Proceedings of the Royal Musical Association, C (1973-74) 33-47, Studies in Musical Science in the Late Renaissance (London & Leiden, 1978).

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sixteenth century were deeply rooted in Aristotelian science. Thus Francesco Barozzi in his translation of Proclus's commentary on Euclid tried to bring out its basic Aristotelian structure by marginal references to the Posterior Analytics 14. Giuseppe Moleto opened his unpublished discourse (in the Ambrosian Library in Milan) on the mathematical sciences with an account of the Aristotelian idea of a demonstrative sciences as presented in the Posterior Analytics15. Writers on mechanics from Alessandro Piccolomini to the Galileis's friend Guidobaldo del Monte all looked, with the Aristotelian Mechanica, for a science of physical causation. The tradition of the rational arts in perspective painting, music and mechanics shared then the Aristotelian conception of a rational science of nature. We could say that Galileo and others were later to use the decisiveness of the mathematical arts in order to replace the Aristotelian causes by discovering the true physical processes of nature 16. Galileo's earliest dated, or easily datable, writings were mathematical, starting in 1587 or early 1588 with his theorems on centres of gravity for which he used Archimedes 1?. Also in 1587 he visited Clavius in Rome (X, 22-3). His mathematical treatises on fortification and on the compass of proportion can be dated by the inclusion of copies in the collection of manuscripts made by G. V. Pinelli, who died in 1601. Also in this collection, now in the Ambrosian Library, Carugo discovered a purely mathematical treatise on cosmography (an extensive summary of the first book of Ptolemy's Almagest), different from that published by Favaro which in one of its copies is dated 1606 18. These mathematical treatises copied for Pinelli were written at Padua and must date therefore from the years 1592-1600. At Padua Galileo had been drawn into the Pinelli circle which included Guidobaldo del Monte and several prominent Jesuits. One was the remarkable Antonio Possevino, a friend of Clavius and author of the encyclopaedic Bibliotheca selecta rationum studiorum (1593), for which Clavius contributed help on mathematics and its history 19. In writing to Guido14

Published at Padua, 1560: cf. A. CARUGO (1983) above n. 2; below n. 46. To be analysed in our book by Carugo. 16 Cf. E. PANOFSKY, "Artist, scientist, genius: notes on the ' Renaissance Dammering'" in The Renaissance: Six Essays by W. K. FERGUSON et al. (New York, 1962); CROMBIE (1975b), (1980), (1981), (1983) above nn. 2, 4, 12, "Historical commitments of European science". Annali dett'Istituto e Museo di Storia della Scienza di Firenze, VII (1982) 29-51, and Styles of Scientific Thinking (London, 1994). 17 I, 179-208; cf. X, 22-36, GALILEO, Discorsi, ed. with notes by CARUGO (1958) 840-7, above n. 2. 18 II, 206-7; the Ambrosian Ms. is being edited by Carugo, and excerpts will be published in our book. 19 Cf. G. Cozzi, "Galileo Galilei e la societa veneziana", Saggi su Galileo Galilei 15

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baldo del Monte in 1602 with his first reference to the isochronism of the pendulum and on the descent of bodies along the arcs and chords of circles, he commented that "when we begin to have to do with matter, because of its contingency the propositions considered in the abstract by geometry begin to alter", so that they could not be regarded as "certain science" such as was mathematics itself (X, 100). To Paolo Sarpi he wrote in 1604 of his earliest (mistaken) law of free fall, that since "I lacked a totally indubitable principle which could be taken as an axiom in order to demonstrate the accidents I have observed, I have been reduced to a very natural and evident proposition (ha molto del naturale et deU'evidente}" (X, 115). From these distinctions much of his future conception of science was to follow20. In 1597 Galileo made his first dated references to Copernicus, in his letters to Jacopo Mazzoni and to Kepler. The purpose of his letter to the former was to refute with a mathematical demonstration (using figures the same as in Clavius's Sphaera) an argument just published by Mazzoni against Copernicus, whose Pythagorean opinion Galileo held to be "much more probable" 21 than the opinion of Aristotle and Ptolemy. To Kepler he wrote with congratulations on his Mysterium cosmographicum (1597), which he promised to read, rejoicing "to have such a companion in the search for truth" when there were so few "who do not follow a perverted method of philosophizing". He would read the book the more willingly "because I came to the opinion of Copernicus many years ago and the causes of many natural effects have been found by me from such a supposition (post'tto) which are without doubt inexplicable by the generally accepted hypothesis. I have written down many reasons and refutations of counter arguments which

(1968), reprinted in his Paolo Sarpi tra Venezia e I'Europa (Torino, 1978); E. C. PHILLIPS, "The correspondence of Father Christopher Clavius S. J. ...", Archivum historicum Societatis lesu, VIII (1939) 193-222; Crombie (1977) above n. 2; below nn. 28 sqq. 20 Cf. W. L. WISAN, "The new science of motion: a study of Galileo's De tnotu locali", Archive for History of Exact Sciences, XIII (1974) 103-306, "Galileo's scientific method: a reexamination" in New perspectives on Galileo, ed. R. E. BUTTS and J. C. PITT (Dordrecht etc., 1978), "Galileo and the emergence of a scientific style" in Theory Change etc., ed. HINTIKKA, GRUENDER and AGAZZI (Dordrecht etc., 1981). 21 II, 198; referring to JACOBUS MAZONIUS, In universam Platonis et Aristotelis philosophiam praeludia, sive De comparatione Platonis et Aristotelis (Venetiis, 1597): Galileo's figures for the dimensions of the world in II, 201 are the same as those in CHRISTOPHORUS CLAVIUS, In Sphaeram loannis de Sacrobosco commentarius (Romae, 1581) 209, 211; cf. W. HARTNER, "Galileo's contribution to astronomy" in Galileo: Man of Science, ed. E. McMuLLiN (New York, 1967); W. R. SHEA, Galileo's Intellectual Revolution (London, 1972); A. VAN HELDEN, "Galileo on the sizes and distances of the planets", Annali dell'Istituto e Museo di Storia della Scienza di Firenze, VII (1982) 70; below n. 45.

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however I have not dared until now to bring into the open, being frightened by the fortunes of Copernicus himself, our master". Copernicus had been derided by an infinity of "fools", hence he would not himself "publish my thoughts" (X, 68). Kepler replied urging Galileo to have confidence and asking for further information (X, 70). He guessed that Galileo had in mind proofs from the tides a, but Galileo did not answer. It seems clear that Galileo's serious commitment to Copernicus came with his telescopic discoveries of 1609-1610. He showed in his remarkable response to the new star of 1604, with his strange Aristotelian explanation, almost an aversion to the new cosmology23. Clavius had argued already in his Sphaera (1585 ed., pp. 191-5) in agreement with Tycho Brahe that, since the new star of 1572 had no observable parallax, it was to be considered a celestial body beyond the Moon. He thought that the new stars and comets might be generated in the celestial region. If this were true, it was up to the Aristotelians to find arguments for Aristotle's opinion on the matter of the heavens. He supposed that probably we should say that was not a fifth essence but a mutable body, though less corruptible than sublunary bodies. Only fragments remain of Galileo's autograph public lectures at Padua on the new star of 1604. After stating some disagreements with Tycho Brahe and Kepler, he gave his own explanation, resembling one given of comets by Aristotle (Meteorologica 1.6, 343al-23, c.7, 344a5-37), that the new star was not a star at all but an effect produced by the reflection of sunlight from condensed vapours rising from the Earth to the celestial sphere (II, 277-84, cf. 269-72). This was scarcely compatible with the immense distance of the fixed stars cited in his refutation of Mazzoni's argument against Copernicus. He cited observations he had made to locate the phenomenon, on which Clavius wrote to him at the end of the year (X, 121, cf. 117-9, 133, 136). He cited also a list of authors who had written on new stars, including the Spanish scholastic philosopher Francisco Valles, or Vallesius, who had published a recent commentary on the Meteorologica (1588) with another optical explanation. Another correspondent Leonardo Tedeschi sent him an account of this and mentioned also Clavius and his opinions (X, 130-2, cf. 124-9, 137-41). Galileo wrote to a further correspondent in 1605 that the planned to publish his lectures, but not wanting to expose "to the censure of the world what I think not only about the location of this light, but also about its substance and generation, and 22 KEPLER, Gesammelte Werke, hrg... W. VAN DYCK und M. CASPAR ... F. HAMMER, XIII 23(1945) 192-3. Cf. HARTNER (1967) above n. 21; below nn. 28-29.

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believing that I have come upon an opinion that has no evident contradictions and that on that account could be true, I must for my own security go slowly" (X, 134). He wanted to make more observa own security go slowly" (X, 134). He wanted to make more observa

that what he had already written applied likewise to the new star of 1604. Galileo published nothing, but we know that he was granted a licence on 26 February 1607, repeated on 1 March 1610, to publish a work entitled Astronomica denuntiatio ad astrologos24. Was this his projected work on new stars and comets? Again as late as 1606 in his Trattato delta sfera ovvero Cosmografia, written for his students at Padua, despite a reference to "the greatest philosophers and mathematicians who, considering the Earth to be a star, have made it mobile" (II, 223), he offered a purely traditional astronomy with the standard Aristotelian and Ptolemaic arguments against such a proposition. The "subject of cosmography" he wrote was the "description of the world" (mondo), but only that part of the theory (la speculazione) dealing with the number and arrangement of its regions and their shape, size and distance and motions found therein. The consideration of their "substance and quality" was left to "natural philosophy". As to "method, usually cosmography proceeds in its theorizing with four". First there are "sensory observations (osservazioni sensate)" of the appearances of phenomena. Secondly there are hypotheses (ipotesi), that is "suppositions (supposizioni) concerning the celestial orbs such that they agree with the appearances", as that the heavens were spherical and moved in circles with diverse motions, and the Earth was at rest at the centre. Thirdly there were geometrical demonstrations by which, from the properties of the circle and the straight line, the particular properties (accidenti) following from the hypotheses were demonstrated. Lastly there were arithmetical calculations which reduced the results to tables for practical convenience. We could distinguish in the world as a whole two regions, and because "it is true that our intellect is guided to knowledge of the substance by means of the properties", we found between these two regions notable differences. In one there were mutable elements always in a process of generation and corruption and with a natural rectilinear motion; the other, celestial region was immutable except for its eternal circular motions (II, 211-2). Whether or not from motives of prudence, or from lack of interest, or because of specific teaching duties, he seems to have paid little attention to Copernicus.

24 A. FAVARO, "Intorno alia licenza di stampa del ' Sidereus Nuncius' di Galileo Galilei", Rivista delle biblioteche, n. 18-19 (1889) 98-103; cf. XIX, 227-8; below n. 37.

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All this changed with the Sidereus nuncius (1610). Describing in his dedication to the Grand Duke Cosimo II of Tuscany how Jupiter with its satellites revolved "round the centre of the world, that is round the Sun itself", he added: "But why do I use probable arguments, when I can decide and demonstrate it with almost necessary reasoning?" (II, 56-7). So, as the Pythagoreans had held, was "the Moon like another Earth" (65). All this he would treat more fully in his book De systemate mundi where, against "those who exclude the Earth from the dancing whirl of stars", he would "demonstrate the Earth to be a wandering body", and "this we will confirm with an infinity of physical reasons (naturalibus rationibus)" (75). Galileo's situation also changed. In writing then with new celebrity on 7 May 1610 to Belisario Vinta to apply for a return to Florence, he listed the works which he proposed to complete there: "two books De sistemate seu constitutione universi, an immense conception full of philosophy, astronomy and geometry; three books De motu locali, an entirely new science in which no one else, ancient or modern, has discovered any of the most remarkable laws which I demonstrate to exist in both natural and violent movement: hence I can reasonably call this a new science and one discovered by me from first principles; three books on mechanics, two relating to demonstrations of its principles and foundations and one concerning its problems". Besides these he had various opuscoli on sound, vision, the tides, the continuum, animal motion and other subjects. He concluded with his request concerning his "title and function" in the service of the Grand Duke: that "in addition to the title of mathematician, His Highness will add that of philosopher; for I claim to have studied more years in philosophy than months in pure mathematics" (X, 351-3). Later in a letter of 16 July 1611 asserting that we knew that the Moon had mountains and valleys like the Earth "no longer from imagination but from sensory experience and from necessary demonstration (per sensata esperienza et per necessaria demonstrazione}", that is from the telescopic "observations from which I deduce (deduco] my demonstrations" (XI, 142), he wrote that "as I show elsewhere" Aristotle had not demonstrated that the heavens were immutable and in substance "quite different from our inferior substances". The contrary was the sounder opinion (147). He referred here again perhaps to De systemate mundi. This list raises some problems. Should we suppose that he had already begun the philosophical work on cosmology which became the Dialogo sopra i due massimi sistemi del mondo, Tolemaico e Copernicano (1632)? We know that during the years 1602-1609 he was developing the theorems on the isochronism of the pendulum and on falling bodies and related problems on which he was to found his new

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kinematics and dynamics, and which were to be published in the treatise "De motu locali" in the Discorsi e dimostrazioni matematiche, intorno a due nuove scienze (1638) 25 . But what were these three books on mechanics? As for his philosophical studies, we should not take Galileo's claims about himself too literally, but we have an indication of his philosophical knowledge and commitments two years later in the First Letter about Sunspots (1612) published in his Istoria e dimostrazioni intorno die macchie solari e loro accidenti (1613). His Jesuit opponent Christopher Scheiner concerning these phenomena, a man he wrote "of free and unservile mind", was "beginning to be moved by the force of so many novelties and to give ear and assent to the true and good philosophy, especially in that part which concerns the constitution of the universe". But he had not freed himself from certain beliefs to which the intellect became "accustomed by long habit to give assent", as where "he continues to keep as true and real" those eccentrics, epicycles etc. "supposed by pure astronomers (posti da i puri astronomi} to facilitate their calculations, but not to be maintained as such by astronomers who are philosophers (astronomi filosofi). These, in addition to the task of somehow saving the appearances, try to investigate, as the greatest and most admirable problem there is, the true constitution of the universe. For such a constitution exists, and exists in only one, true, real way, that could not possibly be otherwise" (V, 102) 26. In these words he stated with great force the goal of truly scientific demonstration as presented by Aristotle in the Posterior Analytics2?. A decade later when in II Saggiatore (1623) Galileo was defending himself against the accusation by another Jesuit opponent that he was ignorant of logic, he displayed a considerable acquaintance with the methods of another part of Aristotle's logic: the probable and persuasive, as distinct from demonstrative argument, and the analysis of fallacies, presented in the Topics and the Sophistici Elenchi. He dated this acquaintance from the time when he "was young and still under a pedantic tutor" and used "to engage with pleasure" in logical 25

Cf. R. CAVERNI, Storia del metodo sperimentale in Italia, IV (1895) 267 sqq.; GALILEO, Discorsi, ed. CARUGO (1958) 694 sqq., above n. 2; L. Sosio, "I ' Pensieri' di Paolo26 Sarpi sul moto", Studi Veneziani, XIII (1971) 315-92; WISAN (1974) above n. 20. Cf. SHEA (1972) above n. 21, CROMBIE (1975a) above n. 2. 27 Post. Anal, 1.2, 71b9-72a24, 6, 74b5-6, 10, 76a31-b31, see translation with notes by J. BARNES (Oxford, 1975); also BARNES, "Aristotle's theory of demonstration", Phronesis, XIV (1969) 123-52; L. A. KOSMAN, "Understanding, explanation and insight in the Posterior Analytics" in Exegesis and Argument, ed E. N. LEE et al. (Assen, 1973); J. H. LESHER, "The meaning of NOUS in the Posterior Analytics", Pbronesis, XVIII (1973) 44-68; and Articles on Aristotle, I: Science, ed. BARNES, M. SCHOFIELD, R. SORABJI (London, 1975).

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"altercations" (VI, 245, question 12). He described one argument made by his opponent as not even "a good topical argument for persuading anyone" (VI, 257, q. 13). It was indeed "possible to reach true conclusions through false arguments, paralogisms and fallacies" (VI, 273, q. 18, cf. 14, 15, 16, 17), but he wanted to do so through true demonstrations. We may suppose that Galileo was given the normal foundation in logic at Pisa, and that he was made as familiar as any educated person with the standard types of Aristotelian argument (cf. IV, 65, 659, VII, 59, XVIII, 234, 248). We are still left with the problem of when he resumed his logical studies in order to write the Disputationes. This treatise as we have said cannot be dated before 1597. 2. We may look briefly at the conception of true science expounded by Clavius, who remained an evident influence upon Galileo to the end of his life. Galileo in this Tractatio de caelo refuted Copernicus's location of the Earth in an orbit round the Sun with the same arguments in the same words as Clavius in his Sphaera (1581)28. What he did not cite in organising the case against Copernicus was Clavius's lucid exposition of criteria for deciding whether or not the circles and their arrangement, postulated in astronomical theory to account for the phenomena, had any real physical existence. Clavius insisted firmly that "just as in natural philosophy we arrive at knowledge of causes through their effects, so too in astronomy, which has to do with heavenly bodies very far away from us, we must attain to knowledge of them, how they are arranged and constituted, through the study of their effects, that is, stellar movements perceived through our senses". Hence it was "highly rational" that astronomers should "search out" the circles and their arrangements that would carry the planets round in their observed motions "on condition that causes can be thereby suitably assigned to all the motions and appearances, and that nothing absurd or inconsistent with natural philosophy can be inferred therefrom". He set out then to rebut the sceptical argument of "Averroes and his followers", who said that "they concede that all the phenomena can be saved by postulating eccentric circles and epicycles, but it does not follow from this that the said circles are found in nature; on the contrary they are entirely fictitious; for perhaps all 28

Compare I, 38-41, 41-7, 47-54, 48-50, 50-4 respectively with CLAVIUS, Spbaera (1581) 42-6, 55-7, 63-4, 134-43, 68-70; Clavius in the 1594 edition of his book referred to "Nicolaus Copernicus Prutenus, nostro hoc seculo astronomiae restitutor egregius" (pp. 67-8) while still opposing his views; cf. CROMBIE (1975a) above n. 2; above nn. 21, 23.

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appearances can be saved in a more suitable way, though it is not yet known to us". Thus "the appearances may be truly saved" by circles that were "themselves entirely fictitious, and in no way the true cause of those appearances, just as one may reach a true conclusion from a false premise, as is evident from Aristotle's Dialectics". This refers to the Priori Analytics (II, 1-4, 53b4-57bl7). Clavius first strengthened the Averroist argument from Copernicus, who "saves all the phenomena in another way" than Ptolemy, so that "eccentrics and epicycles are not necessary for saving the phenomena". Then he countered with a complex rebuttal beginning with a challenge to his opponents, that "if they have a more suitable way of saving the appearances, let them show it to us, and we shall be satisfied and thank them heartily... But if they cannot show us a more suitable way, then they should at least accept this one, deduced as it is from such a variety of phenomena; unless they wish not only utterly to destroy natural philosophy as it is expounded in the schools, but also to bar the way to all the other arts which discover causes through the study of effects. For whenever anyone infers some cause from its visible effects, I will say just what my opponents do; namely that perhaps another cause, at present unknown to us, can be furnished from those effects". The dialectical argument that "a true conclusion can be drawn from false premises" would ruin natural philosophy, but it was "irrelevant", because it was only the syllogistic form that made this kind of inference possible. It was something quite different from accounting mathematically for the phenomena by means of eccentrics and epicycles. Moreover "by the assumption of eccentrics and epicyclic circles not only are all the appearances already known preserved, but also future phenomena are predicted, the time of which is altogether unknown", such as the occurrence of an eclipse. As for Copernicus, "he did not reject eccentrics and epicycles as fictitious and contradictory to philosophy". Indeed "if the supposition of Copernicus involved nothing false and absurd it would certainly be doubtful which opinion, that of Ptolemy or of Copernicus, should rather be adhered to (as regards saving the phenomena of this kind)". But since Copernicus's supposition did contain many absurdities and errors contrary to the established natural philosophy, and also seemingly to the Holy Scriptures, that of Ptolemy was to be preferred. God had perhaps handed over "the constitution of the heavens and their motions" (pp. 434-7) for disputation with always something left over, so that men would never cease to inquire admiringly into his works 29. 29

Cf. P. DUHEM, "SOZEIN TA PHAINOMENA. Essai sur la notion de theorie physique de Platon a Galilee", Annales de philosophic chretienne, VI (1908), reprinted

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Clavius thus decided between rival hypotheses in astronomy by means of two criteria: the variety of phenomena covered, and agreement with accepted natural philosophy. The distinction indicated between mathematical and physical astronomy had of course been made in the well-known passage of Geminus quoted by Simplicius in his commentary on Aristotle's Physics (11.2, comm. 12). The physicist looked for causes inherent in the substance of bodies by which to demonstrate effects, including the consideration of "its being better that things should be as they are"; the mathematical astronomer investigated external qualities and invented hypotheses using epicycles and eccentric circles by which to save the phenomena. He must "go further and examine in how many different ways it is possible for these phenomena to be brought about, so that we may bring our theory concerning the planets into agreement with that explanation of the causes which follows an admissible method". Thus "a certain person" had even postulated that the Earth moved round the Sun30. One notable feature of Clavius's argument was his insistence that the form of reasoning in mathematical science was quite different from the syllogism, so that comparisons between them were irrelevant and misleading31. Another was his failure to meet the central logical point made by Averroes. Averroes wrote of the epicycles and eccentrics in his commentary on Aristotle's De caelo (II.6, comm. 35) that astronomers "suppose the existence of these circles as principles" and deduced from them consequences corresponding precisely to what was observed; but "they demonstrate in no way that the suppositions which have served them as principles are necessitated in return by these consequences". There was then no reciprocal implication between the phenomena and such principles, for phenomena could not uniquely determine their causes. To assert that they did would be to commit the logical fallacy of affirming the consequent. Averroes wanted to undermine the Ptolemaic epicycles and eccentrics in order to establish the Aristotelian homocentric spheres as the true basis of an astronomy consistent with the true physics. Without taking sides on this astronomical issue, Aquinas in the Summa theologicae (I, question 32, art. 1) refined the logical point by distinguishing the kind of "principle as in natural science where Paris, 1982; A. M. BLAKE, C. J. DUCASSE and E. H. MADDEN, Theories of Scientific Method: the Renaissance through the nineteenth century (Seattle, Wash., 1960); CROMBIE (1977) above n. 2; N. JARDINE, "The forging of modern realism: Clavius and Kepler against the sceptics", Studies in the History and Philosophy of Science, X (1979) 141-73; C. NAUX, "Le Pere Christophe Clavius, sa vie et son oeuvre", Revue des questions scientifiques, LIV (1983) 55-68, 181-94; above n. 28. 30 Cf. T. L. HEATH, Aristarchus of Samos (Oxford, 1913) 275-6. 31 Cf. below n. 43.

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sufficient reason can be brought to show that the motions of the heavens are always of uniform velocity" from the kind where the reasons adduced "do not sufficiently prove the principle", as with the astronomical system of eccentrics and epicycles. Here accounting for the phenomena "is not sufficient proof, because possibly another hypothesis might also be able to account for them". This argument became a commonplace. It was repeated by the sixteenth-century Italian Averroi'st Agostino Nifo in contrasting different kinds of demonstration: "a good demonstration is one in which the cause is convertible with the effect". But since the epicycles and eccentrics were not reciprocally implicated by the appearances, they must be regarded as "provisional, until another better cause is discovered, which is convertible with them. Hence their proponents are mistaken, because they argue from a proposition having several causes to the truth of one of them; for these appearances can be saved both in this way and in others not yet discovered" 32. Montaigne used the same argument to illustrate how undecidable were such questions, so that it did not matter whether one believed Ptolemy or Copernicus, and who knew but that one day a third opinion might overthrow both33. Pereira used it in De communibus..., where he also gave an account of demonstration in mathematics and in the Posterior Analytics strongly contrasting with that of Clavius 34. Cardinal Robert Bellarmine was to use it in advising Paolo Antonio Foscarini and Galileo in 1615 to be prudent in their advocacy of the Copernican system35. Clavius ignored the logical point, and looked in the manner indicated by Geminus to natural philosophy to decide between equally accurate mathematical hypotheses. Galileo pursued essentially the same strategy, first to argue in the Trattato delta sfera and Tractatio de caelo against the Earth's motion, 32

AUGUSTINUS NIPHUS, In Aristotelis libros De coelo et mundo commentaria (Venetiis, 1553) f. 90vb; cf. DUHEM (1908) above n. 29; P. MANSION, "Note sur le caractere geometrique de 1'ancienne astronomic", Abhandlungen zur Geschichte der Mathematik, IX: Festschrift... Moritz Cantor (1899) 275-92; G. E. L. OWEN, "TITHENAI TA PHAINOMENA" in Aristote et les problemes de methode, ed. S. MANSION (Louvain, 1961); J. MITTELSTRASS, Die Rettung der Pbdnomene (Berlin, 1962); W. H. DONAHUE, "The solid planetary spheres in post-Copernican natural philosophy" in The Copernican Achie vement, ed. R. S. WESTMAN (Berkeley & Los Angeles, 1975); G. E. R. LLOYD, "Saving the appearances", Classical Quarterly, XXVIII (1978) 202-22. 33 MONTAIGNE, Essais, XII: "Apologie de Raimond Sebond", texte etabli par R. BARRAL avec P. MICHEL (Oeuvres completes, Paris, 1967) 237-8. 34 BENEDICTUS PERERIUS, De communibus omnium rerum naturalium principiis et affectionibus libri quindecim (Romae, 1576) 47-48; cf. CROMBIE (1977) above n. 2. 35 XII, 171-2, cf. V, 351, 357-61; X. M. LE BACHELET, "Bellarmin" in Dictionnaire de theologie catholique, II (Paris, 1905) 560-99, "Bellarmin et Giordano Bruno", Gregorianum, IV (1923) 193-201; G. DE SANTILLANA, The Crime of Galileo (Chicago, 1955); U. BALDINI, "L'astronomia del Cardinale Bellarmino" in the Atti of the Convegno (1983).

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and then later to argue for its motion. He used Clavius's two criteria in the anxious years 1615-1616 to argue for Copernicus from the new evidence of his telescopic discoveries and from his new dynamics and mechanics, with which he aimed to destroy Aristotelian physics and to replace it with a true system. Hoping to persuade above all Bellarmine, he set out these arguments in his letter of 23 March 1615 to Piero Dini, his Considerazioni circa I'opinione Copernicana, his Lettera a Madama Cristina di Lorena, and his Discorso del flusso e reflusso del mare finished in January 1616. Astronomers, he wrote in the Considerazioni, "have made two sorts of suppositions: some are primary and concerned with the absolute truth in nature; others are secondary, and these have been imagined to provide the reasons for the appearances in the movements of the stars, and they show how these appearances are in a certain way not concordant with the primary and true suppositions". Thus Ptolemy supposed "not as pure astronomer but as purest philosopher" that the celestial movements were all circular and uniform, that the Earth was immobile at the centre of the celestial sphere, and so on. Then he introduced his secondary suppositions as epicycles and eccentrics to account for the phenomena, but certainly not as fictions. Copernicus likewise put the mobility of the Earth "among the primary and necessary positions in nature (posizioni prime e necessarie in naturaY'. Galileo then made the remarkable assertion that, "if discursive reasoning is not enough to make us understand the necessity of having to put the eccentrics and epicycles really in nature, we must be persuaded of it by the senses themselves" (V, 357-60), for in the Copernican system the orbits of Venus and Mercury like those of Jupiter's four satellites were literally epicycles and the orbits of Mars, Jupiter and Saturn literally eccentrics. Far from these having been introduced as fictions, "they must be admitted in our time with absolute necessity, since they are shown to us by the senses themselves" (V, 298). This seems vindication of Qavius indeed. Galileo's final argument from the tides in the Discorso was again remarkable for its criteria of decision. He introduced with this a new physical criterion for identifying, the true astronomical system, as that which was uniquely possible within a single uniform system of terrestrial and celestial dynamics. It was an ambitious attempt to extend the Archimedean method, with its use of models, from terrestrial to celestial phenomena. At the same time it was an attempt to give a truly scientific demonstration in the Aristotelian sense, by means of an hypothesis "that seemed reciprocally to harmonize the mobility of the Earth with the tides, taking the former as the cause of the latter, and the latter as an indication and argument for the former" (V, 393). Then cause and effect would be convertible: this cause must necessarily

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produce those effects, and those effects must necessarily entail this cause and no other. The search for convertibility presupposed the framework of the syllogistic modus ponendo ponens and modus tollendo fattens. Here the aim of true demonstration was to discover definitions in which cause and effect, or substance and properties, were convertible: the substance was defined uniquely by those properties and those properties were uniquely properties of that substance. Hence, beginning with the observation of properties, it was necessary to know exhaustively all the possible substances of which they could be properties. Then if those were eliminated one after the other, what remained must be the one true substance and definition concerned. Mersenne and Newton were to object to this form of argument in science. Galileo's scientific originality in the great cosmological debate lay in his use of range of confirmation as the decisive test of a true theory. Thus he insisted in his First Letter about the Sunspots (1612) that his discovery that Venus had phases like the Moon "will leave no room for anyone to doubt what the revolution of Venus is, but will decide with absolute necessity, in conformity with the positions (posizioni] of the Pythagoreans and of Copernicus, that the rotation of Venus is round the Sun, round which, as the centre of their revolutions, revolve all the other planets" (V, 99). This was "indubitably demonstrated" by this "single experience" (199). In this way he wrote later, his telescope had provided through "sensory observations that can in no way be adapted to the Ptolemaic system, but are very sound arguments for the Copernican" (328), evidence not available to Copernicus himself (VII, 349-50, 363). The criterion of range of confirmation gave to the experimental and mathematical sciences their open-ended character. But Galileo never came to see clearly, at least in his Copernican disputes, that their different logical form led to different logical consequences from the Aristotelian truly scientific apodeictic demonstration. Nor did his opponents. Hence the cross-purposes so evident in the later stages of these disputes. Bellarmine had demanded such a demonstration of the Earth's motions. One of Galileo's most hostile critics, the Aristotelian philosopher Antonio Rocco, a former student at the Collegio Romano, dismissed his arguments in the Dialogo (1632) from tides and telescope alike with the challenge: "But come on, if there is a necessary truth and conclusion such that it is also evident as you say, show the evidence, bring in the reasons and the causes, leave persuasion to rhetoric, and no one will contradict you" (VII, 629). Since there were several ways of saving the appearances, Galileo by "putting forward only one, fell into the error of the consequent". Galileo noted in reply: "You are mistaken because you do not understand what you are saying...: but the structure of the world is just

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one, and it has never been otherwise: therefore someone looking for something other than this one that exists is looking for something false and impossible" (699-700). We may introduce at this point a document found by Carugo in the Pinelli collection in the Ambrosian Library which, if authentic, would be profoundly puzzling for the history of Galileo's Copernicanism. This is an unaddressed, unsigned and undated letter in handwriting resembling Galileo's but not clearly identifiable. Since it is among the Pinelli manuscripts it should date from before his death in 1601. The author was writing to replace an earlier letter with "notes on mechanics" which had gone astray. He continued: "Concerning my treatise De motu celesti, I may say that it is in three books which make twenty-one folios... The figures will be rather numerous, as in Sacrobosco's Sphaera ... In my doctrine I show not only the necessity of lines and numbers, but also the necessity of physical (naturali] operations The treatise is by way of introduction... In this way an easy route is opened, not only into the apparent motions of the fixed stars and planets, but also the calculations of the distances and motions of the comet: a thing considered impossible by previous writers. Furthermore by experience I can affirm this, that those who feel uneasy with the usual theories of planets do not find any difficulty whatever in our Pythagorean theory but on the contrary great satisfaction, so that it seems to me that I would not have as many copies as could be sold. The same hypotheses have been followed by Copernicus, a truly singular man to whom I am much indebted. But he left there a gross scale of useless revolutions and fictional motions alien to reason and to the nature of things and to the necessity of appearances" 36. If this letter was by Galileo, what was the treatise De motu celesti? Could it have been a Copernican revision of a now unknown work to which Galileo referred in De motu gravium as "our lost commentaries on the Almagest of Ptolemy, which... will be published in a short time" (I, 314)? Could it have been the projected Astronomica denuntiatio ad astrologos? We know that Galileo once projected a work on comets, which were in fact discussed at length by Clavius in his Sphaera37. The unidentified letter shared Galileo's preference for theoretical simplicity and belief in natural as well as mathematical necessity, but unlike both Galileo and Clavius it seems to accuse Copernicus of introducing fictions. Nothing has been established. Necessity was a central theme alike of Galileo's logical Disputationes and of his scientific writings to the end of his life. An account 36 37

Biblioteca Ambrosiana Ms. I. 231 inf. (Codice Pinelliano), f. 187rv. Cf. above nn. 23-24.

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of his intellectual biography should include an examination of the relation of this treatise, a series of questions on the Posterior Analytics, to the development of the general conception of scientific knowledge within which he always presented his solutions of particular problems. We have done this in detail in our book on Galileo's natural philosophy, in which we are publishing relevant sections of the Latin text with an English translation. Here we can only indicate some relevant points. Galileo started in De praecognitionibus from the fundamental Aristotelian doctrine that it was principles that gave us knowledge: "The primary principles must be in some way presupposed as known, in order that the conclusion itself may be perfectly known" (disputatio II, quaestio 1, Ms. Galileiano 27, f. 4r; cf. II. 3, f. 5v). Principles could be known in various ways: the most universal solely through their terms, as that the whole is greater than its part; others solely through the senses, as that fire is hot; others by induction, division and hypothetical arguments; others by experience, as in medicine; others solely by habit, as those of moral science which we cannot understand unless we practice them. Primary and immediate principles were those that could not be proved in any way. He insisted that principles in\ essendo, that is existing in the objects of knowledge (as distinct from in cognoscendo, principles of knowledge) could be proved in the particular sciences a posteriori from their effects, for otherwise "the question of existence would be excluded from all sciences except metaphysics" (II, 4, f. 6r). "The principles in a demonstration a priori are known beforehand, whereas in a demonstration a posteriori they are sought" (f. 6v). Accepting that "all new knowledge originates from the senses" (III. 1, f. 6v) whose objects must exist, he distinguished scientiae redes which began with actually existing objects from scientiae rationales concerned only with objects of knowledge (f. 7rv). But he insisted that while the sciences, because they considered universals, abstracted formally from the existence of their objects, they must all in the end be concerned with existence. They were concerned not with the contingent existence of individuals, but with the existence of species of things "which, the universe being supposed, is necessary at least in its time". This was "the existence that follows universal nature, not in the abstract but in something individual". For indeed "nature, is more completely realized by species than by individuals" (f. 7v). Mathematics likewise abstracted from existence, but it demonstrated the properties of existing objects (f. 8r). Throughout he used the Aristotelian analogy between the causation of knowledge in man and of effects in nature: "for every natural cause sufficient to produce its effect, provided that its requirements are given, operates by necessity; but the intellect together with the knowledge of principles is a natural

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and sufficient cause to produce scientific knowledge". Still, "why must we necessarily assent to the conclusion once we know the premises?" He replied with Saint Thomas, "because there are some things that necessarily, follow from known principles; therefore, once these are known, the conclusions, which are virtually contained in them and are suited to be inferred, are necessarily known" (f. 12v). But there was a difference for, "because man is free" (f. 13r), he might not assent even when all the requirements were given. The Tractatio de demonstratione was a critical analysis of the account given by Aristotle and later Greek and medieval commentators of scientific demonstration and its kinds according to the subject-matter. The premises of truly demonstrated knowledge according to the Posterior Analytics (I. 2) must be "true, primary, immediate, better known than, prior to, and the causes of the conclusion" (Tr. de dem. I. 1, f. 13v). Immediate meant that the primary premises were not themselves demonstrated, but were self-evident; and the cause must be of that effect alone, which itself could not be otherwise. Galileo argued, with Averroes and St. Thomas, that only true propositions could be actually known. True conclusions could be inferred from false premises only per accident, not per se, and to know something required not only inference but demonstration from true premises. Scientific demonstration gave knowledge of "a thing through the causes by which it exists". The proper object of knowledge was ens reale, something real, not just ens rationis, a thing of reason. Hence of the void and infinite and suchlike "there can be no science, because they are nothing" (II. 1, ff. 17v-18r). Demonstratio quia, ' demonstration that' in the scholastic terminology used by Galileo, demonstrated the cause a posteriori from its effect known through the senses, while demonstratio propter quid, ' demonstration because ', gave us scientific knowledge of the effect by demonstrating it a priori from its discovered cause. Galileo argued that since "only those causes by which a thing exists are true and proper causes in being (in essendo], therefore demonstration propter quid must proceed only through such causes". This kind of demonstration "makes us know a thing without qualification (simpliciterY, but this was not so with "demonstration which proceeds from virtual causes, for these are ex suppositione and therefore do not make us know things without qualification" (II. 2, ff. 18v-19r). To know was simply "to assent certainly and evidently to the conclusion", but such assent required that the premises were not only true but immediate. This was not so when a science was subordinate to another, as astronomy and music to mathematics. Hence "a subordinated science, as imperfect, cannot have perfect demonstrations, since it supposes its primary principles to be proved in a superior science, and

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therefore it generates knowledge ex suppositione and only in a certain respect (secundum quid)" (II. 4, f. 20v). Thus we could have "scientific knowledge (scientia) of something in two ways, either simpliciter and absolutely, or secundum quid and within a determinate genus". The former "required that a resolution should be made into all its principles and causes, even the primary and most universal", and that these should be known per se (II. 5, ff. 21v-22r). As for the requirement that the premises should be better known than the conclusion, whether better known to us or in nature, he agreed with St. Thomas that for an absolute demonstration they must be better known in nature. This was not contradicted by cases where we might assume premises in order to prove something else; or where, as in mathematical demonstrations, "the causes are better known than the effects both to us and in nature, though such demonstrations are not the most powerful (pottssimae)"; or where the conclusion could be better known than the premises as "by the senses or by faith". Sciences were the more perfect according to their object, as the divine was more perfect than the perishable; to their independence, so that subordinate sciences were imperfect; to their certainty; and to their evidence. This could be either intuitive evidence through knowledge of the terms alone, as of first principles; or discursive evidence through the cause, as of demonstrative science. Evidence always carried certainty, but we could assert with "certainty without evidence, as is clear in subordinated sciences and even clearer in our faith" (II. 6, ff. 22rv). In any case "we come to rest in knowledge of the conclusion, but because of knowledge of the principles" (f. 23r, cf. 22v). Galileo concluded his scholastic treatise with a discussion of the main kinds of demonstration distinguished by Aristotle and the commentators: ostensiva, ad impossibile, quia, propter quid, potissima (III. 1-2, ff. 29r-30v; cf. I. 1, f. 13r). Ostensive demonstration was that which proved from true principles that something was true (f. 13r). As a form of inference "a demonstration that leads to an impossibility (ad impossibile) is not a true and perfect demonstration, since it proceeds from false propositions and, by raising questions, comes to deny both premises" (III. 1, f. 29r; cf. 13r, 30r). Avicenna was said to have held that there was only one kind of demonstration, propter quid (f. 29r). Galileo agreed with St. Thomas and others who had maintained that there were two, but only two kinds, quia and propter quid: for "we know a thing either a posteriori or a priori: we know it a posteriori by demonstration quia, a priori by demonstration propter quidn (f. 29v, cf. 30r). That demonstration quia was a true kind of demonstration was proved "on the authority of all commentators" as of Aristotle himself, for it "proceeds from necessary

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propositions and infers something necessary (ex necessariis procedit et insert aliquid necessarium), and does not generate opinion (opinio)\ therefore it generates scientific knowledge (scientiaY'• By contrast "induction is not a demonstration at all,... for it proceeds from particulars" and "by itself does not lead to any necessary conclusion". The demonstration of the cause of some effect showed us by its very nature at the same time the existence of the effect: thus "demonstration propter quid, so far as it is in its power, makes us know the cause and the existence of a thing" (f. 30r, cf. 29r). Hence it was useless of Averroes to add a further kind of demonstration potissima of existence as well as cause. But there were within demonstration propter quid itself " something like two kinds of demonstration, the one proceeding through extrinsic causes, the other showing through intrinsic causes the attribute of its primary and adequate subject by means of principles that are actually indemonstrable, and the latter can with perfect right be called potissima". In a demonstration propter quid "it must be known either in the premises or before them that the cause has a necessary connection (necessaria connexio) with its effect, whereby it will then be possible in the demonstration to give the reason why this connection exists in the subject". By comparison demonstration quia might seem to be "a topical or probable syllogism", but in itself it was a true demonstration which " infers from necessary premises a necessary conclusion" (f. 30r). Continuing his analysis with an example, man's ability to laugh, he wrote: "we know the connection of the attribute with the subject by experience: for from the beginning of the world up to now the ability to laugh has always been known to be connected with man; secondly, by induction...; thirdly, by the light of our intellect, which knows that this connection is necessary: for in most cases those things that always happen are natural; hence, since the ability to laugh always belongs to man, our intellect understands that it is natural. This can be confirmed by the consideration that otherwise nature would have badly provided man with universal properties, since it would not have provided things with their necessary conditions and properties. And... we do not know the cause of the effect, but the connection of the cause with the effect" (f. 30v). Demonstration propter quid and quia were then analogous, for both "proceed from true and necessary propositions". One and the same conclusion could be demonstrated by either, but not formally in the same way. Hence demonstration quia was called by Aristotle "demonstration of sign (demonstratio signi)n and "it proves the existence of a thing"; by Averroes "demonstration of evidence (demonstratio evidentiae), since it proceeds from things that are better known to us"; by Latin writers "demonstration from the effect, or a posteriori-, by the

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Greeks conjectural (conjecturalis}". Within it various distinctions could be made. For example when it "proceeds from an effect to its cause" as "there is smoke, therefore there is fire", the demonstration could proceed also "from one effect to another, or from a sign or whatever accident is necessarily connected with its cause to the cause itself". Another distinction came from considering the middle term of the syllogism, where the demonstration might consist of "convertible terms, such as: there is an eclipse, therefore there is an interposition of the Earth", or not, "such as: it is hot, therefore there is fire". Yet another distinction was between demonstrations of "simple being", as by Aristotle of primary matter and the first mover, and demonstrations a posteriori of more complex propositions. These were especially useful, "since the principles of a science are sometimes unknown and cannot be proved except by demonstrations of this kind", and without their help "we cannot know anything at all about abstract and divine things" (III. 2, f. 30v). Finally Galileo came to the question (III. 3, f. 31rv): Whether a demonstrative regress can occur. The first opinion was that of those more ancient philosophers who are reported by Aristotle to have claimed that in a demonstration a perfect circle is given, so that it is possible to know perfectly both the conclusion by the premises and the premises by the conclusion38.... Aristotle... denies that a perfect circle can be permitted in a demonstration, yet he admits an imperfect circle. We consider this opinion as most true. In order to understand it, we should note, first: two things are required for a demonstration. First, that what proves and what is proved should be connected with each other, otherwise it would not be possible to infer one necessarily from the other. Secondly, that which proves, as it is better known, should come first in the demonstration. We should note, secondly: the cause and the effect can be taken in three ways. In the first way, under the formal relation of cause and effect; in the second way, in so far as they are different things; in the third way, they can be considered in so far as the cause is necessarily connected with the effect...

He argued that a demonstrative regress was not possible in the first way because one relative thing is not better known than the other, and would not be circular in the second way if the things were necessarily connected: for "the demonstrative regress is the progress of reasoning in a demonstration which goes from the effect to the cause 38

Cf. ARISTOTLE, Post. Anal. 1.3, translated with notes by J. BARNES (Oxford, 1975); DESCARTES, Discours de la methode, VI, texte et commentaire par E. Gilson (Paris, 1947) 181-91, 470-4; N. JARDINE, "Galileo's road to truth and the demonstrative regress", Studies in the History and Philosophy of Science, VI (1976) 277-318; above n. 27.

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and vice versa". But a regress was possible in the second way only "provided that it takes place in a different kind of cause, or in the same kind but not in the same respect (ratio] and does not lead to the same thing". For "it could happen that someone knows the effect but not the cause", and then "from the existence of the effect he proves the existence of the cause", but still "he does not know the reason why it belongs to the effect... Now this can be proved through a demonstrative regress, for it has a necessary connection such as that of the reason for the effect with the cause, and one of the two can be assumed as better known in order to prove the other". To an objection that, for example, "vapour is the material cause of rain and rain is the material cause of vapour" was circular, he replied that here the causes were different, for we demonstrated rain by condensation and vapour by rarefaction, so there was no circle. To the question whether the progress from the cause to the reason for the effect showed the existence of the effect, he replied with St. Thomas that here "indeed existence cannot be proved by a perfect demonstration absolutely and simpliciter, but it can be propter quid." Then: You will ask secondly: in which sciences do we think that there is such a circle. I reply: the demonstrative regress is useful to the completion of all sciences, but it is most frequent in the physical sciences. The explanation for this is that in most cases the physical causes are unknown to us. In mathematics there is almost no use for such a demonstrative regress, because in such disciplines the causes are better known both by nature and to us. You will ask thirdly: what are the requirements of a demonstrative regress. I reply, they are these...: that in it there should be two progressions of demonstration, one from effect to cause, the other from cause to effect. Second: that we should start from demonstration quia... Third: that the effect should be better known to us... Fourth: that once the first progress has been completed, we should not immediately start the second, but we should wait until the cause, which we know materially, becomes known to us formally. This is the reason why demonstration propter quid cannot take place unless we know beforehand the cause formally. You will object: then it would follow that the demonstration propter quid is useless, as it is made for the very purpose of knowing the formal cause. I deny this consequence: for although someone who knows the formal cause knows virtually the reason why (propter quid] the attribute belongs to the subject, yet he does not know it actually unless he makes a true demonstration. From this it follows that a regress is not properly a circle, since it proceeds from the effect to the material cause and from the cause known formally to the reason for (propter quid] the effect. Fifth condition: that the demonstrative regress should take place through convertible terms. For if the effect had a wider extension than the cause, it would make the first progress impossible. Therefore the following inference is not valid: there is light, therefore there is the Sun. On the other hand, if the cause has a wider extension than the effect, it would make the

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The Disputationes, with Galileo's other scholastic treatises, give biographical substance to Ernst Cassirer's perception that Galileo shared with his Aristotelian opponents a fundamental agreement on the object of truly scientific knowledge, despite his rejection of their syllogistic methods of trying to reach and form of expressing such knowledge39. They establish the longevity and depth of his enduring commitment to their common assumption that true natural philosophy must demonstrate the necessary connections underlying the regularities of phenomena perceived by the senses. They establish the depth likewise of his commitment to a philosophical strategy aimed at once to solve particular problems and to lead to the apprehension of universal first principles. This he continued to share with contemporary philosophers, even when he came to differ from them sharply in his specification of effective methods of scientific inquiry, and hence of exactly how particular solutions must make it necessary to accept the principles from which he tried to demonstrate that they followed. By this strategy he aimed to establish a new identity at once for natural philosophy and for nature. All three of Galileo's scholastic treatises showed an explicit agreement on many questions with Thomist opinions, for example in the Disputationes on there being only two kinds of demonstration, quia and propter quid, and as in the Tractatio prima de mundo (I, 29-31) on the perfection of the world and its realization rather through species than individuals40. After Aristotle, he cited Averroes and Aquinas more than any other authorities in the three treatises together, with the latter equalled by Themistius and Philoponus in the Disputationes. All three used syllogistic arguments without mathematics. He seems to be siding, in the debate whether the most powerful demonstration was that described in the Posterior Analytics or that provided by mathematics, with Alessandro Piccolomini and Pereira against Francesco Barozzi and Clavius when he wrote in the Disputationes that mathematical demonstrations "non sint potissimae" (f. 22r, cf. 31v)41. He followed in 39 E. CASSIRER, Das Erkenntnisproblem in der Philosophic und Wissenschaft der neueren Zeit (Berlin, 1906) 134-41. 40 Ms. Galileiano 27, ff. 7v, 29r, 30r; cf. I, 29-31 where the argument corresponds almost word for word to AQUINAS, Summa theologica, I, q, 25, art. 6, Summa contra gentiles, 1.75, 81, 11.45, 111.71. 41 P. GALLUZZI, "II ' Platonismo' del tardo Cinquecento e la filosofia di Galileo",

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this treatise the Aristotelian tradition that made demonstration quia and propter quid the central method of natural philosophy, and he kept to that terminology with only a passing reference to "resolutio et compositio" (f. 14r) as belonging to demonstration. At the same time he showed a strong independence. With Aristotle he denied tha argument in a circle could be permitted in a demonstration, and gave an example to show that in a proper demonstrative regress this was not so. But with Aristotle he admitted as "most true" an imperfect circle, of which he made an analysis. For the progression of a demonstrative argument went in two directions: starting from an effect better known that its cause, we searched for its cause so that we could demonstrate that effect from this. A significant condition was that the cause and effect had to be convertible, that is coextensive (f. 31rv). This according to the accepted interpretation of Aristotle was the condition for a perfect scientific demonstration, in which the complete cause and the effect entailed each other reciprocally and uniquely. All three scholastic treatises have the same decisive manner. It seems reasonable to suppose from their resemblance in style and interests that they were written at nearly the same time. If so, Galileo might have followed the traditional order of topics in which commentators began with logic and went on to cosmology and then to physics. This would date them all after 1597. Descartes similarly was to follow in Les meteores (1637) the order of topics discussed in Aristotle's Meteorologica and followed by commentators. There are many resemblances likewise both in terminology and in conception of science between the Disputationes and Galileo's other writings on natural philosophy, but in these another model also makes its appearance: that of mathematics. The sixteenth-century debate on mathematics had centred on the opposing conceptions of its relation to natural philosophy attributed to Plato and to Aristotle. Both sides claimed support from Proclus's commentary on the first book' of Euclid's geometry. Barozzi, in putting the Platonic view against the Aristotelian Piccolomini, argued that mathematics provided in itself the most powerful demonstrations, even if in subordinate sciences like astronomy and music they were not the most certain. Mathematics was necessary to natural philosophy because it was concerned with " mid dle essence" lying between the "sensible essence" of things and the purely "intelligible essence" of the divine. Hence both "in the order with respect to nature" and "in the order of learning and in terms in Ricerche sulla cultura dell'Italia moderna, a cura di P. ZAMBELLI (Bari, 1973); L. OLIVIERI (a cura di), Aristotelismo veneto e scienza moderna (Padova, 1983); CROMBIE (1977) and CARUGO (1983) above n. 2; also n. 34.

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of utility Plato placed the mathematical not only prior to the natural but prior to all sciences " and to all arts 42. Clavius made the same point, again strongly influenced by Proclus, in his own influential commentary on Euclid. For "the mathematical disciplines deal with things without any sensible matter, but really they are immersed in matter". From their intermediate position " they demonstrate everything they undertake to dispute by the firmest reasons and confirm them so that they truly produce scientia in the mind of the hearer, and they utterly remove all doubt; something which we can scarcely ascribe to other sciences". Mathematics were thus an antidote to the Pyrrhonists, "philosophers who decided nothing but doubted about everything". He insisted that the "linear demonstrations" of geometry were not syllogisms, and that dialectical arguments (as in the Topics] were very different from mathematics: "For in a dialectical problem either one or the other part of a contradiction being undertaken is only probably confirmed, so that each man's intellect is in doubt which part of it is true; but in mathematics, whichever part a man chooses he will prove with firm demonstration, so that there is no doubt left at all" 43. Hence his argument that mathematics should be made an essential subject of study at the Collegio Romano, for "natural philosophy without the mathematical disciplines is lame and incomplete" 44. This was matched by the note written by Galileo in 1612 during his hydrostatical controversies that he "being used to study in the book of nature, where things are written in only one way, would not be able to dispute any problem ad utranque par tern or to maintain any conclusion not first believed or known to be true" (IV, 248). Likewise Mazzoni in his In universam Platonis et Aristotelis philosophiam praeludia (1597), the work about which Galileo had written to him in that year, maintained that mathematics was essential to all physical demonstrations. Once more he acknowledged Proclus. Mathematics was not concerned with the final cause, but demonstrated through the formal cause and in "mixed mathematics" which "include matter and motion" also through other appropriate causes: "something 42

FRANCISCUS BAROCIUS, Opusculum, "Questio de medietate mathematicarum" (Patavii,431560) ff. 38r-39v. CHRISTOPHORUS CLAVIUS, Eudidis Elementorum libri XV, Prolegomena (Romae, 1574) and I.I, f. 22; cf. N. W. GILBERT, Renaissance Concepts of Method (New York, 1960) 44 16, 90; above n. 4. CROMBIE (1977) 65, above n. 2; cf. A. P. FARRELL, The Jesuit Code of Liberal Education (Milwaukee, Wise., 1938); G. COSENTINO, "Le matematiche nella ' Ratio Studiorum' della Compagnia di Gesu", Miscellania storica Ligure, II (1970) 171-213, "L'insegnamento delle matematiche nei collegi Gesuiti nelTItalia settentrionale", Physis, XIII (1971) 205-17.

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shown clearly in Archimedes's little book De insidentibus, in which that most acute man very often completes his demonstrations by means of an active cause such as through the impulsive power which is in a liquid or in some other heavy body" (lib. XV, pp. 159-60)45. Then: "The question is whether the use of mathematics in physical science, as an instrument of proof (ratio probandi) and a middle term of demonstration, is opportune or not". He replied that "Plato believed mathematics to be especially fitted for physical investigations" and he proposed to defend Plato, and to show that "Aristotle has run on to the rocks", because just "where good sense showed that mathematical demonstrations should be used... he wrongly rejected mathematics". By postulating geometrical bodies prior to the four elements, and therewith accounting both for physical change and for the production in us of the different sensible qualities, Plato had made "not an error into which his love of mathematics drove him" but "a stroke of the greatest genius". But "Aristotle, from failure to apply mathematical demonstrations in the proper places, has widely departed from the true method of philosophizing (vera philosophandi ratio)" (XVIII, 188-90). Both were mistaken in separating theory from practice, for "theoria and praxis do not divide philosophy into two generically different parts, but everything theoretical also has either as a side-effect or as its fruit something practical" (XXIII, 231). Thus in natural philosophy and mathematics "all theories have their praxis, and conversely praxis their theories" (p. 233 bis). But there was a difference of purpose between theoretical reasoning "for the sake of truth" that aimed to show the "essence" of particular existing things, and reasoning that aimed to "make truth a means" to some practical end, as "when a mathematician is concerned with mechanics". A good example to show that in both cases "experience not only precedes the grasp of universals, but also follows it" was astronomy (XXIV, 245-6). He took up the Copernican debate here in the context of a rejection of Pyrrhonic and other sceptical "doubts against the investigation of truth" (VII, 72), concluding with the argument against the Pythagorean opinion of Copernicus (X, 129-34) about which Galileo was to write. Each in his own way, Mazzoni as Galileo later, was trying to establish criteria for science that would embrace alike the particular sciences of the diverse phenomena perceived by the senses and the "perfect science in an absolute sense, which understands by eternal reasons". For the former kind of science 45

Cf. A. KOYRE, "Galileo and Plato", Journal of the History of Ideas, IV (1943) 420-1; CROMBIE (1969) above n. 2; F. PURNELL JR., "Jacopo Mazzoni and Galileo", Physis, XIV (1972) 273-94; GALLUZZI (1973) above n. 41; JARDINE (1976) above n. 38; also nn. 4, 21.

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Aristotle provided for Mazzoni the best criteria, for the latter Plato, who showed how reason could ascend "to the principles and causes of things" (XVI, 175-6). This was a suitable distribution of favours by the incumbent of the chair at Pisa in both Platonic and Aristotelian philosophy which Mazzoni held from 1588 to 1597. Galileo met him, a friend both of Vincenzo Galilei and of Guidobaldo del Monte, on his return to Pisa as mathematical lecturer in 1589. In writing to his father in 1590 about some volumes of Galen and "la Sfera" which he was expecting, he added that he was "studying and having lessons with Signer Mazzoni", an association evidently pleasing also to Guidobaldo del Monte and to Mazzoni himself (X, 44-7, 55, XIX, 34-41, 627). In his letter to Mazzoni of 1597 Galileo wrote from Padua with warm appreciation of the many kindnesses he had received at Pisa from his old mentor, colleague and friend and of the "universal learning" shown by his book. He continued that he was greatly satisfied and consoled to see Mazzoni, "in some of the questions which in the first years of our friendship we used to dispute together with such delight, incline to the side that had seemed true to me and the opposite to you". Perhaps this had been "to give scope to the arguments", or to save "intact in every detail, the genuineness of the learning of so great a Master, under whose discipline it seems that all who dedicate themselves to search for the truth do and must gather together" (II, 197-8). The Master must have been either Aristotle or Plato, but for Mazzoni surely Plato. The model used in their different ways by Clavius and Mazzoni, and perhaps following these two preceptors also by Galileo, was the account given by Proclus of the relation of mathematics at once to existence and to human understanding and practice, in his In primum Euclidis Elementorum librum Commentariorum ad universam mathematicam disciplinam principium eruditionis tradentium libri IV (1560)46. Proclus gave to the Platonic scheme of existence set out in the Republic the Aristotelian logical structure of the Posterior Analytics. Mathematical existence, in its intermediate position between the highest simple realities grasped only by intellectual intuition and the complex extended objects of the senses, was explored by discursive reasoning. Mathematical knowledge then could lead both upwards to the apprehension of the absolutely intelligible principles of all existence, and downwards into the investigation of the detailed construction of the material 46 Latin translation by Barozzi (Padua, 1560); quotations below are with slight modifications from the English translation by G. R. MORROW (Princeton, 1970): the suggestion that Galileo used Proclus was made by JARDINE (1976) 317, above n. 38; cf. also n. 14, and CROMBIE, Stvles... above n. 16.

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universe and the operations of the practical arts. Going upwards it discovered its own primary principles, and its common axioms as that of equality and common methods as "the method of proceeding from things better known to things we seek to know and the reverse path from the latter to the former, the methods called analysis and synthesis" (Prologue, I. 3). Always "it is the higher sciences that provide the first hypotheses for the demonstrations of the sciences below them" (I. 4). Mathematics "takes its principles from the highest science and, holding them without demonstration, demonstrates their consequences" (I. 10). Mathematical knowledge was generated in its intermediary position by the internal activity of the understanding, but it was at the same time stimulated by and projected downwards upon the objects of the senses. Reaching by its dialectical power both upwards and downwards, the understanding thus replicated with a cosmos of ideas the complex cosmos of existence: "All mathematical are thus present in the soul from the first... This then is a second world-order which produces itself and is produced from its native principles...; and when it projects its ideas, it reveals all the sciences and the virtues" (I. 6). The function of mathematics was "discursive thinking", and in this differed both from pure intellectual intuition and from "opinion and perception, for these forms of knowing fix their attention on external things and concern themselves with objects whose causes they do not possess. By contrast mathematics, though beginning with reminders from the outside world, ends with the ideas that it has within; it is awakened to activity by lower realities, but its destination is the higher being of forms". Thus "it unfolds and traverses the immaterial cosmos of ideas, now moving from principles to conclusions, now proceeding in the opposite direction, now advancing from what it already knows to what it seeks to know, and again referring its results back to the principles that are prior in knowledge". Hence "it advances through inquiry to discovery", working in two ways, sometimes exploring into diverse particulars and speculations, at others assembling these diverse results for reference "back to their native hypotheses... The range of this thinking extends from on high all the way down to conclusions in the sensible world, where it touches on nature and cooperates with natural science, in establishing many of its propositions, just as it rises up from below and nearly joins the intuitive intellect in apprehending primary principles. In its lowest applications therefore it projects all of mechanics as well as optics and catoptrics and many other sciences bound up with sensible things and operative in them. While as it moves upwards it attains unitary and immaterial insights that enable it to perfect its partial judgements" (I. 7). Mathematics then "makes contributions of the very greatest value to

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natural sciences. It reveals the orderliness of the ratios according to which the universe is constructed and the proportion that binds things together in the cosmos... All these I believe the Timaeus sets forth, using mathematical language throughout in expounding its theory of the nature of the universe. It regulates by numbers and figures the generation of the elements, showing how their powers, characteristics and activities are derived therefrom and tracing the causes of all change back to the acuteness or obtuseness of their angles, the uniformity or diversity of their sides, and the number or fewness of the elements involved". Likewise "as Socrates says in the Philebus, all the arts require the aid of counting, measuring and weighing, of one or all of them; and these arts are all included in mathematical reasonings and are made definite by them" (I. 8). Mathematics thus projected upon sensible and imaginable things "its demonstrations about them existing previously in the understanding" (II. 1). Geometry "makes use of synthesis and analysis, always starting from hypotheses and principles that it obtains from the science above it". Then it uses "demonstrations and analysis in dealing with the consequences that follow from the principles, in order to show the more complex matters both as proceeding from the simpler and also conversely as leading back to them" (II. 2). At a certain "level of mental exploration it examines nature, that is, the species of elementary perceptible bodies and the powers associated with them, and explains how their causes are contained in advance in its own ideas". Then "when it touches on the material world it delivers out of itself a variety of sciences, such as geodesy, mechanics and optics, by which it benefits the life of mortals" (II. 3). Geometry like all mathematics in its intermediate position was based on hypothesis: "For no science demonstrates its own principles or presents a reason for them; rather each holds them as self-evident, that is, as more evident than their consequences... This is the way the natural scientist proceeds, positing the existence of motion and producing his ideas from a definite principle. The same is true of the physician and of the expert in any other science or art" (II. 8). Principles had to be clearly distinguished from their consequences. He went on to describe methods discussed by Plato, Aristotle and Euclid common in logical form to both mathematics and natural science. The "best is the method of analysis, which traces the desired result back to an acknowledged principle... A second is the method of division, which divides into its natural parts the genus proposed for examination and which affords a starting-point for demonstration by eliminating the parts irrelevant for the establishment of what is proposed". These were both used by Plato. "A third is the reduction

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to impossibility, which does not directly show the thing itself that is wanted but, by refuting its contradictory, indirectly establishes its truth... Reduction is a transition from a problem or a theorem to another which, if known or constructed, will make the original proposition evident" (Propositions, I. 1). His example was the reduction of the problem of doubling the cube to that of finding two mean proportionals. In the third method he explained: "Every reduction to impossibility takes the contradictory of what it intends to prove and from this as a hypothesis proceeds until it encounters something admitted to be absurd and, by thus destroying its hypothesis, confirms the proposition it set out to establish" (I. 5). This corresponds logically in natural science to a form of experimental falsification within a defined number of possible hypotheses. Galileo combined in De motu gravium mathematical with syllogistic arguments in his analytical search for true relations of cause and effect. The writings, for which following E. Alberi we use this title, are collected in Ms. Galileiano 71. They were first published in part by Alberi in 1854 in his edition of Galileo's Opere, and later in full with the title De motu by Favaro in the first volume of the Edizione Nazionale (1890). Galileo appears in De motu gravium deeply preoccupied with the issues that dominated his scientific life: the proper methods of inquiry and demonstration in natural philosophy, and the discovery with them of the true constitution of the universe. His style of argument came from the twin models of the postulational method of Archimedes and the Aristotelian syllogistic structure leading to either the confirmation or the falsification of the premises by confronting their conclusions with experientia or ratio. This term meant both, reasoning and accepted theory. Terminology in this mixture got some changed applications. Thus he wrote: « The method (methodus) that we shall observe in this treatise will be such that what ought to be said always follows from what has been said; nor shall I ever (if I may) assume as true what ought to be demonstrated. This is the method which my mathematicians have taught me: but it is not adequately observed by certain philosophers..." (I, 285). Notable among these was Aristotle in his physics, "because he assumed as known axioms what are not only not clear to sense, but neither ever demonstrated nor even demonstrable, since they are absolutely false" (I, 277-8). But Galileo habitually put his argument in the form of a hypothetical syllogism, usually to refute some opposing opinion by leading it to a reductio ad contradictionem, ad impossibile, or ad absurdum47. His own characte47

Cf. A. C. CROMBIE, Robert Grosseteste and the Origins of Experimental Science (Oxford, 1953, 1971), and (1975a) above n. 2; LESHER (1973) above n. 27; quotations

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ristic style appears in the use and content of ratio and its relation to experentia. Aristotle, he wrote, had kept too close to superficial experience, but he himself would "always use reasons more than examples (for we search for the causes of the effects, which are not given in experience)" (I, 263). Essential to the ratio of physics was mathematics, and he repeated the criticism that "Aristotle was not very well versed in geometry" (I, 302). An illustration was the demonstration of the falsity of one of his relevant conclusions by "the divine Archimedes" (I, 303). At the same time true ratio must be based on true experientia, but the relation between them was subtle. Sometimes plausible but false opinions gained currency because no one bothered to scrutinize them, as the "common opinion" that things appeared larger under water. When he "could not discover a cause for such an effect, at length turning to experience" he found that there was no such effect, at all with things seen simply under water, but only with things seen through the curved sides of a glass vessel containing water (I, 314). Sometimes our situation was the converse, as he wrote later of odours given off by fruit and flowers. For "we never can observe those odoriferous atoms", whether evaporating or condensing, but "when sensible observation is wanting, argument (discorso) must take its place, by whose help we shall be sufficiently able to apprehend the motion to the rarefaction and resolution of solids, as well as that to the condensation of the finest and most rare substances" (VIII, 105). But it was not always easy to discover the nature of things. So he concluded of the continuing motion of projectiles that such "a movable body moving with other than natural motion is moved by a power impressed (virtus impressa) on it by a mover. But what that power is, is hidden from our knowledge". A deleted addition continued: "And in the same way what power it is that makes strings resound is also hidden from our knowledge" (I, 374). De motu gravium was an essay in physical cosmology. Archimedes supplied Galileo with a new model not only for scientific method, but also for the primary physical problem with which he was concerned, the disposition and motions of the four elements in relation to the central Earth. From this model much else for physics followed. Galileo agreed with Plato in the Timaeus that the disposition and motions of the elements were the result of their relative gravities. He then introduced Archimedes in order to reduce the cosmological order of the elements to a problem of hydrostatics on the model of bodies floating here are with slight modifications from the English translation by I. E. DRABKIN in GALILEO GALILEI, On Motion and On Mechanics, by DRABKIN and S. DRAKE (Madison, Wise., 1960).

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or sinking in water. Thus he transformed Aristotle's teleological arrangement of the universe into the resultant of mechanical forces. He dismissed lightness as a separate property contrary to heaviness; it was simply relative to the heaviness of the medium. Thus the syllogism: "The cause of a positive effect must be positive: therefore the cause of motion cannot be lightness (levitas), which is a negative quality (privatio). It remains therefore that it is heaviness (gravitas); even things that are moved upwards, are moved by heaviness" (I, 416, cf. 362n). Likewise for all "alterative motions" or changes in quality: for "that alterative motion (motus alterativus), when the movable body is moved from lightness to heaviness, is a single and continuous motion. As when water becomes per accidens cold from hot it is moved with a single motion towards coldness, and the motion from hot to warm is no different from the motion from warm to cold", so too when a body moved from being light through neither heavy nor light to heavy. "So far then are these motions from being contraries that they are actually only one, continuous and coterminous. Hence also the effects that flow from these causes should not truly be called contraries, since contrary effects depend on contrary causes" (I, 322-3; cf. I, 159). In this way Galileo came to reject the whole Greek doctrine of pairs of contrary properties, and to replace it by a single linear quantitative scale by which gravity and temperature and so on could be measured and measuring instruments devised. Despite the ambiguity behind Viviani's particular claim that Galileo "discovered thermometers (termometri)" (XIX, 607), there can be no doubt about the effects of this radical conceptual change in the very possibility of quantification upon the fundamental theory and practice of all natural science48. Why then did "provident nature (prudens natura)" distribute the positions of bodies in the order found? It was not sufficient to say that "it pleased Highest Providence" to give them "the capacity to move to some particular place": light bodies upwards, heavy downwards. For "granted that heavy bodies move towards the centre because they move towards the Earth, our next question is: why was the Earth placed at the centre, and not in the place of (say) fire?" He found it "impossible to believe that nature was not constrained by necessity, or at least from expediency, to make this kind of distribution, 48

Cf. Tractatus de dementis (I, 157-60) and VIII, 634-5, XI, 350, 506, 545, XII, 139-40, 157-8, 167-8, XV, 12-15, XVII, 377-8; J. P. ANTON, Aristotle's Theory of Contrareity (London, 1957); G. E. R. LLOYD, Polarity and Analogy: Two types of argumentation in early Greek thought (Cambridge, 1966); F. SOLMSEN, Aristotle's System of the Physical World: A companion to his predecessors (Ithaca, N.Y., 1960); F. S. TAYLOR, "The origin of the thermometer", Annals of Science, V (1942) 129-56; W. K. MIDDLETON, A History of the Thermometer (Baltimore, Md., 1966); below nn. 59, 62.

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but merely did as she fancied and as chance would have it". He racked his brains "to think of some expedient and suitable, if not necessary, cause: and indeed I discovered that it was not without the best of reasons that nature had chosen this order. For since there is a single matter for all bodies, and those bodies are heavier that enclose more particles of that matter in a narrower space, it was certainly rational that those bodies that contained more matter in a narrower space should also occupy the narrower places such as those that are nearer the centre" (I, 344-5, cf. 252-3). Thus, as suggested perhaps by the Timaeus and the atomists, he reduced relative gravity to the relative condensation and rarefaction of matter. "In accordance with reason, therefore, we shall say that motion towards the centre is natural, and motion away from the centre unnatural": the intrinsic cause of all motion was weight, and at the centre bodies came to rest (I, 352-4). Archimedes and "the ancients" (I, 359), which in the scholastic tradition meant the Greek atomists and Plato in contrast to Aristotle, thus taught Galileo how he might reduce the whole physical world to a coherent uniform system of mechanics. Archimedes taught him also the analytical device of reducing physical problems to their mathematical essence by idealized abstractions from which all material accidents such as friction and irregular shape had been eliminated, and in which unimportant departures from strict physical truth were ignored. GaKleo followed his example with skill in his analysis in De motu gravium of motion on an inclined plane. He argued that "a movable body having no external resistance on a plane inclined no matter how little below the horizon will descend naturally, without the application of any external force", whereas on "a plane inclined upwards, no matter how little" it "does not ascend except by force". Hence "on the horizontal plane itself the body is moved neither naturally nor violently" and so "can be made to move by the smallest force of all". In demonstrating this he used an argument from the balance for which he assumed "as true what is false: namely, that weights suspended from a balance make right angles with the balance, when really the weights tending to the centre converge". Covering himself "with the protecting wings of the superhuman Archimedes" who had made the same assumption, he commented that Archimedes "did so perhaps to show that he was so far ahead of others that he could draw true conclusions even from false assumptions". We must not suppose that his conclusion was false, for he had proved it by another demonstration. Hence we must say either that the suspended weights do make right angles "or else that it is of no importance that they make right angles" but enough that the angles are simply equal. The latter seemed sounder, unless we wanted to call it "geometrical licence" as when

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Archimedes assumed that surfaces had weight. That was not the end of the problem of relating mathematics to matter. For "our demonstrations must be understood of movable bodies free from all external resistance. But since perhaps it is impossible to find these bodies in matter, someone making a trial on them (de his periculum faciens) should not be surprised if the experiment fails (si experientia frustretur] and a large sphere, even though it is on a horizontal plane, cannot be moved with a minimal force". Further, there was in addition the fact that "a plane cannot actually be parallel to the horizon. For the surface of the Earth is spherical, and a plane cannot be parallel to this". Since "the plane touches the sphere at only one point (piano in uno tantum puncto sphaeram contingente], if we move away from .such a point, we must be moving up", and so it would be impossible to move the sphere "with an arbitrarily minimal force" (I, 299-301, cf. 296-9, 340, 407-8, VII, 52, VIII, 190, 197, 202-3)49. If Archimedes supplied the mathematical method, De motu gravium remained in much of its physical theory and methods of argument, and in its metaphysical expectations, fundamentally Aristotelian. Galileo based its dynamics on the Aristotelian principle that motion like any positive effect required an adequate cause, hence a continuing velocity required a continuing motive power and a change in velocity a change in effective power. He retained the distinction between natural and unnatural motion. In searching for the changing effective power bringing about the acceleration of falling bodies, he wrote that "we shall use this resolutive method (resolutiva methodo) to track down what we believe to be the true cause of this effect" (I, 318). His resolution was nonmathetaatical, and was in fact based on Pereira's De communibus... as we show below (I, 318-20). Most characteristic in its resemblance to the Disputationes was his search for necessary causes and demonstrations. These were essential likewise to any practical science of mechanics. "Before I descend to the speculation of mechanique instruments," he wrote in the version of Le mecaniche published by Favaro, " I have thought it very fitt to consider in generall the commodityes that are drawen from them. The rather, because (if I deceive not my self) I 49 Cf. on this question N. KOERTGE, "Galileo and the problem of accidents", Journal of the History of Ideas, XXXVIII (1977) 389-408; also Vocabulario degli Accademici della Crusca (Venezia, 1612): "Cimentare, cimento, vedi Esperimentare, Esperimento" (p. 182); "Tentare. Far prouva, cimentare. Lat. tentare, experiri, periculum facere" (p. 881). These terms were common synonyms and were used by Galileo as such, without distinguishing active testing from passive observation, despite C. B. SCHMITT, "Experience and experiment: a comparison of Zabarella's view with Galileo's in De motu", Studies in the Renaissance, XVI (1969) 114 sqq.

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have scene all enginiers deceiv'd, while they would apply their engines to works of their owne nature impossible; in the success of which both they themselves have bene deceiv'd, and others also defrauded of the hopes they had conceiv'd upon their promeses...; as if, with their engines they could cosen nature (ingannando... la natura], whose inviolable lawe it is, that noe resistence can be overcome by force which is not stronger than it. Which belief how false it is, I hope by true and necessary demonstration to make most manifest" (II, 155, cf. 156, 158, 179-80)50. Citing in this treatise not only Archimedes and the Aristotelian Mechanica but also Pappus's Mathematicae collectiones, he stressed the generality of mechanical principles. Thus he wrote of the effects of percussion, as with a hammer: "the cause of which, though it be in nature somewhat obscure and hard to be unfolded", he would try to make "clere and sensible, shewing at last the beginning and original (// principle ed origine] of this effect to be deriv'd from no other fountaine than that from whence flow the causes of other mechanicall effects". Force, resistance, space and velocity "goe alternately following such a proportion and answering such a law (leggeY as they followed in every mechanical operation; "and this is according to the necessary constitution of nature (la necessaria constituzione delta naturaY• "Arguing by the converse,... if it were otherwise, it were not only absurd, but impossible". So "all wonder ceases in us of that effect, which goes not a poynt out of the bounds of nature's constitution" (II, 188-9). Again in his Discorso intorno alle cose che stanno in sull'acqua (1612) Galileo continued to use the terminology of the Disputationes to point to the same scientific objectives. As in De motu gravium he combined Aristotelian with Archimedean models both in form of argument and in physical concepts, and he tried to reduce general questions of the constitution of matter and the universe to specific problems soluble by natural science. This work was his first published contribution to experimental physics. If he contradicted so great a man as Aristotle, he wrote, this was not by caprice or because he had not read and understood him, "but because reasons persuaded him to it, and Aristotle himself had taught him to quieten the intellect (quietar I'intelletto] by what has convinced me by reason, and not only by the authority of the master" (IV, 65). His first aim then was "to introduce true demonstrations" from "the true, intrinsic and total cause" (IV, 67, cf. 79). His method of identifying the true cause was "to remove, in making the experiment (I'esperienza], all the other 50

English translation by ROBERT PAYNE (1636): transcribed by A. CARUGO from British Library Ms. Harley 6976, ff. 317r, 329v-30r; cf. below nn. 57, 58.

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causes that can produce this same effect" (IV, 19), leaving only this one. For the "cause is that which, when present, the effect follows and, when removed, the effect is removed" (IV, 27, cf. 22). The quantitative relation between an adequate cause and its effect had been well defined by Luca Valeric in commenting to Galileo in 1609 on "principles of a middle science". A "geometrical intellect with some light, either natural or acquired, from metaphysics" would, he wrote, understand "that when the power of the efficient cause is multiplied it is necessary that the quantity of the effect should be multiplied according to the same multiplication, deducting from it every kind of impediment". For "we measure the quantity of the cause with the quantity of the effect" (X, 248, cf. 245)51. Archimedes had demonstrated that floating or sinking depended on the excess in gravity of the water or of the body relative to each other. Galileo continued: "By a different method and by other means I shall manage to prove the same, by reducing the causes of such effects to more intrinsic and immediate principles... And since this is required by the demonstrative progress (la progressione dimostrativa\ I shall define some terms and then explain some propositions which I could use, as true and known things, for my purposes" (IV, 67). True scientific demonstration depended then for Galileo upon a conception of laws both of logical reasoning and of nature discovered in existence and confirmed by all experience. This done, as he put it in the Dispufationes, "we come to rest in knowledge of the conclusion,... because of knowledge of the principles" (Ms. Galileiano 27, f. 23r); for, as he repeated in the Discorso (1616) on the tides, "bringing to rest the mind of those who desire, in theorizing (nelle contemplezioni] about nature, to penetrate beneath the skin... is reached only when the reason produced as the true cause of the effect easily and openly satisfies all the particular symptoms and properties (sintomi ed accidenti) that are seen distinctly connected with this effect" (V, 377). During this period 1610-1616 of many disputes over the telescope, floating bodies, the sunspots and the Copernican system, through which he articulated his campaign at once for a new physics and cosmology and for a new conception of natural science, Galileo wrote often on the proper methods of science and the point at which they could bring the mind naturally or by force of available possibilities to rest. He 51

Galileo (IV, 52) cited Francesco Bonamico for the rule of presence and absence, which had been stated in much the same words by William of Ockham: cf. E. CASSIRER, "Some remarks on the question of the originality of the Renaissance", Journal of the History of Ideas, IV (1943) 49-56; also for Galileo's use of this rule and the rule of concomitant variations CROMBIE, Robert Grosseteste (1953, 1971); KOERTGE (1977) above n. 49; WISAN (1978) above n. 20; and for the Topics etc. below.

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developed in print during those years all the main characteristics of his natural philosophy: his insistence that the object of natural science was the one true world existing to be discovered; his methods of exploring and demonstrating that one true world; and what kind of world he expected to find and with what degree of certainty. In fact he used a variety of methods of scientific argument and exploration adapted to different kinds of problems and subject-matters, and related to a variety of scientific and philosophical sources and models. His exploration might be primarily theoretical or primarily experimental according to the simplicity or complexity of the subject-matter and its problems. What he claimed to have been able to demonstrate truly and with certainty might depend again on the subject-matter, on his scientific experience in using different philosophical models, and also on his personal circumstances at different periods of his life. Winifred Wisan in her reexamination of "Galileo's scientific method" (1976) has rightly emphasized the effect on his presentation of his scientific conclusions of the prohibition in 1616 that forbad him to teach or write anything more in defence of the Copernican system. The form of Galileo's scientific argument with problems involving simple variables was postulation or argument ex suppositione on the model of Euclid and above all Archimedes. It was Archimedes who provided the ideal, as in his reduction by purely theoretical analysis of the possible postulates that could yield the phenomena of the balance or lever to an unique set certified by self-evidence or sufficient reason. Thus he could give a complete account of an experimental phenomenon without the need for any experiments. Galileo explicitly followed this model in describing his discovery of his definition or law of acceleration of falling bodies in the Discorsi (1638; VIII, 197, 205-8); and in his letters of 1637 to Pierre Carcavy (XVII, 90-1) and of 1639 to G. B. Baliani (XVIII, 12-13, 78). He postulated ex suppositione a definition without asserting its existence in nature, and demonstrated therefrom the "many properties of such a motion". The subject-matter did not allow him like Archimedes to reduce the possible definitions by a purely theoretical analysis to the one actually true in nature, but "if experiment showed that such properties happened to be verified in the motion of naturally falling heavy bodies, we could assert without error that this is the same motion that was defined and supposed by me" (XVII, 90). His experiments in this kind of situation, here with the inclined plane, were made then to test whether his postulated theoretical world was the one actual world. They amounted to "very little less than a very necessary demonstration" (VIII, 205). Again in using the pendulum as an instrument of analysis he began with "a postulate, the absolute truth of which we shall hereafter find established by seeing

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other conclusions built upon this hypothesis, to correspond to and most exactly to agree with the experiment" (208) 52 . He saw the arguments developed ex suppositione by Ptolemy and by Copernicus for the much more complex motions of astronomy as likewise aiming to demonstrate, as he wrote in 1612, the one "true constitution of the universe" which "could not possibly be otherwise" (V, 102, 351, 357-61, VII, 148-50, 470, XII, 171-2). This was a truly Aristotelian vision of a completed science. A passage from Galileo's hydrostatical controversy specifies a change of model from the Aristotelian to the mathematical conception of analysis and synthesis, or resolution and composition. It also harks back to the Disputationes. The main question in dispute concerning scientific method was the efficacy of mathematics in physics, and hence of Archimedes against Aristotle. A passage in Galileo's hand published in 1615 in a work under Benedetto Castelli's name contrasts the proper method of argument in formulating problems for scientific decision with the circular syllogisms used by their opponents. They "commit the gravest mistakes" because "using mainly, but not well, the resolutive method (// metodo resolutivo] (which, if well used, is the best method of discovery), they take the conclusion as true and instead of going on deducing from it this and then that and then that other consequence, until they come across one that is manifest either by itself of because it has been demonstrated, from which then the intended conclusion is reached by the compositive method (il metodo compositivo}; instead, I say, of making good use of such a progression, they form with their imagination a proposition that squares immediately with the conclusion they intend to prove, and without falling back even a single step, they take it as true, though as false or equally doubtful as the conclusion, and immediately they construct on it a syllogism, which leaves us without any gain in our original uncertainty" (IV, 521, cf. 13-15). This account of resolution and composition corresponds to that given by Pappus in the Mathematicae collectiones (VII, praefatio 1-3) of the two kinds of analysis used by the Greek geometers, and more briefly by Proclus as analysis and synthesis 53. 52 53

Cf. on this WISAN (1974) 124 and (1978) 42, above n. 20. PAPPUS ALEXANDRINUS, Matbematicae collectiones a Federico Commandino in Latinum conversae... (Pisauri, 1588); cf. T. L. HEATH, History of Greek Mathematics, II (Oxford, 1921) 400-1. Pappus and Proclus were both known in manuscript to GIORGIO VALLA, De expetendis et fugiendis rebus opus, X.I (Venezia, 1501); Pappus was cited by GUIDOBALDO DEL MONTE, Mechanicorum liber, Praefatio (Pisauri, 1577); cf. A. P. TREWEEK, "Pappus of Alexandria: the manuscript tradition of the Collectio mathematical, Scriptorium, XI (1957) 195-233; GILBERT (1960) above n. 43; JARDINE (1976) above n. 38; WISAN (1978) above n. 20; also n. 46. For another historical ac-

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Galileo elaborated his account in the Dido go (1632) to embrace both mathematics and physics. He believed that the method by which Aristotle himself had expounded his physical doctrine was not that "by which hee investigated, for I hould for certaine that hee first of all procured, by way of senses, of experiments and observations, to assure himselfe as much as might be of the conclusion, and that afterwards he sought the meanes to demonstrate it; for that is for the most part the use in demonstrative sciences; and this comes to passe because when the conclusion is true, if we make use of a resolutive method, we easily encounter some proposition that hath alreadie beene demonstrated, or we arrive to some principle which is of itselfe knowne (prindpio per se notoY (VII, 75). Of some principles "humane understanding... hath so absolute a certaintie as nature herself e hath, and such are pure mathematical sciences... I beleeve that this knowledge equalls the divine knowledge in the objective certaintie, seeing it arrives so farre as to comprehend the necessitie, above which I cannot see that there is greater certaintie" (VII, 129)54. Physical principles were less certain. He regretted that the great magnetical experimenter William Gilbert's lack of mathematics and especially of geometry had made him so rash "in accepting of those reasons for the concluding demonstrations which hee produceth for the true causes of the true conclusions by him observed". But a well conducted experimental investigation on which to base a conclusive scientific argument could "make it little lesse to mee than a mathematical demonstration". He went on to bring the resolutive method into the experimental argument: "In searching the reasons of the conclusions unknown to us, wee must have the fortune from the beginning to direct our discourse towards the way of truth by which when a man walkes, it easily falls out that hee meets now count following CASSIRER (above n. 39) and its critics cf. J. H. RANDALL, "The development of scientific method in the school of Padua", Journal of the History of Ideas, I (1940) 177-206, The Career in Philosophy, I (New York, 1962) 256-360 and "Paduan Aristotelianism reconsidered" in Philosophy and Humanism: Renaissance essays in honor of Paul Oskar Kristeller, ed E. P. MAHONEY (Leiden, 1976); CROMBIE (1953, 1971) above n. 47; N. W. GILBERT, "Galileo and the school of Padua", Journal of the History of Philosophy, I (1963) 223-31; W. F. EDWARDS, "Randall on the development of scientific method in the School of Padua - - a continuing reappraisal" in Naturalism and Historical Understanding: Essays in the Philosophy of John Hermann Randall jr., ed. J. P. ANTON (Albany, N.Y., 1967), "Niccolo Leoniceno and the origins of humanist discussion of method" in Philosophy and Humanism, ed. MAHONEY (1976); H. SKULSKY, "Paduan epistemology and the doctrine of the one mind", Journal of the History of Philosophy, VI (1968) 341-61; C. B. SCHMITT (1969) above n. 49 and A Critical Survey and Bibliography of Studies on Renaissance Aristotelianism 1958-1969 (Padova, 1971) 38-46. 54 English translation by Joseph Webbe, British Library Ms. Harley 6320 (c. 1634): quoted here and below.

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with some, and then with other propositions knowne for true, either by discourse or by experience, from the certaintie whereof the truth of ours getts force and evidence" (VII, 432, 434-5). Castelli in writing to Galileo in 1637 described an experimental analysis of a problem concerning the absorption of heat from the Sun's rays as "ordering all the reasoning first by the resolutive method and then by the compositive" (XVII, 160). Galileo's form of scientific argument with more complex subjectmatters was a combination of experimentally controlled postulation with more immediate experimental and observational exploration. He conducted his experimental analysis of the causes of effects according to the "laws of logic" (leggi logicali) or "physical logic" (logica naturale) (VI. 252, 333), which were the scholastic rules of inference: presence and absence, and concomitant variations. The last was specified by Aristotle in the Topics as a rule for the predication of properties by which to "argue from greater or lesser degrees... See whether a greater degree of the predicate follows a greater degree of the subject... Now... if an increase of the property follows an increase of the subject,... clearly the property belongs; while if it does not follow, the property does not belong. You should establish this by induction" (Topics, II. 10, 114b37-115a6, cf. IV. 6, 127bl8-25, VI. 7, 145b33-6a36; FRANCIS BACON, Novum organum, II. 13). These were the logical rules that Galileo stated for his inquiries into hydrostatics and sunspots, into comets in II Saggiatore (VI, 339-40, q. 45), and into the connection between the motions of the tides and of the Earth in the Dialogo: "I say therefore, that if it be true that of one effect one only is the primarie cause and that betweene the cause and the effect there is a firme and constant connection, it is necessarie that whensoever there is a firme and constant alteration in the effect, there is a firme and constant alteration in the cause". Then since annually and monthly the tides "have their firme and constant periods, wee must of force say that there falleth out a regular alteration in the same times in the primary cause of the fluxes and refluxes". Demonstrating this with his model of water moving in a vessel, he argued that the motion observed was "a compounded motion resulting from the coupling together of the two proper motions whereof the diurnall whirling with its now adding to, and then drawing from the annuall moving, is that which produceth the difformitie in compounded motion". Similarly to account for the regular seasonal variations in the tides "(if we will retayne the identitie of the cause) we must finde out alterations in these additaments and subtractions which make them more or less powerful! in producing these effects which have dependance on them" (VII, 471-2).

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The Aristotelian rules of inference used the criterion of range of confirmation to establish that a given property belonged to a given subject. Galileo extended the quantification of the argument "from greater or lesser degrees" from the example of mathematics and the practical mathematical arts. These rational arts, of perspective painting and measured music but above all of mechanics and engineering, provided a distinctive intellectual model for Galileo's experimental investigations no less important than those taken from his other sources. The rational arts offered a distinctive method of analysis by means of artificial models imitating the processes of nature. Thus the Venetian Daniele Barbaro wrote in his well known commentary on Vitruvius (1556) that "the architect must think out very well and, in order to make more certain of the success of the works, will proceed first with the design and the model... Yet he will not search for impossible things, either as to the matter or as to the form, which neither he nor others can accomplish. Whence art, observer of nature, wanting also to make something, takes the matter of nature put into existence with sensible and natural form... and forms that matter with that idea and with that sign which is reposing in the mind of the artist" 55. The engineer Giuseppe Ceredi of Piacenza, inspired at once by Greek mathematical thinking and by the example of "nature itself, as if become mechanical in the construction of the world", offered in 1567 as a method of antecedent analysis in designing any desired result the construction of "models (modelli}, adding, changing and removing many things" as required. In this way he could bring together conveniently the many observations needed to bring about "some new and important effect", recognize errors by experience and correct them by reason, and so direct the whole enterprise "to the stable production of the effect that is expected" 56. Again Guidoba'ldo del Monte, taking up ideas from the influential Aristotelian Mechantca in a paraphrase of Archimedes published in 1588, wrote that "if art overcomes nature by imitating her so that those things which are done by art happen contrary to nature", that was possible because "art with wonderful skill overcomes nature through nature herself, by so arranging things as nature herself would do if she decided that such effects should be produced by herself" 57. Galileo was to write likewise in Le mecaniche, and in 55

DANIELE BARBARO, 7 died libri dell'Architettura di M. Vitruvio, tradotti e commentati... 1.3 (Vinegia, 1556) 26; cf. V. P. ZOUBOV, "Vitruve et ses commentateurs du XVIe56siecle" in La science au XVIe siecle: Colloque de Royaumont 1957 (Paris, 1960). GIUSEPPE CEREDI, Tre discorsi sopra il modo d'alzar acque da' luoghi bassi (Parma, 1567) 5-7; cf. CROMBIE (1982) and Styles... above n. 16. 57 GUIDOBALDUS E MARCHio MONTIS, In duos Archimedis Aequeponderantium libros paraphrases scholiis illustrata, Praefatio (Pisauri, 1588) 2; cf. the Aristotelian Me-

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criticizing "the model of a machine" proposed by an engineer, that "already a long time ago I had found, and confirmed by many many experiences, the concept that nature could not be overcome and cheated (defraudata) by art" (VIII, 572)58. Galileo's writings on natural philosophy were all disputations in which he combined his scholastic and mathematical methods to argue for or against the various positions or hypotheses being proposed. His method of argument was to eliminate rival proposals by means of these rules of inference, and then to try to demonstrate the truth of his own favoured proposal by showing that it alone was confirmed by agreement with the whole range of the known phenomena. Thus he wrote in his Second Letter on the Sunspots (1612) of two rival suppositions, that the spots were either small circling stars or actually on the solar body, "this second, it seems to me, is true, and the other false; just as any other supposition (posizione] whatsoever that might be assumed will be found false and impossible, as I shall try to demonstrate by means of obvious disagreements and contradictions. All the appearances agree concordantly with the hypothesis that they are contiguous with the Sun and that they are carried round by its revolution, without meeting any inconvenience or difficulty" (V, 118, cf. 117, 127). Having shown that this rival which did save a good part of the phenomena was nevertheless false, he did not want "to waste time in disproving every other imaginable supposition" (V, 130). If his true observations meant that celestial matter must be alterable, this was a conclusion closer than the opposite view to Aristotle himself, who surely would have agreed if he had known "the present sensory observations. For he not only admitted manifest experience (le manifeste esperienze] among the powerful means of reaching conclusions about natural problems, but gave it first place". For "I am sure that he never held the conclusion of inalterability to be as certain as that all human reasoning must take second place to evident experience (evident e esperienza)". For all that he continued, "in order to remove every ambiguity, to some come, inspired by a superior power, necessary methods (metodi necessarily by which we understood these phenomena, "though this is not enough to persuade those whose minds cannot be reached by the necessity of geometrical demonstrations" (V, 138-40). Repeating this interpretation of Aristotle in the same context in the Dialogo (1632), he made Sagredo challenge his opponent as represented chanica (847a); S. DRAKE and I. E. DRABKIN, Mechanics in Sixteenth Century Italy (Madison, Wise., 1969); P. L. ROSE and S. DRAKE, "The pseudo-Aristotelian Questions of Mechanics in Renaissance culture", Studies in the Renaissance XVIII (1971) 65-104. 58 Cf. VIII, 559-61; above n. 50.

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by Simplicio "to produce all the particular reasons, experiments and observations, as well naturall as astronomicall, whereby others may be persuaded" of their opinion (VII, 71, cf. 75-6). As for Galileo's own preliminary arguments for the Earth's motion from simplicity and economy and so on, these "I bring you not as lawes infrangibile (leggi infrangibili], but as motives (motivi] which have some appearance. And because I know full well that one onely experience, or concluding demonstration, which could be brought to the contrarie were sufficient to beat downe these and an hundred thousand other probable arguments unto the ground, we must not stay heere, but go forward..." (VII, 148). There is a striking contrast between Galileo's apodeictic confidence about astronomy and mechanics and his much more cautious estimate of what could be truly and certainly discovered about the real world existing behind the more complex and enigmatic problems of matter and its composition and properties 59. This corresponded to the distinction which placed the former in the mathematical middle sciences and the latter in natural philosophy or physics. Natural philosophy he had written in the Trattato della sfera (1606) was concerned with "substance and quality" and "our intellect is guided to knowledge of the substance by means of the properties (accidenti}" (II, 211, 212). The proper object of natural scientific inquiry was then the substances and hence causes bringing about the properties which made up the world we could observe. With his first telescopic discoveries he set out to destroy the Aristotelian division of the world into regions of celestial and elementary substances (XI, 147, cf. 280-5, 289, 298-303; above nn. 23-24), just as in De motu gravium and the Discorso (1612) on floating bodies he set out to destroy the division of properties into contrary pairs. Both he wanted to reduce to a linear quantitative uniformity amenable to mathematics and measurement. His problems began in looking beyond that to the physical substance and causality 59

Cf. for Galileo's scientific style especially L. S. OLSCHKI, "The scientific personality of Galileo », Bulletin of the History of Medicine, XII (1942) 248-73, "Galileo's philosophy of science", Philosophical Review, III (1943) 349-65; A. C. CROMBIE, Galilee devant les critiques de la posterite (Les Conferences du Palais de la Decouverte, Paris, 1956), translated in part as "Galileo: a philosophical symbol", Actes du VHIe Congres International d'Histoire des Sciences, Florence-Milan 19% (Vinci & Paris, 1958) 1089-95, (1969), (1975a), (1981) and (1983) above n. 2, and Styles... above n. 16; JARDINE (1976) above n. 38; KOERTGE (1977) above n. 49; WISAN (1978) and (1981) above n. 20; with his researches into different subject-matters classically exemplified by A. KOYRE, Etudes galileennes, I-III (Actualites scientifiques et industrielles, nos. 8552-4; Paris, 1939); L. GEYMONAT, Galileo Galilei (Torino, 1957), English translation (New York, 1965); E. McMuLLiN (ed.), Galileo: Man of Science (New York, 1967); M. CLAVELIN, La philosophic naturelle de Galilee (Paris, 1968); SHEA (1972) above n. 21; WISAN (1974) above n. 20; also nn. 47-58.

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behind the phenomenal world. One such problem arising out of the Sidereus nuncius (1610) was the nature of light, the means by which the telescope gave us its information. The Roman philosopher Giulio Cesare La Galla reported an occasion in Rome in 1611 when he had lamented the impossibility of deciding even on "our general classification of it, as to whether it is substance or property, body or something incorporeal, quality or relation; for such is the weakness of our intellect that it can easily be made to fit all these categories or equally be excluded from them". Galileo agreed "and firmly avowed that he would willingly allow himself to be shut up in a dark cell and fed on bread and water, provided that, when he was restored to light in due course, he could perfectly grasp its nature and understand it" 60. Again in his First Letter about the Sunspots (1612) he wrote that "for me it is much more difficult to find the truth than to show convincingly what is false, and it seems, to me that I know what the sunspots are not, rather than what they are" (V, 95). So "we could not blame in any way the philosopher who confessed that he does not know, and cannot know, what the matter of the sunspots may be" (106). He was prepared to speculate but, he wrote in his Third Letter, "in our speculating we either try to penetrate the true and intrinsic essence of natural substances, or content ourselves with coming to know some of their properties (affezioni]. An attempt upon the essence I hould to be an undertaking no less impossible and a labour no less vain in the nearest elementary substances than in the most distant and celestial ones... But if we wish to stop at the apprehension of some properties, it does not seem to me that we should despair of being able to reach them in the bodies most distant from us as well as in the nearest ones" (V, 187-8). Perhaps Winifred Wisan (1976, p. 24) was correct in detecting a further nuance from the prohibition of 1616 in the Platonic imagery of the remark in the Discorso delle comete (1619) published under Mario Guiducci's name, that "we must be content with what little we can conjecture here among the shadows, until we are shown the true constitution of the parts of the world" (VI, 99). But this expressed yet once more a consistent estimate of our knowledge of physical causes, if not of geometrical structures. He commented famously in the Dialogo (1632) on the assertion that everyone knew that the cause of bodies falling downwards was gravity, that rather "every man knows that it is called gravitie", but of the "essence you know no whitt more than you 60

JULIUS CESAR LA GALLA, De phoenomenis in orbe Lunae, De luce et lumine disputatio (Venetiis, 1612) 57-8; cf. GALILEO, Le opere, III, 325-6; CROMBIE (1969) above n. 2.

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know of the essence of the movent (movente] which turnes the starres about, excepting the name..." (VII, 260-1). Likewise in the Discorsi (1638) he refused "to inquire into the cause of the acceleration of natural motion, concerning which various opinions have been pronounced by various philosophers". It was enough at present for him "to search out and demonstrate to us some passions (passtones] of an accelerated motion (let the cause of that acceleration be what it will)..." (VIII, 202). Galileo suggested in the Discorsi (VIII, 87-89) methods for deciding by measurement whether or not light was a form of motion with a finite speed. But from his first discussions of the nature of light, through II Saggiatore (VI, 350, 352), down to his last correspondence on the subject with Fortunio Liceti in 1640-41 he maintained that the evidence could show us only how light behaved, not what it was. His comment to Liceti in 1640 on "the essence of light, about which I have always been in the dark" could be applied to his physical investigations over many years: "Here I would not like to be told that I have not stopped at the truth of fact; for experience shows me that it happens in this way; which, I could say, in all the effects of nature admired by me, assures me of the an sit but brings me no gain in the quomodo" (XVIII, 208). Galileo's philosophical campaign was dedicated to establishing the identity at once of the true science and, as he wrote in his First Letter about the Sunspots, of "the true and real world which, made by God with his own hands, stands always open in front of us for the purpose of our learning" (V, 96, cf. XI, 530, XII, 20). What he expected to find by reason in existence behind the appearances perceived by the senses was governed by the interaction between his philosophical and scientific sources and his scientific experience in exploring nature by means of geometrical postulation, the logic of experimental elimination and confirmation, analogical modelling, measuring instruments, and the extension of the natural senses with the telescope and microscope, to say nothing of the exigencies and expediencies of debate and persuasion. Galileo's rhetorical image in // Saggiatore (q. 6) of the mathematical book of philosophy recalls Proclus's account of the Timaeus "using mathematical language throughout in expounding its theory of the nature of the universe" and the generation of the elements and their powers "by numbers and figures" (1.8: above, n. 46) and recalls also Clavius and Mazzoni (cf. nn. 42-45). Galileo had quoted biblical passages comparing the heavens to a book in his Tractatio de caelo (I, 64). His point in II Saggiatore was to distinguish the book of philosophy from books of fiction like the Iliad and Orlando furioso "in which the least important thing is whether what is written in them is true" (VI, 232). By contrast, as he repeated in his last account of the image to

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Liceti in 1641, "the book of philosophy is that which stands perpetually open before our eyes, but because it is written in characters different from those of our alphabet it cannot be read by everybody; and the characters of this book are triangles, squares, circles, spheres, cones, pyramids and other mathematical figures fittest for this sort of reading" (XVIII, 295, cf. XIX, 625). Thus, as in the Timaeus, Euclid and Proclus it was essentially a geometrical, not an arithmetical book61. The Timaeus and related Greek sources offered Galileo also something further in his search for a rational philosophy of nature. He had been forced to defend the validity not only of his telescopic observations but also of unaided vision against sceptical doubts about the certainty of mathematics when applied to sensible subjects. Practical difficulties in using this unfamiliar instrument reinforced the suspicion that the telescope was just another of the optical devices for producing illusions well known to theatrical magic. Clavius and other mathematicians at the Collegio Romano formed this opinion when they tried to confirm Galileo's observations in the autumn of 1610, until with advice from Galileo himself they succeeded. Christopher Grienberger wrote to him frankly that things so difficult to believe should not be accepted lightly and that it was hard to give up opinions held for so long by so many philosophers, but that at length "I have examined with my own eyes the wonders you were the first to introduce to the world... I have learned from experience (experientia) that it is not an illusion that you have seen four satellites in motion around Jupiter,... the irregularities of the Moon..." and so on (XI, 33, cf. X, 430-45, 480-501, XI, 253, 272-7). La Galla in his ambiguous defence of the telescope in 1612 linked the question to Aristotle's critique of Plato for his prejudicial introduction of mathematics into physical inquiries and to the further question of "sensible forms and qualities". It was he wrote "asserted by philosophers and known from experience" that "the senses are deceived over the common sensibles, namely motion, rest, number, size and shape; although they are normally either not at all or to the least degree at fault over the proper sensibles, such as colour or taste" (III, 323-5). He gave as an illustration the ancient illusion of a stick half in water which appeared bent to vision but straight to touch. Galileo replied like Plato (Republic X. 602C-E) that such optical illusions were corrected by optical science (III, 323-5) and likewise for other such apparent deceptions. Later in II Saggiatore (q. 48) he argued that "when I conceive of a 61 Cf. for the book of nature M. CURTIUS, Europaische Literatur und lateinisches Mittelalter (Bern, 1948) 323-9, English translation (New York, 1953) 319-26; E. GARIN, La cultura filosofica del Rinascimento italiano (Firenze, 1961) 451-65.

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piece of matter or a corporal substance, I certainly feel myself necessarily obliged at the same time to conceive" that there must be attributed to it a set of irreducible minimum "conditions (condizioniY': shape, relative size, location in place and time, motion or rest, touching other bodies or not, and number. He felt "no compulsion to hold that it must necessarily be accompanied by such conditions" as colour, taste, sound etc. "Rather, if the senses had not escorted us, reason or imagination by itself would perhaps never have arrived at them". Having no justification by reason, these qualities evidently had no place in his theory of the real physical world. They "are on the side of the object in which they seem to be placed no more than mere names (puri nomi], but have a place only in the sensitive body (corpo sensitivo}" of living things. The "primary and real properties (primi e reali accidenti}" required in external bodies for exciting these sensory qualities in us were no more than "sizes, shapes, numbers and slow or swift motions" (VI, 347-50). Galileo's primary properties apart from one refinement had been listed by Aristotle (De anima III. 1, 425al5-17, cf. II. 6, 418a8-19, III. 1, 425al4-blO; Categoriae c.6, 4b20-6a35, cf. c.8, 9a27-bll; De sensu c.l, 437a4-16, cf. c.4, 442a30-b!7) as quantities not qualities, and as objects common to more than one sense rather than proper to each sense. His distinction between the mere names and the real properties corresponded to the account given by Galen of Democritus's distinction between the qualities "by convention (lege}" or for us and those existing "in reality (vere}n in things 62 . Again according to Sextus Empiricus "Plato and Democritus held that the only real things were those discernable by reason" 63. Both recognized as real only actual as distinct from potential qualities, and both agreed also in reducing all the other senses to modes of touch. Aristotle had criticized his predecessors for precisely these opinions (cf. I, 123-9, 157-60). Except for making irreducible geometrical shapes and not solid atoms the primary constituents of matter, Plato in the Timaeus (56B-68D) added to the real properties listed by the atomists two fundamental items: numbers, and variations in the speeds of motion. Thus the numbers of particles accounted for density and texture, their shapes and speeds accounted for the different sensations of heat, and above all variations in speeds expressible in numerical 62

GALEN, De elementis secundum Hippocralem libri duo, I, Latin version by Niccolo Leoniceno in GALEN, Omnia quae extant in Latinum sermonen conversa, I (Venetiis, 1556) f. 2rv; cf. CROMBIE (1969) above n. 2 and his Appendix: "Sources for Galileo's accounts of the primary properties and secondary qualities etc." in our book; SHEA63 (1972) 100-4, above n. 21; also nn. 48, 59. SEXTUS EMPIRICUS, Adversus mathematicos, VIII.6, Gentiano Herveto Aurelio interprete (Parish's, 1569) 184-5, (Genevae, 1621) 222.

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ratios accounted for the different qualities of sensation experienced as the pitch and consonance of sounds (67A-C, 80A-B). This was the refinement of "slow or swift motions" that Galileo added to Aristotle's common sensibles in listing his primary and real properties. It had been developed by the Greek musical theorists from Archytus of Tarentum and Plato, Aristotle himself (De anima II. 8, 419b4420b4) and Aristoxenus, to Ptolemy and Theon of Smyrna, and was discussed explicitly by Boethius in his influential textbook on music. The connection of the frequencies of vibratory impulses with musical sensations had been investigated in the sixteenth century by Giovanni Battista Benedetti and by Vincenzo Galilei probably assisted by Galileo himslef64. Galileo like Plato (61C-62A) introduced the question of the causation of the sensory qualities by asking what we meant by heat, looking then for the "true property, affection and quality (vero accidente, affezzione e qualitd] that really resides in the material" (III, 347). Like Plato he was concerned to distinguish between things and sensations designated by names. After considering common problems of sensation he followed Plato's order and essential ideas in explaining the five special senses (65B-68D). It seems evident that he based his treatment on the Timaeus, and possible that these were the subjects of the De sono et voce and De visu et coloribus included in his programme for Vinta in 1610. By defining in this way a stable and calculable relation of perception to the world perceived, Galileo met one essential condition for a rational science of nature. He provided against the sceptics for the validity, and against the magicians for the consistency of the information received through the senses. He focused attention on the relevance to this question of the scientific study of the senses themselves and of sound and light as the media of hearing and vision. In his analysis of the more complex properties of materials and of heat and light in the Discorsi he introduced yet another ancient model, Hero of Alexandria. Whereas Plato and the atomists had been concerned primarily with the general problem of establishing what existed through changing appearances, Hero had aimed to find more limited explanations of specific physical phenomena of the structure of matter. Likewise in his treatment of sound Galileo gave preference to technical over philosophical questions and authors in acoustics. In keeping with these sources he shifted his focus from that of // Saggiatore to more technical and experimental aspects of the argument from observable phenomena to the inobservable structures and motions postulated by reason to 64 Cf. CROMBIE (1969) above n. 2, (1971) and the forthcoming volume on Mersenne etc. above n. 13.

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produce them. He appeared at his most sophisticated as a philosopher who was an engineer, looking not so much for the nature of things as for the way to specify precisely in defined situations how to get accurately reproducible results. His search for the true identity of science and of nature then seems to have ended in the conclusion that in practice it was this rational experimental art, and not any vision of a completed and demonstrated necessary truth of the essence of things, that could lead us most truly to the only science of nature available. 3. We turn now to the difficult problem of placing in Galileo's intellectual biography important undated writings on natural philosophy. The problem has two aspects: the order of composition, and the dates. The only evidence available comes from comparisons of contents, from references and citations, and from material connections in the same or related manuscripts. Much has to be probable and persuasive, little demonstrative. There are more questions than answers. Hence our approach must be problematic, despite any temptation there may be to play the role as Galileo put it "of someone who has conceived some perfect demonstration but who does not assent to its conclusion" (Ms. Galileiano 27, f. 13v): to offer irrefutable proofs for what cannot be believed, like the clever Oxford scholar who proved irrefutably that Queen Victoria was the author of the Iliad. The main problem is the dating of the Latin dialogue and treatise De motu gravium (Ms. Galileiano 71) and the scholastic Tracfafiones de mundo et de caelo and Tractatus de alteratione et de elementis (Ms. Galil. 46) all in Galileo's hand. The last pages of Ms. Galileiano 46 which contains these scholastic treatises are filled with fragmentary notes (excerpts from books and drafts of passages) on motion. The second note was written in dialogue form for insertion in the dialogue and so must have followed it (I, 375-8, 409) 65 . Then comes a series of notes used in the treatise De motu gravium, which Galileo must have written after the unfinished dialogue and before or while writing, or while revising, the treatise. All the fragmentary notes are written on paper with the same watermark as the dialogue which they follow immediately in the manuscript. The first draft of the treatise (Ms. Galileiano 71, ff. 115-24; I, 247, 326-40) is on paper with the same watermark as the Tractatus de alteratione et de elementis. The Tractationes de mundo et de caelo is on a third kind of paper66. These

65 Cf. I. E. DRABKIN, "A note on Galileo's De motu", his, II (1960) 271-7, and in GALILEO, On Motion... (1960) 124, above n. 47; WISAN (1974) above n. 20. 66 Cf. CROMBIE (1975a) above n. 2.

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material connections are matched by the use made of Pereira's De communibus..., which use matches the order of composition: dialogue, notes, treatise. There are no references to Pereira in the dialogue, but Galileo used his textbook for some of the notes for the treatise and for the treatise itself. He used it also for the Tratatio prima de mundo where he cited it for a specific argument concerning the eternity of the world (I, 22-24, 32-37; cf. Pereira XV) and for the Tractatio de dementis (I, 123-4, 138-9, 143-6,151-2; cf. Pereira III. 1, X, 10-11, 22-3). Three passages in De motu gravium offer compelling evidence that Galileo was using Pereira's textbook here. The first is that in which he adopted a theory that projectiles were kept in motion by a virtus impressa (I, 307-15, 412) in the form which Pereira (XIV. 4-5) had expounded in order to reject. The other two passages are those in which he discussed Philoponus's criticism of the Aristotelian argument for the impossibility of motion in a void and Hipparchus's theory of the acceleration of falling bodies. The former began as a fragmentary note (I, 410) which was expanded into an addition to the chapter on the question in De motu gravium (I, 284). Galileo reported the argument in a way not presented by Philoponus in his commentary on the Physics IV, but evidently conflated from two passages by Pereira (XL 10-11). Again in reporting Hipparchus's theory Galileo falsely referred to Alexander of Aphrodisias instead of to Simplicius's commentary on De caelo (comm. 86) where it is to be found, and reported it in an incomplete and distorted form which he proceeded to criticize (I, 31920). A clue is found in a fragmentary note on Hipparchus's theory (I, 411), with in another fragment (ibid.} and in a marginal note to De motu gravium (I, 318 n. 1) an explicit quotation from the chapter in which Pereira (XIV. 3) presented it in the same incomplete and distorted form as that criticized by Galileo. Further, Galileo's account of the "horizontal plane" of the Earth (I, 299-301, cf, 340, 407-8; above n. 49) is the same as that given by Clavius in his Sphaera (1581, pp. 132-2). In view of his very detailed use of Clavius for his Tractatio de caelo it is reasonable to suppose that he based his account on this textbook here also67. De motu gravium was linked then with the scholastic treatises through these common Jesuit sources, and this link we have to take into account in trying to place both in Galileo's intellectual biography. 67

Cf. for the same point with the same diagrams FRANCESCO MAUROLICO, Dialogbi de cosmographia (Venetiis, 1543), whose work was known to Clavius; A. MASOTTI, "Maurolico, Francesco (1494-1575)", Dictionary of Scientific Biography, IX (New York, 1974) 190-4; above n. 28.

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Unhappily there seems to be no firm evidence for the date when he read any of these sources. All we have are some fragile hints for Clavius. It seems likely that Galileo used figures for the dimensions of the world taken from Clavius for his letter of 1597 to Mazzoni (above n. 21). One later manusctipt (c. 1624) of the version of his Trattato della sfera (1606) published by Favaro contains a "Tabula climatum" (II, 244-5, cf. 207, 209) closely similar to that in Clavius (1581, pp. 413-4) but not found in earlier copies or in the earlier unpublished version of the Trattato (1601) in the Ambrosian Library. Although he did not mention Clavius in what remains of his lectures on the new star of 1604, where he cited a series of other authors, it seems certain that he must have known of his extensive discussion in the Sphaera of the earlier new star of 1572 (above n. 23). This was mentioned by one of Galileo's correspondents at the end of 1604 (X, 132), when Clavius himself also wrote to him about his own observations (X, 121). Evidence for the dating of De motu gravium is to say the least undecisive. The main physical issue with which it was concerned was the nature of gravity and hence the cosmological arrangement and motions of the four terrestrial elements. The geocentric cosmology made explicit in the introduction to the final version but also assumed throughout (I, 252-3, 342-5) could hardly have been written during the period of Galileo's public campaign for Copernicus opened with the Sidereus nucius (1610). He cited Copernicus's De revolutionibus once in De motu gravium (I, 326) but not in connection with the motions of the Earth. He named him also in the Tractatio de caelo (I, 43, 47-54; cf. above n. 28) explicitly to refute his opinion. These geocentric doctrines might seem to place both treatises before Galileo's Copernican declarations of 1597 to Mazzoni and Kepler, but he continued after that for whatever reason to assume the old cosmology in his lectures on the new star of 1604 and in his Trattato della sfera in 1606. He introduced in De motu gravium a critique of Aristotle, based on Plato and Archimedes, for his general failure to understand mathematics and his particular theory of gravity. This is absent from the Tractationes de mundo et de caelo. If we assume a progressive intellectual development this would place De motu gravium after the Tractationes. If all three scholastic treatises were written about the same time, and all after 1597 because of the use of Carbone for the Disputationes, this would place De motu gravium still later. Their common use of Jesuit sources might suggest composition at nearly the same time. So might their common syllogistic style of argument. This might not seem a specific resemblance because Galileo continued to combine scholastic with Archimedean methods in his later works, but the Aristotelian dynamics of De motu gravium seems to link it more

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definitely with his scholastic treatises on cosmology and natural philosophy 68. A reference in the dialogue De motu gravium (I, 379) to his reconstruction in La bilancetta of the exact method by which Archimedes assessed the proportion of gold and silver in King Hiero's crown places that and hence the treatise after this work. Then can we date La bilancetta? The story of Hiero's crown had been told by Vitruvius, but according to Galileo with a crude method unworthy of Archimedes's superior intellect. After examining Archimedes's treatises on floating bodies and the balance he had found his true method (I, 215-6, cf. 211-4). Galileo's boasted reconstruction resembles a version of Archimedes's method given in the Carmen de ponderibus et mensuris, a work on weights and measures dating from about 500 AD which is the second extant source for the story of Hiero's crown. It was published with the grammarian Priscian's works in 1516 and 1584 69. An account of the method closer to the Carmen than to Galileo was published by Giovanni Battista della Porta in the edition of his Magia naturalis of 1589 70. Like Galileo he claimed to be offering a new discovery of Archimedes's method. Galileo and Porta seem to have become acquainted only after the publication of the Sidereus nuncius, when they were put in touch by Federico Cesi and both became members of the Accademia dei Lincei (X, 252, 508, XI, 175, 345, XX, 511). Galileo referred to Priscian in his undated commentary on Tasso (IX, 130, cf. 12-16, X, 244, XIX, 627, 645). His autograph manuscript of La bilancetta is followed by an autograph table of relative weights of metals in air and in water (I, 223-8). The values given here and in the Carmen and by Porta are sufficiently different for it to be supposed that he and Porta made independent measurements. La bilancetta is not mentioned in Galileo's earliest surviving correspondence of 1588-90 which is devoted largely to Archimedes (X, 22-30). It seems to have had some circulation in manuscript before its eventual publication in a work entitled Archimede redivivo in 1644 (I, 213), but neither it nor Porta nor the Carmen were mentioned by Mazzoni in his discussion of Hiero's crown in his In universam... 68 Galileo's reference to a question "amicissimi nostri Dionigii Fontis" (I, 368) could have been written before or after his friends's death and so does not help with dating; nor in fact does the discussion in the Discorso (1612) on floating bodies of a problem similar to one in De motu gravium, for the problems were different and so the one discussion was not a correction of the other: cf. SHEA (1972) 19-20, above n. 21. 69 PRISCIANI CAESARIENSIS, Institutiones grammaticae, adiectis nuper praetermissis Libello de XII carminibus (Parrhisiis, 1516) f. 127rv and Libri omnes (Basileae, 1584) 863-4. 70 lo. BAPT. PORTA NEAPOLITANUS, Magiae naturalis libri XX, XVIII.8 (Neapoli, 1589) 285-6.

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(1597, p. 232). Another reconstruction of Archimedes's method resembling Galileo's with a description of the hydrostatic balance was published by Marino Ghetaldi in his Promotus Archimedis (Romae, 1603), writing in the preface that he had been urged to publish it by Clavius 71. But since the Carmen had been available in print throughout most of the sixteenth century all this throws no clear light on the date of La bilancetta. The date often given as 1586 is based on the sole evidence of a manuscript note added by Viviani in the margin of his life of Galileo in 1654 (XIX, 605, cf. I, 211). A further problem is presented by Le mecaniche. This exists in two versions, a shorter version of lectures dated 1594 in a manuscript discovered by Favaro72 too late to be included in the Edizione Nazionale, and the longer and much more developed version which he did include. This longer version contains a discussion (absent from the shorter version) of the motion of a body on an inclined plane which seems less developed than that found in De motu gravium. Both discussions were based on the idea that heavy bodies could be moved on a horizontal plane by any force however small. This was presented in the former work as an obvious consequence of "the constitution of nature with regard to the movements of heavy bodies" and stated as an "undoubted axiom" (II, 179-80). But in the latter Galileo thought that it "seems quite hard to believe" and set out to demonstrate it from the principle of the balance (I, 299; cf. above n. 49). He referred also to an earlier discussion of the problem (I, 296). On this rather slender evidence should we conclude that De motu gravium was written after the longer Le mecaniche? Then when was the latter written? He mentioned to Vinta in 1610 that he had in hand "tre libri delle mecaniche" (X, 352). In a short piece of uncertain date from Florence about a machine he wrote that he had formed "already a long time ago" (VIII, 572; cf. above nn, 50, 58) the concept given prominence in Le mecaniche that nature cannot be cheated by art. These remarks suggest composition well before he returned to Florence in 1610. But it appears that a demonstration in the work concerning the proportion of the force required to pull a weight on planes with different inclinations was unknown to Galileo until G. B. Baliani sent it to him on 17 June 1615 (XII, 186-8). From a much later letter by 71 See "Quomodo Archimedis argenti mixtionem deprehendit in auro" (pp. 51 sqq.); L. CAMPEDELLI, "Ghetaldi (Ghettaldi), Marino (1566 [1568?] -1626)", Diet. Set. Biog., V (1972) 381-3. 72 Cf. FAVARO, "Delia meccaniche lette in Padova 1'anno 1594 da Galileo Galilei", Memorie del R. Istituto Veneto di Scienze, Lettere ed Arti, XXVI (1899) and WISAN (1974) above n. 20, for the resemblances between Le mecaniche and De motu gravium.

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Baliani of 1 July 1639 (XVIII, 68-71) we learn that many years before Baliani had sent Galileo, from a manuscript treatise on mechanics by Francois Viete in his possession, an improvement on a solution by Pappus concerning the inclined plane, and that Galileo had replied claiming the treatise as his own. In the longer Le mecaniche the solution is introduced with a criticism of Pappus (II, 181). Again this version contains a precise definition of the concept of momenta absent from the shorter version (II, 159). Does all this place the longer Le mecaniche after Baliani's letter of 1615? Some further circumstantial evidence might support such a dating. When in 1620 Elie Diodati wrote to Galileo saying that he had never seen any work by him on mechanics, Galileo replied that this was no wonder, since his many disputes over several years had delayed the completion both of "my Mechanics and my System", ie. of the World (XIII, 48, 53). There is no copy of Le mecaniche in the Pinelli collection, where one might expect to find it if Galileo had written it at Padua before 1601, since Pinelli was interested in the subject. The titles of other treatises written at Padua describe Galileo as "matematico dello Studio di Padova" or "lettore di matematica nello Studio di Padova" (e.g. II, 207), but in the manuscript copies of Le mecaniche the author is indicated simply as "il Galileo" or as Galileo Galilei "Accademico Linceo" or just "Fiorentino". This seems to point to a later date, when he was famous, living in Florence, and a member of the Lincei. Again in Le mecaniche Galileo discussed the apparent paradox of the Archimedean screw in the same way as Guidobaldo del Monte in De cochlea, published posthumously in 1615. But how can composition after this date be squared with his remarks quoted above? But we could go on. If this various evidence displaces Le mecaniche to a date so much later than the traditional 1590s based on Vincenzo Viviani's notoriously unreliable witness, it might seem to make De motu gravium even later. We may suppose that it was written with revisions over several years. The mature style of arguing in this treatise, with its sophisticated use of Archimedes, should warn us against considering it as an unsuccessful attempt by a young mathematical lecturer at Pisa or Padua to discuss traditional questions relating to the motion of bodies. The mention of an extensive commentary on Ptolemy's Almagest, which the author claims to have just completed and to be about to publish (I, 314), confirms the impression that here we have the work of an experienced scholar. Since no such commentary is extant among Galileo's writings, can this refer to something that was to be incorporated in the Dialogo? We know from correspondence that it was in 1624 and 1625 that what was originally planned as a Dialogo del flusso e reflusso developed into a larger discussion of the

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Ptolemaic and Copernican systems (XIII, 236, 282) 72a . The eventual Dido go (1632) was linked again with both De motu gravium and the scholastic treatises on cosmology and natural philosophy through the fragmentary notes in Ms. Galileiano 46 and through their use of common Jesuit sources. Thus two of these notes (I, 416) on Aristotle refuting Plato's involvement with geometry became the celebrated assertion by Simplicio in the Dido go (VII, 229) that mathematics might be true in the abstract but not so true in matter, both citing the same example of sphaera tangit planum in puncto (cf. I, 301) 73 . Again Salviati's criticism of Aristotle's merely probable reasons for there being only three dimensions and demonstration of the same thing by mathematics (VII, 34, 38) are identical with those given in Clavius's Sphaera (1581, pp. 13-15). In a further exchange between Simplicio and Sagredo (VII, 256) we find at least an echo of the distinction made by Pereira in De communibus... (I. 16) between physics as a science based on sensory evidence and probable reasons and mathematics as a science based on intellectual evidence and necessary demonstrations, even if mathematical demonstrations were not potissimae. We find a specific citation in the expression used by Simplicio for Plato's theory of knowledge: nostrum scire est quoddam reminisci. This appears nowhere in Ficino's Latin translation of Plato, but is given by Pereira as a quotation from Plato saying "nostrum scire nihil aliud esse, quam quoddam reminisci" (III. 6). Can we find a date for De motu gravium? We know from correspondence that Galileo was writing a general treatise on motion in the years 1628-31. Cesi wrote on 9 September 1628 urging him not to waste time in answering opponents, but to carry on working to complete his writings on various subjects including the "knowledge of... the nature of all motions (la natura di tutti i moti}" (XIII, 448). Cavalieri wrote on 3 December 1630 saying that he was glad to hear that Galileo had resumed his "theorizing on motion (speculationi del moto}... seeing that with such science and mathematics coupled together it is possible to undertake theorizing about natural things" (XIV, 171). Galileo himself wrote on 29 November 1631 to Cesare Marsili to say that he was planning to publish the "first book on motion (primo libro del motoY (XIV, 312) immediately after his forthcoming Dialogo. Was this the treatise "De motu locali" to be published in the Discorsi (1638)? Its three books correspond to his description to Vinta in 1610. Parts of this treatise can be dated to the years 1602-9, and 724

Cf. CARUGO, Gli avversari di Galileo ed il loro contribute alia genesi e immediata fortuna del Dialogo..., Saggi su Galileo Galilei, IIP (Firenze, 1972) 128-207. 73 Cf. ARISTOTLE, Metaphysics, 11.2, 995al4-16, III.2, 997b34-998a6; above n. 49.

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Galileo could have resumed work on it after his many years of controversy. But it is a purely mathematical treatise and if the correspondence refers to a philosophical treatise on the nature of motion, it may refer to the De motu gravium, which is such a treatise on the causes of the natural motion of heavy bodies. To what else could it refer? Was he writing two treatises, the one to complement the other? Does the assorted evidence we have indicated justify so massive a displacement of De motu gravium from its conventional dating at Pisa or Padua to the eve of the Dido go or even later? If this seems like attempting to prove the unbelievable that is not our intention. We put the question for the evidence itself to reveal a believable answer. The answer must affect the dating also of Galileo's scholastic treatises on cosmology and natural philosophy and on logic. All are linked with each other and also, though not necessarily immediately, with the Didogo through their common use of Jesuit sources. We know that the logical Disputationes must have been written after 1597, but apart from that we have no direct evidence for dating any of the other scholastic treatises. Did they all belong to the years of philosophical studies, some time between 1597 and 1610, of which he boasted to Vinta? We can date Galileo's use of another work by Pereira, a commentary on Genesis published in 1589 which was the source of the exegetical rules for relating demonstrated science to scriptural revelation discussed in his Lett era a Madama Cristina de Lorena (1615; V, 333-4)74. Likewise he used for this letter a comment added by Clavius on the recent astronomical discoveries to his last edition of his Sphaera in 1612 (V, 328). May we then suppose that Galileo read his other scholastic sources some time during these years 1610-1616 when his various cosmological controversies had launched him firmly beyond mathematics into philosophy? His disputes obliged him to clarify his ideas of science and of nature, and his writings of that period are an evident product of such a clarification. A stylistic feature may also relate De motu gravium to this period or later. Galileo in one of the fragmentary notes in Ms. Galileiano 46 complained of people who read his writings not to see "whether what I have said is true" but only to "undermine my arguments" (I, 412). This may seem to belong to a context of controversy and it became a familiar complaint in his writings on floating bodies (1612), sunspots (1612), science and the interpretation of Scripture (1613-15), and comets (1618-23). Alternatively his assumption that the world was inhabited largely by hostile fools and knaves may simply be an enduring diagnostic symptom of 74

Cf. CROMBIE (1975a) 165, above n. 2.

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Galileo's character. Another stylistic feature relating to the Jesuits but not to the question of dating is the dialogue form used by Galileo in the Dialogo. Galileo's dialogues differ from Plato's, where Socrates's interlocutors simply raise questions and listen patiently to his answers. They are an elegant form of the scholastic disputatio, revived by the Jesuits, in which each speaker put forward a definite point of view closely argued from experience, reason and relevant authorities, and all aimed to clarify the topic and reach critical assessments of the solutions proposed. Galileo in his disputes aimed clearly to win not only the truth but also the argument. He showed himself a master of all the dialectical and topical skills of debate and persuasion7S. At the same time he continued to be haunted to the end by an apodeictic vision of certainty, however unobtainable. His scientific experience with a diversity of problems made him well aware in practice of the degrees of certainty, analysed by logicians, available in different kinds of subject-matter. Central to his treatment of cosmology to the last was the distinction such as made by St. Thomas Aquinas and discussed in the Dialogo (VII, 30, 369, 488) between possible mathematical hypotheses which saved the astronomical appearances and demonstrations through true causes. He adapted his scientific methods and his immediate expectations to the subject-matter. The on-going physical argument through all his major writings on natural philosophy aimed to dispute and reject the Aristotelian conception of physical causes and to establish in its place the truly certified conception which in the end he saw as uniformly mechanical. If we may so characterize Galileo's contribution to the promotion of a rational philosophy of science and of nature articulated by the Jesuits, against on one side scepticism and on the other Neoplatonic and Hermetic magic, the direction of his argument led him inevitably into often bitter disputes with the Jesuit Aristotelians themselves. But these should not blind us to the underlying similarity of their rational policy. Nor was Galileo in this alone among prominent natural philosophers. Mersenne, Gassendi and Descartes promoted the same sort of rational philosophy against the same sorts of opponents. "Car la nature ne peut etre trompee, ni ceder a ses droits", wrote Mersenne with evident satisfaction in opening his Les mecaniques de Galilee (1634) 76 . Together with others of similar outlook they established an 75

J. D. Moss, "Galileo's rhetorical strategies in defense of Copernicanism" in the Atti 76of the Convegno (1983). Ed. B. ROCHOT (Paris, 1966); cf. LENOBLE (1943), POPKIN (1979), CROMBIE (1971) and (1975b) above nn. 3-4, 13; and R. PINTARD, La libertinage erudit dans la pre-

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identity for natural philosophy in their time, by closing many still open questions through their insistence upon specific rational criteria for Admitting questions, as well as answers, into acceptable scientific inquiry. Galileo himself wrote no explicit critique of scepticism or magic or Neoplatonism, which he.virtually ignored except for the brief period of his Neoplatonic theological letters of 1613-15, but his sharp awareness of these different kinds of philosophy is obvious in numerous comments specifying his own. An interesting difference is that Mersenne and Gassendi were sufficiently sceptical to disbelieve that certainty was possible in the search for causes in natural science. Mersenne therefore insisted upon experimental precision. Galileo and Descartes still on this question stayed with Aristotle. This could considerably affect the relative weight given to experimental measurement as distinct from mathematical or logical demonstration in scientific inquiry. "The most subtle Galileo, easily the chief of the mathematicians of our time, and likewise a noted philosopher", Liceti wrote of him towards the end of his life in a book devoted to many questions unanswerable by Galileo's criteria, including whether or not the universe was infinite77. Galileo in 1639 acknowledged his copy with its account of opposing opinions: "I cannot stop wondering how one single human mind can store all the doctrines scattered in a thousand books by a thousand other rare minds". As for the question of infinity: "The reasons given for both sides are very acute, but in my brain neither of them reaches a neceessary conclusion". Perhaps in the end "this is one of those questions that happen to be inexplicable by human reasonings, resembling perhaps predestination, free will and other matters, where only the Holy Scriptures and the divine assertions can set us piously at rest" (XVIII, 106).

mitre moitie du XVIIe siecle (Paris, 1943); I. DAMBSKA, "Meditationes Descartes'a na tie sceptycyzmu frankuskiege XVII wieku", Kwartalnik filosoficzny, XIX (1950) 1-24 with French summary; H. COURIER, "Doute methodique ou negation methodique? ", Etudes philosophiques, IX (1954) 135-62, La pensee religieuse de Descartes (Paris, 1972); T. GREGORY, Scetticismo e empirismo: Studi su Gassendi (Bari, 1961); O. R. BLOCK, La philosophic de Gassendi (La Haye, 1971); G. RoDis-LEWis, L'oeuvre de Descartes (Paris, 1971); R. MANDROU, Des humanistes aux hommes de science XVIe et XVlle siecles (Paris, 1973); J. A. SCHUSTER, "Descartes' Mathesis universalis: 1619-1628" in Descartes: Philosophy, mathematics and physics, ed. S. GAUKROGER (Brighton, 1980); B. V. BRUNDELL, Pierre Gassendi 1592-1655: From Aristotelianism to a new natural philosophy (University of New South Wales Ph.D. dissertation, 1982). 77 Cf. CROMBIE (1969) 23, above n. 2.

Galileo Galilei, by Mario Leoni 1624 (Musee de Louvre).

11 Galileo and the Art of Rhetoric with A. Carugo Galileo's idea of rhetoric and his attitude towards it are unequivocally conveyed by the following passage from the Dialogo (1632) on the two greatest systems of the world, which carries in the margin the note: «In the natural sciences the art of rhetoric is ineffective ». He wrote: If this about which we are disputing were some point of law or of other human studies, where there is neither truth nor falsehood, we could rely a lot on sharpness of wit, on quickness in replying and on better knowledge of writers, and hope that whoever excelled in these matters would make his own reasoning appear and be judged superior. But in the natural sciences, the conclusions of which are true and necessary, and where there is no place for human judgment, one should be cautious not try to maintain something that is false. For a thousand Demosthenes and a thousand Aristotles would be left defenceless by anyone of little intelligence who has had the chance of knowing the truth (VII, 78) *. i

Despite Galileo's disparagment of rhetoric recent literary critics have claimed to have unveiled what they call « rhetorical strategies» devised by him in his battle for a new idea of science and a new philosophy of nature. Jean Dietz Moss, in her study of « Galileo's rhetorical strategies in defence of Copernicanism»2, has claimed that in his Lettera a Madama Christina di Lorena (1615) Galileo closely followed the conventions of letter writing developed by medieval rhetoricians and 1 The Roman and Arabic numbers in brackets refer by volume and page to the National Edition of Le opere di Galileo Galilei, 20 vol. (Firenze, 1890-1910). See for a full discussion of Galileo's intellectual style A. C. CROMBIE and A. CARUGO, Galileo's Arguments and Disputes on Natural Philosophy (forthcoming); also A. CARUGO and A. C. CROMBIE, The Jesuits and Galileo's ideas of science and of nature, « Annali delTIstituto e Museo di Storia della Scienza di Firenze », VIII.2 (1983) 3-67; A. C. CROMBIE, Styles of Scientific Thinking in the European Tradition (London, Gerald Duckworth, 1994). 2 Novita celesti e crisi del sapere, a cura di P. Galluzzi (Supplemento agli « Annali ...», 1983, 2), 95-103.

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adopted by the humanists, in particular the an dictamini which formulated the principles of epistolary composition with its distinctions of salutatio, captatio benevolentiae, narratio, petitio and conclusio. But Moss's own paraphrase of Galileo's letter hardly justifies the application to it of such rigid distinctions. As far as the Dialogo is concerned, she maintains that the arguments presented by Galileo «are not rigorous demonstrations in the sense of fulfilling the canons of Aristotle's Posterior Analytics. They are instead dialectical in nature, the probable type of reasoning treated in Aristotle's Topics and Rhetorica». She has also remarked that «the manner in which Galileo presents his arguments is rhetorical, in that they are intended to induce assent from his fictional and real audience ». But statements like these only show that Moss seems to be unaware of the clear distinction made by Aristotle and familiar to Galileo between dialectical and rhetorical arguments and to have vague and confused ideas about the nature of rhetorical arguments, an impression confirmed by her random discussion of scattered passages from the Dialogo. A more rigorous and systematic analysis of the rhetorical structure of the Dialogo, and a more subtle discussion of the rhetorical devices exploited by Galileo in presenting various forms of arguments, are be found in Brian Vickers's essay on « Epideictic rhetoric in Galileo's Dialogo »\ Vickers claims to be the first to have noticed that «the dominant rhetorical technique in the Dialogo is the simultaneous use of praise and blame, elevating the Copernican world-system and debasing the Ptolemaic » (p.71). In other words, the Dialogo exemplifies a brilliant application of epideictic rhetoric as described in Aristotle's Rhetoric, book I, chapter III. Moreover, according to Vickers «the epideictic mode clearly lent itself to the dialogue form»(p:73), not so much to the Platonic one, in which a priviledged and dominant speaker exposes the limitations of his partners' thinking, but rather to the Ciceronian form, in which distinct characters espouse distinct philosophical points of view and each speaker argues for his case. Hence Galileo's adoption of the rhetorical concept of persona or mask, which protected him from being identified with his characters and allowed him to give a living reality to philosophical ideas. Analyzing the topics that are praised or blamed in the Dialogo, Vickers argues that, beside the encomia to God and to the acuteness of human mind, which are part of the stan3

«Annali dell'Istituto e Museo di Storia della Scienza di Firenze», VIII.2 (1983), 69-102.

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dard epideictic repertoire, «the truly original feature of the Dialogo [is] the fact that every other instance of praise and blame concerns the new science, its heroes and enemies, and its positive contribution to knowledge »(p. 81). Despite the brilliance of Vickers's arguments and the evident care with which he has studied the Dialogo, he does not seem to have paid sufficient attention to what Galileo understood by rhetoric and to what it meant for him. A clear indication of this can be gathered from the passage of the Dialogo which we have quoted at the beginning. Rhetoric was regarded by Galileo as an art of speaking wittingly and brillantly on legal or ethical and political issues so as to persuade an audience to judge a case in one way rather than another, by means of arguments that are only apparently conclusive and that lead to conclusions that are not necessarily true and may even be false. The natural sciences or natural philosophy, on the other hand, were conceived by Galileo as a form of knowledge based on arguments not only persuasive but also logically sound, that is to say necessary demonstrations leading to true conclusions. Therefore rhetorical arguments according to Galileo were not only ineffective, but had no place in natural philosophy and ought to be avoided in any philosophical discussion. If any philosopher tried to resort to this sort of argument in a dispute on how nature is structured and how it operates, he should be exposed by those philosophers who were aiming at the knowledge of truth. The classical distinction between modes of discourse aiming at truth and at mere persuasion had been made by Plato in the Phaedrus. This became well known in Marsilio Ficino's Latin version composed at the end of the 15th century and was echoed by Galileo as will appear later. Socrates in his analysis of true love starts by trying «to discern the nature of soul» (245 C). He characterizes the essential human soul as «the soul that has beheld truth» and «the soul of the philosopher alone » as that which could rise on wings so that it « ever approaches to the full vision » of divine perfection (249 B-C). Thus «those who live a life of philosophy » did honour to the music of the eldest of the Muses, Calliope and Urania, «whose theme is the heavens and the story of gods and men, and whose song is the noblest of them all» (259 D). Then what was good discourse? Must it « presuppose a knowledge in the mind of the speaker of the truth about his subject? » Must the intending orator know, for example, what is truly just, or good or noble, or only « what will be thought so, since it is on the latter, not the former, that persuasion depends» (259 E - 260 A)?

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Supposing, Socrates continues, that neither he nor Phaedrus knew what a horse was, he might persuade his companion to buy a donkey by calling it a horse. It was the same «when a master of oratory, who is ignorant of good and evil, employs his power of persuasion on a community as ignorant as himself, not by extolling a miserable donkey as being really a horse, but by extolling evil as being really good, and when by studying the beliefs of the masses he persuades them to do evil instead of good» (260 C). The «art of rhetoric» was «a kind of influencing of the mind by means of words, not only in courts of law and other public gatherings, but also in private »; and anyone possessing the art « can make the same thing appear to the same people now just, now unjust, at will», and likewise «now good, and now the reverse of good». The trick was «to make out everything to be like everything else », but then « anyone who intends to mislead another, without being mislead himself, must discern precisely the degree of similarity and dissimilarity between this and that». How can he do this «if he does not know the truth about a given thing» (260 C - 2A)? Socrates contrasted rhetoric with dialectic, the method of inquiry for the truth by means of correct question and answer using the taxonomic procedures first of collection, by which « we bring a dispersed plurality under a single form» in order to define it, and then of division, by which in reverse « we are enabled to divide into forms, following the objective articulation ». Thus by dialectic we could « discern an objective unity and plurality» (265 D - 6B) and discover the truth. But rhetoric aimed not at truth but at mere persuasion. According to the manuals of rhetoric, after opening a speech with a preamble, « next comes exposition accompanied by direct evidence; thirdly indirect evidence; fourthly probabilities »; then in addition «proof and supplementary proof», followed by «refutation and supplementary refutation both for prosecution and defence»; with «covert allusion and indirect compliment and ... indirect censure » and other tricks of those like «Gorgias, who realized that probability deserves more respect than truth» (266 D - 7 A). But it was not enough simply to have picked up the antecedents of the art, as if people who had done that with medicine or dramatic poetry or music knew anything about the actual practice of those arts; for «it is because they are ignorant of dialectic that they are incapable of defining rhetoric » (269 B) or of practising or teaching it. «The true rhetorician, the real master of persuasion» aimed at that and nothing else, but the art shared certain common methods

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with scientific argument aiming to find the truth. « All the great arts need supplementing by a study of nature» (269 D - E). Socrates likened the method of rhetoric to that of medicine. Each, in order to reach its goal, had to discover the true nature of its object. Rhetoric had to grasp the nature of the soul in order to see how it was persuasible; medicine had to grasp the nature of the body in order to see how it was healthy or curable: «In both cases you must analyze a nature ... if you are to proceed scientifically, not merely by practice and routine, to impart health and strength to the body by prescribing remedies and diet, or by proper discourses and training to give to the soul the desired belief and virtue ». This was the method attributed to Hippocrates, «but we must no,t just rely on the authority of Hippocrates, but we must see also if our reason agrees with him on examination». At the end of his analysis the scientific rhetorician «will classify the types of discourse and the types of soul, and the various ways in which souls are affected, explaining the reasons in each case: suggesting the types of speech appropriate to each type of soul, and what kind of speech can be relied upon to create belief in one soul and disbelief in another, and why ». For « a certain type of hearer will be easy to persuade, by a certain type of speech, to take such and such action, for such and such reason, while another type will be hard to persuade. All this the orator must fully grasp, and next he must watch it actually taking place in men's conduct». When the student of rhetoric, having grasped the theory, could place any individual person in this classification of characters, and could know how to seize the occasion for the appropriate tricks, «then and not till then he has well and truly achieved the art». There was « absolutely no need for the budding orator to concern himself with the truth about what is just or good conduct» or «who are just and good men ... In the law courts nobody cares about the truth in these matters, but only about persuasion, and that is concerned with what seems most likely» for the purpose. The would-be master of persuasion must then suppress or substitute facts according to need and say «goodbye to the truth forever». Then he will be «equipped with the art complete» (269 D - 73 A). If « the multitude get their notion of probability as the result of a likeness to truth, ... these likenesses can always be best discovered by someone who knows the truth » (273 D). Socrates rebuked Phaedrus for suggesting that « apparently it makes a difference who the speaker is, and what country he comes from; you do not ask

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simply whether what he says is true or false » (275 C). The «art of dialectic » transcended rhetoric because its aim was truth, and when the dialectician wants to persuade he «selects a soul of the right type, and in it he plants and sows his words founded on knowledge, words that can defend both themselves and him who planted them, words that instead of remaining barren contain a seed from which new words grow up in new characters, giving the seed immortality, and its possessor the greatest blessedness attainable by man». The conditions were that « first you must know the truth about the subject that you speak or write about; ... secondly you must have a corresponding discernment of the nature of the soul» being instructed and «arrange your discourse accordingly». Then you will become competent «as a scientific practitioner of speech, whether you propose to expound or to persuade » (276 E / 7 C). Someone who has thus « done his work with a knowledge of the truth, and can defend his statements when challenged», could fittingly be called a «philosopher ». But a composer of merely literary works «on whose phrases he spends hours, twisting them this way and that, pasting them together and pulling them apart, will rightly I suggest be called a poet or speech writer or law writer» (278 C - E). Galileo's assessment of the scope and limits of rhetoric was not particularly new and original, for similar ideas were commonly shared by any learned person of his time. A clear and detailed picture of what was generally understood by rhetoric in the learned circles in which Galileo moved can be found in an Italian paraphrase of Aristotle's Rhetoric produced in 1565 by Alessandro Piccolomini, a philosopher whose works were familiar to Galileo and with whom he had many points in common. Piccolomini had acquired a great reputation as a philosopher when, still very young, he published in 1547 an enlightening commentary in Latin to Aristotle's Mechanical Questions, together with a learned treatise also in Latin on the question of what degree of certainty can be achieved in the mathematical sciences. Both these works were very influencial in promoting among philosophers new debates on the principles of mechanics and on the nature of mathematics and its place among other speculative disciplines such as natural philosophy and theology. Subsequently Piccolomini produced a series of works covering the whole range of philosophical disciplines. They were written in Italian and aimed to show that the vernacular was as powerful and as flexible as Latin in conveying philosophical and scientific ideas and arguments. Copies of some of Piccolomini's works

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were owned by Galileo, whose style of writing in Italian show sometimes a striking resemblance to Piccolomini's. For instance a phrase such as «sensate esperienze e certe dimostrazioni» which is recurrent in Galileo's writings was coined by Piccolomini4. After publishing treatises in Italian on logic, natural philosophy and cosmology as well as on ethics and politics Piccolomini produced a series of three volumes giving an extensive and detailed commentary or «paraphrase » on Aristotle's Rhetoric. In the preface to the first volume, published with the title Copiosissima pamfrasi nel primo libro delta Retorica d'Aristotele (Venice 1565), Piccolomini praised Aristotle's style or method of exposition for being straightforward and free from rhetorical embellishments, and preferred it to Plato's poetic style which veiled the truth with obscure fables: If we consider carefully the reason why of the two greatest luminaries of learning, Plato and Aristotle, the latter has for so many centuries predominated and is still predominating in the schools of sciences, we shall find that undoubtedly this is so not because he is superior in learning: in fact, although there have been and still are many who would not agree to put Plato before Aristotle as far as sciences are concerned, nevertheless no learned man has yet considered Plato inferior in learning. But we shall clearly see that the true reason for Aristotle's superiority is none other than the method, that is the way of presentation that he has followed in his books: he has presented and expounded the matters of his treatises in a clear, neat, proper and ordered manner, free from superfluities, without enveloping them in obscure fables or veiling them with poetical imagery (senza velo di poetica imitatione) and, lastly, without masking them with rhetorical ornaments (senza maschera di retorico omamento).

Aristotle's unrhetorical style of writing was regarded by Piccolomini as the most suitable for the study of nature. He warned natural philosophers against using rhetorical trappings which would unnecessarily increase the natural difficulty of discovering what is hidden in nature: « Nature has unfortunately concealed and hidden its things more deeply than man would wish or need: therefore > for learned men, who struggle to discover and explain them, their intrinsic and natural difficulty should be enough, without adding further dif4 ALESSANDRO PICCOLOMINI, La sfera del mondo (Venezia 1566), p. 4: « E mancando le frequent! sensate esperientie tnanca ancora la certezza delle conclusion!»; p. 246: «La certezza ... delle loro dimostrationi puo supplire in gran parte a quanto in prima, per Pimperfettione che portano le cose sensate, si fusse mancato ». A. FAVARO, Miscellanea Galileiana inedita, xii: La libreria di Galileo, « Memorie del R. Istituto Veneto di Scienze, Lettere e Arti», XXII (1887), 982-1034, lists three of Piccolomini's works (nos. 384-386) including La sfera del mondo.

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ficulty by resorting to poetical and rhetorical complications (con poetici e retorici involgimenti)» (p. 2). Piccolomini's warning against the use of rhetoric in natural philosophy was clearly echoed in the passage from Galileo's Dialogo which we quoted at the beginning. The same note was struck by Galileo over and over again in his writings, as we shall see later. For the time being we stay with Piccolomini and we follow his competent guidance in order to get a proper understanding of Aristotelian rhetoric. To justify why he thought it necessary to produce and publish his own account of Aristotle's rhetoric, Piccolomini denounced the inadequacy of existing translations of and commentaries on it. He argued that previous translators had corrupted and made a mess of the Aristotelian text either by producing an unintelligible word for word translation or by giving a misleading interpretation of their own: When I examined those who have translated these books into another language to see if I could find in their translations anything that could throw light on some passage ... I found that they had really not translated, but rather corrupted the whole text, since most of the passages had been either painted (depinti) or misunderstood (contro il vero sentimento intesi}. By « painted » I mean those passages which the translators, being aware that they do not understand them, transpose from one language to the other by using the same number of words in the same order. As a result, since different languages require different arrangements of words and different forms of locution, those passages which are translated so closely to the original are rendered unintelligible, besides being misunderstood by the translators themselves. This is the way in which the translators paint the passages which they are aware that they do not understand. On the other hand, as far as those passages are concerned which they presume that they understand though they do not, they depart from the author's true meaning (p. 3).

Faced with the task of expounding Aristotle's Rhetoric, Piccolomini soon realized that he had to adopt a different method of exposition from the one that he had used in his previous works, in which he had given accounts of Aristotle's treatises on logic, natural philosophy, ethics and mechanics, and of Ptolemy's work on astronomy. In those works be had faithfully followed the opinions of the authors so far as the substance of the matters treated was concerned, whereas for the method he had adopted a freer style, « writing as it pleased me, by expanding or abridging the original, by adding things or leaving things out, by explaining and clarifying, and by doing anything that could show more clearly the author's meaning and mind and make the matters easier »(pp. 7-8).

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But in expounding Aristotle's Rhetoric it was necessary not only «to show clearly, to penetrate, to expand and to disentangle its substance and its pith and marrow», but also «to explain step by step Aristotle's meaning and mind». To do this Piccolomini decided that the best method of exposition was to paraphrase, since this was «most suited to express the auther's mind by sometimes freely expanding the original in order to unveil and show the substance of his ideas without ever departing from him» (p. 8). The kind of paraphrase adopted by Piccolomini was one that allowed him to make long digressions in order to strengthen and clarify Aristotle's opinions by adding arguments and examples of his own without abandoning his footsteps. By doing this Piccolomini was explicitly following the example of the ancient commentator Themistius and particularly of his commentary on Aristotle's De anima. Rhetoric, says Piccolomini at the beginning of his paraphrase closely following Aristotle's text, bears great resemblance and affinity to dialectic in dealing with subjects that are not confined to any particular science, and in using «propositions, terms, concepts and arguments that are adapted to the common knowledge of men rather than belonging to any particular science or to the deep and precise knowledge of a specialist» (p. 13). Knowledge of rhetoric as well as of dialectic is so easily accessible to everyone that anyone can understand and practise these arts without difficulty. «Rhetoric and dialectic are different from particular sciences in that, whereas the latter treat their subject-matters with a precise scientific method which is proper to each of them, rhetoric and dialectic instead form their propositions and arguments in a way that is adapted to the common understanding of men». In fact they use propositions that are not scientific and precise, but apparently true and probable, and by means of such propositions they form probable arguments and proofs, so that their way of proceeding is entirely proportionate and suited to the judgment and understanding of men most of whom are unskilled »(p. 14). In rhetoric as well as in dialectic «propositions, premises, causes and arguments are derived not from specific sciences and arts, but from common life, and are adapted, formed and used in such a way that anyone can understand them who is not mentally blind and deprived of almost all the senses» (p. 15). But whereas dialectic concerns equally all sorts of subject-matters, «rhetoric deals more usually with civil affairs» (ibid.}.

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The strength of rhetoric consists in the ability of an eloquent public speaker to persuade his listeners by means of arguments that have only the appearance of demonstration, such as that which is called enthymeme, which is an imperfect form of syllogism lacking one of the premises. The enthymeme is different from the syllogism in that, whereas in the syllogism both the premises are explicitly formulated and arranged in their proper order, in the enthymeme one of the premises is always omitted, and it is left to the listener himself to supply it in his own mind. This is so because «the speaker does not have to talk in a learned manner nor for the purpose of teaching, as he must in scientific disputations, but he can speak in a popular manner suited to his listeners and therefore very similar to the common way of speaking that is normally used in the activities of everyday life. As a consequence, he does not need to lay out and arrange terms, propositions and arguments according to the schemes and rules of deduction, as one must do when treating or discussing some scientific topic the purpose of which is not just to persuade, but to find truth itself» (p. 33). Rhetoric or the art of speaking (arte del dire, as Piccolomini called it from the Latin expression ars dicendi which was often used to translate the title of Aristotle's treatise) deals not just with what is «truly probable and persuasive », but also with what is only apparently so. And it requires knowledge not only of the true enthymeme, but also of the apparent one. From this point of view rhetoric is again similar to dialectic which requires knowledge not only of the true syllogism, but also of the syllogism that is not true but has only the appearence of being so. But from another point of view there is a fundamental difference between rhetoric and dialectic which derives ultimately from their different aims, dialectic aiming at gaining the truth, rhetoric at gaining the listener's approval. Though the dialectician must know the apparent as well as the false syllogism besides the true syllogism, yet he knows it not for the purpose of using it deliberately, but in order to be on his guard against being deceived by it and to be able to expose and demolish it if it is used against him. Someone who uses a false syllogism deliberately must be regarded as a sophist rather than a dialectician, that is as someone who uses false and deceitful arguments. But in the art of speaking things are different: the rhetorician or orator does not aim to win the argument in a dispute by using probable arguments in order to get as near as he can to the truth, but he aims to win the audience over by any possible means. Therefore whether he achieves this result by means of a true enthymeme and of a

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truly probable or apparently true proof, or by means of an only apparently probable argument, nevertheless he is still essentially an orator or a rhetorician, and is still called by that name (p. 41).

Piccolomini did not agree with other commentators who believed that the difference between a rhetorician and a dialectician in the use of apparent and fallacious arguments was only a difference of names. He maintained that when a dialectician uses apparent arguments, he only changes his name and is called a sophist, while nevertheless remaining truly a dialectician, whereas a rhetorician does not change his name because he uses such arguments. Piccolomini argued instead that «their difference lies in the thing itself: the deliberate use of fallacious syllogisms is forbidden to a dialectician, whereas it is allowed to a rhetorician for reasons based on the different aims of these two arts» (p. 42): for the dialectician tries to get to the truth, whereas the rhetorician tries to persuade an audience. The practice of the art of speaking required three things: a speaker, an audience and the cause for which one speaks. Correspondingly there are three ways of inducing belief and persuasion: one is based on the good opinion that the audience has of the speaker's behaviour; the second consists in making the audience favourablely disposed towards one's cause; and the third consists in being able to argue and to show that one's cause is reasonable. In order to master these three ways of persuading one must know three things: first, one must be capable of arguing with good reason and of exploiting the strength of syllogisms; secondly, one must know «the qualities and conditions of virtues and good behaviour so that one's speech may produce a good opinion of one self »; and finally, one must have «a good knowledge of all human feelings», that is one must know what they are, how and by what they are aroused, and what effect they have. Knowledge of the various forms of reasoning and argument depends on dialectic which deals with the nature of the syllogism and therefore helps to strengthen any sort of reasoning and argument. The other two kinds of knowledge, one relating to the behaviour and virtues of man and the other to the motion of the passions, derive their strength from the moral and political disciplines: it belongs indeed to the moral and civil philosopher to know what sort of actions depend on human will and produce an inclination either to vices or to virtues, which entail either praise or blame and induce people to have a good or bad

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opinion of us. As for the feelings, though it belongs to the natural philosopher to consider in what part of the soul they are placed; nevertheless, since we are influenced by our feelings in taking a good or bad decision in our actions, knowledge of how they are aroused and of what their effects are belongs to the moral or political disciplines. Piccolomini defined the art of rhetoric as «a branch or shoot of dialectic and of moral or political philosophy» and separated it from natural philosophy. He argued that whereas the natural philosopher studies the feelings from the point of view of the subject in which they are placed, which is the appetite sensitive or physical desire, a faculty of the soul, the rhetorician instead considers them as the stuff of which our virtues and vices are made and as the principles of most human actions. From this point of view they are the concern rather of the civil or political philosopher than of the natural philosopher. Therefore civil and political actions are the subject-matter proper to rhetoric. From what has been said so far we can draw the conclusion that Piccolomini's account of the Aristotelian rhetoric or art of speaking eloquently stresses its distinction from a speculative discipline such as natural philosophy and its close connection with a practical discipline such as political or moral philosophy. Rhetoric has nothing to do with knowledge of nature and with the acquisition of truth, but its main aim is to influence human actions. Rhetorical arguments are entirely different from scientific arguments: they are based on reasonings that are only apparently conclusive and lead to conclusions that may be false, whereas scientific arguments are based on necessary demonstrations leading to true conclusions. A rhetorical speech is addressed generally to an unlearned audience, who can easily be persuaded to take one course of action rather than another by an eloquent speaker who knows how to stir their feelings and passions. But a scientific argument can be followed and understood only by a learned person who is trained in the techniques of necessary demonstrations. It was to this idea of rhetoric so competently described by Piccolomini that Galileo referred in his arguments and disputations every time he wanted to define as clearly and as precisely as possible what he thought natural philosophy was about, that is its proper object, its method and its aim, in order to expose his opponent as incompetent or deceitful in using rhetorical arguments to support a false picture of nature. Galileo's familiarity with and high esteem of

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Aristotle's Rhetoric is confirmed by one of his earliest biographers, Niccolo Gherardini who, writing in 1654, pointed out that «it is far from truth that he ... did not think very highly ... of Aristotle, as some of those who profess to be his followers foolishly say ... Among Aristotle's works he praised above all the Rhetoric and the Ethics, saying that he had written beautifully on this art» (XIX. 645). Among the notes and drafts that Galileo jotted down in 1612 while he was engaged in the controversy on the cause of the floating of bodies, there is a passage in which he sets nature's operation in opposition to human actions. Nature, argued Galileo, follows necessary laws and is not influenced by the sort of probable reasons that form the rhetorical arguments by which some tried to persuade other men to follow their deliberations and opinions: Since nature does not change its operations in the least as a result of men's consultations, what is the point of arguing so fiercely between ourselves in order to win the argument for one of our opinions: in fact our influence on nature's deliberations is no greater than the effect that the disputes and controversies between the members of the Venetian council of nine magistrates have on the resolutions of the Emperor of China. Nature's deliberations are good, univocal and perhaps necessary, so that our opinions and advice have no place in them; nor do probable reasons: hence whatever argument we produce about them is either good and true, or bad and false. If it is bad and false, we must laugh at it and demolish it, but we should not hate whoever has produced it. If it is good and true, the hatred against whoever has put it forward is impious, perfidious and sacriligious. It is nonsense to say that truth is hidden so well that it is difficult to distinguish it from lies: it remains well hidden for as long as nothing but false opinions are produced, leaving large room for probability; but as soon as truth comes forward, its light shines as brightly as the Sun's and dispels the darkness of falsehood (IV, 24).

From this contraposition between nature's operations and man's deliberations, between the necessary laws of nature and the contingent laws of men, between demonstrative arguments leading to true consequences and fallacious arguments which, though persuasive and apparently convincing, entail false consequences, Galileo derived the idea that rhetoric has no place in discussions on natural philosophy. This opinion, which he shared with such authoritative philosophers of the time as Piccolomini, was expressed by Galileo with strength and conviction over and over again in many different writings, especially in the Dialogo where three interlocutors respectively voicing Aristotle's opinions and reasonings (Simplicio), Galileo's arguments

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and ideas (Salviati) and an amateur's observations (Sagredo), gather together for the purpose of « arguing », as the full title reads, « about the two greatest systems of the world, the Ptolemaic and the Copernican, by producing philosophical and natural reasons for the one and for the other». At the beginning of the Dialogo, after Simplicio has produced Aristotle's argument to prove that the world is perfect from the fact that it has only three dimensions and that three is a perfect number, Salviati exposes the fallacy of this apparent syllogism which turns out to be no more than a rhetorical trick: I do not feel bound by all these reasonings to grant any more than that what has a beginning, a middle and an end can and must be called perfect: but I cannot grant by any reason that, because beginning, middle and end are three, the number three is perfect and has the power of conferring perfection on those things that have such a number. I can neither understand nor believe, for instance, that for legs the number three is more perfect than the number four or two; nor do I think that the number four is an imperfection in the elements, and that they would be more perfect if they were three. It would have been better, therefore, if Aristotle had left such plaisanteries to the rhetoricians and had proved his point by a necessary demonstration, since this is what one has to do in the demonstrative sciences (VII, 35).

Again Galileo warns against mixing rhetoric with science and against entangling rigorous demonstrations with rhetorical embellishments in the second Day of the Dialogo, during a discussion of some of the traditional objections to the Copernican system of the world. Simplicio relates an argument put forward by an Aristotelian philosopher, Scipione Chiaramonti, in his book De tribus novis stellis (1628): «the Copernican hypothesis would bring a great confusion and darkness into the system of the world» by placing the Earth, which is «the dump of all corruptible matters», among the « uncorruptible celestial bodies», which are regarded as «noble» and «pure» even by Copernicus, who states that they are arranged in the best order and removes from them any changeable property. «What better arrangement, and more suitable to nature and to the Divine architect himself, than to separate the pure from the impure, the mortal from the immortal, as they do in the other schools, where they teach that those impure and perishable matters are enclosed within the narrow bounds of the concave surface of the sphere of the Moon, above which the celestial things rise in an unin-

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terrupted series» (VII, 292). Salviati agrees that the Copernican system brings disruption into the Aristotelian world, but he points out that what is being discussed is «the true and real world». He goes on then to expose the fallacy of Chiaramonti's argument: When this author, following Aristotle, derives the essential difference between the Earth and the celestial bodies from the incorruptibility of the latter and the corruptibility of the former, and then from this difference he pretends to draw the conclusion that motion must belong to the Sun and the fixed stars and immobility to the Earth, he is falling into a paralogism by supposing that which is in dispute. For Aristotle derives the incorruptibility of the celestial bodies from their motion, whereas it is disputed whether motion belongs to them or to the Earth. But we have already talked more than enough about the vanity of these rhetorical illations. Besides, is there anything sillier than to say that the Earth and the elements are separated from the celestial spheres and relegated and confined to the sphere of the Moon? Is not the sphere of the Moon one of the celestial spheres and, according to their opinion, placed in the middle of all the other spheres? This a new way indeed of separating the pure from the impure and the healthy from the sick by providing room for the infected right in the heart of the city! I tought that the lazaret should be removed as far away from it as possible. Copernicus admires the arrangement of the parts of the world because God placed the great lamp, which was to illuminate the whole of his temple with the greatest brightness, right in the middle of it, and not on one side (VII, 292-293).

Salviati rounds off his tirade with the usual attack on the improper use of rhetoric in scientific arguments: « But, please, let us not entwine the firm foundations of demonstrations with these rhetorical florid ornaments, and let us leave them to rhetoricians or rather to poets, who have been able to extol and praise worthless, and sometimes even wicked, things by means of their pleasantries » (VII, 293). The identification of rhetorical arguments with fallacies and paralogisms which have only the appearance of demonstrations had been strongly stressed by Piccolomini, and was reiterated by Galileo, who exploited it in the many disputes in which he was involved by denouncing his opponents as being more rhetoricians than philosophers. In a draft containing a reply to objections raised against his Discorso on floating bodies by Aristotelian philosophers such as Cristoforo delle Colombe, Galileo stigmatized him for behaving more like a rhetorician than a philosopher, and for using rhetorical tricks to win popular applause:

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My opponents, moved by those feelings towards me that they clearly show in their writings, try any trick that could gain them popular applause or at least could keep the crowd undecided. One of such tricks is that of shouting frequently in to their ears, pointing out the apparent strangeness of conclusions which are simple and true but which are removed from the commonly accepted opinions of those who have the reputation of being learned. And they do so in order that their listeners will keep to their old ideas and will not bother to listen to any of the contrary arguments. Another trick, which is amazingly exploited by Signer Colombo, is that of answering all the arguments produced by his opponent, even those that are insoluble. I said «answering», though neither has he in the least understood those arguments, nor is there anyone who could understand his answer, which are not even understood by him. I think that he has learned at a good school of rhetoricians how effective it is, in order to gain general approval, to speak a lot and with boldness, so that the simple reader remains confused and undecided whether to give or to refuse his assent to that which he thinks he does not understand because of his own limitations (IV, 445). Galileo's concluding remark shows the usual mixture of irony and complacency with which he scores another victory on one of his opponents: I cannot deny that I have taken particular pleasure in seeng with what skill Signer Colombo finds answers where there are none, forms arguments from meaningless ideas and produces doctrines which he has never seen, let alone studied. And he does all this with subtle smartness in order to gain from cunning the profit that he cannot hope to obtain from reasoning (IV, 445). Galileo's disparaging comments on the use of rhetorical arguments in scientific discussions were tactical moves within a wider strategy aiming at defining with clarity and precision the scope and the methods of natural philosophy as distinct from other intellectual activities such as historiography and poetry as well as rhetoric. The purpose of rhetoric was to choose the most effective words and to construct the most apparently persuasive, though often fallacious, arguments in order to influence the decision and judgment of the unlearned crowd. The aim of philosophy, on the other hand, was to read the book of nature, and this task required men of great intellectual skill. The proposition that philosophy is the proper nourishment for men of great intellectual power and is what separates them from

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common people was vigorously asserted by Galileo right at the outset of the Dialogo, in the dedicatory epistle addressed to the Grand Duke of Tuscany. He argued that the book of nature was made by an omnipotent Craftsman and that those parts of nature are more noble and worth studying that reveal his craftsmanship to a higher degree. The most noble of all is the system of the world, and accordingly the investigation of this subject is reserved for those who are endowed with the greatest mental powers: The difference between men and animals, however great, can reasonably be said to be very similar to that between men themselves ... Such differences depend on the different powers of their minds, and I regard this as amounting to being or not to being a philosopher: for philosophy, as a nourishment suited to those who can be nourished by it, separates them from the common people to a higler or lower degree according to the variety of such nourishment. Those who look higher are separated by a greater difference; and to look at the great book of nature, which is the proper object of philosophy, is a way of raising one's eyes: though everything that can be read in such a book is extremely well proportioned, since it has been made by an omnipotent Craftsman, nevertheless that part is better constructed and more worthy in which we can see more clearly his work and craftsmanship. The system of the world can be ranked, in my opinion, among the highest natural things that can be apprehended by our mind: since as a universal container it surpasses everything else in size, as the rule and support of all things it must also surpass everything in nobility. Therefore, if ever there was a man who surpassed everybody else in intellectual ability, Ptolemy and Copernicus were such men, for they raised their eyes so high as to be able to read the book of nature and to philosophize about the system of the world (VII, 27).

If then natural philosophy as a form of intellectual knowledge for which only a few speculative minds are suited was to be kept separated from rhetoric which is a kind of pratical knowledge accessible to common people of lower intellectual capability, likewise, since it is based on sense experience and on necessary demonstrations, it must be clearly distinguished also from historical knowledge which is based on recollection and on authority. At the beginning of the second Day of the Dialogo Simplicio asks with dismay: « But if we abandon Aristotle, who is going to be our guide in philosophy? Name some author, please!» (VII, 138). Salviati replies: «We need to be escorted in unknown and wild countries, but in open and clear places only the blind need a guide. Those who are blind would better stay at home, but those who have

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eyes in their face and in their mind must use them as their guide ». But Salviati's rejection of Aristotle's guidance is immediately qualified as a refusal to subscribe to Aristotle's statements, not as a refusal to understand his arguments: I do not say that we should not listen to Aristotle; on the contrary, I approve of reading and studying him carefully, and I blame only those who let themselves become enslaved to him so that they blindly subscribe to every statement that he has made and, without looking for other reasons, take it for granted and regard it as a decree that cannot be violated. This is an abuse which entails another extremely dangerous consequence, that is that others give up any effort to try to understand the strength of his demonstrations (ibid.).

Those who rely on Aristotle's authority and quote Aristotelian texts in the course of philosophical disputations should be called rather historians than philosophers, since they replaced arguments with compilations of text: What is more shameful than to see, during public disputes about conclusions that can be demonstrated, someone coming in with a text written often for another purpose to shut his opponent's mouth with it? But if you want to carry on with this way of studying, you should give up the name of philosophers and call yourselves historians or doctors of memory (VII, 139).

Galileo took care to define as clearly as possible the scope of natural philosophy by separating it not only from rhetoric and history, but also from poetry. Natural philosophy aims at reaching true conclusions about the real world by means of necessary arguments based on mathematical demonstrations; poetry, instead, aims at creating a fictional world by imitating the style of celebrated authors. This point is eloquently illustrated by Galileo in a famous passage in // Saggiatore (1623) (chapter 6) which contains the powerful image of the book of nature written in mathematical language. This passage is usually misunderstood as a declaration of philosophical allegiance to Platonic ideas. A more appropriate understanding of it can be obtained if it is interpreted in the light of Galileo's constant efforts to give a precise characterization of natural philosophy: I think I perceive in Sarsi the strong belief that in philosophy it is necessary to rely on the opinions of some famous author, so that our mind would remain completely sterile and infertile if it were not married to someone else's reasoning. And perhaps he thinks that philosophy is a book produced by a man's imagination, such as the Iliad and Orlando Furioso, books in

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which the least important thing is that what is written is true. Signer Sarsi, this is not how the things stand. Philosophy is written in this great book which stands always open in front of our eyes (I mean the universe), but it cannot be understood unless one first learns the language and the characters in which it is written. It is written in mathematical language and the characters are triangles, circles and other geometrical figures, without which it is impossible for man to understand a single word of it (VI, 232).

As a natural philosopher Galileo would not resort to the kind of rhetorical arguments which he was so keen to expose in his opponents. Similarly he would neither rely on quotations from authorities nor let his imagination create a fictional picture of the world like those concocted from various sources by such Renaissance philosophers as Ficino, Cardano, Telesio and Bruno, all of whom Galileo ignored or at least claimed that he had never read. « What has been written by Cardano and Telesio, I have not seen » he declared in // Saggiatore (chap. 9), rejecting Sarsi's insinuation that « Galileo seemed to have derived something relating to the comets from the sterile and barren philosophy of Cardano and Telesio » (VI, 236, 118). But as a natural philosopher Galileo was also constantly engaged in disputes on issues raised by his published works, and in order to fight successfully with his opponents he had to learn the art of arguing. He could find little help in rhetorical tricks, but had to turn to the more subtle techniques of arguing developed by Aristotle in the Posterior Analytics, the Topics and the Sophistical Refutations. The theory of scientific demonstration contained in the Posterior Analytics was closely studied by Galileo in a series of still unpublished logical disputations (preserved among the MSS of the Galilean Collection at the National Library in Florence, with the shelfmark MS Gal. 27) on the nature of principles of scientific knowledge and on the structure of scientific demonstrations, that is demonstrations that lead to true conclusions by means of necessary arguments'.As for the Topics and the Sophistical Refutations, there is no evidence that Galileo devoted to them the same attention as he paid to the Posterior Analytics. Nevertheless many of his works, particularly II Saggiatore and the Dialogo, show him as a skilful practitioner of the art of developing the kind of dialectical and sophistical arguments described in these two Aristotelian treatises. 5

See references in note 1. above; also A. C. CROMBIE, « Sources of Galileo's early natural philosophy », in Reason, Experiment and Mysticism in the Scientific Revolution, ed. M. L. Righini Bonelli and W. R. Shea (New York, Science History Publications, 1975), 157-175, 303-5 : ch. 9 above.

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The Topics treats forms of reasoning which, while syllogistically correct, fall short of the conditions of scientific accuracy. The purpose of the Topics is «to discover a method by which we shall be able to argue from probable opinions about any subject or problem presented to us, and shall ourselves, when sustaining a dispute, avoid saying anything self-contradictory» (methodum invenire per quam poterimus syllogizare de omni proposito problemate ex probabilibus, et ipsi disputationem sustinentes nihil dicamus repugnans)6. In other words, it has the purpose of making the two participants, the «questioner» and the «answerer», able to sustain their parts in a dialectical discussion. The subject of the Topics was described by Aristotle as «the dialectical syllogism based on premises that are merely probable» (dialecticus syllogismus est qui ex probabilibus est collectus] and was contrasted with the demonstrative or scientific syllogism, the subject of the Posterior Analytics, which is based on premises that are true and immediate (demonstratio est quando ex veris et primis syllogismus erit}. In the Sophistical Refutations Aristotle deals with the sophistical syllogism, which is based on premises that seem to be probable, but are not really so (litigiosus est syllogismus ex us, quae videntur probabilia, non sunt autem}. A knowledge of this way of arguing was part of the necessary equipment of a philosopher, as was pointed out by Piccolomini, not in order that he might himself make use of it, but that he might avoid it and prevent being trapped in sophistical arguments used by his opponents. Galileo followed Piccolomini's advice and learned the techniques of the dialectical and sophistical syllogisms so that he could expose any fallacy in the arguments produced by his opponents. Throughout the Dialogo Galileo does not miss any chance of showing off his mastery of the art of arguing and disputing by exposing fallacies and paralogisms in most of the arguments put forward by Aristotelians against the motion of the Earth. After arguing that, whether the Earth moves or stands still, the shots of a piece of artillery would not show any observable variation, Salviati warns Simplicio «to be cautious in acknowledging as true many experiences produced by those who never made them, but insistently claim that they are exactly as they should be in order to support their case» (VII, 208). «The simple truth», adds Salviati, «is 6 This is the old mediaeval Latin translation of Aristotle which was still largely used in the 16th century: see for example ARISTOTELIS STAGIRITI Opera omnia, i (Lugduni, 1580), 390-1, Topicorum libri, i, c. 1 on demonstratio, syllogismus, dialectus, syllogismus litigiosus and paralogismus.

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that the effects of these shots must be exactly the same whether the terrestrial globe moves or is at rest. The same will be true of all the other experiments that have been or can be produced, which at first sight appear to be true in so far as the old idea of the immobility of the Earth keeps us caught among equivocations » (VII, 209). Salviati's argument is further supported by Sagredo who joins forces to unmask the fallacy of the traditional argument: «I understand very well that whoever will imprint in his imagination this idea of all terrestrial things sharing the daily rotation as something that belongs to them by nature, in the same way as in the old idea they thought that it belonged to them to be at rest around the centre, will discern without difficulty the fallacy and equivocation which made the argument produced for the immobility seem conclusive» (ibid.). For all his admiration for Aristotle's skill in arguing, Galileo does not hesitate to attack some of the most commonly established Aristotelian arguments by showing that they are based on paralogisms. After Simplicio has presented Aristotle's argument to prove that heavy bodies move in order to go to the centre of the universe, Salviati not only does not agree with Simplicio in regarding it as a conclusive demonstration, but he declares: I am amazed that you need to be shown Aristotle's paralogism, since it is so obvious, and that you have not noticed that Aristotle presupposes what is in question (VII, 59).

This direct attack delivered against Aristotle's reputation as the greatest authority on logic and the art of arguing provokes Simplicio's immediate reaction: I beg you, Signer Salviati, to speak with a greater respect for Aristotle. How could you persuade anyone that he who was the first and only one to explain wonderfully the form of syllogism, demonstration, sophistical refutations, the way of discovering sophisms, paralogisms, and in a word all parts of logic, could then equivocate and make such a serious mistake as to suppose as known that which is in question? (VII, 59).

Simplicio's rhetotical tirade in defence of Aristotle is effectively deflated by Salviati who, wittingly playing on words and deliberately exploiting the equivocal or ambiguous meaning of the word organum traditionally used as the title for the collection of the Aristotelian logical treatises, compares logic to an organ and argues that one thing is to know the rules of an art, another thing is to be skilful in practicing it:

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Logic, as you know very well, is the organ with which we philosophize. But, as it can happen that a craftsman is excellent in building organs, but is not trained to play them, so someone can be a great logician but have little skill in using logic. Similarly, there are many who know the whole of the art of poetry by heart, but are incapable of composing even four lines. There are others who have learned all Leonardo's prescriptions, but would be incapable of painting a single chair. One does not learn to play the organ from those who build organs, but from those who play them; one learns poetry by reading poets all the time; one learns to paint by makins drawings and paintings all the time; one learns to make demonstrations by reading books full of demonstrations, and such are only the mathematical, not the logical, books (VII, 59-60). This impressive and convincing use by Galileo of the literary form of the simile should not be regarded as an example of rhetorical ways of arguing, but only as a document of his mastery of the art of poetry. Galileo's poetical style was not a substitute for philosophical arguments, but an important aspect of them. In fact the simile is used by Salviati as an essential part of his argument aiming at showing that even Aristotle sometimes resorts to paralogisms: Now — he goes on — returning to the object of our discussion, I say that what Aristotle sees in the motion of light bodies is the moving away of the fire from any place of the surface of the terrestrial globe and its rising straight upwards. This motion is truly towards a circumference greater than the Earth; indeed Aristotle Jihnself makes it move towards the concave surface of the sphere of the Moon. But that such a circumference is that of the world or is concentric with it, so that to move towards it is also to move towards the circumference of the world, this cannot be stated unless one presupposes first that the centre of the Earth, from which we see light bodies rise and move away, is the same as the centre of the world, that is to say that the terrestrial globe is placed in the centre of the world. This is what we doubt, and what Aristotle intends to prove. And do you say that this is not a manifest paralogism? (VII, 60). This stringent argument leaves Simplicio's position defenceless; his reaction is an acknowledgment of defeat: «This way of philosophizing aims to overthrow the whole of natural philosophy and to ruin the heavens and the Earth, and the whole world » (VII, 62). Salviati, being the winner, can afford to be more confident and to reassure Simplicio that « philosophy itself cannot but benefit from our disputes, for if our ideas are true, we shall have gained new ac-

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quisitions; if they are false, by refuting them the old doctrines will be further confirmed. You should instead worry about some of the philosophers and should try to help and support them, for as far as science itself is concerned it cannot but advance» (VII, 62). Salviati's remark about the benefits to be derived from philosofical disputes is further stressed by a marginal note stating that « philosophy can receive increment from disputes and oppositions between philosophers». This remark draws our attention to an important aspect of Galileo's way of philosophizing, that is to the fact that throughout his life he produced and developed his ideas of science and of nature by engaging in disputes with his opponents. Most of his works, from the Discorso on floating bodies of 1612 to the Dialogo of 1632, are in the form of disputations on specific and precise questions, for which different and opposing arguments are analyzed. In them Galileo displays all his skill in the art of arguing. He seemed to take such pleasure in the practice of this art that often in his disputes he aimed clearly to win not only the truth but also the argument. This is particularly noticeable in those cases where he is so keen to show off his virtuosity in arguing that he first pretends to add arguments apparently supporting his opponent's point of view, only to surprise in the end both him and his audience by revealing their faults and paralogisms and thus destroying the thesis being maintained. An example of this way of arguing is offered by Salviati when he discusses in the second Day of the Dialogo Ptolemy's objection that a rotation of the Earth would fling off everything on its surface. At first Salviati pretends to add further support to the argument, which Simplicio considers so strong as to be irrefutable: «I want also, Signor Simplicio, to strengthen even further the knot of the argument, by showing in a way which is even more obvious to the senses how true it is that heavy bodies which are turned at a great speed around a stable centre acquire an impetus or impulse to move away from this centre, even though by nature they have a tendency to go there » (VII, 216). Salviati's refutation of the argument is all the more surprising as it is accomplished through reasoning based on simple mathematical ideas which even Simplicio can understand and accept. Salviati brings Simplicio step by step to acknowledge that, in the case of the rotation of the Earth, the impulse to fly off along the tangent to the surface is overcome by the tendency to move towards the centre of the world, so that all heavy bodies lying on the surface of the Earth are kept firmly in their

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place. At the end of a long and complicated discussion where all the concessions apparently made by Salviati to Simplicio turn out to weaken and finally destroy the latter's position and to consolidate that of the former, Salviati cannot hide his satisfaction and pride in having won: You can see now how great is the strength of truth, for while you try to knock it down, your very attacks help it to stand up and to become stronger (VII, 230).

The disputational style of the Dialogo was not just a literary form based on rhetorical conventions, as some recent critics believe, but was required by the nature of Galileo's scientific enterprise, which aimed to provide new solutions to old problems by showing that the old solutions were based on unacceptable principles and on fallacious arguments, and by building new arguments on the ruins of the old ones. That style also reflects Galileo's experience of public debates in which he was engaged at crucial moments of his life. A vivid portrait of Galileo in the act of disputing and of displying his extraordinary skill in arguing to overpower his opponents emerges from Antonio Quarengo's letters written from Rome between December 1615 and January 1616 to inform the Cardinal Alessandro d'Este about the developments of the discussions which Galileo was having with opponents of the Copernican system in order to persuade influental members of the Church to take a position in favour of it. « Galileo is here », announced Querengo on the 30th of December, «and often in gatherings of people endowed with intellectual curiosity he produces stupenduous arguments about the Copernican opinion, which he believes to be true» (XII, 212). On the 20th of January Querengo sent a description of what was going on in these gatherings that would be perfectly fitting for most of the discussions in the Dialogo between Salviati and Simplicio: You would enjoy it greatly if you could hear Galileo argue, as he often does, among fifteen or twenty people who deliver cruel assaults on him, sometimes in one house sometimes in another house. But his position is so fortified that he can make fun of everybody: though the novelty of his opinion is not very convincing, nevertheless he convincingly shows that most of the arguments by which his opponents try to knock him down are fallacious. Particularly last Monday, in Signor Federico Ghislieri's house, he put on a wonderful show. What gave me the greatest pleasure was that, before answering his opponent's reasons, he amplified and strengthened

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them with new arguments which seemed very well grounded, but only in order to destroy them later and make his opponents appear the more ridiculous (XII, 226-7).

Galileo was after all sincere in his deposition at the trial in Rome on the 30th of April 1633, when he acknowledged that his main mistake in writing the Dialogo had been to indulge in that « natural complacency which everybody has of his own subtelties, by showing that I was more clever than any common man in finding ingenious and apparently probable arguments even for false conclusions» (XIX, 342).

D I ALD O G O I GALILEO GALILEI LINCEO MATEMATICO SOPRAORDINARIO D E L L O S T V D I O DI P I S A .

£ Filofofo, e Matematico frimario dd SERENISSIMO

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IN FIORENZA,PerGio:BatiftaLandini MDCXXXII. CON L1CENZA DE' SVPE^IORI. Galileo Galilei, Dialogo (1632): title page: the disputation that precipitated Galileo's trial, and made him a cultural symbol to suit many tastes.

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Galileo Galilei: A Philosophical Symbol

Commenting some half century ago on the conventionalist view of the Copernican system put forward by Cardinal Bellarmine1, following the example of Osiander, Pierre Duhem famously declared2 that it was they, and not the scientific realists Galileo and Kepler, who had grasped the exact significance on the experimental method. Protesting, in his recent study3, against this assertion, Professor de Santillana has pointed out that a wider reading of Bellarmine's writings shows that his view of astronomy, so much in keeping with Duhem's own philosophy of science, is an isolated island of conventionalism surrounded by a sea of scholastic metaphysical realism concerning all other subjects. De Santillana questions, moreover, whether Duhem's conventionalist or positivist conception of science could in fact give an adequate account of the work of the great constructive geniuses who have actually created our experimental science - of the work of Galileo, for example, as distinct from that of critics like Bellarmine or of other, more systematic, logicians. It is an indication of the permanent philosophical interest of Galileo's writings that any historical account of his scientific activity must involve the issue of interpreting his philosophy of science. Was his new science of inertal motion, the 'very new science dealing with a very ancient subject'4 upon which he pinned his conviction of the physical truth of the Copernican system, a discovery of the real physical world or a conceptual invention, a fiction that enabled him to predict? If it were necessary to defend Galileo's intransigently absolute conception of verified scientific theories against such critics as Duhem, one could legitimately do so by pointing out that with the concrete philosophical and scientific

1

Roberto Bellarmino a Paolo Antonio Foscarini, 12 aprile 1615\ in Le Opera di Galileo Galilei, ed. naz., (Firenze, 1902, xii), pp. 172-2. 2 P. Duhem, Essai sur la notion de theorie physique de Platan a Galilee, 'Annales de philosophic chretienne', vi (1908), 588, 584-5. 3 G. de Santillana, The Crime of Galileo, (Chicago, 1955), pp. 107-8. 4 Galileo, Discorsi e dimonstrazioni matematiche, intorno a due nuove scienze, iii (Opere, ed. naz., viii), p. 190.

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situation and the actual methodological and technical problems which he had to face, it was the one most calculated to be effective. But when one looks at the many different and contradictory interpretations that have been given of Galileo's philosophy of science and of its significance in the history of thought, one is tempted to conclude that no such defence is is really necessary. The critics may safely be left to cancel each other out. In fact Galileo has been made to occupy almost every position on the line of antithesis between his and Bellarmine's contributions to the Copernican debate. Philosophers looking for historical precedent for some interpretation or reform of science, which they themselves are advocating, have all, however much they have differed from each other, been able to find in Galileo their heart's desire. For his contemporaries, Galileo's fame was chiefly that of the telescopic observer of the heavens, the discoverer of the mountains on the moon, the rotation of the sunspots. Jupiter's satellites and the author of the mathematical law of free fall, who had destroyed the Aristotelian cosmology and won the martyr's palm by his advocacy of the new system of Copernicus5. By a direct appeal to observation he had ruined the dogmatic belief of the schools that the great problems of physics could be solved by pure reason alone, and by the use of mathematics he had shown how to solve them. Although Mersenne failed to be able to get Galileo's results when he repeated his famous experiments with a ball rolling down an inclinical plane6, Galileo was regarded by the end of the seventeenth century, for example in the Royal Society, as the founder, with Francis Bacon, of the experimental method, of the New or Experimental Philosophy7. This was his chief reputation during the eighteenth century also, when Voltaire8 and David Hume9 pointed out that whereas Bacon had only preached the use of experiment, Galileo had both practised it and married it with mathematical reasoning. Montucla10 and Lagrange11 asserted that the laws Galileo discovered in mechanics implied a profounder genius than the novelties he detected in the sky. It was no doubt his reputation as the founder of the experimental method, accepted for example in Whewell's Philosophy of the Inductive Sciences (1840)12, that encouraged the strange elaboration in the 5

R. Dugas, Le mecanique au XVHe siecle, (Neuchatel, 1954), p. 88. Marin Mersenne, Traitez de la nature des sons, et des mouvements de toutes sortes de corps', ii, prop, vii, corollaire i, ii, Harmonic Universelle (Paris, 1636), i, 112; A. Koyre, Etudes Galileennes, (Paris, 1939), ii, 73. 7 Cf. Dr Wallis's Account of some Passages of his own Life in Peter Langtoft's Chronicle, ed. Thomas Hearne, (London, 1725), I, clxi. 8 Siecle de Louis XVI (1752), Ch. 31, Oeuvres, (Geneva, 1769), xii, 36-38; Essai sur les moeurs et I'esprit des nations (1756), Ch. 121, Oeuvres, ix, 371-2. 9 History of Great Britain, under the House of Stuart, 2nd. ed., (London, 1759), i, 129. 10 S.F. Montucla, Histoire des mathematiques, (Paris, 1758), ii, 260. 11 J.L. Lagrange, Mecanique analytique, 2nd. ed. (Paris, 1811), i, 221. 12 Book xii, Ch. 10 (London, 1840), pp. 379-83; cf. Whewell's History of the Inductive Sciences (1837), Book v, Ch. iii, §3 and Book vi, Ch. ii, §5. For other examples see J.F.W. Herschel, A Preliminary Discourse on the Study of Natural Philosophy, (London, 1830), pp. 113 sqq., 167-8; Biographic universelle, 2nd by M. Michaud, (Paris, 1856), xv, 412, 417. 6

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nineteenth century of the story of Galileo dropping two different weights from the Leaning Tower of Pisa, in order to prove, as his law of falling bodies stated, that all bodies fall with the same acceleration, and to disprove the Aristotelian teaching that the speed would be proportional to the weight. In his account of the history of this story, Lane Cooper13 has shown that half a page written sixty years after the date of the alleged event by Galileo's disciple and biographer, Viviani, is the origin of the full nineteenth-century version14 of the young professor toiling up the winding stair of the Leaning Tower with two different weights (in some accounts the larger one was almost as large as himself) to make his great challenge to the elderly Aristotelians, and of the gasp of surprise and indignation from the vast assembly of the professors and students gathered below when the two objects struck the ground with the same resounding blow. An experiment of this kind had in fact been mentioned in various writings since late classical times, and in his De Motu, written about 1590 when he was at Pisa, Galileo claims to have performed it 'from a high tower'15. In 1612, and again in 1641, two acquaintances of Galileo claimed to have dropped weights from the Leaning Tower.16 The results were always the same. The heavier body always reached the ground considerably before the lighter. 'Oh how readily are true demonstrations drawn from true principles!'17, exclaimed Galileo in 1590, when in fact he was not disagreeing with Aristotle on this point. The truth is that it was not on experimental grounds, but because he came to re-think the whole theory of motion, that Galileo finally parted company with Aristotle. The experimental results in fact disagreed with both the old and the new dynamics, for the Aristotelians had predicted an incorrect proportion between the velocities of different weights, and Galileo predicted that the velocities would be the same. But this did not upset Galileo at all. He incorporated the inconsistency into his new dynamics, and made it agree with his experiment, by attributing it to air resistance.18 In making this move he showed that genius not for pure experiment but for theoretical reasoning using experiment, and that confidence in theoretical reasoning even in the face of immediate experimental contradiction, which marks the success of all his scientific inquiries. One reason for the nineteenth-century elaboration of this story is undoubtedly that Galileo's reputation as the founder of the experimental method had led Auguste Comte, equally unembarrassed by any great knowledge of the actual historical circumstances of his experiments, to annex him in 1830 as also a founder of positivism. Comte held that the real object of science had always been 'savior, pour prevoir', knowing in order to foresee, and foreseeing in 13 14 15 16 17 18

Lane Cooper, Aristotle, Galileo, and the Tower of Pisa, (Ithaca, 1935), pp. 26-7. See Lane Cooper, op. cit.; cf. O.M. Mitchell, The Orbs of Heaven, (London, 1851), pp. 63-5. Galileo, De Motu (Opere, i), p. 334: Lane Cooper, op. cit., pp. 86-7, 54-5. Lane Cooper, op. cit., pp. 28-32. De Motu, p. 334. Galileo, Discorsi, i (Opere, viii), p. 116; iv, p. 279.

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order to gain control. His view of the history of the matter was very clearly described by his friend J.S. Mill. The fundamental doctrine of a true philosophy, according to M. Comte', wrote Mill, 'and the character by which he defines Positive Philosophy, is the following: - We have no knowledge of anything but Phaenomena: and our knowledge of phaenomena is relative, not absolute. We know not the essence, nor the real mode of production, of any fact, but only its relations to other facts in the way of succession or of similitude. These relations are constant: that is, always the same in the same circumstances. The constant resemblances which link phaenomena together, and the constant sequences which unite then as antecedent and consequent, are termed their laws. The laws of phaenomena are all we know respecting them. Their essential nature, and their ultimate causes, either efficient or final, are unknown and inscrutable to us'. 'M. Comte claims no originality for this conception of human knowledge. He avows that it has been virtually acted on from the earliest period by all who have made any real contribution to science, and became distinctly present to the minds of speculative men from the time of Bacon, Descartes, and Galileo, whom he regards as collectively the founders of the Positive Philosophy'.19 Even more explicit was the positivist interpretation of Galileo given towards the end of the century by the great Viennese historian and critic of mechanics, Ernst Mach, the grandfather of the modern school of logical empiricism. 'The modern spirit that Galileo discovers is evidenced here, at the very outset', he wrote of Galileo's treatment of the problem of falling bodies, 'by the fact that he does not ask why heavy bodies fall, but propounds the questions, How do heavy bodies fall? in agreement with what law do freely falling bodies more? The method he employs to ascertain this law is this. He makes certain assumptions. He does not, however, like Aristotle, rest there, but endeavours to ascertain by trial whether they are correct or not. We see thus . . . that Galileo does not supply us with a theory of the falling bodies, but investigated and established, wholly without preconceived opinions, the actual facts of falling'.20 The great opponent of Comte and Mill in the philosophy of science and the interpretation of scientists was William Whewell21, and Whewell's views were largely influenced by Kant, who is the principal source of the modern school most opposed to positivism. Embracing the apparent paradox that it was Aristotelian science and not Galileo's that was primarily empirical, Kant characterised the the significance of Galileo's methods as residing in their recognition of the essentially theoretical character of scientific inquiry. The

19

J.S. Mill, Auguste Comte and Positivism, 2nd. ed., (London, 1866), p. 6; cf. Auguste Comte, Cours de philosophic positive, (Paris, 1830), i, Premiere lecon. 20 E. Mach, The Science of Mechanics, Ch. 2, §§2,8, transl. from the second German ed. by T. J. McCormack, (London, 1893), pp. 130, 140. 21 Prilosophy of the Inductive Sciences, 2nd. ed., (London, 1847), ii, 295 sqq., 317, 320 sqq.

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'new light that flashed upon all students of nature', with the great work of Galileo and his contemporaries, as seen for example in Galileo's treatment of falling bodies, was their recognition that physics must determine its objects a priori. 'They comprehended', he wrote, 'that reason has insight into that only, which she herself produces on he own plan. . . . Reason, holding in one hand its principles, according to which concordant phenomena alone can be admitted as laws of nature, and in the other hand the experiment, which it has devised according to those principles, must approach nature, in order to be taught by it: but not in the character of a pupil, who agrees to everything the master likes, but as an appointed judge, who compells the witness to answer the questions which he himself proposes'.22 Developing this line of thought, that Galileo's chief merits were rather as a theorist than an experimenter, some modern critics have been tempted to suppose that Galileo was really indifferent to experimental tests.23 'Io senza experienza son sicuro che 1'effetto seguira come vi dico', said Salviati, Galileo's spokesman in the Dialogue, 'perche cosi e necessario che segua'.24 And indeed it is very often difficult to distinguish Galileo's thought experiments from his actual ones. Turning from this sample of Galileo's critics to his own words and deeds, it is clear that he was neither an early Comtean positivist nor a Machian phenomenalist nor a Kantian rationalist, neither a Millian empiricist nor an unempirical theorist, neither an unqualified Platonist nor a wholesale enemy of Aristotle. Galileo's normal method was to deal with problems piecemeal, and he often used different arguments for tactical reasons which cannot each be generalised into a total point of view. When he decided to ignore the cause of the acceleration of falling bodies and concentrate on the descriptive law, 'whatever the cause may be',25 as he said, and when he showed up the Aristotelian causes and substances in physics as mere names, he wrote like a positivist. But this was in order to put aside irrelevant questions and isolate his problem. It was certainly no positivist who debated so passionately the truth of the Copernican system or who claimed to be reading in mathematical language the real book of Nature and to be discovering in verified theories the real physical world of the primary qualities and their laws. These were no economical summaries such as Mach conceived scientific laws to be, but a world of real substances and causes, Platonic in that they were mathematicall determined, Aristotelian in that they were inherent in matter, but Archimedean in their mathematical form.

22

Kant, Critique of Pure Reason, Preface to the second edition (1787). Cf. Koyre, Etudes Galileennes, ii, 72-3, iii, 60, 66-67; Dugas, Le mecanique au XVIIe siecle, pp. 80-89. 24 Galileo, Dialogo sopra i due massimi sistemi del mondo, ii (Opere, ed. naz.), p. 171. 25 Discorsi, iii (Opere, viii) 202. See A.C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700, (Oxford, 1953), pp. 285, 303-10. 23

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Similarly, when Galileo wrote cavalierly of experiment, he did so to assert the superiority of the theoretician, able to foresee yet unobserved results, over the pure empiricist who can see only the facts already observed.26 On other occasions he wrote that one negative instance was enough to demolish a theory.27 It is clear, as Kant perspicaciously indicated, that the method of theoretical and experimental enquiry which Galileo described in so many passages is what we should now call hypothetico-deductive, and the final test of a true hypothesis was by agreement with experiment. It is the utterly metaphysical character of a science that was so technically successful that is the most arresting feature of all Galileo's inquiries. We may disagree with his conviction that a verified theory is an absolute truth, we may treat his Neoplatonic realism as a regulative belief and his mathematical primary qualities as physical models, we may see his methods as a new syntax and as the origin of philosophies that developed only after he was dead. All these are the insights we may get into our own problems from the study of a great thinker of the past. But these insights are not the same as the dead man's own philosophy. Faithful to the paradoxical battle-cry of reform, stare super vias antiquas, philosophers have extracted from Galileo's writings an almost endless variety of meanings suited to present objectives. To justify this use of history, Comte proposed the dangerous formula, that if no precedent can be found in what the chosen authority states his methods and aims to be, then precedent can be claimed in what he must really have been doing to be successful28, even if he denies it. Certainly this distinction is not totally invalid. But the formula universally applied would destroy the validity of historical evidence altogether and would make all historical distinctions and precedents entirely meaningless. It is not by reading our own problems backwards that historical experience is enlightening, but by exposing ourselves to the surprise that thinkers so effective should have had aims and presuppositions so different from our own. Postscript See above, ch. 10, with Appendix (a), for the dating of Galileo's writings.

26

Discorsi, iv (Opere, viii), p. 296. Dialogo, ii (Opere, vii), p. 148. 28 i.e. what the scientist was 'really' doing according to the interpreter's view of the methods and content of science. 27

13 Alexandre Koyre and Great Britain: Galileo and Mersenne I REMEMBER vividly the occasion when I first encountered the work of Alexandre Koyr6. It must have been in 1946. By this time I had been introduced at Cambridge by CD. Broad to the classical study of the history of philosophy through conceptual analysis, and I had been much taken by the advice given by R.G. Collingwood to look in the study of texts for the questions assumed in the answers given. I had become particularly interested in the approach to the subject made by L6on Brunschvicg in Les etapes de la philosophie mathematique and by the work of Etienne Gilson on the history of medieval philosophy. In 1946 I had just accepted an academic post in the history and philosophy of science, and I was completing my last biological paper, which was published in 1947. I was checking some French publications which had arrived in the Cambridge University Library after the gap of the war years, among them the Actualites scientifiques et industrielles, where in the volumes for 1939 I found the three parts of Koyre"'s Etudes Galileennes. About the same time I encountered also another French wartime publication, Robert Lenoble's Marin Mersenne ou la naissance du mecanisme (1943). Contact with these captivating intelligences (as I said on another occasion) was like Galileo's description of the stimulation given to the ear by the musical interval of the fifth, seeming at the same time to kiss and to bite, at once seducing and awakening.1 They showed the enlightenment that can be gained only by looking beneath the surface of immediate scientific results and by seeking to identify the intellectual assumptions and the technical capabilities that made certain discoveries possible and explanations acceptable to a particular generation or group, and the assumptions and capabilities that made them impossible or unacceptable to earlier generations. They focused attention on the need to study in depth the particular intellectual contexts in 1. Galileo Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze (1638), i, in Le opere, direttore A. Favaro, 20 vol., Firenze, G. Barbera, 18901909, ristampa 1968, viii, p. 149; A.C. Crombie, "Premio Galileo, 1968", Physis, 1970, xii, p. 106-108.

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which scientific changes have been brought about, and with them the assumptions about both the nature of scientific knowledge and the nature of the world that have generated resistence to change. This conception of the history of science was very inspiring, and it was especially Koyre who through his series of publications and his personal influence inspired those of us in Great Britain, as also in the U.S.A. and of course in France, who took up the subject professionally just after the Second World War. Koyre and Lenoble, and also we should add Edwin Burtt with his much earlier Metaphysical Foundations of Modern Physical Science (1924, revised 1932), intellectualized the historiography of science. They made it part, and showed that it had to be often a central part, of a more general historiography of thought. I knew them all, and especially Alexandre Koyre, whom I first met in Brussels, and then many times in Paris, London, Oxford and Princeton during the 1950s and later. In many long conversations I discovered this extraordinary man, always fascinating in the intellectual perceptions deployed over his formidable range of learning, not easily persuaded to change but always open to disagreement, from which with his beguiling smile he would draw some fresh and unexpected insight. I spent some time with him in Paris about six months before he died, when he was being treated for leukemia, and I saw him for the last time in hospital just before his death on 28 April 1964. He greeted me with his usual courage and gentleness, and we said farewell.2 One might say that by intellectualizing the historiography of science Koyre risked disembodying the history of scientific ideas. It is true that his example may have entailed a risk, despite the perception and skill evident in all his work, although I cannot think of any damage that may have come from his particular style of deploying his insights. But one can both benefit and differ from even the most inspiring of examples. This I shall illustrate briefly from some more recent work on Galileo and Mersenne, but first I want to establish a viewpoint, relevant to Koyre's own vision of the history of science. The Western scientific movement with which we are concerned has been, as I have said elsewhere, the history of men's relations with nature and their fellow beings as perceiver and knower and agent, mediated through particular visions of existence from which the arts

2. Cf. C.C. Gillispie, "Koyre, Alexandre (1892-1964)" om Dictionary of Scientific Biography, New York, Charles Scribner's Sons, 1973, vii, p. 482-490; for publications A. Koyre, De la mystique a la science, ed. P. Redondi, Paris, Ecole des Hautes Etudes en Sciences Sociales, 1986, p. 216-221; and for comments on myself and on the historiography of science A. Koyre, "Les origines de la science moderne", Diogene, 1956, xvi, p. 3-31, and "Commentary" in A.C. Crombie (ed.), Scientific Change, London, Heinemann, 1963, p. 847-865.

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and sciences have followed.3 It can be identified most precisely as an approach to nature effectively competent to solve problems of two kinds: those presented by particular phenomena, and those concerned with general systems of explanation. By the scientific movement I mean then the history of a specific vision created within Western culture, initially by the ancient Greeks, at once of knowledge and of the object of that knowledge, a vision at once of natural science and of nature. We can trace this vision to the commitment of some ancient Greeks, within a much wider intellectual movement, to the decision of questions of all kinds, ethical and practical as well as scientific and metaphysical, by argument and evidence as distinct from custom, edict, revelation or some other habitual means. The Greek philosophers, mathematicians and medical thinkers developed thereby the notion of a problem as distinct from a doctrine, and the consequent habit of envisaging thought and action in all situations as the perceiving and solving of problems. They developed with this the conception of a rational scientific system incorporating the solutions of particular problems, a system in which formal reasoning matched natural causation. From these two fundamental matching conceptions, of formal proof and of causal demonstration, each entailing a capacity for self-correction, have followed all the essential character and style of Western philosophy, mathematics and natural science and their competence to control subject-matters of all kinds, from abstract ideas to material things. This specific and selective Western scientific vision at the same time closed elsewhere open questions of what kind of world men found themselves inhabiting and so of what means they should use to explore, explain and control it. Historical questions arise then at different levels, some given by nature, and some made by man. At the level of scientific thinking, both in the perception and solution,of problems within the technical possibilities available, and in the justification of the enterprise whether intellectual or moral or practical, the history of science has been the history of argument. Scientific argument has been diversified explicitly through its history into different particular forms in accordance with the demands of different subject-matters, of different theories of scientific demonstration, and of different conceptions of the nature of things as the object of scientific inquiry. It has proceeded by postulating principles as in the Greek mathematical sciences, by deploying within its discourse designed observation and 3. Cf. A.C. Crombie, "Historical commitments of European science", Annali dell' Istituto e Museo di Storia della Scienza di Firenze, 1982, vii. 2, p. 29-51, "What is the history of science?", History of European Ideas, 1986, vii, p. 21-31, "Experimental science and the rational artist in early modern Europe", Daedalus, cxv. 3, Summer 1986, pp. 49-74; Styles of Scientific Thinking in the European Tradition, London, G. Duckworth, 1994.

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experiment using appropriate instruments and apparatus, by hypothetical modelling and analogy, by taxonomy, by probabilistic and statistical analysis, by historical derivation as in the study of languages and of living organisms. It has been aimed in different social contexts almost as much at persuasion as at demonstration. But always if an argument was either to demonstrate or to persuade acceptably it has been expected to satisfy the stable criteria of logical consistency and agreement with the evidence: criteria formalized by the Greeks themselves and their successors within the scientific movement. Of course this kind of stratospheric view of nearly three millenia of intellectual history sweeps insouciantly over periods or circumstances of incompetence or indifference; but whenever Western scientific thinking has been revived or refocused or transferred from one culture to another, this has been done explicitly as the revival or appropriation of an existing tradition. This is not very surprising since the tradition has had its existence both in living people and in texts available for recovery and translation, and whether from the one or from the other there has been an explicit continuation of education in the same styles of thought and practice. The historiography of science is concerned then with the history of scientific argument, and with intellectual and moral behaviour in relation to such argument. On this I shall make two further comments. First, if we insist upon the cultural specificity of the Western scientific tradition in its origins and initial development, and upon its enduring identity in diffusion to other cultures, we do not have to look far below the surface of scientific inquiry and its immediate results to see that the whole historical process has gone on in a context of intellectual and moral commitments, expectations, dispositions and memories that have varied greatly with different periods, societies and circumstances. These have affected both the problems perceived and the solutions found acceptable, and also the evaluations of desirable and undesirable ends and their motivations. The whole affair as I have said elsewhere is an invitation to treat the historiography of science as a kind of comparative historical anthropology of scientific thinking. Before all we must be concerned with people and their vision, with their perceptions of problems and their expectations in the uncertainty of an unknown future, and with their response both in accepting and in opposing innovation and change. As ourselves products of a particular time and culture, we may then give ourselves the therapeutic surprise that effective scientific thinking could be based on assumptions and have aims and motivations so various and so different from our own. Secondly, accepting all this, we do not likewise have to look far into the scientific tradition to see that the whole programme has presupposed the stability at once of nature and of human thinking.

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Nobody knows what nature is, Koyre once said to me, except that it is whatever it is that falsifies our hypotheses. The scientific movement has comprised distinct kinds of knowledge which have had to be tested in different ways. Propositions asserting factual regularities could be tested directly by observation and have been the most stable. Propositions asserting theoretical explanations must be tested by their observable consequences and have tended to be replaced with the development of more precise or more general theories. Propositions asserting beliefs about the fundamental nature of the world have not usually been proposed for testing but have been assumed in the development of theories, until they have been replaced by the rethinking of the foundations. From whatever level of its activity, the Western scientific movement has generated through its history a progressive accumulation of objective and reproducible knowledge, and of methods and techniques for acquiring and developing it, that are communicable to all mankind. This is an historical phenomenon of the profoundest human importance of which historians and philosophers are, or should be if they have any intellectual responsibility, obliged to take account. When Galileo insisted that we cannot cheat nature, however much we may cheat our fellow men, he was defining the identity at once of nature and of natural science.4 For it was impossible to solve problems in nature whether theoretical or practical by magic or by commercial bargaining or political convenience or chicanery. A large part of the argument within the scientific movement, notably in the 17th century, has been directed towards establishing its identity as distinct from other forms of contemporary erudition. The specific history of science as a problem-solving activity is not then the same as the history of ideas or ideology lacking its identifying modes of self-correction and criteria of acceptability. Only someone with no grasp of scientific knowledge, little of the history of thought, and motivated no doubt by some catastrophic ideology, would want to think it was.5 The illumination given by Koyre to our understanding of Galileo came from his perception of Galileo as primarily a theoretical thinker by contrast with the dedicated experimenter then currently presented. There can be no doubt of the importance and influence of that illumination, which has guided the reshaping of all subsequent studies of 4.

Galileo, Le mecaniche, in Le opere, ii, p. 155, cf. Lettera a Madame Cristina di Lorean (1615), in ibid. \, p. 326-327. 5 Unawareness of a specifically scientific movement seems to be exemplified by Paolo Rossi-Monti, so far as one can diagnose from his somewhat undiscriminating comments on Koyre, Ernst Cassirer, J.H. Randall and myself: see his "Aristotelici e moderni: le ipotesi e la natura" in L. Olivieri (ed.), Aristotelismo veneto e scienza moderna, Padova, Antenore, 1983, i, p. 125-129, published also in English in Annali... (as above n. 3), 1982, vii. 1, p. 3-7.

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Galileo and of much else. In his brilliant demolition of this older image of Galileo, he argued ingeniously that Galileo's Platonism had led him to believe that experiments were really unnecessary to confirm demonstrations established by reason.61 suppose that no one would now agree with that extreme interpretation. Koyre also showed that Galileo's principal model for mathematical physics was not Plato but Archimedes. This gives us a better insight into Galileo's conception of the place of experiment in a scientific argument. Archimedes, for example in his treatise On the Equilibrium of Planes, set out by purely theoretical analysis to reduce the possible postulates that could yield the phenomena of the balance to an unique set, rationally certified either by self-evidence or by sufficient reason: for what sort of world would we have if they were not true? Then, since he had so discovered the one possible set of true postulates, he could derive from these a complete account of the experimental phenomena without any need for experiments. Galileo took the "superhuman Archimedes"7 as his model, but he realized very clearly that in the more complex subject-matter of the science of motion he could not reduce the postulates to the one true set by a purely theoretical analysis. He went as far as he could in postulating possible theoretical worlds but, as he pointed out on several occasions, notably in describing how he discovered the ratio of distance to time in falling bodies, he had to decide by experiment whether his postulated ratio was that found in the one actual world.8 To control theoretical postulation was then one way in which Galileo brought experiment into a scientific argument, but he did so even more extensively in another way: in order to explore ever more complex subject-matters by experiment, as distinct from controlling a primarily theoretical exploration. This was ignored by Koyre, but

A. Koyr6, "Galileo and Plato", Journal of the History of Ideas, 1943, v, p. 400428; cf. A.C. Crombie and A. Carugo, Galileo's Natural Philosophy, (forthcoming), with full bibliography. 7. Galileo, De motu gravium, in Le opere, i, p. 300. 8. Cf. Galileo to Pierre Carcavy, 5 June 1637, in Le opere, vii, p. 90-91, and to G.B. Baliani, 7 January 1639, in ibid, xviii, p. 11-13; A.C. Crombie, "The primary properties and secondary qualities in Galileo Galilei's natural philosophy", in C. Maccagni (ed.), Saggi su Galileo Galilei, Firenze, G. Barbera, preprint 1969, "Sources of Galileo's early natural philosophy", in M.L. Righini Bonelli and W.R. Shea (ed.), Reason, Experiment, and Mysticism in the Scientific Revolution, New York, Science History Publications, 1975, p. 157-175, 303-305, "Philosophical presuppostions and shifting interpretations of Galileo", in J. Hintikka, D. Gruender and E. Agazzi (ed.), Theory Change, Ancient Axiomatics, and Galileo's Methodology: Proceedings of the 1978 Conference on the History and Philosophy of Science, Dordrecht, D. Reidel, 1981, i, p. 271-286; A. Carugo and A.C. Crombie, "The Jesuits and Galileo's ideas of science and of nature", Annali... (as above n. 3), 1983, viii. 2, p. 3-68, with further references; A.C. Crombie and A. Carugo, Galileo's Natural Philosophy (forthcoming). 6.

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without it any account of Galileo would be incomplete, and in relation to Koyre's image of Galileo it is interesting because here Galileo was strongly Aristotelian. In his inquiries into hydrostatics and sunspots, into comets, and into the connection between the motions of the tides and of the Earth, he conducted his experimental and observational analysis of the causes of effects according to the "laws of logic" or "physical logic",9 which were the Aristotelian rules of inference as developed by scholastic natural philosophers: presence or absence, and concomitant variations in degree, together with the reductio ad contradictionem or ad impossible. Thus Galileo used two main forms of scientific argument: (1) the Archimedean theoretical postulation controlled by experiment for the simpler phenomena of motion; and (2) these Aristotelian rules of inference for the more complex phenomena of material change. Both can be found together in De motu graviwn. Both led to demonstration, with a shift during the years 1612-16 from an Aristotelian scholastic conception of the demonstrative progression and of analysis and synthesis (or resolution and composition) to a mathematical conception akin to that described by Pappus and Proclus. But Galileo retained to the end of his life the fundamentally Aristotelian expectation, coming from a conception of a completed and closed system of knowledge, that scientific inquiry could discover the one "true constitution of the universe" which "could not possibly be otherwise"10 and could be established by "necessary demonstrations".11 Yet despite this apodeictic talk, he based his scientific practice on the open-ended conception of inquiry coming from mathematics and experiment and on range of confirmation as the test of a theory. The paradox is that Galileo never seems to have recognized the difference being made to the traditional logic and epistemology of science by the mathematical thinking in physics of which he was himself a supreme virtuoso. I have discussed much of this long ago in various papers and most recently in my joint paper with Adriano Carugo on "The Jesuits and Galileo's ideas of science and of nature" (1983).12 Clearly of the greatest significance for Galileo's intellectual biography is Carugo's discovery of Galileo's use for his scholastic essays on natural philosophy, and for De motu gravium, of well known- textbooks by Jesuit 9. Galileo, // Saggiatore (1623), questioni 12 and 42, in Le opere, vi, p. 252, 333. 10. Galileo, Prima Lettera circa le Macchie Solari (1612) in Le opere, v, p. 102. 11. Galileo, Lettera a Madame Cristina di Lorena (1615), in Le opere, v, p. 330; cf. Crombie, 1975, and Carugo and Crombie, 1983, note 8 above. 12. Note 8 above, with Crombie 1975 and other references; also Galilee devant les critiques de la posterite, Paris, Les conferences du Palais de la D6couverte, , ser. D, no. 45, 1956, Augustine to Galileo, 2nd ed., London, Heinemann Educational Books, and Cambridge, Mass., 1959, reprinted with revisions 1979.

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professors, Benito Pereira and Francesco di Toledo, of the Collegio Romano. This wholly unexpected new perspective focused attention on that institution, and was followed by my own identification of Christopher Clavius as another and very influential source there; and finally by Carugo's identification of Ludovico Carbone as a further source, again connected with the Collegio Romano, for his logical Disputationes de praecognitionibus et de demonstratione, essentially a commentary on the Posterior Analytics. All this we have discussed in the revised version of our book, Galileo's Natural Philosophy, in which we are publishing Carugo's edition of the Disputationes, with an English translation.13 If this new work, and that of other scholars, notably Winifred Wisan and Maurice Clavelin, seems to take us beyond the image of Galileo presented so brilliantly by Alexandre Koyre, that indeed is just what he would have wished, and it does nothing to dim the light he cast upon the whole subject and thereby upon the whole historiography of science. In conclusion I shall move again farther from Koyre's own contributions, yet to a subject on which he again cast light: Galileo's relations with Mersenne. I shall not retread Koyre's ground. Mersenne as I have said elsewhere makes an interesting contrast in scientific style with both Galileo and Descartes: they aimed at certainty in physical science; he, disbelieving in the possibility of certainty, aimed at precision.14 Hence the priority he gave to experimental measurement, and his criticism of Galileo's experiments. I am going to sketch a detective story about the discovery of the ratio of the period to the length of the pendulum and some related matters in the science of music. It was Cornelis de Waard who noted that Mersenne had published this ratio in his Harmonic universelle (1636) and Harmonicorum libri (1636) two years before Galileo published it in his Discorsi e dimostrazioni matematiche intorno a due nuove scienze (1638) and one year before he mentioned it in his letter of 5 June 1637 to Laurens React.15 In fact Mersenne published this ratio four years before Galileo, by 30 June 1634, in Les mechaniques de Galilee.^ I have established from correspondence and references 13. This book was awarded the Galileo Prize in 1969, and is deposited in the Domus Galileana, Pisa; cf. note 1 above. 14. Cf. A.C. Crombie, "Mersenne Marin, (1588-1648)", in Dictionary of Scientific Biography, 1974, ix, p. 316-322, with further references, "Marin Mersenne (1588-1648) and the seventeenth-century problem of scientific acceptability", Physis, 1975, xvii, p. 186-204, Marin Mersenne: Science, Music and Language (forthcoming). 15. Galileo, Le opere, xvii, p. 100-102; cf. Marin Mersenne, Correspondance, ed. C. de Waard, 1955, iv, p. 444-455, appendice iii: "Les etudes de Mersenne sur le funependule"; cf. notes by A. Carugo in Galileo, Discorsi... (1638), ed. Carugo e L. Geymonat, 1958, Torino, Paolo Boringhieri, p. 699-708. 16. Ed. B. Rochot, Paris, Presses Universitaires de France, 1966, viie Addition.

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within their works that Mersenne must have written his theorems, deriving the ratio by considering bodies falling perpendicularly, on an inclined plane, and then in a circle, by the end of 1633,17 whereas Galileo seems almost certainly to have written his first statement of it between 7 April and 9 June 1635. The former date is established by his correspondence with Fulgenzio Micanzio in Venice who with others there commented on his progress in writing the First Day of the Discorsi (dealing with the pendulum and acoustics) as he sent him successive pages of his manuscript; the latter date is established by Galileo's letter to Elie Diodati saying that on it he had sent a manuscript including the First Day to Giovanni Pieroni in Germany. This survives in Florence as the only extant manuscript of the Discorsi.18 There is no positive evidence that Galileo knew the pendulum ratio before he wrote this part of the Discorsi, and there is negative evidence that he did not.19 But Diodati sent Galileo a copy of Mersenne's Les mechaniques de Galilee on 10 April 1635, just when he would have reached the appropriate point in his manuscript.20 Galileo has left no comment. Apart from these dates, other circumstances and coincidences are sufficiently arresting to invite the suspicion that Galileo learnt the ratio from Mersenne. First, his bare announcement in the Discorsi of so important a proposition contrasts strikingly with his usual practice of offering full mathamatical and experimental demonstrations of his novelties. Again, even if he never received or never read Les mechaniques de Galilee, Mersenne had sent in advance of publication printed sections of his Harmonie universelle containing his theorems both to Nicolas Fabri de Peiresc in Aix-en-Provence and to Giovanni Battista Doni in Rome during 1634.21 Both were in touch with Galileo and his close friends in Florence, and these in turn were in touch with over17. See for the pendulum ratio Mersenne, Harmonie universelle, "Traite des instrumens", i, props, xix-xx, and "Traitez de la nature des sons et des mouvemens de toutes sortes de corps", ii, props, xii-xvi; and Mersenne to Peiresc, 10 March 1634, and subsequent correspondence in Correspondance, iv, p. 81-82, 105, 134, 175-177, 181-182, 186-187, 218-219, 225-227, 240-241, 253-255, 259-260, 267-269, 280-281, 286-287, 345, 368, 379, 388, 392-394, v, p. 33, 35, 136-137; cf. A.C. Crombie, "Mathematics, music and medical science", in Actes du XII* Congres International d'Histoire des Sciences, Paris, 1968, Paris, Albert Blanchard, 1971, i. B, p. 295-310 (reprinted in Science, Optics and Music in Medieval and Early Modem Thought, London, Hambledon Press, 1990), Crombie 1974 (note 14 above), Styles . . . ch. 10, (note 3 above), Marin Mersenne (note 14 above), Crombie and Carugo, Galileo's Natural Philosophy (notes 8,13 above). 18. MS Banco Raro 31; cf- Galileo, Le opere, xvi, pp. 271-274 with Pieromi to Galileo, 11 and 18 August and 15 December 1635, ibid. pp. 300-304, 359-361; Crombie 1971, n. 24, with other references in note 17 above. 19. Cf. Crombie, Styles . . . ch. 10,1994 (note 3 above), Crombie and Carugo, ibid. 20. Galileo, Le opere, xvi, p. 255; Mersenne, Correspondance, v, 132, cf. vi, 242. 21. Cf. Crombie, Crombie and Carugo (notes 17, 19 above).

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lapping circles of Galileo's friends in Rome, round Benedetto Castelli which included Rafaello Magiotti, round Cardinal Francesco Barberini which included Doni, and round Francois de Noailles. These circles included friends with whom Mersenne corresponded about his work, besides Doni especially two Frenchmen, JeanJacques Bouchard and Pierre Michon Bourdelot.21 The correspondence in particular of Magiotti shows how aware Galileo's friends were of Mersenne and his writings, an awareness sharpened by hostility and suspicion after his criticisms of Galileo's experiments. It also points to a possible channel of relevant information from Rome to Galileo. On 5 November 1634, Magiotti wrote to Galileo urging him to get his work into print, because there were people ready and eager to trick him out of "a great part of your long labours". He added that the young mathematician Famiano Michelini, just returning to Florence after a visit to Rome, "will talk to you more openly about this".22 In Rome Michelini had formed a warm friendship with Castelli, who appreciated especially his attachment to Galileo.23 Before he left Rome a relevant section of Mersenne's Harmonic universelle and probably also Les mechaniques de Galilee had reached Doni.24 If it was Mersenne who was Magiotti's putative plagiarist, Michelini could have got information about his writings from Doni, Bouchard or Michon Bourdelot. There is no evidence that either he or Galileo did receive any such information from Rome, but later in 1637 Magiotti directly accused Mersenne in letters to Galileo and to Michelini of both denigrating and appropriating Galileo's work. He had read his "large and numerous bad books" in French.25 Mersenne himself in his comments on the Discorsi, which he read first in manuscript during the winter of 16361637, claimed priority only for some of the contributions to the science of music which Galileo also announced in the First Day.26 These are a further complication of the story which I do not have

22. Galileo, Le opere, xvi, p. 152; Michelini was known in his order as Francesco di San Giuseppe or delle Scuole Pie. 23. Cf. Castelli to Galileo and Michelini to Galileo, both 8 April 1634, in Le opere, xvi, p. 75-76. 24. Mersenne to Peiresc, 28 July 1634, Correspondence, iv, p. 267-268, Doni to Mersenne, ibid., p. 384-385, and 392-394 on Harmonie universelle, "Traite des instrumens", ii; cf. note 17 above. 25. Magiotti to Galileo, and to Michelini, both 25 April 1637, in Le opere, xvii, p. 6364, and again to Galileo, 16 May 1637, in ibid., p. 80-81; also in Mersenne, Correspondance, vi, p. 241-243, 255. 26. See Mersenne, "Premiere observation" and "Seconde observation" inserted in the second volume of Harmonie universelle (1637) immediately following the "Table des matieres", and Les nouvelles pensees de Galilee (1639), livre i, arts. 17, 2024, ed. P. Costabel et M.-P. Lerner, Paris, J. Vrin, 1973; cf. Crombie, references in notes 14 and 17 above.

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space to discuss here. So impressed was Mersenne with Galileo that he seems to have supposed that Galileo must have discovered the pendulum ratio for himself. The evidence points otherwise. We have then a detective story about a possible murder without a body, but with strong circumstantial grounds for suspicion.

Vincenzo Galilei, Dialogo della musica antica, et della moderna (1581): title pageGalileo's father Vincenzo Galilei (c. 1520-1591) was a leading and controversial musical theorist, experimenter and scholar, and a skilled lutanist. It was he who may have introduced Galileo to experimental science by his investigations into the laws of vibrating strings, while Galileo was living in his house during 1585—89. Galileo reported results, corresponding to those described in his father's books and manuscripts, in his DLscorsi e dimostrazioni matematiche intorno a due nuove scienze (1638).

14

Marin Mersenne and the Origins of Language

Mersenne made language an exemplary subject of analysis into its elements and of modelling from those elements.1 There were a number of distinct questions: whether there was an original natural language of mankind, the relation of the diverse existing languages to each other and to any supposed original language, the language of the deaf and dumb, the relation of human to animal language, and the invention of an artificial universal language for communication among all men and of a philosophical language capable of representing the truth of things clearly and without equivocation. Treatment of these questions came from a variety of approaches guided by the basic principles enunciated by Aristotle in De interpretatione (c.l, 16a 4-8), that spoken sounds were symbols of affections of the soul and written marks were symbols of spoken sounds, and that although these symbols were not the same for all men, the affections and the things they referred to were the same. The question whether there was a natural original human language in which the names of things signified their natures, or whether all languages had grown up by fortuitous use in which words acquired their meaning by convention, went back to ancient Greek discussions of the origins of mankind and of civilisation. The former view was implied by the story in Herodotus's History (ii.l) of the isolation of children from birth to find out what unprompted words they would first utter, and was presented ambiguously by Plato together with the latter especially in the Cratylus. The conventional theory of language and its origin, asserted briefly in the Hippocratic treatise The Art (§2), had been developed especially by the Greek atomists and was reported by Lucretius (v. 1028-90), Diodorus Siculus (i.8) and Diogenes Laertius (x.75-6). The question became complicated by the account in Genesis (2. 19-20) of how God arranged for Adam to name all the other creatures, which led to the Patristic and scholastic supposition that the original and natural language of mankind was Hebrew, and again from the thirteenth century by the Neoplatonic and Cabalistic

1 This essay is based on my book Styles of Scientific Thinking in the European Tradition, ch. 14 (London, 1994) with full bibliography; the subject is elaborated in my Marin Mersenne: Science, Music and Language (forthcoming).

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assertion that possession of the true name gave occult power over the thing named.2 The need for an effective means of intellectual communication among men of different languages and cultures had been stressed by Augustine (De civitate Dei, xix.7), and the problem was recognised with renewed urgency in the thirteenth century in the theological and geographical context of Western Christendom. The natural language of mankind might be Hebrew, but its pristine universality had been lost in the confusion of Babel. The universality of Latin stopped at the boundaries of the West. Christians had a religious obligation to communicate the truth revealed to them. At the same time, whether there was a natural language of mankind and whether it was Hebrew, again became disputed questions. The Emperor Frederick II was said to have 'tried to find out by experiment what language or speech boys would have when they grew up, if they could speak to no one'.3 Roger Bacon located the problem within Augustine's distinction in De doctrina Christiana (ii.2-4) between natural and conventional or given signs. Natural signs were those which, 'without any desire or intention of signifying, make us aware of something beyond themselves', as smoke signified fire, or a track a passing animal. Given signs were those which living creatures made to each other intentionally in order 'to produce and transfer to another mind what happens in the mind of the person who makes the sign'. Bacon, after citing Augustine, went on to ask what was 'the first language of Adam and how he gave names to things; and whether boys reared in solitude would use any language by themselves, and if they met each other how they would indicate their natural states of mind'.4 Dante, in De vulgari eloquentia (i.6), had no doubt that the original human language was Hebrew, for 'a certain form of speech was created by God, together with the first soul', comprising both names and grammatical structure, and this was inherited after the confusion of Babel only by the Hebrews. Others took a different view in a much more scientific spirit. Thus his French contemporary Jean de Jandun in his questions 'Super De sensu' returned critically to the case of the isolated child, which he compared to that of a deaf mute: It has been said that because such a mute has not heard any meaningful speech, he cannot utter any. In question is: if a boy were reared in a forest, where he had never heard any kind of language, whether he would speak any language. . . . Some say that he would speak Hebrew, and that that language is natural; but this is not true, because then it would be adapted to all men and all would speak naturally that, which is false and evident to sense. Likewise there is no habit of 2 Cf. Roger Bacon, Opus mains, iv, ed. John Henry Bridges (Oxford), i, p. 395-7, Opus tertium c.26 (as below n. 4); Marsilio Ficino, De vita coelitus comparanda, iii.21 in Opera (Basileae, 1576); Henricus Cornelius Agrippa, De occulta philosophia, i.69-74 (Antwerpiae, 1531). 3 Salimbene de Adam, Cronica, a cura di Giuseppe Scalia (Bari, 1966), i, p. 510. 4 Roger Bacon, Opus tertium, c.27 in Opera quaedam hactenus inedita, ed. J.S. Brewer (London, 1859), i, p. 100-2.

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any speech unless through the social intercourse of men, and hence I say that he would not speak a language; he could well from natural appetite form sounds, but no consistent expressions unless he were later to have intercourse with others 5

(q-7).

Later in the fourteenth century, in a commentary attributed to Nicole Oresme and Albert of Saxony, Hebrew was again rejected and the case of the isolated child analysed further: It must be said therefore that that boy would speak a single language entirely peculiar to himself, and when he saw outside things he would have concepts naturally representing them and therefore he would be able to impose on them an idea and express them by a word; and if two boys were brought together and fed at the same time, they would speak a language common to both; the same would happen if there were several boys. But if they were placed separate, then it would be possible for them to speak a similar language and it would be possible for them to speak totally different ones. From this it seems to follow that it would be possible for there to be two men, of which one never saw nor knew the other, who would speak each in his own way, and yet they would mutually understand each other and agree in language (q.3).6

Another contemporary philosopher, Marsilius of Inghen, yet again rejected the naturalness of Hebrew as 'silly and ridiculous' and concluded 'that that boy would remain mute until he was established by other men in a definite language; but if there were two boys placed together . . . these could mutually set up between themselves a new language'.7 Renewed linguistic efforts made in the sixteenth and seventeenth centuries towards restoring the religious unity of Europe, and towards realising through conversion the ancient ideal of the unity of mankind, by finding a common means of communication for all nations and peoples, took two directions. One was the examination of the relation of existing languages to each other; the other was the attempt to devise a new artificial universal language. The deaf and dumb would likewise be restored to humanity by scientific knowledge and by devising means of communicating through the eyes and other senses. A new search for the common elements of diverse human languages began with the comparative studies of ancient and modern tongues carried out among others notably by Sigismundus Gelenius in his Lexicon symphonicum (1537), by 5

Joannes de Janduno, Quaestiones super Parvis naturalibus (Venetiis, 1589), f. A7r; cf. Agrimi as in next note. 6 Le 'Quaestiones De sensu' attribute a Oresme e Alberto di Sassonia, a cura di Jole Agrimi (Firenze, 1983), pp. 71-2.1 am grateful to Chiara Cristiani for this important reference. There are certain parallels in the story by the 12th-century Hispano-Muslim philosopher Ibn Tufail, Hayy Ibn Yaqzdn, texte arabe . . . et traduction franchise par Leon Gauthier, 2e ed. (Beirut, 1936). The story was translated first into Latin by Edward Pococke (1671); cf. Gul A. Russell,' "The Rusty Mirror of the Mind": Ibn Tufayl and Avicenna's Psychology' in Interdesciplinary Perspectives on Ibn Tufayl, ed. Lawrence I. Conrad (Oxford, forthcoming). 7 Marsilius of Inghen, Questiones De sensu et sensato, q. 3, quodlibet 1, MS Erfurt F. 334, f. 7(8)r: translated from Agrimi as in preceding note.

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Conrad Gessner in his Mitridates (1555) where he applied the methods of natural history to the problem, and by Joseph Just Scaliger in his 'Diatriba de Europaeorum lingua' (1599) published in his Opuscula varia (1610). From this work emerged the recognition that languages formed groups, each united by grammatical structure and vocabulary in which it differed from others, so that all ancient and modern European languages (and Persian) formed one group, all Semitic languages another, Chinese and related languages yet another. Scaliger introduced an important principle by distinguishing in the first group more ancient matrices linguae from their more recent derivatives, an idea that was to be taken up by Mersenne's friend Nicolas Fabri de Peiresc,8 and was to control subsequent inquiries into the genetic history of human languages, into the supposed original language of mankind, and into the causes of its diversification through time and place. Parallel with this line of comparative analysis was that into the anatomy and physiology of the human and animal vocal organs and into the language of animals. Following Aristotle in the Historia animalium (iv.9; cf. De anima, ii.8), Girolamo Fabrici took up the first subject in his De visione, voce, auditu (1600) and De locutione et ejus instruments liber (1601), and the second in his De brutorum loquela (1603). In an area dominated from antiquity by philosophical disputes over sceptical doubts cast on the uniqueness of human language and reasoning by alleged examples of the same in animals, and over the alleged occult magical power of words and related issues, Fabrici introduced systematic observations of the actual ways in which such animals as the domestic hen and dog communicated with each other. The conception of a new universal language that could compensate for the division into national tongues had its dual origin in the Aristotelian linguistic principles developed by the scholastic grammarians, and the scholastic vision of the unity of truth evident in such as Roger Bacon and Ramon Lull. 'In order to convert the infidels easily and quickly from universal principles' wrote Lull, 'one should make a treatise which is universal to all sciences, and which leads by necessary conclusion to the truth, and can teach the way to find the specific object desired'.9 Lull offered in his combinatory symbolic logic an infallible art providing a universal method capable of demonstrating the one and certain truth to all who learnt to use it. The grammarians who advanced on scholastic ideas in the sixteenth and seventeenth centuries came to offer essentially universal lexicons as means of multilingual communication. It was Francis Bacon, in the Advancement of Learning (1605), who gave a fresh direction to the project by insisting that a true universal language must be more than simply verbal, but must be capable of communicating true notions of the real world 8

See Nicolas-Claude Fabri de Peiresc, Lettres a Claude Saumaise et a son entourage (16201637), ed. A. Bresson, (Firenze, 1992). 9 Raimundus Lullus, Tractatus de modo convertandi infideles' (1292) in Opera latina, ed. Maioricensis Scholae Lullisticae, Mallorca, Publicaciones de la Consejo Superior de Investicaciones Cientificas, 1954, fasc. iii, p. 104-5.

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based on a proper understanding of nature, that is on true scientific observation and reasoning. Hence his analysis of language became an essential part of his novum organum or new scientific method, and an ideal artificial language became what was to be called not simply a universal but also a philosophical language. Mersenne entered these disputes and projects in order to refute both the magical and the sceptical assertions of those whom he regarded as enemies of truth, continued Fabrici's empirical methods and a form of combinatory calculus, and developed his own theory of language. The originality of Mersenne's approach to language and its modelling by symbols or gestures lay in his combination of scientific with historical analysis, starting in his earliest publications. He encountered the question of natural human language first in the Cabalistic belief in the power of words, a doctrine which in Quaestiones celeberrimae in Genesim (1623) he violently rejected along with the whole of magic and the occult. He left open the possibility that God might have revealed the natural names of things to Adam in Hebrew, and he remained at first undecided whether language had developed by chance or by revelation. He still supposed in his discussion of Timposition des noms' in La verite des sciences (1625) that, since 'les noms ne nous servent que pour entendre et signifier ce que nous voulons dire, et ce que nous avons dans I'esprit', in our dealings with other men 'plus les noms approachent des choses qu'ils signifient, et plus les representent ils naiifvement, et meillieurs sont-ils'. Perhaps with the ancients, before they were given Hebrew letters, du moins leurs prononciations representoient les choses: c'est peut estre pourquoy les Chinois ont quasi autant de characteres que de choses. . . . On pourroit aussi former autant de dictions diverses comme il y a de diverses individus au monde, mais on ne peut en inventer, qui signifient la nature, et 1'essence des choses, d'autant que nous ne la cognoissons pas; il n'y a que Dieu qui le puisse faire, ou qui le puisse commander aux anges: peut estre que les noms qu'Adam imposa, avoient ce privilege: mais depuis ce temps la les noms se sont tellement eloignez de leur premiere origine, que nous n'en recognoissons plus aucun vestige. Nous voyons neantmoins que les peuples inventent diverses langues a cause de leurs divers temperamens. . . . Voyla d'ou sont venues en partie les diverses langues, ce qui a commence a la confusion de Babel avec une grande perte des sciences, car s'il n'y avoit qu'une langue au monde, on s'entrecommuniqueroit plus facilement les sciences, et on emploieroit tout le temps a les apprendre, qu'on passe a etudier aus langues etrangeres (i.6).

Later in his unpublished continuation of Quaestiones in Genesim he hardened his position, insisted that spoken words were simply physical sounds made with the mouth and tongue which functioned as arbitrary signs by means of which the same meaning could be expressed in different languages, and firmly concluded that 'there is no language natural to men besides this or that which they learn from parents or teachers'.10 It was false to say that Hebrew was natural. 10

Bibliotheque Nationale, Paris, MS lat. 17, 262, pp. 511, 536, cf. MS lat. 17, 261, pp. 3-6;

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Mersenne set out his notable theory of the origins, history and empirical science of language finally in his Harmonie universelle (1636-37) and Harmonicorum libri (1636). He insisted that a true language must be a vehicle of conscious meaning, and that this was possible only for human beings. Spoken words were physical sounds just as written words were visible symbols which had been given meanings in the course of human history arbitrarily by use. The sounds made by animals, like their visible signals, were means of communication with functions in their bodily lives, but they operated within systems of unconscious physical stimulus and response. They were no more a language in the human sense than the communications within a machine, even though the analogy of animal and mechanical communication could provide a means of analysis of true human language. He proposed to model meaning. Just as the effects of music varied with race, way of life, period and culture, so different groups of men had come to express their common understanding of meaning in a variety of languages diversified by their different historical experiences, environments, needs, temperaments and customs. Because men shared reason it was possible to translate the expression of a common meaning from any language into any other, but no existing language was naturally prior to all others. He ingeniously explored the acquisition of language in Harmonie universelle. Traitez de la voix, et des chantes', i: 'De la voix, des parties qui servent a la former, de sa definition, de ses proprietez, et de 1'ouye'. He insisted: La voix des animaux est necessaire, et celle des homines est libre; c'est a dire que 1'homme parle librement, et que les animaux crient, chantent, et se servent de leurs voix necessairement . . . ; car leur appetit sensitif estant echauffe par 1'impression de 1'imagination, commande necessairement a la faculte motrice de mouvoir toutes les parties qui sont necessaires a la voix (prop. viii).

This led to the question: 'A scavoir si 1'homme pourrait parler ou chanter s'il n'entendoit point de sons ni de paroles'. The answer seemed to depend on a virtually impossible experiment, that was to isolate a child from all sounds and words from the day of its birth for twenty or thirty years. C'est pourquoy il faut se servir de la seule raison, qui dicte qu'un homme ne parleroit point s'il n'avoit iamais ouy de paroles, parce qu'il ne s'imagineroit pas que les paroles peussent servir a expliquer les pensees de 1'esprit, et les desirs de la volonte: et quand il se 1'imagineroit, il ne sc.auroit pas de quelles dictions il devroit se servir pour se faire entendre. On peut done ce semble conclure que 1'homme ne parleroit point s'il n'avoit appris a parler.

Nevertheless, since birds sang naturally, and a man could imagine that high and low notes could represent different things, Ton peut dire que 1'homme parleroit encore qu'il n'eust point oily parler, pourveu qu'il eust quelqu'un a Robert Lenoble, Mann Mersenne ou la naissance du mecanisme (Paris, 1943), p. 514-5, 517.

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qui il addressast ses paroles' (prop. x). If the experiment with one isolated child was too difficult: Suppose que Ton nourrist des enfans en un lieu ou ils n'entendissent point parler, a sc.avoir, de quelle langue ils se serviroient pour parler entr'eux. le suppose que les enfans . . . inventeroient des sons, et des dictions pour signifier leurs desirs, car nous ne sommes plus dans la difficulte precedente, qui considere un homme tout seul qui n'a personne a qui parler. Or si nous ne supposions la verite de la foy, qui nous apprend que le premier homme a este cree droit, juste et servant, nous croirions avec les philosophes payens, que les premiers hommes ont invente la premiere langue, qui peut estre appellee langue originaire ou matrice, d'ou les autres ont este tirees: . . . ie dy premierement qu'ils formerent des sons pour se communiquer leurs pensees. Secondement, qu'il est impossible de sc.avoir de quels sons ou de quelles paroles ils useroient pour se faire entendre les uns aus autres; car toutes les paroles estant indifferentes pour signifier tout ce que Ton veut, il n'y a que la seule volonte qui les puisse determiner a signifier une chose plustost qu'une entre (prop. xi).

This led again to the question of a natural language, or failing that whether through 'la science des sons dont les langues sont formees . . . un musicien philosophe . . . peut inventer la meillieure langue de toutes les possibles'. He was not asking for 'une langue qui signifie naturellement les choses', for 'il n'est pas necessaire qu'une langue soit naturelle pour estre la meillieure de toutes, mais il suffit qu'elle exprime le plus nettement et le plus briefvement qui peut se faire les pensees de 1'esprit, et les desirs de la volonte'. But by means of a combinatory calculus described in the Traitez . . . ' book ii, 'Des chants', showing how many dictions could be made with any number of letters, it could be possible 'establir une langue universelle, qui seroit la meillieure de toutes les possibles, si 1'on sc,avoit 1'ordre des idees que Dieu a de toutes choses' (prop. xii). He went on to ask: Si nous avions une langue naturelle, . . . si nous la pourrions establir, suppose qu'elle se perdist: et parce que nous confessons que nous ne sgaurions maintenant trouver une langue naturelle, encore que nous soyons de mesme condition que celle ou nous serions apres 1'avoir perdue, il faut semblablement avoiier que 1'art et la raison que nous avons ne pourroit nous fournir les mesmes voix qui nous servent naturellement a expliquer nos passions, si nous en avions perdu 1'usage.

For no one could foresee that, among various possible signs, tears and sobs would indicate sadness and laughter joy. Moreover 'si Ton remarque les voix dont les animaux expriment leurs passions et leurs affections, on les iugera aussi indifferentes pour signifier lesdites passions, comme sont les paroles pour signifier nos conceptions, ou les autres choses dont nous voulons parler'. Thus the syllable kik, by which a hen (as described by Fabrici in De brutorum loquela) told her chickens to run and hide, had no more relation to events than the syllable glo by which she called them back. The fundamental difference between animal and human speech was not that 'la nature les auroit privez des organes necessaires a la parole', as we might have thought if we had not taught birds to speak, but that TAuteur de la nature, ou la nature intelligente

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determine les animaux, et les conduit tellement, qu'ils n'ont nulle liberte en leurs actions' (prop. xiv). He went on to discuss in some detail how the muscles of the vocal organs of different peoples became habituated to pronouncing their own languages and refractory to pronouncing others (prop, xxxvii), and to raise again the question, presented by the comparative anatomy studied by Fabrici, of what was lacking in some birds and in all quadrupeds that prevented them from being taught to imitate human speech. As for animal language, 'il n'y a nul doute que le jargon des oiseaux, et les cris des animaux, leurs servent de paroles, que Ton peut appeller la langue, et I'idiome des bestes, car Ton experimente que celles qui sont de mesme espece s'entendent aussi bien par leur voix differentes, que les hommes par leurs paroles' (prop, xxxix). The elements of speech could be explored also by the imitation of the animal and human voice by musical instruments, and by the methodical study of comparative anatomy and physiology. For 'la langue et les autres instrumens de la voix usent de differens mouvemens en prononc,ant les syllables et les lettres, comme il est difficile de les expliquer, a raison que nous ne pouvons voir ces mouvemens' (prop, xliii). Mersenne saw in his analysis of human knowledge and of its expression through the common elements of language an opening into the possibility of inventing a perfect system of communication for all men, a new universal language capable of conveying information without error. He began experimenting with the idea of making a new artificial universal language by means of the combinatory calculus showing the number of possible permutations and combinations of a given set of elements with which he had tried, in La verite des sciences (iii.10), to devise the best tune from among the number that could be composed from a given set of notes. In 1629 he forwarded to Descartes a project by an unnamed author for a new universal language. Descartes in his reply proposed as a model for the true, as distinct from an artificial, universal language, not the generalised structure that could be extracted from existing languages, but mathematics. But Tinvention de cette langue depend de la vraie philosophic', and even if it were achieved so that it represented to the judgement 'si distinctement toutes choses, qu'il lui serait presque impossible de se tromper', this could be expected only in 'un paradis terrestre'.11 Mersenne went ahead on the assumption that such an universal language could be usefully established before the perfection of the true philosophy. He argued that the only certain knowledge of things available to us was of their measurable quantities. He proposed then to combine his linguistic with his musical investigations by using his combinatory calculus to construct a system of sounds and notation for representing such quantities. Thus he wrote in Harmonie universelle, 'Traitez de la nature des sons', i: 'L'on peut se servir des sons de chaque instrument de musique, et des differens mouvenmens que 1'on

11

Descartes a Mersenne 20 novembre 1629, in P. Marin Mersenne, Correspondance, edits et annote par Cornelis de Waard avec la collaboration de Rene Pintard (Paris, 1945), ii, pp. 327-8.

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leur donne pour discourir de toutes sortes de suiets, et pour enseigner et apprendre les sciences' (prop. xxii). Then Ton peut representer tout ce qui est au monde, et consequemment toutes les sciences par le moyen des sons, car puis que toutes choses consistent en poids, en nombre et en mesure, et que les sons representent ces trois proprietez, ils peuvent signifier tout ce que Ton voudra, si Ton excepte la metaphysique. . . . D'ou il s'ensuit que le parfait musicien peut inventer des dictions, et une langue parfait, que signifie naturellement les choses, et qu'il peut enseigner les sciences sans user d'autre langage que celuy d'un luth, ou de quelque autre instrument (prop. xxiv).

'Je me suis imagine une sorte d'escripture et un certain idiome universel', he wrote of this language of quantities in a dedication to Peiresc, 'en dressant un alphabet qui contient tous les idiomes possibles, et toutes les dictions qui peuvent servir a exprimer chasque chose en telle langue qu'on vouldra. II a ceste propriete que sa seule lecture peut tellement enseigner la philosophic accomodee a son ordre, qu'on ne peut 1'oublier ou si on 1'oublie, qu'on peult la restablir sans 1'ayde d'aulcun'. He hoped that it would help 'pour inventer la maniere de communiquer avec tous les peuples du Nouveau Monde'.12 He described this language in his 'Livre de la voix', propositions xlvii, where he showed that Ton peut inventer la meillieure langue de toutes les possibles', and xlviii-xlix, and in his 'Livre des chants', propositions xiii-xix, specifying that the best language must be both economical and clear, applying to languages his tables for all possible tunes, and providing tables for all possible pronunciations. Besides mathematics and music and the comparative philology of ancient and modern phonetic tongues, the discovery of Chinese characters as both ideophones and ideographs had opened European eyes yet further to the variety of human language and its potentiality for constructed innovation. Mersenne's insights into the question were to have a decisive influence on later English projects for universal languages.13 Mersenne's study both of the physiology and comparative phonetics of natural human speech, and of the imitation of human vowels and consonants by musical instruments and by animals, led him to a further question: that of deaf mutes and how to communicate with them. Here again his empirical approach promoted scientific and experimental analysis by contrast with philosophical speculation. Thus he rejected the widely accepted ancient idea that there was a sympathetic association between the nerves of the ear and the vocal organs, so that the deaf were incurably dumb. This had been questioned from the end of the thirteenth century. Thus Jean de Jandun asked in his Quaestiones super Parvis naturalibus, 'Super De sensu', q.7: 12 A Monsieur de Peiresc vers 20 avril 1635, in Mersenne, Correspondance, ed. cit., 1959, v, p. 136-7. 13 Cf. Hans Aasleft, 'Wilkins, John (1614-1672)' in Dictionary of Scientific Biography (New York, 1976), xiv, pp. 366-8; Mary M. Slaughter, Universal Languages and Scientific Taxonomy in the Seventeenth Century (Cambridge, 1982).

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Whether all the congenitally deaf are dumb. Some have maintained that speech is convertible, namely that all the deaf are dumb and vice versa because, since some powers are mutually connected, if there is an impediment in one there will also be one in the other. . . . But this is not valid. . . . And therefore I say that someone congenitally deaf is necessarily dumb because anyone who cannot learn how to form meaningful speech at will is in that way necessarily dumb. This is selfevident, because knowing how to form meaningful speech at will comes about only through habit and social intercourse with people, but someone congenitally deaf cannot become accustomed to the expression of meaningful speech, because this requires that he hears speech of this kind.14 Again in the sixteenth century some medical authorities recognised that the deaf were dumb only because they had never heard speech. Girolamo Cardano insisted that deaf mutes were just as intelligent as the rest of humanity and could be educated through vision.15 Mersenne reported with enthusiasm the pioneering Spanish work in teaching deaf-mutes to speak. He cited in 'De la voix' the account given by the king's physician Francisco Valles of the method devised by Pedro Ponce de Leon: Quant aux muets, encore que plusieurs croyent qu'ils n'est pas possible qu'ils parlent autrement que par les signes ordinaires qu'ils font avec les mains, les yeux, et les autres parties du corps, parce qu'ils ne peuvent oiiir aucune instruction, a raison qu'ils sont sourds; il n'y a neantmoins nul doute que Ton peut tellement leur apprendre a remuer la langue, qu'ils formeront des paroles, dont on pourra leur apprendre la signification en leur presentant devant les yeux, ou leur faisant toucher les choses qu'elles signifient. D'ou Ton peut conclure qu'il faut commencer par 1'escriture pour faire parler les sourds, comme Ton commence par la parole pour enseigner a parler aux autres: de sorte que la parole et 1'escriture sont quasi une mesme chose. . . . Or 1'unique moyen d'enseigner a lire et a escrire aux sourds et aux muets consiste a leur faire comprendre que les caracteres dont on use, representent ce que Ton leur montre, et ce qu'ils voyent: car la pronunciation des lettres et des vocables, c'est a dire la parole, ne represente pas plus naturellement les choses signifiees que 1'escriture quelle qu'elle soil, puis qu'elles dependent toutes deux egalement de la volonte et de 1'institution des hommes, sans laquelle elles ne significient rien. . . . Cecy estant pose, il est facile d'enseigner a escrire toutes sortes de choses aux sourds, pourveu qu'elles puissant tomber sous le sens de la veue, ou du toucher, ou qu'elles puissent estre goustees, ou flairee; main il est plus mal-aise de les faire parler, dautant que Ton ne peut leur monstrer tous les mouvemens de la langue, et des autres parties qui forment la parole. . . . Valesius dit que son amy Ponce enseignoit tellement les sourds par le moyen de 1'escriture, qu'il les faisoit parler en leur monstrant premierement au doigt les choses qui estoient signifiees par 1'escriture, et puis en leur faisant remuer la langue jusques a ce qu'ils eussent profere quelque parole, ou fait quelque espece de son ou de voix (prop, li).16 14

Cf. above n. 5; and for the supposed irremediable link between the ear and the vocal organs Galen, Deplacitis Hippocratis et Platonis, ii.4. 12-15, 40-2, 5.1-97, De usu partium, xvi.3-4, ix.12, xi.10, De locis affectis, iv.9. 15 Cardano, Opera omnia, ii (Lugduni, 1663), pp. 72-3, x, p. 462. 16 Cf. Franciscus Vallesius, De sacra philosophia, c.3 (Lugduni, 1588), p. 78; Lorenzo Hervas y Panduro, Escuola Espanola de sordomudos (Madrid, 1795), 2t.; Abraham Farrar, 'Histrocial Introduction' to Juan Pablo Bonet, ^implication of the Letters of the Alphabet and Method of

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It was especially in France that effective teaching methods were to be developed systematically, as described by the Abbe Charles-Michel de 1'Epee in La veritable maniere d'instruire les sourds-muets, confirmee par une longue experience (1784). These, as Mersenne indicated, were a consequence of the empirical theory of language which he had done so much to promote, and which thus restored the deaf and dumb to the full human dignity and responsibility of which they had been for so long deprived by nature and society.

Teaching Deaf-Mutes to Speak, transl. H.N. Dixon (Harrogate, 1890); Ruth Elaine Bender, The Conquest of Deafness (Cleveland, Ohio, 2nd ed., 1970); Harlan Lane, When the Mind Hears: A History of the Dea/(New York, 1984); with also A.C. Crombie, 'Mathematics, Music and Medical Science' (1971), reprinted in Science, Optics and Music in Medieval and Early Modern Thought (London, 1990), pp..363-78.

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Further References Mersenne, Les mechaniques de Galilee, ed. B. Rochot (Paris, 1966), Les nouvelles pensees de Galilee (Paris, 1639), ed. P. Costabel et M.-P. Lerner, 2 vol. (Paris, 1973); C.S.F. Burnett, M. Fend and P. Gouk, The Second Sense: Studies in hearing and musical judgement from antiquity to the seventeenth century (London, 1991); V. Coelho (ed.), Music and Science in the Age of Galileo (Dordrecht, 1992); H.F. Cohen, Quantifying Music (Dordrecht, 1984); P. Dear, Mersenne and the Learning of the Schools (Ithaca, NY., 1988); A.E. Moyer, Musica scientia: Musical scholarship in the Italian Renaissance (Ithaca, N. Y., 1992); and for language K. O. Apel, Die Idee der Sprache in der Tradition des Humanismus von Dante bis Vico (Bonn, 1963, 3rd ed. 1980); H. Arens, Sprachwissenschaft (Miinchen, 1955, 2nd ed. Freiburg, 1969); A. Borst, Der Turmbau von Bable, 4 vol. (Stuttgart, 1957-63); O.V.C.M. Funke, Zum Weltsprachenproblem in England im 17'.Jahrhundert (Anglistische Forschungen, xlix; Heidelberg, 1929); G. Gusdorf, Les sciences humaines et la pensee occidentale, ii, iii.2 (Paris, 1967-69); J.R. Knowlson, Universal Language Schemes in England and France 1600-1800 (Toronto, 1975); G. Mounin, Histoire de la linguistique (Paris, 1967); R.H. Robins, A Short History of Linguistics (New York, 1967); Paolo Rossi, Clavis universalis (Milano/Napoli, 1960), V.G. Salmon, The Study of Language in 17th-Century England (Amsterdam, 1979); M.M. Slaughter, Universal Languages and Scientific Taxonomy in the 17th Century (Cambridge, 1982); G.F. Strasser, Lingua universalis, Kryptologie und Theorie der Universalsprachen in 16. und 17. Jahrhundert (Wiesbaden, 1988); F.A. Yates, Giordano Bruno (London, 1964), The Art of Memory (London, 1966), Theatre of the World (London, 1969), Collected Essays, 3 vol. (London, 1982-84); see also A.C. Crombie, Science, Optics and Music. . . chs. 9, 13, 14, 15 (1990), Styles of Scientific Thinking . . . chs. 10, 14 (1994), and above ch. 13, below ch. 15.

Appendix Nicolas-Claude Fabri de Peiresc Lettres a Claude Saumaise et a son entourage (1620-1637), edited by Agnes Bresson (Florence, 1992). A Monsieur, M. Nicolas Claude Fabry Sieur de Peiresc et de Callas, Baron de Rians, Abbe et Seigneur de Guistres, et Conseiller du Roy en la Cour de Parlement d'Aix en Provence. 'In this dedication to Peiresc of the Traitez des Consonances. . . . ', which formed part of his great Harmonic universelle (1636), Marin Mersenne offered a portrait of his friend, whose 'liberalite' had provided so much for the 'honnestes gens' and 'hommes sgavans' of all of Europe. 'Car vous ne leur fournissez seulement pas les tres-rares manuscrits, 1 es medailles et les autres reliques de la venerable antiquite dont votre Cabinet est enrichi . . . mais vous leur faites venir tout ce qu'il y a plus curieux au Levant, et dans toutes les autres parties de la terre, sans en pretendre autre chose que d'ayder a faire valoir le talent d'un chacun, et a faire paroistre la portee et 1'estendue de 1'esprit humain.' Anyone who visited Peiresc was left with the impression 'que vous n'ayez dresse vostre Cabinet que pour luy, et que tous vos biens soient aussi communs aux sgavans, que 1'air et 1'eau a tous ceux qui respirent'. Belonging to a family original from Pisa, Nicolas-Claude Fabri (1580-1637) took the name Peiresc from a village in the Alpes de Provence inherited from his mother. Education, travel and a wide circle of friendships established his style of erudition essentially as a collector, patron and organiser, but also as a practical researcher, over almost the whole range of the liberal arts and sciences. His interests were eclectic in the style of his sixteenth-century predecessors, by contrast with that of the contemporary generation of systematic philosophers, but his curiosity had a purpose and could be sharply focused. A Jesuit schooling introduced him to astronomy. On a journey to Italy during 1599-1600, he met at Padua the antiquarian Giovanni Vincenzo Pinelli and Galileo, and visited galleries, stimulating an interest in Antiquity, and in the diversity of nature, that was to mature in the study of law at Montpellier under the philologist Jules Pacius. Travel to England and the Netherlands brought him in touch with Dutch botanists, to whom he was to send seeds and the names of Provencal plants. After reading Galileo's Sidereus nuncius, he and the Provencal astronomer Joseph Gaultier were the first in

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France to observe in 1610 the four satellites of Jupiter with a telescope. Afterwards, by organising systematic observations of their positions, and of a lunar eclipse, from different points of the Mediterranean, he and Gaultier, with Pierre Gassendi, were able to calculate the length of that sea with considerably improved accuracy. Other scientific investigations carried out at Belgentier, his country house near Aix-en-Provence, led to the discovery of the lacteal vessels in man; to comparative dissections of the eyes of a variety of animals; and to the collecting for his impressive garden of seeds and plants, and of some exotic animals, from many parts of the world. With equal energy, he collected objects of art and archaeology of all kinds, materials for comparative investigations into the origins and filiations of languages, and manuscripts and books for his library, all of which he made generously available. In the early seventeenth century, scholarly and scientific communication still took place mainly be personal correspondence, and that of Peiresc, as of Galileo, Mersenne and Descartes, is a major source for the intellectual and practical life of the time. His regular exchange of letters with Mersenne over twenty years has been published in the admirable edition of Mersenne's Correspondance, begun by Cornelis de Waard and now completed by Armand Beaulieu. Mersenne sent him material concerning the science and art of music for forwarding to Rome; they discussed Galileo; Peiresc tried through Cardinal Francesco Barberini to ease the restrictions imposed on Galileo after his trial. A large part of his correspondence was published a century ago as Lettres de Peiresc by Philippe Tamizey de Larroque in seven volumes (188898), with many inconvenient omissions; this was accompanied by Les correspondants de Peiresc in twenty-one parts (1879-97). Raymond Lebegue published Les correspondants de Peiresc dans les anciens Pays-Bas (1943), and shortly before his death completed with Agnes Bresson a supplement with corrections to Volume Seven of the Lettres (1985). Now Agnes Bresson has published a major and immaculate edition, dedicated to the memory of her late preceptor, who has written a foreword, of Peiresc's letters to the philologist Claude Saumaise. This edition of Peiresc's Lettres a Claude Saumaise et a son entourage (16201637) is a major event. It begins with a perceptive and informative historical and textual introduction, which is followed by sixty-six previously unpublished letters to Saumaise occupying 375 pages, omitting those from Saumaise which are available in Tamizey de Larroque, but including in an appendix important and relevant unpublished materials by him. The letters are accompanied by historical exegeses in notes of extraordinary richness and erudition often as long as the letters themselves. The result is a model of expert editing and historical analysis, and a major contribution to intellectual and cultural history. Equally impressive are the source and bibliographical materials, glossary and indexes, comprising a further 170 pages. These, with their clear analytical presentation and ample coverage, will be a necessary instrument of research for all future students of the intellectual and cultural history of the

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period. The volume will be of particular value for the new historical interest in collectors, collections and museums, for the history of science, for the history of languages and for orientalists. Peiresc is properly located for the first time in this splendid volume in the variegated life especially of the Mediterranean world in the early seventeenth century. He emerges as a savant for whom the natural sciences belonged as much as literary learning to a humanist culture, and who organized his collecting in the service of the whole Republic of Letters. The enthusiastic intelligence of these letters and their vivid detailing of so many objects of his curiosity make them a continuous pleasure to read. We meet his competition with Lord Arundel for the purchase of the Arundel marbles now in the Ashmolean Museum; postal facilities and travel in the Mediterranean area; Turkish pirates who captured and threw overboard Pinelli's library, and the recovery from the sea of those sections of it now in the Ambrosiana and Marciana libraries. Pursuit of aspects of life in the ancient Mediterranean area, Egyptian, Etruscan, Greek, Roman, Byzantine, leads to requests for information and manuscripts about systems of money, numerals and computing, weights and measures, military arms and uniforms, strategy and tactics, chronology, astronomy, music, divination, plants and animals. Peiresc acquired in manuscript 'un livre arabe assez ample de 1'histoire des animaulx ou il se trouvera possible quelque chose de plus que ce que nous en avons dans les anciens grecs, puis qu'ils sont sur les lieux ou les animaulx estranges habitent'. There is a long saga of attempts to identify a particular 'animal etrange' which arrived from Ethiopia at Marseilles for the King: a kind of antelope now called Oryx beisa. He collected ancient inscriptions, medals, coins and bronzes, ivories, enamels, paintings and other works of art; he researched into the history of medicine, drugs, epidemics and hygiene; and from all these inquiries built up an important collection of manuscripts in Greek, Latin, Italian, Arabic, Coptic and other European and oriental languages. It was in his investigations into the origins and filiations of languages that Peiresc appears at his most inventive in this remarkable correspondence. He was a pioneer in historical derivation by the comparative method. This had been initiated for languages in the sixteenth century by Sigismundus Gelenius and Guillaume Postel, and developed among others by Conrad Gessner, using the methods of Aristotelian biological taxonomy. By the end of the century, it had been recognised that there were correspondences between apparently diverse languages, such as German and Persian, as between Arabic and Hebrew. The guiding principle was introduced in 1599 by Joseph-Juste Scaliger, by using common elements of European languages to show that these could be arranged in a genetic order of more ancient matrices linguae and their more recent derivatives. Scholars then looked for rules of etymological derivation to explain the transition of one language into another. The first approaches to historical philology could be arbitrarily formal and limited only to the derivation of words, but the horizon was expanded empirically by such

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scholars as Saumaise, and later conceptually by the recognition, notably by Leibniz, that linguistic affinities must be determined also by grammatical structure. Meanwhile, attention was given both to the circumstances promoting the preservation of forms of speech and writing, and to the causes of linguistic diversification in time and space. It was to answer these questions that Peiresc outlined a programme in this correspondence. One central theme was his attempt to find in Coptic the key to the Egyptian hieroglyphs, but he envisaged a comparative historical philology encompassing all the ancient and modern languages of Europe, the ancient Near Eastern as well as classical languages of the polyglot Bible, Persian, Scythian and languages farther East, with the decipherment of ancient texts and inscriptions and of the occult symbolism of the Cabbala. The fundamental task of historical philology was to trace the history of languages back through their secular diversifications to the matrices linguae of each group and thence perhaps to the original universal language of mankind. The Jesuit Athanasius Kircher, whose interest was inspired by Peiresc, hoped to achieve this by using a Lullian art of combinations, first to decipher the hieroglyphs and then to reduce all languages to their pristine original. By contrast, the empirical method used by Peiresc and Saumaise was to distinguish by comparative analysis the words and idioms belonging to the matrix from the additions, modifications and losses brought about by the contingencies of historical experience. Peiresc noted in his study of Coptic that an older language could be preserved in a more recent script, as when some ancient inscriptions on precious stones used Greek letters for Egyptian or Hebrew words. He argued from analogies with the processes of change observable in modern languages, for example through mixing, addition or loss at the frontiers of France with Flanders, the Basque regions and Genoa, and through invasions and migrations, how changes in remote Antiquity could have come about. He looked behind the distortions of pronunciation and spelling for the original 'matrice racine' of names of rivers and towns, and thinking of the Etruscan inscriptions in his large collection of ancient medals he wondered 's'il y avoit moyen de penetrer dans cette langue etrusque par les regies de cez mattrices langues septentrionales'. He begged Saumaise 'd'excuser la liberte possible trop grande de mes conjectures, qui sont si subjectes a equivoque et par consequent a tomber dans 1'abbus'. The style is the man, and for both correspondents the learned author of this fascinating and elegantly produced edition cites Isaac Casaubon: 'Ubi cum studio veritatis, viget studium antiquitatis.'

15 Le Corps a la Renaissance: Theories ofPerceiver and Perceived in Hearing

Music has been strangely neglected by historians of science until very recently, yet music was one of the fundamental Greek mathematical sciences, an important part of the medieval mathematical quadrivium, and from the middle of the 16th century the subject of active mathematical and experimental research1. The science of music, like that of optics, was concerned primarily with the relation of perceiver to perceived: with the identification and quantitative analysis of clues to sensations. For music there were two basic questions : the discovery of the acoustical quantities expressible in numbers that stimulated the diversities of auditory perception, and the discovery of the anatomical structure and physiological functioning of the ear as the receiver of those quantitative clues. In the first question science entered immediately 1. Cf. G. Reese, Music in the Middle Ages (New York, 1940), Music in the Renaissance, 2nd ed. (London, 1954); M.R. Cohen and LE. Drabkin. A Source Book in Greek Scince (New York, 1948); C.A. Traesdell, "The theory of aerial sound. 1687-1788" in Leonhard Euler, Opera omnia, 2 series, ed. A. Speiser, E. Trost, C. Blanc, LG. du Pasqrier, xiii (Lausaimae, 1955), pp. vii-cxvii, "Hie rational mechanics of flexible or elastic bodies, 1638-1788" in ibid, xi 2 (Turici, 1960). 15-141 ; C.V. Palisca, "Scientific empiricism in musical thought" in Seventeenth Century Science and the Arts, ed. H.H. Rhys (Princeton, NJ., 1961), 91-137, "The science of sound and musical practice" in Science and the Arts in the Renaissance, ed. J.W. Shirley and F.D. Hoeniger (Washington, D.C., 1985a), 59-73 ; D.P. Walker, Studies in Musical Science in the Late Renaissance (1967-76) (London, 1978) ; A.C. Crombie, "Mathematics, music and medical science" (1971) in Science, Optics and Music in Medieval and Early Modern Thought (London: Hambledon Press, 1990), Styles of Scientific Thinking in the European Tradition, chs 3, 7, 10 (London: G. Duckworth, 1994), Marin Mersenne: Science, Music and Language (forthcoming), A.C. Crombie and A. Carugo, Galileo Galilei's Natural Philosophy (forthcoming); S. Dostrovsky, "Early vibration theory : physics and music in the seventeenth century", Archive for History of Exact Sciences, xiv (1975), 169-218 ; F.W. Hunt, Origins in Acoustics : The science of sound from antiquity to the age of Newton (New Haven, Conn., 1978) ; J.C. Kassler, The Science of Music in Britain, 1714-1830, 2 vol. (London & New York, 1979), introduction : "The 'science' of music to 1830" reprinted in Archives Internationales d'histoire des sciences, xxx (1980),

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into the problems of art through the analysis of consonance and dissonance, resonance and related phenomena, and the devising of scales (to be embodied in the tuning of musical instruments) that were at once ordered on some rational principle and able to satisfy the needs of the ear. Why was the number of consonances limited, and what determined the frontier between consonances and dissonances ? These were fundamental questions for musical theory from the 14th century. Musical theory in the medieval quadrivium was based primarily on Boethius's De institutione musicae. Sound was propagated through the air as a succession of impulses. Pitch depended on their frequency. Consonances were produced by the blending of high and low notes with frequencies in the ratios of the perfect set of numbers 1 to 4. They affected the soul because of its structural conformity through these ratios with the harmonies alike of the cosmos and of musical sound. Hence the moral power of music stressed in the Timaeus (35B-36B, 46C-47E), by Aristotle in the Politics (viii, 5) and by Augustine. Within this context at once of educational doctrine, natural philosophy and mathematical science, medieval students of music had a choice of two main types of theory : that of Plato and the later Pythagoreans, which related the consonances to purely numerical ratios, and was associated with cosmic numerology ; and that of the Aristotelians, which began with experience and looked beyond mere numbers for physical and causal explanations of sound and its effects in sensation. Thus Aristoxenus made the ear and not numerical theory the proper judge of consonance and dissonance. Grosseteste offered a sophisticated explanation both of the physical propagation of sound and of its effects on sentient beings. Later in the 13th century knowledge of Aristotelian theories was greatly extended by the translation into Latin of the commentary or paraphrase by Themistius on De anima, and of the Problemata then believed to be by Aristotle himself. Scientific discussion of the whole subject entered a new phase with the exposition of this work by Pietro d'Abano in the commentary which he completed at Padua in 1310. Pietro d'Abano promoted a causal as distinct from simply numerical treatment of the phenomena of sound (in particular pitch and consonance) that was to re-establish the Aristotelian as opposed to the Platonic or late Pythagorean approach to the science of music. His influence on musical theory was comparable to that of Roger Bacon on optical theory through his exposition of Alhazen2. From this time a number of different factors promoted the development of musical science along with musical practice and of disputes that accompanied both. 111-36, "Music as a model in early science". History of Science, xx (1982), 103-39 ; P.M. Gouk, "Tlie rede of acoustics and musical theory in the scientific work of Robert Hooke", Annals of Science, TOO. vii (1980), 573-605, "Acoustics in the early Royal Society 1660-1680", Notes and Records of the Royal Society, xxx vi (1982), 155-75, The Anatomy of Music : Sound and science in seventeenth - century England (London : G. Duch worth, forthcoming) ; H.F. Cohen, Quantifying Music : The science of music at the first stage of the scientific revolution, 1580-1650 (Dordrecht, 1984) ; F. de Buzon, "Science de la nature et theorie musicale chez Isaac Beeckman (1588-1637)", Revue d'histoire des sciences, xxx viii (1985), 97-120. 2. Cf. Palisca (1985), Crombie, Styles..., chs. 7,10.

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The attention given in the 14th century by mathematicians such as Walter of Odington and Philippe de Vitry to musical problems, arising especially out of the innovations of polyphony and in musical instruments, greatly improved the precision of musical notation. Later in the 15th century knowledge of Greek musical theory was extended far beyond that presented by Boethius and used in the medieval quadrivium by the recovery and new availability of Greek and Latin texts. New sources included Aristoxenus, Euclid, Nicomachus, Ptolemy, Porphyry, Adrastus, Aristides Quintilianus and Theon of Smyrna. At the same time the revival of Platonism led by Marsilio Ficino brought late Pythagorean purely numerical musical theory into fresh confrontation with the Aristotelian insistence on starting from experience and looking beyond numbers for causes. The new sources pulled musical theorists, and practitioners concerned with scales and the tuning of instruments, in both directions. Between the middle of the XVIth century and the middle of the XVIIth the science of music was tranformed by a number of happenings. Musical theorists were forced by the striking innovations in more recent polyphony and in musical instruments to reconsider the whole question of the theoretical limit fixed to consonances by restricting them to ratios between the numbers 1 to 4. Recent music exploited popular song in using intervals beyond this boundary and tunings other than that of the Pythagorean scale of the Timaeus (35B-36B) as set out by Boethius. Musical theorists following Aristoxenus in basing their perception of consonances primarily on the complex factual responses and demands of the ear came to doubt whether there was any precise boundary between consonance and dissonance. At the same time they looked systematically for enlightenment on this question and on acoustics generally in the texts of Greek authors, especially of Aristoxenus and Ptolemy and of the Aristotelian De audibilibus and Problemata, becoming readily available in Latin translations and sometimes in the vernacular. The problem for the mathematical scientists was to discover what the grounds of music were in the physical motions and propagation of sound and in the process by which sound stimulated hearing in a percipient organism. They had to ask how numerical ratios became sensations of pitch, consonance, dissonance and so on, and why some were pleasant and others unpleasant. Their point of departure was in effect a physical analysis of the relation between the quantitative primary properties of sound and the secondary qualities of sensation generated by physiological and psychological happenings through the ear. Central to the whole of 16th-century acoustical theory was the musical problem of devising on some mathematical principle scales and systems of tuning that would meet the demands of the ear. This involved explanations of consonance and dissonance. Gioseffo Zarlino in Venice broke new theoretical ground by extending the realm of consonance from ratios within the first four numbers to ratios within the first six, the so-called senarius or senario. In this he took into account recent

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polyphonic practice by including among the consonances the major third (5:4), minor third (6:5) and major sixth (5:3), and he also proposed rules of composition based on the new limit3. It was in offering to the composer Cipriano de Rone an analysis of the musical problems involved in tuning that the mathematician Giovanni Battista Benedetti took the first step towards the mathematical and physical demonstration of the fundamental proposition that pitch depended on frequency of vibrations or impulses, and hence that the musical intervals were ratios of these frequencies, whatever instrument produced them4. Benedetti proposed a physical explanation of consonance which would account for these phenomena. Starting from the proposition that the frequencies of two strings with the same tension were inversely proportional to their lengths, he argued that the consonance of intervals depended on the coincidence of the terminations of their vibrations. Then, since the the more frequent the coincidence the higher the degree of consonance, he could arrange the consonances in an order by multiplying the two terms of each of their ratios. This put relative consonance and dissonance alike on a continuous scale which ignored the boundary of the senario. The complexity of the relation of science to art in this period is exemplified by Vincenzo Galilei. He again was led by musical problems of consonance and tuning to a scientific study of sound. As a skilled lutanist he was sent by his humanist patron Count Giovanni Bardi in Florence to study musical theory with Zarlino in Venice, just before Zarlino succeeded Cipriano de Rore at St. Mark's. On his return, Galilei then became musical preceptor to the musical academy of the Camerata which met at Bardi's home, and a composer. Starting in agreement with Zarlino he turned, under the influence of the humanist musical scholar Girolamo Mei, who worked in the Vatican Library, into his most ruthless critic. Mei argued for an empirical conception of the art of music. How was it Galilei asked him "that the practitioner does not follow at all the designs of the theorist, as he should, since the theorist gives the reason why" ? Mei replied that "considering and understanding are one thing and putting into operation another. The former belongs to the intellect and the latter to sense. But the sense of hearing is not as perfect as the judgement of the intellect because of the material and other circumstances that always necessarily accompany the former". Hence "the practitioner, having simply to satisfy the sense"5, needed no further precision than would achieve that end. The ear could tolerate considerable deviations from any mathematical scale. 3. Gioseffo Zarlino da Chioggia, U istitutioni harmoniche (Venetia, 1558; new eds. 1573,1589); M. Shirlaw, The Theory of Harmony (London, no date : 1917? reprinted De Kalb, DI, 1955) ; J.M. Barbour, Tuning and Temperament, 2nd ed. (East Lansing, Mich., 1953) ; cf. Palisca (1961). Humanism in Italian Renaissance Musical Thought (New Haven, Conn., 1985b) ; D.P. Walker (1978). Music, Spirit and Language in the Renaissance (London, 1985). Cohen (1984). 4. Cf. Baibour (1953), Shirlaw (19177). Palisca (1961). (1985a). Cohen (1984). 5. C.V. Palisca, Girodamo Mei (1519-1594) : Letters on Ancient and Modern Music to Vincenzo Galilei and Giovanni Bardi (American Institute of Musicology, 1960), 65, 66,103,125-6.

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Galilei's main target became Zarlino's attempt to restrict music to consonant ratios within the numerical senario. He launched his attack on Zarlino in his Dialogo della musica antica et della moderna (1581), dedicated to Giovanni Bardi. His work is a good example of the contemporary search at once for the best system and for its true ancient model. He gave in the Dialogo an analysis of the vohime published in 1562 of Latin versions by Antonio Gogava of Aristoxenus, Ptolemy and the Aristotelian De audibilibus, as well as of the Latin version by Jean Pena of Euclid's Sectio canonis (1557). Among the manuscripts inherited by his son Galileo he left a translation of Aristoxenus into Italian6, and he explicitly followed Aristoxenus in trying to build a rational art of music up from auditory sensation instead of imposing on it a rigid mathematical scheme in the style of the Platonists and Pythagoreans. He pointed out that intervals and tunings that sounded pleasant or harsh on some instruments could sound the reverse on others, and that familiarity could accustom the ear to change its preferences7. Galilei was unsympathetic towards the more numerological and cosmic aspects of Platonism, and he looked in the Dialogo beyond the mere numerical harmony of Zarlino's "harmonic numbers" or "sounding numbers" for the physical basis of sounds and their effects on the ear. To a reply by Zarlino, Galilei again pressed his attack with \\isDiscorso intorno all' opere di messer Gioseffo Zarlino da Chioggia (1589). Central to the interest of the dispute for scientific and artistic thought was Galilei's rejection of Zarlino's conception of what was natural, in the sense of given in nature as distinct from made artificially by man or in man by his cultural experience and history. Galilei argued that it was "natural" that the ratios of the octave and the fifth were concords, but that the division of the former into seven and the latter into four intervals "is entirely a matter of art" (p. 21). All scales were made by man and so were "artificial" (p. 31). "In the same way it can be said of speech that it is natural and artificial" (pp. 81-82). Thus all systems of intonation had to be learnt. For although "the material of singing, which is the voice..., is given by nature, to know then how to place it to form the intervals both consonant and dissonant, and also what are needed in measure and proportion, belong to an" (p. 99; cf. 127-8). Systems of intonation like languages in so far as they were made by man could undergo historical development. In the course of his critique Galilei described an important acoustical discovery which he used against Zarlino's numerical explanation of consonances. He showed in the Discorso, and in manuscripts apparently written between its completion and his death in 1591, that the traditionally accepted Pythagorean ratios of the consonances were ratios only of lengths. Thus while the octave ratio for the lengths of strings was 6. Biblioteca Ntzionale Centrale di Firenze, MSS Gtlilciani 8, ff. 3'-38* ; cf. A. Procissi, La colltxione Gal'deiana della Biblioteca Nazionale Centrale di Firenze, i (Roma, 1959), 8 ; Aristoxeni... Harmonicorwn elemenlorium libri iii, Q. Ptolemaei Harmonicorum seu De musica libri Hi, Aristotelis De obiecto auditus fragmentum ex Porphyrii commentafiis, omnium mine primum latine conscript* et editt ab Ant Gogavino Gnwknsis (Venetiii, 1562). 7. Vincentio Galilei, Dialogo... (Fiorenza, 1587), 32,47-8,55.

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2:1, for their tensions it was the squares of these numbers 4:1, and he asserted that for organ pipes it was their cubes 8:1, the ratio of their volumes. Likewise the ratios of tensions of strings were for the fifth 9:4 and for the fourth 16:9. It seems clear that, as he claimed, Galilei must have made his experiments with strings, but he cannot have reached his proportion for pipes by experiment for the pitch of a pipe is proportional to its length, not its volume. He could easily have discovered this from an organ builder. Galilei seems to have been captivated by a neat mathematical sequence making the consonances depend successively on the unit, square and cube (for the octave 2:1, 4:1 and 8:1) of the three quantities he considered8. Nevertheless he showed not only that the accepted story of Pythagoras's experiments with hammers must be false, but also that if other quantities besides length of strings were considered, ratios outside Zarlino's senario produced recognized consonances. Like Benedetti (who had not explicitly drawn this conclusion) Galilei showed that there was no natural or numerical boundary between consonance and dissonance, but that they were distinguished by ear. Moreover an could complement nature, could yield conclusions about nature, and could transcend nature in artificial things. Galilei's analysis of the relation of perceiver to perceived in hearing was to be developed into a systematic doctrine by Isaac Beeckman, Descartes and Mersenne. Using essentially Benedetti's theory of consonances, Descartes wrote in 1630 to Mersenne that the "calcul que je faisois des retours des sons pour faire consonances" showed that in terms of the physical motions or blows producing them some intervals were simpler than others. "Je dis plus simple, non pas plus agreable [...] Mais pour determiner ce qui est plus agrdable, il faut supposer la capacit6 de 1'auditeur, laquelle change comme le goust, selon les personnes [...]; de mesme que Tun aime mieux ce qui est doux, et 1'autre ce qui est un peu aigre ou amer, etc."9. Thus concerning the perfection of consonances, "il y a deux choses a distinguer, a s^avoir ce qui les rend 8. Vincentio Galilei, Discorso... (Fiorenza, 1S89), replying to Zarlino, Sopplimenti maicali (Venelia, 1588), with Galilei, "Discorso particolare intomo alia diversita delle forme del diapason" MSS Galileiani 3, ff. 45'-47r, 54", "Discorso partioolare intomo all* unisono", ibid., ff. 5^-57'; cf. Procissi, i (1959), 3-6, 8 ; Nicomachus, Harmonicos manuale c.6, Macrobius, Commentarii in Somnium Scipionis ii.l, and Boethius De institution* musica i. 10-11 for the story of Pythagoras's alleged discoveries ; Galileo Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze Giomata i (Leida, 1638) in Le Opere, ed. nazionale, viii (Fircnze, 1898), 138-50, cf. x, 86-87, xix, 594, 599, 602, 604, and the Discorsi a cure di A. Carugo e L. Geymonat (Torino, 1958) for similar acoustical experiments perhaps bagun with his father at Florence ; Palisca (1961), (1985a), D.P. Walker, "Some aspects of the musical theory of Vincenzo Galilei and Galileo Galilei", Proceedings of the Royal Musical Association, c (197374), 33-47, reprinted with changes in (1978). Unfortunately Walker's assertion in this article, that Galileo could not possibly have made his famous experiments with a file and with a goblet of water to show that the musical intervals were ratios of frequencies (Opere, viii, 141-5), was based on his failure to understand that Galileo was dealing not with vibrations but with what are now called standing waves: cf. Crombie, Styles..., ch. 10. 9. Descartes to Mersenne L 1630 in Mersenne, Correspondence, publiee et annotee par C. De Waard avec R. Pintard, ii (Paris. 1937), 370-1 ; cf. A. Pino, Descartes et la musique (Paris, 1907) ; B. Augst, "Descartes'* Compendium on Music", Journal of the History of Ideas, xxvi (1965), 119-32 ; Buzon, (1981), Cohen (1984).

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plus simples et accordances, et ce qui les rend plus agreables a 1'oreille. On, pour ce qui les rend plus agr&bles, cela depend des lieus ou elles sont employees, et il se trouve des lieus ou mesme les fausses quintes et autres dissonances sont plus agreables que les consonances, de sorte qu'on ne scauroit determiner absolument qu'une consonance soit plus agitable que 1'autre." Musical perceptions then were often subjective and influenced by their context. "Mais on peut dire absolument quelles consonances sont les plus simples et plus accordantes, car cela ne depend que de ce que leurs sons s'unissent davantage Tun avec I'autre, et qu'elles approchent plus de la nature de 1'unisson ; en sorte qu'in peut dire absolument que la quarte est plus accordante que la tierce majeure, encore pour I'ordinaire elle ne soit pas si agr6able; comme la casse est bien plus douce que les olives, mais non pas si agr&ble a nostre goust"10. Mersenne was to elaborate this line of analysis into a comparative physiological and ethological inquiry into the variation of the effects of music on the ear and the emotions according to age and temperament, to the musical context, to the cultural habits of different peoples, and in different kinds of animals. In his great Harmonic universelle (1636-37), in which he presented his own fundamental researches, together with those of relevant predecessors, into the mathematical physics and the psychology of sound, he established for the first time a systematic science of music in all its aspects11. Those inquiring into the way in which sound effected sensations in a sensitive body found themselves confronted by a number of different kinds of problem : the physical propagation and motions of sound and their acoustical quantities, the physiological mechanisms by which the ear responds to them, the means of relating these physical quantities and motions to the sensations they produced, and the empirical phenomena of auditory perception. Before the work of Mersenne, Descartes and other contemporaries made these distinctions explicit, invertigators working in different intellectual and academic contexts did focus during the 16th century on different kinds of problems which they developed into different subjectmatters for research. Thus while students of music as a mathematical science and art were inveitigating the acoustical quantities and their effects in musical sensation, and philosophers were explaining in their own ways the interactions between body and soul, anatomists in the medical schools had been looking into the physiology of the ear. Anatomical research, starting in Italy early in the 16th century not far in advance of where Galen had left off, had by the beginning of the 17th century clarified and in large part discovered the main macroscopic details of the human auditory mechanism and its innervation12. According to the current theory derived from Aristotle (De 10. Descartes to Mersenne 13.i. 1631, ibid., iii, 2* ed. par B. Rochot (1969), 24-25. 11. Cf. R. Lenoble, Marin Mersenne, ou la naissance du mecanisme (Paris. 1943) ; A.C. Crombie, "Mersenne, Marin (1588-1648)" in Dictionary of Scientific Biography, ed. C.C. Gillitpie, ix (New Yoik. 1974), 316-22, Styles... ch. 10, Science, Optics and Music..., Marin Mersenne. 12. Cf. A. Politzer, Geschichte der Okrenkeilkunde, i (Stuttgart, 1907); A.C. Crombie, The study of the senses in Renaissance science" (1964) in Science, Optics and Music...

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anima ii. 8), the motion transmitted from a sounding body through the air produced a corresponding motion of the air enclosed in the ear. Elaborating this with anatomical details, the Dutch physician Volcher Goiter in his "De auditus instrumento" (1573)13, the first special monograph to be written on the ear, identified the proper organ of hearing as the internal air in the cavity of the middle ear. "To have a sensation of anything" he wrote, "there must be a mutual action and affection (actio et passio) between the sentient thing and the thing sensed, and for this there must be mutual agreement between the two. Whence it follows that when the external air acts, the internal or implanted air is affected, the internal air receiving the alteration of the external air and being moved in the same way from outside. But this does not happen immediately, but through the interposition of the membrane and of certain ossicles wonderfully designed by nature". The external air "affected by the quality of sound" transmitted its pulsations to the drum, whence they were transmitted through the ossicles to the "enclosed air" and thence through the windings of the ear unaltered to "the auditory nerve. By means of this passage and agency, the image of the sound (strepitus imago) is at last transmitted to be seat of sensation (principiwn sentiendi)" (c. 1). He thought that the bony labyrinth and cochlea of the inner ear acted like the coils of a musical instrument to augment the sound (c. 15). Discussion of the physiology of hearing concentrated on the identification of the sensitive organ and on its mode of operation with that of the other parts, on the analogy of the operation of the eye in focusing visual images. Somewhat earlier than Goiter the Italian anatomist Guido Guidi had proposed that "the principal instrument of hearing" was the air enclosed in the inner ear, adding that his proposals "are to be understood more as conjectures than as scientific knowledge"14. Later in 1600 Andre* du Laurens located the proper organ of sensation in the cochlea, but insisted that it was not the enclosed air but must be the termination of the auditory nerve15. Guilio Casserio insisted on this likewise in his De vocis auditusque organis historia anatomica (1600-01), a marvellously illustrated work which with Girolamo Fabrici'sDe visione, voce, auditu (1600) systematized auditory anatomy16. Attempts at more quantitative investigations of auditory physiology followed Mersenne's prescription that no one could succeed in this "unless he combines the 13. Volcher Colter, "De auditus instrumento" in Exiernarum et internarum principalium Humani corpora partium tabulae (Nurembergae, 1573) ; cf. Politzer (1907), Crombie (1964), R. Herrlinger, Volcher Colter, 1534-1576 (Nuremberg, 1952). 14. Vidus Vidius, De anatomia carports humani libri vii, vii, c.5 (Ars medicinalis, iii, Venetiis, 1611), 322-3. 15. Andrea Laurentius, Historia anatomica humani corporis, xi, quaestiones 9-10 (Francofurti, 1600), 428-9. 16. Cf. L. Premuda, "Casseri (or Casserio), Giulio (c. 1552-1616)" in Diet. Sci. Biog. iii (1971), 98 100 ; B. Zanobio, "Fabrici, Girolamo (or Fabricius ab Aquapendente, Geronimo Fabrizio) (c. 15331619)" in ibid., iv (1971), 507-12.

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principles of physics and medecine with mathematical reasoning"17. This was to be done at the Academic Royale des Sciences, with a considerable debt to the still qualitative comparative studies of Thomas Willis of Oxford18. In 1667 Claude Perrault proposed for the Academic a programme of comparative research into the structures and functions of all the organs composing the bodies of animals ; in 1677 he undertook "d'examiner a fond tout ce qui appartient au sens de 1'ouye"19. The culmination of this pan of his programme was the Traitt de I'organe de I'owe (1683) by Joseph Guichard Duverney in which, with acknowledgements to the physicist Edme Mariotte, Duvemey proposed an explanation of the analysis of pitch by the ear modelled on the selective sympathetic resonance of the strings of a lute. He would "tirer de la mechanique de ces parties quelques consequences par lesquelles on peut expliquer leur usage et la maniere dont nous appercevons les sons et les bruits differens... ; mes conjectures me paroissent asses vraisemblables, mais d'autres seront peut-estre d'un autre goust. Quoy qu'il en soit, je croiray avoir bien reussi, si je puis les obliger par cette essay a nous dormer quelque chose de meilleur"20.

17. Marinus Mersennus, Quaestiones in Genesim, c.iv., vers 21, q. 57, art. 16 (Lutetiae Parisiorum, 1623), 1696b. 18. Thomas Willis, De anima brutorum, pan i, cc. 10, cf. 3-15 (Oxonii, 1672) ; G.S. Brett, The Philosophy of Gassendi (London, 1908) ; P.P. Cranefield, "A sevcntcenth-ccntuiy view of mental deficiency and schizophrenia : Thomas Willis on 'stupidity or foolishness", Bulletin of the history of Medicine, xxxv (1961), 219-316 ; A. Meyer and R. Hierons, "On Thomas Willis's conception of neurophysiology", Medical History, ix (1965), 1-15,142-55. \9.Histoire de I'Acadtmie Royale des Sciences, i (Paris, 1733), 18, 35-37 (1667), 117 (1670), 223 (1677). 20. Joseph Guichard Duvemey, Trait/ de I'organe de I'owe (Paris, 1683), 68-9 ; cf. R.S. Stevenson and D. Guthrie, A History of Oto-Laryngology (Edinburgh, 1949) ; Crombie (1964).

Rene Descartes, curious portrait by an unknown artist, drawn perhaps in 1642 in Holland (see Oeuvres, ed. C. Adam et P. Tannery, xii, 1910, pp. xv—xvi, 75).

16

Expectation, Modelling and Assent in the History of Optics Part I: Alhazen and the Medieval Tradition KEPLER'S MEDICAL friend Johann Brengger wrote to him in 1604 after the publication in that year of his account of the formation of the optical image in the eye: 'From what I have seen before on the operation of the camera obscura of Giambattista Porta . . . I have always persuaded myself that vision occurred by the reception of the images (species) of visible things on the retina. But I am in doubt, for everything would be received there inverted, whereas vision occurs erect'.1 The contemporary force of this to us perhaps trivial difficulty directs us at once to the presuppositions and expectations that gave rise to it. From there in turn we can reach some measure of Kepler's originality and of his limitations. Brengger's comment alerts us also to the role of models, in particular during the preceding century that of the camera obscura, in the investigation of ocular physiology. A model of course embodies a theory, whether it is a scale model of selected significant features of the situation modelled or an analogical model of the formal relations between phenomena without identity of material parts, whether it is an abstract postulate or is actually constructed, and whether its function in scientific argument is exploratory or explanatory. A model according to the 16th-century Italian engineer Giuseppe Ceredi, with 'nature itself as if become mechanical in the construction of the world and of all the forms of things', could enable the investigator, by modifying it as required, to come 'to the perfection of art and to the stable production of the effect that is expected'.2 Likewise Leibniz was to point to the

'Brengger to Kepler 23.xii.1604, in Kepler's Gesammelte Werke, W. von Dyck, M.Caspar, F. Hammer (eds), 18 vol. (Munich, 1937-1959), xv, pp. 90-91. See on the subject of this paper A. C. Crombie, The mechanistic hypothesis and the scientific study of vision', Proceedings of the Royal Microscopical Society, 2 (1967), 3-112 with extensive bibliography, reprinted in Science, Optics and Music in Medieval and Early Modern Thought (London, 1990); 'Science and the arts in the Renaissance', History of Science 18 (1980), 233-246; 'Experimental science and the rational arts in early modern Europe', Daedalus 115 (1986), 49-74; 'La Dioptrique et Kepler', in Le Discours et sa methode, N. Grimaldi and J.-L. Marion (eds) (Paris, 1987), pp. 131-144; and Styles of Scientific Thinking in the European Tradition (London, 1994), with further discussion, documentation and bibliography. 2 G. Ceredi, Tre discorsi sopra il modo d'alzar acque da' luoghi bassi (Parma, 1567), pp. 5-7.

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Fig. 1. Euclid: the geometry of vision.

usefulness of 'analogies . . . in making predictions about matters of which we have as yet little experience' and 'in investigating the true causes of things, for it is always easier to discover the cause of a phenomenon which several things have in common'.3 A model then offered a means of exploring a natural phenomenon through the known properties of an artifact, by reducing both to a common form provided by an appropriate general theory which defined their common scientific provenance and guided the inquiry to their common explanatory principles. It offered an antecedent theoretical analysis that could suggest new questions to put to nature. It operated in scientific argument within a framework of generally accepted theoretical commitments, concerning both the nature of the world and the appropriate style of reasoning, which determined the expectations of those involved and the assent they would give to its conclusions. For the historian attempting to unravel these commitments and their consequences it is essential to pay close attention to the contextual meanings of terms, to philosophical philogy: Ceredi's term mecanica for example meant not simply machinary in its later sense, but rather as the Greek mechane a contrivance or device of any kind. To understand the commitments of the science of vision at the time of Kepler, as at that of Alhazen, we must take a long view. The Greek natural philosophers in their search for the simplest and most economical principles of nature established theoretical modelling as a method of inquiry at the very beginning of Western scientific thinking. Thus they exploited the speculative power of geometry by reducing astronomy to the properties of the sphere and its radii, and the phenomena of visual perspective to those of the straight line and the angle. They could then develop their research into the phenomena primarily theoretically within the model itself, with a minimum of immediate reference to observations. Greek optical theory was essentially a theory of visual perception which aimed to make the process of vision yield the perceptions we had of the visible scene. Euclid created the science of geometrical

3 Leibniz, Elementa physicae, ii (c. 1682-1684) in Philosophical Papers and Letters, ed. and transl. L. E. Loemker (Dordrecht, 1969), p. 284.

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vision: from

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Robert Fludd, Utriusque cosmi... historia: Microcosmus (Oppenheim, 1618).

optics and perspective by taking the eye as the point of origin of lines of vision, of which he postulated the essential properties: that they were rectilinear, that they formed a perspective cone with its apex at the eye and its base at the object seen, that things appeared to be equal, larger or smaller according to whether the angles subtended at the eye were equal, larger or smaller, and so on. In this way he could demonstrate from his premises, without immediate observation, the appearances that things must have in direct vision and in the extension of visual space in plane and curved mirrors (Figs 1 and 2). The problems recognized in Greek optics all followed from the primary commitment of all its theories after Euclid, whether geometrical, physiological or philosophical, to making the process by which vision was effected yield an immediate explanation of visual perception. This was the commitment of Ptolemy in his combination of experimental measurement with geometry, of Galen in his inquiry into the physiological functions of the different parts of the eye and his identification of the anterior surface of the crystallinus (the modern lens) as the sensitive receptor, and of the philosophers whether Platonic, Aristotelian, Stoic or Epicurean in their theories of how vision was caused.

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The specific character of Greek optics can be defined by comparison with what happened later. This exemplifies the need in the history of thought to examine problems not only at their own horizon of time but also in the sequence of subsequent insights offering solutions in other contexts. The striking difference between Greek and later medieval and modern optical theory is the absence of any Greek conception of the eye itself as an imageforming optical instrument and hence of any analysis of its dioptrical function. This was surely related to the absence of any purely physical conception of light, independent of the perceptions it generated but the only intermediary between object and eye. Related to this again was the absence of any understanding of the dispersion of light into colours (despite well-known examples of this phenomenon) and hence of any understanding of the physical nature of colour. The explanation of perception by the Stoic visual flux emitted from the eye, or by the entry into it of the ready-made Epicurean images, or by some incorporeal process, made any geometrical analysis of the formation of images irrelevant. The technical capacity was there, but conceptually attention was directed elsewhere. The conceptual change that made this the central problem for visual theory was initiated in the context of 1 Ith-century Arabic thought by the physicist Ibn al-Haytham, known in Latin as Alhazen. Taking the eye as an optical instrument analagous to any other, Alhazen carried out a mathematical and experimental analysis to show how it formed images within itself of the objects from which it received rectilinear rays of physical light. His essential postulate was that the image was formed by the stimulation on the sensitive anterior surface of the crystallinus of points corresponding to the points in the visual field from which the rays came. The image was a pattern of stimulation, not a focused optical image. But by offering this as an immediate explanation of visual perception, he left still unanalysed the different categories of question involved but not distinguished in the Greek theory of vision. The most obvious difficulty was to show how the eye, which on his optical analysis formed an inverted and reversed image, could yet cause us to see as we did. The eventual solution was given by a second change in conceptual strategy initiated by Kepler and made explicit by Descartes. A dead eye as Aristotle had insisted might be an eye only in name. Kepler's reply was effectively that in order to find out how the living eye enabled us to see as we did, the physiological problem of how it functioned as an optical instrument had first to be solved in isolation. He separated the optical geometry of the eye from the perspective geometry of visual perception. Then he turned this round and showed how the rays coming from an apex at each point in the visual field made up a multitude of cones with a common base on the crystallinus, now recognized as a focusing lens, whence each was brought to a focus on the retina where together they formed an inverted and reversed image. Thus the eye functioned dioptrically

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like a dead camera obscura containing a lens. The other problems of the relation of perceiver to perceived, the empirical psychology of perception, and the causation by a physical agent of sensation in sentient beings, could then likewise all be liberated from each other, investigated separately, and their relations re-examined. From the viewpoint of the seventeenth century we can distinguish then four quite different kinds of question wrapped up together in the visual theory inherited from the Greeks, which were separated in the new theory coming from Kepler and Descartes. The first was physical and physiological: the operation of the eye as an optical instrument like any other physical instrument. Secondly there was the relation of the formation of images in the eye to the perception of the objects of these images, and more generally the relation of visual perception to the physiological clues involved. Thirdly there was the ontological question of the relation of a physical stimulus as cause to sensation as an effect in a quite different category. Fourthly there was the empirical psychology of visual perception as a matter of independent autonomous observation apart from physiological or philosophical theory. Alhazen accepted as his starting point the Greek commitment of optics to finding an immediate explanation of visual perception, but he transformed the subject both conceptually and by his style of argument. He transformed optical theory by explicitly distinguishing light from vision, and by investigating first the properties of light and then on that basis the process by which light effected vision by means of the eye. At the same time he developed systematically a specifically experimental as well as mathematical argument in exemplary combination. He took from Alkindi the basic principle that everything in the world emits rays in every direction and applied this to light. In a series of experiments with sighting tubes and other devices, and with a camera obscura of which he studied the operation, he demonstrated the basic postulates of his optics: that light was emitted rectilinearly in all directions from all points on the surface of both luminous and illuminated bodies, whether these were terrestrial or were celestial like the Sun and Moon; and that its propagation was rectilinear whatever its form, whether direct, reflected or refracted. He recognized with brilliant originality that the eye did not simply receive the likenesses of things seen, but must be treated as an optical instrument that itself formed images of them from the light entering it. He rejected the extromission theory that sight was brought about by some kind of action sent out by the eye as supposed in their different versions by Euclid, Ptolemy and Galen; and he rejected the Epicurean intromission theory supposing that already-formed copies of objects entered the eye. The pain inflicted by very bright light, after-images both of bright objects and of bright colours, and a variety of other observations showed that 'light produces some effect in the eye', that 'illuminated colours act on the eye' and that light and colour were

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Fig. 3. The anatomy of the eye from a contemporary illustration inserted by Risner in editing Alhazen, Optica I, 4 (Basel, 1572).

virtually identical so that colours were apprehended only through light.4 His problem then was to discover how the eye formed images of bodies from the light emitted from all their points in all directions. Alhazen adopted the basic ocular anatomy which Galen had related to Ptolemy's geometrical optical analysis and which had been described in detail by Hunain ibn Ishaq (Fig. 3).5 In the globular body of the eyeball with its coats *Opticae thesaurus Alhazeni Arabis libri septem . . . Vitellionis Thuringopoloni libri x, omnes instaurati... a Federico Risnero (Basel, 1572); i, 1.1, p. 1 and i, 3.3, p. 3. All references in the text are to this edition. See Al-Hasan ibn al-Haitham, The Optics, books i-iii: "On direct vision", transl. with introduction and commentary by A. I. Sabra, 2 vols. (London, 1989). On Alhazen see also M. Schramm, 'Zur Entwicklung der physiologischen Optik in der arabischen Literatur', Sudhoffs Archiv 43 (1959), 289-316; M. Schramm, Ibn al-Hay (hams Weg zur Physik (Wiesbaden, 1963); M. Schramm, 'Ibn al-Haythams Stellung in der Geschichte der Wissenschaften', Fikrun Wa Fann 6 (Hamburg, 1965), 1-22; G. F. Vescovini, Studi sulla prospettiva medievale (Turin, 1965a); Crombie (1967: above n. 1); R. Rashed, 'Le Discours de la lumiere d'Ibn al-Haytham (Alhazen)', Revue d'histoire des sciences, 21 (1968), 197-224; R. Rashed, 'Optique geometrique et doctrine optique chez Ibn al-Haytham', Archive for History of Exact Sciences 6 (1970), 271-298; S. M. Straker, Kepler's Optics (Indiana University Ph.D. Thesis, 1971; Ann Arbor, Mich., 1980); A. I. Sabra, 'Ibn al-Haytham... (965-c. 1040)', in Dictionary of Scientific Biography 6 (New York, 1972), pp. 189-210 (for writings in Arabic including those on the camera obscura, etc. not translated into Latin); A. I. Sabra, The physical and the mathematical in Ibn al-Haytham's theory of light and vision', in Commemoration volume of Biruni International Congress in Tehran (Tehran, 1976), pp. 439-478; A. I. Sabra, 'Sensation and inference in Alhazen's theory of visual perception', in Studies in Perception, P. K. Machamer and R. G. Turnbull (eds) (Columbus, Ohio, 1978), pp. 160-185; D. C. Lindberg, Theories of Vision from al-Kindi to Kepler (Chicago, 1976); G. A. Russell, 'The emergence of physiological optics', in Science in Islamic Civilisation, R. Rashed and R. Morelou (eds) (London, 1990). For Greek geometrical optics see Euclid, L'optique et la catoptrique, transl. into French by P. Ver Eecke (Paris and Bruges, 1938); Ptolemy, IS optique, A. Lejeune (ed.) (Louvain, 1956); A. Lejeune, Euclide et Ptolemee (Louvain, 1948); A. Lejeune, Recherches sur la catoptrique grecque (Brussels, 1957). 'Hunain ibn Ishaq, The Book of the Ten Treatises on the Eye, M. Meyerhof (ed.) (Cairo, 1928).

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Fig. 4. From The 'Opus Majus' of Roger Bacon, v. /. Hi. 3, ed. Bridges ii. 24 (Oxford, 1897). The diagram is not anatomical, but a geometrical model showing the curvatures of the different refracting media according to Alhazen's optical theory of the eye. The 'centre of the eye' (centrum oculi, b) coincides with the centres of curvature of the cornea, the aqueous humour (albugineus) and the anterior surface of the glacialis. In front of this are the centres of the vitreous humour and the choroid (uvea), and behind it is the centre of the sclerotic (consolidativa). The object al sends rays which pass perpendicularly through the cornea at m, o and strike the anterior surface of the glacialis perpendicularly at c, d, thus passing through without refraction. At the posterior surface of the glacialis the rays are refracted away from the centre so that they do not intersect; thus an erect image of the object reaches the entrance of the optic nerve at the back of the eye.

surrounding its transparent humours each part had its ordained function. He accepted and extended Galen's argument showing that the anterior surface of the crystallinus and that alone was the sensitive receptor, of which all the other parts were the instruments. (The crystallinus formed the anterior part of the spherical glacialis, and was sometimes called the anterior glacialis or simply

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glacialis; the posterior part was the vitreus humor.) But he formulated the problem of image-formation in the tradition not of medical physiology but of the mathematical sciences. His stroke of genius was to impose on ocular anatomy and physiology a geometrical-optical model that would meet the requirements of his theory of visual perception. He postulated that in the optical system of the eye all the surfaces were spherical, with centres on the line passing from the centre of the pupil to the centre of the termination of the optic nerve at the back (i.4.4-12, pp. 3-7; Fig. 4). When light entered through the pupil, it was known 'that it is a property of light to act on the eye and that it is the nature of the eye to be affected by light' (i.5.14, pp. 7-8). But if all the forms of light and colour entering the pupil from every point on the surface of an object stimulated the crystallinus, all would be confused and no clear image could be formed. His solution was to postulate that only the forms striking its anterior surface perpendicularly, and without weakening by refraction, would cause sensation. As Risner (the editor of the 1572 Latin edition) summarized it in his heading: 'Distinct vision is brought about by straight lines coming from the visible object perpendicular to the surface of the eye and thus single points of the visible object maintain the same position on the surface of the eye as on the visible object'. Alhazen justified his choice of the perpendicular by arguing that among all the lines that reached the eye at different angles it was unique, whereas none of the others could be distinguished from any other as 'more fitting', and that 'the action of the light coming along that perpendicular is stronger than the action of light coming along oblique lines. It is therefore more fitting that the crystallinus should sense from any point only the form coming to that particular point along the rectilinear perpendicular, and should not sense from that point what comes to it along refracted lines' (i.5.18, pp. 9-10). This postulate of his theory of visual perception required the further postulate of his anatomical geometry that the centres of curvature of both surfaces of the cornea, of the albugineous (or aqueus) humour, and of the anterior surface of the crystallinus should all coincide at the centre of the eyeball, so that the forms falling perpendicularly on the first should pass perpendicularly without refraction through them all (i.4.4-12, pp. 3-7; Fig. 4). Thus his style of argument was to impose on both ocular anatomy and on optical physiology geometrical postulates that would satisfy the immediate expectations of vision. 'Vision is brought about through a pyramid of which the apex is in the eye and the base on the visible object' (i.5.19, pp. 10-12), as Risner headed Alhazen's account of the construction of the visual cone or pyramid which he followed Ptolemy and Galen in taking over from Euclid. This would be geometrically the same whether vision took place by intromission or extromission, but Alhazen having refuted extromission composed it only of the forms of light and colour entering the eye along the perpendiculars. Because the

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crystallinus was optically both transparent and dense, it received the forms but prevented them from passing right through: 'Thus the forms are fixed in its surface and body, but weakly: it is the same with any transparent body that is somewhat dense'. Now 'the glacialis is disposed (praeparatus) both to receive those forms and to sense them. Therefore the forms pass into it because of its receiving and sensing power (propter virtutem sensibilem recipienteni). When the form reaches the surface of the glacialis it acts on it and the glacialis is affected (patitur) by it, because it is a property of light to act on the eye and a property of the eye to be affected by light'. This action passed into the glacialis 'only along straight radial lines, because the glacialis is disposed to receive the forms of light vertically on radial lines'. The light was accompanied by colour, 'and from this action and affection will arise the sensation of the glacialis from the forms of visible things that are at its surface and pass into its whole body; and from the ordering (ordinatio) of the parts of the form at its surface and in its whole body will arise its sensation from the ordering of the parts' (i.5.25, p.15). This action which light effects in the glacialis is of the same kind as pain . . . . From there this sensation occurring in the glacialis is extended to the optic nerve and comes to the anterior part of the brain, and there resides the ultimate sensation and the ultimate sentient (ultimus sensus et sentiens ultimum), which is the sensitive power (virtus sensitiva) that is in the anterior part of the brain. That power apprehends the sensible things (comprehendit sensibilia), but the eye is only an instrument of that power, because the eye receives the forms of things seen and sends them to the ultimate sentient, and the ultimate sentient apprehends those forms and apprehends from them the visible things that are in them. That form at the surface of the glacialis is extended into its body, and thence into the subtle body that is in the concavity of the nerve until it reaches the common nerve, and with the arrival of the form at the common nerve vision is completed. By means of the form arriving at the common nerve the ultimate sentient apprehends the forms of things seen (i.5.26, pp. 15-16). Alhazen thus took over from Galen both his basic ocular anatomy and his conception of the process of visual sensation and perception completed in the brain. He also adopted and adapted from Aristotle his conception that the forms of light and colour, transmitted in straight lines as qualities of visible objects, brought about vision by altering in turn the transparent medium and through that the eye, where they endowed the anterior glacialis with those qualities. Thus 'essential light (lux essentialis) is apprehended by the sentient from the illumination of the sentient body, and colour is apprehended by the sentient from the alteration (alteratio) of the form of the sentient body and from its coloration'. Accidental light coming from illuminated objects was apprehended in the same way (ii. 2.18, p. 35; cf. i.5.28, i.5.30, pp. 17-18; ii. 2.16, pp. 34-35). The anterior glacialis was naturally disposed or prepared (nr0nnmtu
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selectively in the direction of the perpendicular, from which they were also stronger (i.5.14, pp. 7-8; i.5.18, pp. 9-10; i.5.25, p. 15; ii.1.4, p. 26; ii.2.42^4, pp. 57-58). Of the forms emitted by each point of the visible object, those which stimulated corresponding points of the anterior glacialis reproduced there the form of the whole object, made up of the forms of these separate points which maintained the order they had in the object. This form was a pattern of stimulations perceptible only from within by the sensitive power itself; it was not an optical image visible to an external observer such as was produced in a camera obscura.6 Each of the eyes corresponded exactly to the other in structure and in position relative to the common nerve, so that in normal binocular vision, when both their axes were directed towards an object, the form of the object would be reproduced at corresponding points in each eye. Thus the object was seen as one 'because the two forms coming from a single thing to the two eyes run together on reaching the common nerve and are superimposed one on the other and made into one form: and by means of that form made up of two forms the ultimate sentient apprehends the form of that thing'. If the spectator pushed one eye out of place he would see two things instead of one, so that the thing must be apprehended, sometimes as one and sometimes as two, not in the eyes but beyond them in 'another sentient' to which the two forms came either united or separately. The evidence that the forms of things seen are extended through the concavity of the nerve and come to the ultimate sentient, and after that vision is completed, is that an obstruction in that nerve destroys vision and when the obstruction is destroyed vision is restored. The art of medicine attests this'. But what it was that passed beyond the eyes was a problem. 'It could be said that the forms coming to the eye do not come through to the common nerve, but a sensation (sensus) is extended from the eye to the common nerve, just as the sensations of pain and touch are extended, and the ultimate sentient then apprehends that sensible thing'. Certainly 'the sensation reaching the common nerve is a sensation of light and colour and ordering, and that by means of which the ultimate sentient apprehends light and colour in some kind of form' (i.5.27, pp. 16-17). The problem was: what kind? The relation of the forms of light and colour to the optical physiological requirements of his theory of visual perception remained a problem to the end. Alhazen argued that 'transparent bodies are not changed by colours, nor are they altered (alterantur) by them with a fixed alteration, but the property of colour and light is that their forms are extended along straight lines' (i.5.28, p. 17). Nor were the lights and colours passing through a transparent medium affected by each other, as he showed by an experiment with a camera obscura. For 6

Cf. Sabra (1972: above n. 4).

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when in one place several candles are put at various different points, all opposite an opening leading into a dark place (locus obscurus), with a wall or an opaque body opposite the opening, the lights of those candles appear on the body or that wall distinctly according to the number of the candles. Each one of them appears opposite one candle on a line passing through the opening. If one of the candles is screened off, only the light opposite that one candle disappears, and if the screen is removed the light reappears. This can be tried at any time: for if the lights intermixed in the air they would become intermixed in the air in the opening and would have to pass through intermixed, and they would not become separate later. But we do not find this so. Hence the lights are not intermixed in the air, but each one of them extends on straight lines. Thus the 'form of each and every light' was extended through the transparency of the air 'which does not lose its own form. And what we say about light and colour and air is to be understood of all transparent bodies, and the transparent coats of the eye' (i.5.29, p. 17). But the camera obscura was not a model for the eye, for in it all the forms of light and colour passing rectilinearly through the aperture to the screen would contribute to the image there, whereas in the eye only those falling on the anterior glacialis perpendicularly would contribute to the form of the object seen. 'Indeed the sentient member (membrum sentiens), namely the glacialis, does not receive the form of light and colour as the air and other nonsentient transparent bodies receive it, but in a way different from that way. Since that member is disposed (praeparatum) to receive that form, so it receives it in so far as it is sentient and in so far as it is transparent'. As he had already explained (i.5.26), 'its affection (passio) by that form is of the same kind as pain. Hence the quality of its reception from that form is different from the quality of reception by nonsentient transparent bodies'. Thus 'the glacialis is altered (alteratur) by light and colour to the extent that it senses (sentiat)\ by an 'alteration (alteratioy that 'is necessary but with a nature not fixed', for it disappeared when the light did. The glacialis was so 'disposed to be affected by colours and lights and to sense them' in a way that air and other transparent bodies and the transparent coats of the eye anterior to it were not. As again he had already explained (i.5.19), of the many forms of light and colour emitted into the air and transparent bodies, 'the eye... apprehends those according to the pyramid which is distinguished between them and the centre of the eye' (i.5.30, pp. 17-18). In the whole process the eye and all its parts 'are instruments by which vision is completed'. The cornea covering the pupil (foramen uveae) retained the fluid albugineous humour, which like the cornea was transparent 'so that the forms would pass through it and reach the glacial humour'. The black, strong, spherical uvea which contained the albugineous humour 'is black so that the albugineous humour and glacialis would be obscured in such a way that the forms of light would make their appearance in them weak: because weak light is more visible in a dark place and escapes notice in a place full of light'. This seems to suggest

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Fig. 5. From Roger Bacon, Opus maius, v. i. viii. /: Oxford MS Bodleian Library, Digby 234 (15 cent.) f. 247.The rays from the right (dextrum m) and left (sinistrum p) ends (labelled in reverse in MS) of the visible object pass perpendicularly through the anterior surface of the flattened glacialis (g, f) and are refracted at its posterior surface (q, u) so that instead of intersecting (below a) they reach the optic nerve (c) with the image correctly orientated. The rays passing into the vitreous humour (held to be optically denser than the glacialis) are refracted according to Ptolemy's rules towards the perpendiculars (bl, bs) meeting at its centre of curvature (b).

that the eye was like a camera obscura with the glacialis as its screen. The glacialis had 'many properties by which sensation is completed', but it was still an instrument to that end. 'But the optic nerve, on which the whole eye is constructed, is hollow so that the visual spirit may run through it from the brain and may reach the glacialis and may in turn give to it sensitive power (virtus sensibilis), and so that the forms may pass through in the subtle body running in its concavity until they reach the ultimate sentient which is the anterior part of the brain' (i.6.33, pp. 20-21). Alhazen's treatment of the fundamental problem that followed from this analysis exemplifies the decisive dominance of his optical theory by his commitment to finding an immediate explanation of visual perception. For

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how did the 'sensible image' of the object made on the anterior glacialis maintain its necessary order in its passage through the posterior transparent media of the eye to the common nerve where it was finally perceived by the ultimate sentient? The first stage of the problem was geometrical, for if the forms coming on the visual pyramid reached its vertex at the centre of the eye they would be reduced to a point, which being dimensionless had no order; and if they passed beyond the vertex their order would be inverted and reversed. His solution again was to contrive further optical and anatomical postulates to prevent these happenings. He supposed that the centre of curvature of the posterior surface of the anterior glacialis — forming its interface with the posterior glacialis or vitreous humour — and that interface itself were in front of the centre of the eye, and that the anterior and posterior glacialis had different transparencies, that is optical densities. Then, applying Ptolemy's rules and constructions for refraction at plane surfaces to sections of spheres, he argued that the forms would be refracted at the posterior surface of the anterior glacialis in the directions preventing their meeting at the vertex of the pyramid (Figs 4 and 5). This would require that the vitreous humour was the denser. He structured his argument formally in hypothetical syllogisms leading by elimination to the one true conclusion: If therefore the form does not reach the concavity of this nerve arranged as it is on the glacialis, neither will it reach the common nerve with its proper arrangements. But the form cannot extend from the surface of the glacialis to the concavity of the nerve in straight lines and still preserve the proper positions of its parts: for all those lines meet at the centre of the eye, and when they continued straight on past the centre their positions would be reversed: what is right would become left and vice versa, and what is above would become below and below above. Thus, if the form was extended on straight radial lines it would be congregated at the centre of the eye and become as it were a single point. And . . . if it was extended on straight radial lines and passed through the centre, it would become reversed in accordance with the reversal of the intersecting lines along which it was extended. Therefore the form can come from the surface of the glacialis to the concavity of the nerve with its parts in their proper positions only on refracted lines, cutting across radial lines.... This refraction must occur before it reaches the centre, because if the lines were refracted after passing through the centre they would be reversed. It has been shown [i.5.18] that this form passes through the body of the glacialis on straight radial lines:... therefore the form is refracted only by its passage through the body of the glacialis. It has been said [i.4.4]... that the body of the glacialis is o unequal transparency and that its posterior part, called the vitreous humour, has a different transparency from the anterior part. There is no body in the glacialis different in constitution (forma) from the anterior body except the body of the vitreous. It is a property of the forms of light and colour that they are refracted when they meet another body of different transparency from the first. Therefore the forms are refracted only at their entry into the vitreous humour. This body has a transparency different from that of the body of the anterior glacialis only in order

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that the forms can be refracted in it. Its surface must be in front of the centre of the eye so that the forms are refracted at this surface before they pass through the centre; and this surface must be correspondingly ordered, because if it were not the form would appear monstrous after refraction (ii.1.2, p. 25).

The second stage of the problem concerned what happened after the forms had passed into the vitreous humour. For the radial lines play no part in the ordering of the thing seen except only at the glacialis, because at this member is the origin of sensation. It has also been shown [i.5.15, 16, 18] that it is impossible for the form of the thing seen to be ordered on the surface of the eye with the likeness (imago) of the thing seen and the smallness of the sentient thing except through these lines. These lines are then nothing but the instrument of the eye through which the apprehension of things seen is completed with their proper arrangement. But the arrival of the forms at the ultimate sentient does not require the extension of these lines rectitudinally (ii.1.3, pp. 25-26; cf. ii.1.8, p. 29).

Moreover, as he had asserted (i.5.30), the glacialis did not receive the forms like other transparent bodies 'because the sentient member receives these forms and senses them and they pass through it because of its transparency and the sensitive power that is in it. Thus it receives these forms according to the reception of sensation (sensus). But transparent bodies receive them only with the reception by which they receive for reflection (ad reddendwri), and they do not sense them'. Because of this difference 'the extension of the forms into the sentient body does not have to be in straight lines, as transparent bodies demand'. Hence 'only the anterior part of the glacialis is made appropriate for the reception of the forms on straight radial lines; but the posterior part, which is the vitreous humour, and the receptive power which is in that body, is not made appropriate to the sensation of those forms but only to the preservation of their ordering' (ii.1.4, p. 26). Therefore forms are refracted at the vitreous humour by two causes, of which one is the difference of transparency of the two bodies, and the other the difference of the quality of reception of sensation between these two bodies'. If their transparencies were the same, the form would be extended into the vitreous humour along the straight radial lines without refraction; 'but it would be refracted because of the difference of the quality of sensitivity (sensus); and thus because of refraction the form would be monstrous, or because of its arrangement there would be two forms'. In fact both causes acted corroboratively so that after refraction a single form passed from the glacialis through to the optic nerve. Therefore the forms reach the vitreous humour ordered according to their order on the surface of the eye, and this body receives them and senses them'. They were refracted by the two causes on entering the vitreous humour, and 'then this sensation and these

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forms are extended through this body until they reach the ultimate sentient', by way of the hollow optic nerve, 'like the extension of the sensations of touch and of pain to the ultimate sentient' (ii.1.5, p. 26; cf. i.5.25, p. 15; i.5.27, p. 16). The forms were not refracted on passing through the posterior surface of the vitreous humour into the visual spirit or 'sentient body, which is in the concavity of the nerve', because their transparency or density was the same (ii. 1.6, p. 27). Despite his geometrical model, Alhazen confined his whole analysis of the properties of the eye within the inherited Greek conception of it as a living sentient organ. He did not distinguish exclusively and consistently the different kinds of question involved in vision, which were to become clear only in the different conceptual context of the 17th century: fundamentally those of the physical properties of light and the operation of the eye as an optical instrument independently of its function in perception. It operated like a dead optical instrument only in so far as it shared the optical properties of insentient transparent bodies, but it was unlike them in being itself an active agent of perception. Alhazen's forms of light and colour were emitted in straight lines by all luminous or illuminated bodies whether or not there was an eye present to see them, and they entered the pupil just as they might enter any optical instrument. But once they had struck the anterior glacialis they were sorted, not by a purely geometrical optical process but by its selective directional sensitivity, into a sensible and not a geometrical optical image of the object seen. He tailored ocular anatomy to the requirements of this theory of sensation. These included the symmetry of the two eyes and optic nerves so that each of their images would be formed at corresponding points and could unite as a single image at the common nerve filled with the visual spirit, so to reach the ultimate sentient (i.5.27, pp. 16-17; cf. ii.1.6, pp. 26-27; ii.2.16, pp. 34-35; Hi.2.2-17, pp. 76-87; vii.6-36, pp. 267-268). He described how the eye, by its selective directional sensitivity operating through the central axis of the visual pyramid on which the forms struck the surface of the anterior glacialis perpendicularly, certified its perception of the whole visible object by means of rapid movements taking the axis over the separate points from which the forms were emitted (ii. 1.7-9, pp. 27-30; ii.2.42-44, pp. 57-58; ii.3.64-69, 75, pp. 67-71, 73-74; vii.6.37, pp. 268-270). But he never made clear whether it was the form of light and colour coming from the object seen, or its action in producing a sensible image in the anterior glacialis, or both together, that passed inwards from the posterior surface of that body to the ultimate sentient located in the region extending from the common nerve to the anterior part of the brain. Exactly how far its propagation continued to be optical and rectilinear, and where it became something different, remained ambiguous. Following Galen he distinguished between the sensation occurring in the anterior glacialis and the discriminative perception made by the ultimate

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sentient. Essential to this was that the sensation should retain its order as it passed through the visual spirit connecting them. Again the ambiguity over what passed produced a matching ambiguity as in Galen over the relative functions of those sentient bodies, but Alhazen explained the process of perception very clearly. The particular qualities (intentiones) that are distinguished by the sense of vision' he wrote 'are many, but generally divided into 22'. These included light, colour, distance, location, shape, size, number, motion, transparency, shadow. Others were perceived by combinations of these, as straightness or curvature, increase or decrease, dryness or wetness by the relative stability or movement of the parts, and emotions by the expressions produced by the movements of the face (ii.2.15, p. 34; cf. ii.2.12, p. 31). The qualities of light and colour going from the object seen into the eye thus differed in different ways which had to be distinguished and interpreted: And since it is so, distinction and inference (argumentatio) by the distinctive power (virtus distinctivd), and recognition of the forms and their signs, will occur only by the recognition or distinction of the distinctive power of the forms coming into the concavity of the common nerve to the apprehension of the ultimate sentient, and by the recognition of the signs of these forms. And so the sentient body extended from the surface of the sentient member all the way to the concavity of the common nerve, namely the visual spirit, is sentient throughout, because the sensitive power is in the whole of this body. Since therefore the form is extended from the surface of the sentient member all the way to the concavity of the common nerve, any part of the sentient body will sense the form; and when the form reaches the concavity of the common nerve, it is apprehended by the ultimate sentient, and then distinction and inference will occur.... In this way apprehension of the forms of visible things will occur in the sensitive power, the ultimate sentient, and the distinctive power..... But distinction occurs only by the distinctive, not the sensitive, power (ii.2.16, pp. 34-35).

Alhazen's Optica provided on its arrival in the Latin West in the 13th century a model of scientific argument, a guide to the relation of perceiver to perceived not simply in vision but in general, and the definitive treatment of optics in all its aspects for nearly four hundred years. The Latin Optica established the subject as a major experimental and mathematical physical science in the scheme of medieval theoretical and practical knowledge. Historically most important of all was the adoption by Roger Bacon, especially in the Opus maius (completed by 1267), followed by John Pecham and Witelo, of Alhazen's geometrical model of the eye as an image-forming device. Witelo wrote his Perspectiva or Opticae libri decem (in 1270 or soon afterwards) as a compendium of Alhazen's Optica and provided jointly with the latter the essential account of the subject (eventually to be published by Risner in 1572 in one integrated volume) until the 17th century. Bacon (in Opus maius v. 3.2.2-4) also developed Robert Grosseteste's conception of a magnifying glass by

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means of constructions based on those of Ptolemy for plane and of Alhazen for curved refracting surfaces. Spectacles were invented in northern Italy at the end of the 13th century.7 Some particular questions arose in two different contexts, that of the camera obscura and that of the eye, over Alhazen's assertion that rectilinear propagation was a fundamental property of light. The camera obscura became a familiar instrument in the second half of the 13thcentury, used for example in observing solar eclipses.8 The question here was how to account by means of rectilinear propagation for the circular shape of the image cast through an angled aperture with straight sides of a certain size at a certain distance from the screen. Why was it that when the aperture was relatively small or its distance from the screen relatively large the image assumed the shape of its luminous source independently of the shape of the aperture? Lacking the analysis into superimposed images made by Alhazen in an Arabic work not translated into Latin, different kinds of answer were proposed. Their essential features for present purposes, without going into details, was that they preserved the principle of rectilinear propagation within the wider principle that nature always acts for the best, and they made the operation of the camera obscura a familiar problem. The question for the eye was that faced by Alhazen concerning the propagation of the sensible image from the crystallinus or anterior glacialis through the vitreous humour and then through the winding optic nerves to the ultimate sentient in the brain. Bacon expounded Alhazen with an interesting new terminology. Since the rays of the visual pyramid or cone carrying the image must travel rectilinearly through the vitreous humour in accordance with the principles of geometrical optics, if they continued all the way in the same straight line they would intersect and then 'what was right would become left and vice versa, and what was above would be below, and so the whole order of the thing seen will be changed'. To prevent this 'nature has contrived' the position and the transparency of the vitreous humour so that the rays would be refracted at its interface with the anterior glacialis, and that there would be no further refraction of the images (species) on their passage from the vitrous humour into the nerve which 'is filled with a similar vitreous humour as far as the common nerve' (Opus maius v. 1.7.1). These optical principles belonged to what he called the common laws of nature and they operated necessarily in all inanimate media. But propagation in an animate medium 7

See E. Rosen, The invention of eyeglasses', Journal of the History of Medicine and Allied Sciences 11 (1956), 183-218; Crombie (1967: above n. 1); V. Illardi, Occhiali alia corte di Francesco e Galeazzo Maria Sforza (Milan, 1976a), and 'Eyeglasses and concave lenses in fifteenth-century Florence and Milan', Renaissance Quarterly 29 (1976b), 341-360. "See D. C. Lindberg, The theory of pinhole images from antiquity to the thirteenth century', Archive for History of Exact Sciences 5 (1968), 154-176; 'A reconsideration of Roger Bacon's theory of pinhole images', ibid. 6 (1970a), 214-223; The theory of pinhole images in the fourteenth century', ibid. 6 (1970b), 299-325. See also Straker (1971: above n. 4), and his 'Kepler, Tycho, and the 'Optical part of astronomy': the genesis of Kepler's theory of pinhole images', Archive for History of Exact Sciences 24 (1981), 267-293.

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Fig. 6. Alberti's grid (1435): from Diirer, Underweysung der Messung (1538).

Ciuitaiij I poM

Fig. 7. A painting as a cross-section of the visual pyramid: from Fludd (1618).

does not hold to the common laws of nature (leges communes nature), but claims for itself a special privilege. This propagation does not take place except in an animate medium, as in the nerves of the senses; for the image follows the tortuosity of the nerve and pays no attention to the straight path. This happens through the power of

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the soul in regulating the path of the image, according to what the operations of an animate thing require (iv.2.2).

Thus for the benefit of natural order 'the capability of the power of the soul' could dispense the image from the 'common laws of natural propagations (leges communes multiplicationum naturalium)' (v. 1.7.1) shared by light and other forms of energy.9 Pecham a little later used similar terminology and noted in discussing the possibility of deviation from rectilinear propagation in the camera obscura that this must happen in the visual spirits in the optic nerve in order to preserve the image. Here 'the mode (via) of the spirits brings about that advance of the image partly outside the rectitudinal', but in the camera obscura this would be done by a 'natural fittingness (convenientta)'. But, he added, 'these things are asserted without prejudice to a better opinion'.10 The Latin perspectivists established Alhazen's geometrical model of vision and made these related optical problems familiar in the West equally for mathematical natural philosophers and for visual artists. Thus Lorenzo Ghiberti, belonging to the first generation of artists to exploit the new technique of linear perspective invented early in the 15th century by Filippo Brunelleschi, used in his discussion of the theory and practice of the method in sculpture all the main optical writers from Aristotle and Euclid to Bacon, Witelo and Pecham and an Italian version of Alhazen's Optica made in the century before.11 The theory of perspective, described for the first time by his younger contemporary Leon Battista Alberti, was based on the visual pyramid or cone extending from the eye as its apex to the object seen as its base. A drawing in true perspective was then a plane cross-section of this pyramid: he described how to make it correctly by viewing the object through a chequered screen or grid (Figs 6 and 7).12 The technique of perspective, showing by means of calculated visual clues how to represent a three-dimensional object on a plane surface, produced in effect a perceptual model of the scene before the eyes. Its exact measurement and true scaling introduced into science and technology a completely fresh means of communicating information through pictorial illustrations, and at the same time a new conception of modelling. Especially dramatic were the effects on the depiction of the external and 9 Cf. Roger Bacon, De multiplicatione specierum, ii.2, ed. and transl. by D. C. Lindberg in Roger Bacon's Philosophy of Nature (Oxford, 1983), pp. 102-103; Lindberg (1970a: above n. 8). '"John Pecham, Perspectiva communis, ed. and transl. by D. C. Lindberg in John Pecham and the Science of Optics (Madison, Wisconsin, 1970), i. 7 revised, pp. 78-81. "Lorenzo Ghiberti, 7 Commentarii, i. 1, ii. 12, 22, iii. 2, J. von Schlosser (ed.) (Berlin, 1912); cf. G. F. Vescovini, 'Contribute per la storia della fortuna di Alhazen in Italia', Rinasdmento 2nd Series, 5 (1965b), 17-49. 12 Leon Battista Alberti, De pictura (1435) in On Painting and On Sculpture, C. Grayson (ed.) (London, 1972); cf. Albrecht Diirer, Underweysung der Messung (Nuremberg, 1525, revised 1538); E. Panofsky, The Life and Art of Albrecht Diirer (Princeton, N.J., 1943, revised 1955); S.Y. Edgerton Jr., The Renaissance Rediscovery of Linear Perspective (New York, 1975); F. Borsi, Leon Battista Alberti (Oxford, 1977; M. Kemp, The Science of Art (New Haven, Conn., 1990).

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internal structures of animals, plants and minerals and their arrangements and of those of machines. Depiction became an instrument of research. Most compelling in the exact information they could provide were the views showing sections cut through an anatomized corpse or a machine at different angles and through different parts, the views with the outside cut away to reveal the internal parts in position, the rotated view as developed by Albrecht Diirer, and above all the transparent view of the internal arrangements and the exploded view depicting both the whole and the parts taken out and shown separately in accurately scaled diagrams. Through the 15th century the new techniques of perspective and chiaroscuro rapidly transformed the working drawings of architecture and engineering as they had the design of paintings. The Sienese engineer Mariano di Jacopo called Taccola, who knew Brunelleschi, and a generation later Francesco di Giorgio Martini, both seem to have designed their machinery by means of inventive drawing on paper before building it. The new pictorial language was used with even greater sophistication by Leonardo da Vinci, and with the printed book it became in the 16th and 17th centuries as normal a means of finding out and conveying information as the written word. Thus appeared the presentation of the mechanisms of pumps, water-driven mills and other devices by Agricola in his treatise on mining and metallurgy, and by Jacques Besson, Agostino Ramelli and Vittorio Zonca in their richly illustrated volumes on machines. There was likewise the increasingly sophisticated presentation of their anatomical researches by Leonardo da Vinci with his drawing of the skull and its contents; by Andreas Vesalius with his illustrations also of the skull, of the opened heart and its valves, and of the eye as a whole and in transverse vertical section accompanied by the dissected parts taken out and shown separately; by Felix Plater with his exploded views of the parts of the eye; by Girolamo Fabrici da Aquapendente and later by Giulio Casserio depicting the organs of the five senses with attention to comparative anatomy.13 Comparisons of living organs with inanimate artifacts were not at this time new, but the familiarity of two such artifacts provided especially efficacious conditions for modelling the eye. The glass or crystal lens became well known during the 16th century as a focusing device in spectacles. The camera obscura was likewise widely used both in astronomy for observing solar eclipses and in art for demonstrating the projection of a scene in perspective upon its translucent screen. Artists as well as mathematicians and natural philosophers began to turn their attention to how the eye itself, receiving the visual clues from the scene or painting in front of it, operated as an instrument of vision. It seems to have been Leonardo who first proposed a camera obscura "Cf. S. Y. Edgerton Jr., The Renaissance development of scientific illustration', in Science and the Arts in the Renaissance, J. W. Shirley and F. D. Hoeniger (eds) (Washington, D.C., 1985), pp. 168-197; Crombie, Styles chs. 8,13 (above n. 1).

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Fig. 8(a). From Leonardo da Vinci, Codex Atlanticus, f. 337 illustrating his comparison of the eye with a camera obscura. In this construction the rays intersect for a second time in the centre of the lens in order to preserve the correct orientation of the image at the optic nerve. The ocular anatomy is peculiar, showing the aqueous humour extending all round inside the dark choroid (uvea), and the vitreous humour in front of the spherical crystallinus.

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Fig. 8(b). From Codex D,f.3v: model of the eye (top right). A hollow glass sphere cut away at the top (— right) is fitted in a box with a small hole in the bottom as the pupil, and filled with water: inside is a smaller glass sphere as the crystallinus. With his face in the water the observer's eye would receive the image of the object seen on the visual pyramid entering the pupil hole on the rays coming from s t. At the left is a matching diagram of the eye itself with the optic nerve emerging on the right at a place corresponding to the observers eye in the model.

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Fig. 9. From Gemma Frisius, De radio astronomico et geometrico (Antwerp, 1545) f.31rv: observing a solar eclipse in a camera obscura.

incorporating a glass lens as a model of the eye, and thus he introduced the conception of the image formed in the eye as a picture on a screen (Fig. 8).14 He introduced at the same time into the analysis of vision the idea of exploiting the conformity of nature with art and of living with dead. But he still looked with Alhazen his analysis for an immediate explanation of visual perception. He recognized the need to explain optically the path through the eye of the rays forming the image. He assumed that the visual power lay not in the crystallinus but in the widened extremity of the optic nerve, which received the images and transmitted them to the common sense in the seat of judgement. The crystallinus was simply a refracting device whose essential function was to prevent the image from reaching the visual power inverted, as in a camera obscura. The eye was not simply a passive instrument like a camera obscura, but a living organ with active vital powers of selection, but for it to see correctly the image must be orientated as well as ordered in the same way as its object. This brilliant model was not known in print in time to have any influence, but the camera obscura itself was widely publicized by writers both on astronomy and on art. Gemma Frisius described and illustrated how to observe solar eclipses in a darkened room in which sunlight admitted through a small hole would produce an inverted image of the Sun on a suitably placed 14 Leonardo da Vinci, Codex D in Les manuscrits, M. C. Ravaisson-Mollien (ed.), 6 vols. (Paris, 1881-1891); // Codico Atlantico nella Biblioteca Ambrosiana di Milano, transcribed by G. Piumati, 8 vols. (Milan, 1894-1904); cf. The Notebooks, arranged etc. by E. MacCurdy, 2 vols. (London, 1938); M. Kemp, Leonardo da Vinci: The marvellous works of nature and art (London, 1981).

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screen (Fig. 9).I5Daniele Barbaro in his standard textbook on perspective gave an account of a similar darkened room with an eyeglass set in the small hole, through which the external scene would be projected onto a sheet of paper placed at the correct distance. There it could be traced with a paint-brush.16 The attention given meanwhile to the eye itself indicates the problems perceived and the characterization of its essential visual parts. Vesalius in his classical dissection published in De humanis carports fabrica libri septem (1543), with woodcuts of the whole eye in transverse vertical section and of the parts taken out and drawn separately, established the standard ocular anatomy to be copied or imitated even when corrected for nearly a century (vii. 14, pp. 643-646). He described the crystallinus as magnifying like eyeglasses (specilla) and its shape, flattened front and back, as 'like a lentil' (ad lentis similitudinem): hence what was to become the standard term 'lens' (p. 646).17 He doubted whether this was the principal organ of the eye, but on how the eye functioned and the controversies of philosophers and medical men he could say nothing (pp. 649-650). Of the retina he wrote enigmatically that 'this c o a t . . . is considered by many the principal organ of sight' (iv. 4, p. 424) but nothing further. Vesalius was corrected later on some important details by Realdo Colombo who pointed out that the lens was located forward of the centre of the eyeball and was flatter in front than behind; and by Giulio Cesare Aranzi who noted that in horses and cattle the optic nerve entered the eyeball to one side, although he still supposed that it entered centrally in man. Aranzi tried to demonstrate vision by means of an experiment on the eye of an ox. After dissecting it out of its socket, he cut an opening in the back as far as the vitreous humour, set it 'in a dark place' illuminated in front of it, then closed one eye and applied the other to the opening in the position of the optic nerve: 'the visual power (vis visiva) of the observer comes through the vitreous to the crystallinus and thence to the cornea through the opening of the uvea to the objects' illuminated.18 Later Felix Plater, professor of medicine at Basel, asserted for the first time explicitly that the retina was the sensitive visual receptor. In his De corporis humani structura et usu (1583) he wrote that through the pupil: 'The illumination of external things irradiating the cornea is sent into the dark chamber (camera obscura) of the eye'. This led him to: l5

Cf. Straker (1981: above n. 8). Daniele Barbaro, La prattica della perspettiva (Venice, 1568). The term specilla, short for ocularia specilla as used by Girolamo Fabrici, meant eyeglasses, as perspicillum used by Felix Plater meant eyeglass (see below), not mirror as supposed by Lindberg (1976: above n. 4) 173 n. 137, 275 n. 151; similarly Francesco Maurolico used conspicilia (below), and later Galileo in the Sidereus nuncius (1610) introduced his telescope under the name perspicillum, in which he was followed by Francis Bacon, Novum organum, ii.39 (1620) in Works, J. Spedding, R. L. Ellis and D. D. Heath (eds), i (London, 1857), pp. 307-308. 18 Iulius Caesaris Arantius, Anatomicarum observationum liber, cc. 18, 21 (Venice, 1587), pp. 71. l6

17

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The primary organ (pars) of vision, namely the optic nerve dilated into the grey hemispherical retina (retiformis) after it enters the eye: which receives and discriminates the forms (species) and colours of external things that fall with the illumination into the eye through the aperture of the pupil and are presented to it by its eyeglass (perspicillwri) It has affinity with the substance of the brain, with which through the nerve it is continuous. Later he came to: Three very clear humours, which in distinct situations fill the cavity of the eye and assist the act of vision.... First, the crystalline humour, which is the eyeglass of the visual nerve: placed facing this nerve and the aperture of the pupil, it collects the images (species) or rays falling into the eye and, spreading them over the area of the whole retiform nerve, it presents these magnified, in the manner of an internal eyeglass (perspicilli penitus modo), so that the nerve can take possession of them more easily (pp. 186-187)." Plater like Vesalius did not consider how the eye operated as the instrument of vision. Hence the question of the inverted image did not arise. They illustrate the insulation of the anatomists of the medical faculties from the mathematical sciences and arts and the fundamental illumination they had brought to the physiology of vision, as likewise of hearing. But clearly, besides Plater's radical identification of the retina as the sensitive visual receptor, reducing the crystallinus simply to a lens, an accurate general ocular anatomy was essential for a true optical analysis of its physiology. The culmination of these anatomical investigations was the superbly illustrated triple treatise by Girolamo Fabrici, De visione, voce, auditu (1600), with 'De oculo visus organo liber' as its first book. Fabrici incorporated in 'De oculo' the corrections to Vesalius made by Colombo and others, with an accurate woodcut of the crystallinus (p. 35), but he still showed the optic nerve entering the eyeball centrally (iii.8, p. 105). His visual theory was essentially a combination of the formulations of the problem by Aristotle and Galen with a version of the optical scheme with which Alhazen had prevented the reversal of the image as the visual cone passed through the transparent media. He likened the crystallinus to eyeglasses (ocularia specilla), 'in which art excells nature' in restoring youth to old eyes by means of refraction (iii.5, pp. 82-83; cf. iii.l, 2, pp. 61, 73-78, iii.7, pp. 102-103). But the crystallinus was also 'the special organ of vision' (iii.7, p. 96) entirely responsible for visual perception within the eye (ii.7, pp. 51-54; iii.7, pp. 96-104). He specifically denied visual sensitivity to the retina and the arenea (iii.8-9, pp. 104-106), and insisted that any transmission of images beyond the crystallinus was both anatomically and optically impossible (iii.10-11, pp. 106-114). With some concessions to optical science, he remained firmly within the medical tradition. "Cf. Crombie (1967: above n. 1); H.M. Koelbing, Renaissance der Augenheilkunde 1540-1630 (Bern. 1967).

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It was the mathematicians who came to reform visual theory by proceeding through an optical analysis of ocular physiology, exploiting the models of eyeglasses and the camera obscura, and thus reformulating the problem itself. The Sicilian mathematician Francesco Maurolico completed in 1554 an optical analysis of both the camera obscura and the eye without connecting the two. His Photismi de lumine et umbra with Diaphanorum panes containing these original results were published only in 1611, and although his manuscripts may have been known, through Christopher Clavius or otherwise, they had no known influence. He based his optics on Alhazen, Roger Bacon, Pecham and Witelo and departed from them only in specific innovations. In Photismi he solved for the first time the fundamental optical problem of how the camera obscura focused the image on its screen. The essential variables were the size of the aperture and its distance from the screen. Maurolico demonstrated geometrically that the inverted image, formed by the superimposed images of the separate points of a luminous source, must come to conform to the shape of the source, regardless of that of the aperture, as these variables came to a certain ratio. He gave the solar and lunar images, in eclipse or not, as particular examples of this general theorem (Theorem 22, corol. 1 and 2, 1611, pp. 17-22).20 He defined the problem of vision in Diaphanorum panes iii: 'On the structure of the visual organ and the forms of spectacles (conspicilid)\ writing that 'since the organ is transparent, the matter is entirely one of transparent bodies'. Sharing the accepted commitment to the orientation of the image in the eye, he attempted to trace the paths of the rays through it, by the conformity of its refractions to those of eyeglasses, in such a way that this orientation would be preserved. 'Among those parts that pertain to vision' he wrote, 'the summit of rank is held by the glacialis or crystalline humour, which in my opinion we can call also the pupilla, in which the visual power takes its position as on a throne. This is convex on both sides, but not spherical but compressed, and more so in front'. Under the heading 'On spectacles' he made apparently for the first time an analysis of nonspherical lenses as exemplified by spectacles and applied the properties of this model to the eye. The crystallinus or pupilla was in effect a biconvex lens, placed in front of the middle of the eyeball but not spherical lest the perpendicular visual rays should pass through the centre of the sphere, intersect there, and carry to the optic nerve an altered, that is inverted orientation (situs) of the thing seen, so that things appear inverted to the spectator . . . . So it happens that the visual rays falling on the anterior surface of the 20 Cf. Crombie (1967: above n. 1), Straker (1971: above n. 4), Lindberg (1976: above n. 4): the last by a double misreading (pp. 180, 276 n. 7) applied to Maurolico what I wrote of Leonardo da Vinci in my Robert Grosseteste (Oxford, 1953, 1971), p. 281, and my 'Kepler: de modo visionis', in Melanges Alexandre Koyre, i (Paris, 1964) p. 141; cf. Crombie (1967), 45-46 n. 72 for my correction of a mistake I did make in supposing that Maurolico had shown the focusing of the image on the retina.

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pupilla and carried through its depth without meeting, that is before coinciding, are carried in their own proper orientation (in suomet situ) to the optic nerve and present the image (species) in its proper position (in sua positione).

The pupilla (crystallinus) was not simply a lens but also the sensitive visual receptor, constituted 'for suffering affection' (adpatiendwri) and 'for sensation' (ad sentiendwri): it received the images of things at its anterior surface and transmitted them from its posterior surface through the optic nerve to the common sense. 'But how vision is effected, whether under some law of refraction (lex fractionis) or of spirits, was by no means easy to decide'. He wished that he could take his account either 'from natural philosophy (physica) or from mathematics alone: because we would reach the goal of truth by following either the one or the other, whether by borrowing the sensitive power from natural philosophy or the law of the refraction of rays from mathematics' (pp. 72-74). He went on to adapt Alhazen's construction for bringing about a point-point correspondence between object and image to show how the crystallinus, with its 'lenticular shape' (figura lenticularis) (p. 75, cf. 76), must refract and transmit the rays according to the law of refraction in such a way that there was no inversion. If he remained bound by the spell of the erect and correctly orientated image, his technical analysis of lenses marked a considerable advance in scientific knowledge of the natural organ and the artificial model alike. He related defective types of vision to the shape of the lens, and prescribed different kinds of spectacles to 'correct the failure of nature' in short and long sight (pp. 76-78). Thus, again using pupilla for crystallinus, 'because the transmission of the visual rays through the pupillae happens no differently from that through spectacles convex on both sides, we may not at all unjustly define the pupillae as the spectacles of nature' (p. 80). Maurolico's optical writings, like Leonardo's, did not become publicly known until after the crucial period of these investigations. It was Giovanni Battista Benedetti who, two years after Plater, published a geometrical comparison of the eye with a camera obscura in which the images of external things were projected through the pupil onto the retina. Benedetti was familiar with Daniele Barbaro's account of a camera obscura with a lens, which he paraphrased in one of the letters included in his Diversarum speculationum mathematicarum et physicarum liber (1585; p. 270). He published his geometrical comparison of the optics of the eye with that of a camera obscura in another brief letter 'De visu'.21 In the eye the rays that would form the optical image of an object were projected through the small pupil and the refracting humours onto the branching nerve (i.e. retina) at the back of the eye as onto the screen of a camera obscura, and the same would happen if they were to proceed directly without refraction 'yet not in its place (in suis locis)\ By this laconic 2l Cf. T. Frangenberg, 'II "De visu" de G. B. Benedetti', in Giovan Battista Benedetti e il suo tempo, presented by A. Ghetti (Venice, 1985), pp. 271-282.

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comment he seems to have meant that without refraction the image would be inverted, as it was in his geometrical account of the camera obscura which had no lens or other refracting medium. These puzzles indicate how difficult these optical problems were both technically and conceptually even for a mathematical scientist as sophisticated as Benedetti. Benedetti's analysis of vision like that of music published in the same volume was apparently not read by contemporaries, but a comparison of the eye with a camera obscura first mentioned briefly by Giambattista della Porta in the first edition of his Magia naturalis (1558) became widely known in the much enlarged edition of 1589. He presented it in the context not of science but of entertainment and optical conjuring. After describing the inverted and reversed scenes that could be projected onto the screen of a camera obscura, he wrote: 'If you put a small lenticular crystal glass (crystallina lens) to the hole', these could be made clearer and restored 'upright, as they are'. The instrument could be used to copy a sunlit picture by placing a white sheet of paper inside the hole, and moving it forwards or backwards until a 'perfect representation' of the picture was cast upon this table (tabula) or screen: then one 'must lay on colours where they are in the table', so that when all is done and the original picture removed, the picture (impressio) will remain on the table.... From this it may be clear to philosophers and opticians where vision is effected; and an end is put to the question of intromission agitated for so long, nor can both be demonstrated by any other artifice (artificium). The image (idolum) is sent in through the pupil, as by the opening of a window, and the part of the crystalline sphere located in the middle of the eye takes the place of the screen (tabula).... It is described more fully in our optics (xvii. 6, pp. 266-26V).22

In his optical work De refractione (1593) Porta firmly located the full power of vision in the crystallinus, where the image was received correctly orientated to correspond to the object seen. To prevent inversion he argued contrary to Vesalius that the crystallinus must be found in front of the centre of the eyeball where the intersection of the rays would occur (iii.l, 13-15, pp. 65-68, 83-86). It was then the anterior surface of the crystallinus that corresponded to the screen of the camera obscura: 'I say that just as light passing through the confined opening of a window represents bodies illuminated by the Sun on a paper underneath, so likewise it depicts on the crystallinus the images (spectra) of seen things entering through the opening of the pupil' (iv.l, p. 91; cf. iv. 1-2, pp. 87-95). He rejected as anatomically impossible Alhazen's theory that vision was completed by the transmission of images beyond the crystallinus through the optic nerves (vi. 1, pp. 139-146).

"Porta, Magiae naturalis libri xx (Naples, 1589), transl. as Natural Magick (London, 1658) with corrections; De refractione optices parte libri novem (Naples, 1593).

Part II: Kepler and Descartes WHEN KEPLER took up the problem of vision no one had questioned the essential assumption that ocular physiology must yield an immediate explanation of visual perception, so that what was seen in the object was only and exactly what was present in the image formed in the eye. The essential geometry remained that of the Euclidean perspective cone, with its base on the visible object and its apex in the eye, as developed by Alhazen into a pointpoint correspondence between the image and the object. Alhazen's account of the ocular image as an internal pattern of stimulated points formed by a combination of optical refraction and selective sensitivity left the relation of the physical to the animate aspects of the process ambiguous, and his theory that visual perception was completed in the common sense located in the brain left the persistent enigma of the nature of the image or information transmitted from the sensitive ocular receptor inwards through the non-optical medium of the optic nerves. The separation of the physical from the animate began with the identification of the crystallinus with a glass lens and the analogy of the whole eye with a camera obscura which formed a wholly different kind of image, an optical image focused on its screen. But the essential commitment to finding an exact correspondence in orientation and order between the image and the visible object remained as an obstruction to a purely optical analysis. Porta made the front of the crystallinus analogous to the screen in his eye. When Plater identified the retina and not the crystallinus as the sensitive ocular receptor he did not consider the optical geometrical consequences. If Benedetti's optical analysis located an inverted image on the retina as on the screen of a camera obscura he did not consider the consequences for the whole science of vision. It remained for Kepler to begin the explicit separation of the distinct questions involved. Kepler was led to his reluctant philosophical innovation, breal^ng with fundamental commitments of the Greek conception of optics, by the inescapable precision of his scientific argument. To the form and expectations of that argument we must pay close attention. Kepler had been introduced to the problem of image formation in a camera obscura by the anomalous results obtained by Tycho Brahe in using this

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instrument to measure the apparent sizes of the sun and moon in solar eclipses. Having adapted a form of dioptral camera for the purpose, Tycho came to realize that systematic allowance had to be made in his observations for the size of the aperture. He measured this and subtracted it from that of the image from which he computed the apparent solar diameter. Then he found to his surprise that the apparent diameter of the moon calculated from observations of the solar eclipse of 1598 was about one fifth smaller during the eclipse than it was at other times when astronomical theory showed the moon to be equally distant. Since he found the same anomaly on all occasions he revised his lunar tables accordingly, and looked for an optical cause in the moon itself. When Kepler, already familiar with the camera obscura for observing solar eclipses, heard of this 'optical paradox' he looked first in the same direction, but he refused to accept Michael Mastlin's anodyne comment that 'observation cannot be perfectly exact', and hoped that 'I could elicit a sure response by means of skilful methods'. After visiting Tycho near Prague in 1600, he returned in June to Graz ready for the solar eclipse expected in July 'with a skilful observation which I am considering' and 'especially to explore by observation ... the striking affirmation' made by Tycho.1 This he did with a dioptral camera with a movable screen. Having learnt from Tycho to measure not only the object being observed but also the essential variables of the size of the aperture and its distance from the screen in the instrument, what he came to explore was the optics of the camera obscura and the experimental error to which the method of observation itself gave rise. He recorded his results in his 'Eclipse Notebook' written during July 1600 and concluded with a set of numbered propositions.2 Early on he asserted the principle that light was propagated rectilinearly in all directions from all points of a luminous source (proposition 6), and then developed his analysis by treating a finite aperture as an assembly of points through each of which an inverted image of the source was cast on the screen (proposition 13). Like Maurolico he demonstrated that at a given ratio between the size of the aperture and its distance from the screen the composite image must conform to the shape of the source; if the aperture were enlarged or its distance decreased the image would assume the shape of the aperture (proposition 14). During July, he reported later in the year to Mastlin, 'I have written a Paralipomena to the Second Book of the 'Kepler to Herwart von Hohenburg 30.v. 1599, in Kepler's Gesammelte Werke, edited by W. von Dyck, M. Caspar and F. Hammer. 18 vols (Munich, 1937-1959), xiii, 339; Mastlin to Kepler 2.V.1598 and Kepler to Mastlin 8.xii.l598, ibid., 213, 253; cf. S.M. Straker, Kepler's Optics (Indiana University Ph.D. thesis, 1971; Ann Arbor, Mich., 1980), and 'Kepler, Tycho, and the "Optical part of astronomy": the genesis of Kepler's theory of pinhole images', Archive for History of Exact Sciences 24 (1981), 267-293. On Kepler's optics see also F. Hammer, 'Nachbericht', in Gesammelte Werke, ii (1939), 393-436; A.C. Crombie, 'The mechanistic hypothesis and the scientific study of vision', Proceedings of the Royal Microscopical Society 2 (1967), 3-112, reprinted in Science, Optics and Music in Medieval and Early Modern Thought (London, 1990); and D.C. Lindberg, Theories of Vision from al-Kindi to Kepler (Chicago, 1976). 2 So named with essential references and analysis by Straker (1981: above note 1).

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Optics of Witelo'. As for Tycho's anomaly, this was an artifact arising from the instrument: 'Therefore any eclipses that have been observed in this manner stand in need of correction'.3 He wrote again about the camera obscura in December 1601: 'Why should it not happen in the eye what I demonstrated in the aperture, that lights are amplified and shadows are constructed? For there is an aperture in the eye'.4 Kepler's Eclipse Notebook was in effect a draft for Ad Vitellionem paralipomena, quibus astronomiae pars optica traditur (1604): Things appended to Witelo, in which the optical part of astronomy is treated, a critique using Risner's standard Latin edition of 1572 of the texts of both Witelo and Alhazen. This he set out over the following three years in the same order of topics, linked by his analysis of image formation in the camera obscura. In the first five chapters he covered critically the optical questions of the nature of light and colour, the camera obscura, the location of the image reflected by plane and curved surfaces, the measurement of refraction in different media, and the operation of vision. In the last six chapters he dealt with the application of optics to astronomy. He explained this programme in his dedicatory letter to the Emperor Rudolph II, concluding: '... nor have I satisfied the mind with the speculations of abstract geometry, to wit with pictures . . . but I have tracked down geometry through the manifest bodies of the world, having followed the footsteps of the Creator with sweat and panting'.5 Since light was the vehicle of observation and also of its deceptions, knowledge of its properties was necessary for scientific practice. Because, he wrote in chapter I 'De natura lucis', 'nature must exhibit God the primary founder of all things in so far as it could', and the spherical form assumed by light was 'the image of the Trinity', and light was likewise 'the natural and fittest image of the corporeal world', introduced by Moses as 'a sort of instrument of the Creator' and 'the link between the corporeal and the spiritual world', knowledge of it was essential for fundamental physical and metaphysical theory. Kepler started from 'Euclid, Witelo and others'. Light he continued 'illuminates everything all around' (chapter I, proposition ii); 'the lines of these emissions are straight, called rays' and 'the shape of a sphere is assumed by light' (proposition iv); its 'motion is not in time, but in a moment' therefore 'the speed of light is infinite' (proposition v). But the 'ray of light is not the light itself going out' for 'the ray is nothing but the motion of light. Just as in physical motion the motion is a straight line, but the physical thing that moves is a body, so in the same way in light the motion itself is a straight line but what moves is a certain surface' (proposition viii). This led to the photometric law: 'As with spherical surfaces having a source of light for centre 'Kepler to Mastlin 9.ix.l600, Ges. Werke, xiv, 150-151. Kepler 10/20.xii.l601, ibid. 207. s Ges. Werke, ii, 8-10. References in the text are to this edition, where they are indicated by GW.

4

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the wider is to the narrower, so is the strength or density of the rays of light in the narrower to that in the wider spherical surface, that is conversely' (proposition ix; GW\\, 18-22). He devoted the whole of chapter II 'De figuratione lucis' (GW ii, 46-61) to the camera obscura, starting with the history, from Aristotle through Witelo and Pecham to Gemma and Tycho, of unsuccessful attempts to solve the problem of the shape of images projected through small openings, and concluding with a long presentation of his true solution in its most general form. He described how he came to see the truth by an experiment in which the geometry was displayed by threads replacing rays so that he eliminated 'the cover of the arcane nature of light' into which both Pecham (called here Pisanus) and Witelo had retreated. Diirer had explained perspective in 1525 by means of a similar physical model, but Kepler did not mention that.6 Kepler showed how the threads, and likewise the rectilinear rays, would produce an image either of the aperture or of the luminous or illuminated source entirely according to their geometrical disposition. Later in the astronomical part of his book he showed how he made the camera obscura an essential instrument for his solar observations, corrected Gemma's and Tycho's understanding of it, published his own computations, and so on (chapters VIII, XI; GW ii, 256257, 288-301). Essential for the accuracy of astronomy was the measurement of refraction to which he devoted his long chapter IV (GW ii, 78-143). He developed a theory of the causes of refraction explicitly by the use of varieties of analogy. This involved a study of conic sections, presented as a system, for which he introduced the term focus (literally, hearth). 'We must use the geometrical languages (voces) of analogy' he wrote; 'for indeed I greatly love analogies, the most trustworthy of my instructors, the confidants of all the secrets of nature: especially to be esteemed in geometry', where 'they brilliantly put in front of the eyes the whole essence of any thing' (chapter IV, pp. 91-92). He proposed an approximation to the still undefined ratio between the angles of refraction and incidence, and improved on Ptolemy's tables as published by Witelo.7 He came to the central subject in chapter V: 'De modo visionis' (GW\\, 143197).8 The 'deception of vision' in the recorded measurements of planetary diameters and of solar eclipses, he began, 'arises partly from the instruments of observation, as we discussed above in chapter two, and partly just from vision itself; and this, as long as it is not counteracted, makes considerable trouble for 'Straker (1971: above, note 1) 390 sqq. (1981, above note 1), and The eye made "other": Diirer, Kepler, and the mechanization of light and vision', in L. A. Knafla, M. S. Staum and T. H. E. Travers (eds), Science, Technology, and Culture in Historical Perspective (Calgary, Canada, 1976), pp. 7-24. 7 Cf. G. Buchdahl, 'Methodological aspects of Kepler's theory of refraction1, Studies in History and Philosophy of Science 3 (1972), 265-268. "Translated by Crombie, 'Kepler: de modo visionis', in Melanges Alexandre Koyre, i (Paris, 1964), p. 141, with slight changes; see also»Crombie (1967: above note 1).

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Fig. 1. From Kepler, Ad Vitellionem paralipomena, v. 2 (Frankfurt, 1604), after Plater, De corporis humani structura et usu, tabula xlix (Basel, 1583). The two unshaded diagrams at the bottom right are of the middle ear.

investigators and detracts from scientific judgement. The source of the errors in vision is to be sought in the structure and functioning of the eye itself. Had Alhazen and Witelo and then the anatomists dealt with the matter properly he would not have had to add this chapter to his Paralipomena ad Vitellionem. As

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it was he would 'put together, as it were as principles, an account of the relevant parts of the eye based on the most approved anatomists'; secondly 'sketch in summary the way vision takes place'; thirdly 'demonstrate each particular point'; fourthly 'lay bare what escaped the reasonings of the opticians and medical men concerning the functioning of the eye'; and lastly 'explain deceptions of vision arising from instruments, and apply this to astronomical practice' (pp. 143-144). His authorities for ocular anatomy, for which he had 'never seen or taken part in' a dissection, were 'the illustrations in Felix Plater's De corporis humani structura et usu, which were published in 1583 and reprinted this year, 1603' (Fig. 1); and the Anatomia Pragensis (1601) of his friend Johannes lessen. In 1600 lessen had been professor of medicine at Prague where he had assisted in the negotiations for Kepler to work there with Tycho Brahe, leading on Tycho's death in 1601 to his own appointment as Imperial Mathematician.9 lessen, according to Kepler, had profited 'by following Aquapendentius' (Girolamo Fabrici) as well as from his own 'anatomical experience'. He himself was a 'mathematician' (v.l, p. 144), but he did not hesitate to choose what he thought correct and relevant to his problem. Contrary to lessen, 'I agree more with Platter' he wrote on the important question whether the crystallinus was anatomically joined to the retina. lessen needed this because he followed Witelo in supposing that 'the power of recognizing visible things' lay in the crystallinus to which it was transferred through this connection from the optic nerve. Platter did not need the connection because he 'left the power of recognizing in the retina, which is nearer the truth' (v.l, p. 150, cf. v.2, pp. 156-157, v.4, p. 183). Kepler disagreed with lessen also on the shape of the crystallinus (p. 151), and noted the control of the light entering the eye by the dilation and contraction of the circular pupil (v. 2, p. 158). He reproduced Plater's plate with its explanatory notes showing the whole eye in vertical section and the parts dissected out and drawn separately, with the slightly bulging cornea (as observed by Leonardo de Vinci) indicated by a dotted line (Fig. 1; v.2, pp. 159-161). In his account in Ad Vitellionem paralipomena (v.4; GW \\, 183-189) of the failings of his predecessors, Kepler identified two sources of ideas for his new theory of vision and stated how he differed from them. 'Plater' he wrote after discussing lessen 'grasped the office of the crystallinus much better, although again not clearly its function. Vision he said happens by the ministry of the retiform coat'. But Kepler corrected Plater's conception of the crystallinus as an internal eyeglass, and showed exactly how changes and defects of vision corresponded precisely to what was painted on the retina: 'For as is the picture, so is vision'. Plater had not understood the difference between the image seen when we looked through a lens at something and the real picture 9 Cf. M. Caspar, Kepler, translated and edited by D. Hellman (New York, 1959), pp. 105-107, 121-123, 166.

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painted on our retina, which Kepler had pointed out in his proposition xxiii (below). 'It seems that Plater was led to this opinion by that anatomical experiment, of which I have heard from other medical men, namely that if the crystalline humour, having been taken out from the other humours, is placed on top of tiny letters it shows those larger. But this is something different from this matter. For vision occurs by means of the picture on the retina. But this deception happens not through a picture, but because of the image. Hence this magnification of letters by the crystallinus (or something analogous to it in the eye) does not fashion vision'. Thus he concluded: 'Compare the true mode of operation (modus) of vision proposed by me with that given by Plater, and you will see that this famous man is no farther from the truth than is compatible with being a medical man who deliberately does not treat mathematics' (pp. 185-187). Of Porta he wrote that it was he who 'in Magia naturalis xvii.6 first proposed the artifice (artificiwri) of that matter of which in the second chapter above I have set out a formal demonstration: namely by what cause all the things outside illuminated by the Sun are seen with their colours in the darkness' of the camera obscura. Next, Kepler continued, Porta 'added a few words de modo visionis1, and he quoted Porta's passage on making it 'clear to philosophers and opticians where vision is effected' and how 'the crystalline sphere located in the middle of the eye takes the place of the screen'. But, he addressed Porta, 'if I understand you well, when you ask where vision is effected, you reply on the surface of the crystallinus or screen'. For Porta had said that 'vision comes from that kind of picture (picturd)' which Kepler had demonstrated in his second chapter (prop, vii): 'and so to conclude, most skilful Porta, if you had added to your opinion only this': that the picture on the crystallinus is still confused by the wide opening of the uvea, and vision does not come about by the conjunction of light with the crystallinus, but the light descends onto the retina, with the separation and then reunion of the radiation to a point, 'and the place of gathering together to a point is on the retina itself, which exhibits the clearness of the picture, and it comes about that through that intersection the image (imago) is inverted and through this gathering together that it is most distinct and clear: if you had added this I say to your opinion, clearly you would have unravelled the mode of operation (modus) of vision' (pp. 187-189; cf. v.2, pp. 151-158; below). Kepler here made explicit his debt to Porta's artifice or model. He followed Porta in his comparison between a camera obscura and the eye as far as the anterior surface of the crystallinus onto which an optical image was cast as onto a screen (cf. v.2, p. 155; v.3, pp. 162, 177-178; below); then going beyond Porta he identified the function of the crystallinus as a lens which focused the image onto the retina, and he dealt with the geometry of how this happened. The image, as Porta had failed to understand, was inverted and reversed on the crystallinus and remained so on the retina. In an autographical passage Kepler

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described how he himself like all his predecessors was at first embarrassed by the inverted and reversed image and looked hard for means to show that it was rectified (p. 185; see below). But he was forced to accept the conclusions of his geometrical optical analysis which he set out in chapter V 2-4. In a new intellectual context Kepler's treatment of the operation of the eye as an optical instrument marked a radical change in the conception of vision accepted by his ancient and medieval predecessors, which enabled him to open a new approach to the relation of physiology to perception, even while he used many of the same analytical techniques. The analogy of the camera obscura, a formal analogy without identity of material parts, enabled him to isolate the geometrical optics of the eye as an immediately soluble physical problem to be treated first and apart from all questions of sensation and perception. With this new conception of the subject-matter he could reduce physiological optics to inanimate physics and banish from this passive physical mechanism any active sensitive power to look at an object or to receive stimuli selectively. He could formulate the fundamental problem of the image not as Alhazen had done, as that of how the eye produced an internal pattern of stimulated points, but as the wholly different problem of how the eye focused a completely different kind of image, an optical image itself visible from without like the inverted image focused on the screen of a camera obscura. Alhazen's eye did not focus but selected the image; he attributed to it explicitly vital sensitive properties which enabled it to deliver to the back of the eye an erect image both ordered and orientated as its object appeared to the viewer. Kepler's image made the need to avoid confusion by the selective perception only of the perpendicular rays irrelevant. The camera obscura became the true model of the eye. Kepler's restructuring of optical geometry to make it not a vital perceiver of a correctly ordered and orientated image conducted on the Euclidean persective cone, but like any inanimate focusing device, immediately raised in a precisely geometrical form the question of the identity and location of the sensitive receptor on which the image was cast. He could undertake a purely geometrical analysis of the paths of the rays of physical light through the crystalline lens and other physical refracting media until they were focused as an optical image on the retina as a screen. Of the innumerable physical rays, going in all directions from every point of a luminous or illuminated source, some fell on the pupil. He demonstrated how an inverted and reversed image must be focused in the eye by means of a construction which at the same time showed that the image must fall on the retina, and hence that this (as Plater had suggested) must be the sensitive receptor. He demonstrated how from an apex at each point on the visible object a multitude of radiant cones passed through the pupil, intersected, and went to a common base on the anterior surface of the crystalline lens, where their positions were reversed and inverted. This surface corres-

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Fig. 2. From Descartes, La dioptrique, v (Leiden 1637): illustrating Kepler's ocular dioptrics. Rays from each point on the object (VXY) are refracted through the cornea (BCD) and lens (L) to foci (RST) on the retina where they form an inverted image of the object. The man looking at the eye, with its back removed, set in a camera obscura would see the inverted image on the translucent retinal SCREEN.

ponded in this way to the screen of a camera obscura, which became as Porta had recognized the true model of the eye up to this location. But Kepler for the first time and for good anatomical reasons carried his optical analysis beyond this. He showed how the lens then focused each radiant cone from the common base in a matching cone to a point on the retina corresponding to that on the object from which it came. The multitude of such points recomposed the image SHIPS 22:1-G

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of the object (Fig. 2), just as did analogously the multitude of double pyramids in the camera obscura without a lens.10 He related this inverted and reversed image to the scene perceived by a simple geometrical rule making the points of this composite picture correspond to their sources on the object but not in orientation. But at the retina optics ended and the rays of light were succeeded by a different kind of motion. This, and how the visual faculty of the soul effected perception by means of the retinal image, he put outside his optical analysis as a problem for natural philosophy. Thus: I have described how vision takes place in such a way that the functions of each separate part can be seen, these so far as I know, having been investigated and discovered by no one else. And so I ask mathematicians to study this carefully, so that something certain about this noblest of functions may at last take its place in philosophy. I say that vision occurs when the image (idolum) of the whole hemisphere of the world which is in front of the eye, and a little more, is formed on the reddish white concave surface of the retina (retina). I leave it to natural philosophers (physici) to discuss the way in which this image or picture (picturd) is put together by the spiritual principles of vision residing in the retina and in the nerves, and whether it is made to appear before the soul or tribunal of the faculty of vision by a spirit within the cerebral cavities, or the faculty of vision, like a magistrate sent by the soul, goes out from the council chamber of the brain to meet this image in the optic nerves and retina, as it were descending to a lower court. For the equipment of opticians does not take them beyond this opaque surface which first presents itself in the eye. I do not think that we should listen to Witelo (book iii, proposition xx), who thinks that these images of light (idola lucis) go out farther through the nerve, until they meet at the junction half way along each optic nerve, and then separate again, one going to each cerebral cavity. For, by the laws of optics (leges optices), what can be said about this hidden motion which, since it takes place through opaque and hence dark parts and is brought about by spirits which differ in every respect from the humours of the eye and other transparent things, immediately puts itself outside the field of optical laws? (And yet it is this motion that brings about vision, from which the name optics is derived; and so it is wrong to exclude it from the science of optics simply because, in the present limited state of our knowledge, it cannot be accommodated in optics)... This image (species) existing separately from the presentation of the thing seen is not present in the humours or coats of the eye, as shown above; hence vision takes place in the spirits and through the impression (impressio) of these images (species) on the spirit. But really this impression does not belong to optics but to natural philosophy (physicd) and the study of the wonderful. But this by the way. I will return to the explanation of how vision takes place. Thus vision is brought about by a picture of the thing seen being formed on the concave surface of the retina. That which is to the right outside is depicted on the left on the retina, that to the left on the right, that above below, and that below '"See Straker (1981: above note I) 291-292. Lindberg (1976: above note 1) 202-206 seems perverse in denying this debt and in continuing to maintain that 'Kepler himself remained firmly within the medieval framework' (p. 207), and similarly later, e.g. 'Continuity and discontinuity in the history of optics: Kepler and the medieval tradition', History and Technology 4 (1987), 431448; followed in this by J.V. Field, Two mathematical inventions in Kepler's Ad Vitellionem Paralipomena', Studies in History and Philosophy of Science 17 (1986), 449-468.

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above. Green is depicted green, and in general things are depicted by whatever colour they have. So, if it were possible for this picture on the retina to persist if taken out into the light by removing the anterior parts of the eye which form it, and if it were possible to find someone with sufficiently sharp sight, he would recognize the exact shape of the hemisphere compressed into the confined space of the retina. For a proportion is kept, so that if straight lines are drawn from separate points on the thing seen to some determined point within the eye, the separate parts are depicted in the eye at almost the same angle as that at which these lines meet. Thus, not neglecting the smallest points, the greater the acuity of vision of a given person, the finer will be the picture formed in his eye. So that I may go on to treat this process of painting (pingendi) and prepare myself gradually for a demonstration of it, I say that this picture (picturd) consists of as many pairs of cones as there are points on the thing seen, with both always having the same base, namely the width of the crystallinus or part of it. Thus while one of the cones has its vertex at the point seen and its base on the crystallinus (varied to some extent by refraction on entering the cornea), the other has the same base on the crystallinus as the first one and the vertex extends to some point of the picture on the surface of the retina; this cone undergoes refraction on passing out of the crystallinus (Figs 2 and 3). All the outer cones meet in the pupil, so that they intersect in that space, and right becomes left... In fact more or less the same thing happens as we showed in chapter ii in a closed chamber (camera clausd). The pupil (pupilld) corresponds to the window and the crystallinus to the screen (tabula) opposite it, provided that the pupil and crystallinus are not so near that intersection is incomplete and everything is confused.... And so if finally straight lines are drawn from points on the visible hemisphere through the centre of the eye" and the vitreous humour, these lines will imprint points forming a picture of the radiating points on the retina opposite. If this did not happen the size of things seen indistinctly to the side would keep changing when the eyes were turned, as happens when spectacles are worn. For these, although fixed immovably in relation to the eye, if they are moved round with it represent things at rest as having some motion, because of the varying amount of the hemisphere appearing at the sides Finally the sensory power (virtus sensorid) or spirit diffused through the nerve is more concentrated and stronger where the retina meets direct cones, because of its source and where it has to go: from that point it is diffused over the sphere of the retina, gets farther from the source, and hence becomes weaker Thus when we see a thing perfectly, w see it within the whole surrounding area of the visible hemisphere. For this reason oblique vision satisfies the soul least and only invites the turning of the eyes in that direction so that they may see directly . . .

The pupil did not affect the focusing of the light, but by dilating or contracting controlled the amount of light entering the eye. Thus the position of the aperture (foramen) is where the rays intersect, and it exists for the sake of the crystallinus...' (v. 2, pp. 151-158). Demonstration of the conclusions stated concerning how vision takes place through the crystallinus. Nearly everything said so far about the crystallinus can be observed in everyday experiments with crystal balls and glass urinary flasks filled with clear water. For if one stands at the glazed window of a room with a globe of this kind of "The sense requires oculi instead of retinae as in the printed texts.

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Fig. 3. From Kepler, Ad Vitellionem paralipomena, v. 3, prop xxiii (Frankfurt, 1604): illustrating his model for demonstrating ocular dioptrics using for simplicity a spherical lens made of a flask of water (a) placed inside the small window fe f) of a camera obscura. Kepler explained how rays from each point (i) of the object were brought together through n m to form in his model a somewhat indistinct image on the screen placed at k 1.

crystal or water, and arranges a sheet of white paper behind the globe at a distance equal to half the diameter of the globe, the glazed window with the fluted wooden or leaden divisions between the lights will be very clearly painted on the paper, but inverted. The same effect can be obtained with other things, if the place is darkened a little. Thus, using a globe of water set up in a chamber opposite a small window, as we described above in chapter ii, proposition vii, everything that can reach the globe through the width of the small window or opening will be depicted very clearly and

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delightfully on the paper opposite. Since the picture is clear at this one distance (namely with the paper a semi-diameter of the globe away from it), it will become indistinct at positions in front of or behind this one. But the direct opposite happens using the eyes...

If the eye were put in the place of the paper, things would be seen erect where they had been inverted on the paper. Since the crystallinus is convex and is denser than the surrounding humours, just as the water in the glass flask is denser than the air, therefore whatever we have demonstrated in this way with the globe of water, and using these media, will have been proved also for the crystallinus, except in so far as it has a different convexity from the globe. So let us proceed with the demonstration of matters belonging to the crystalline or glass globe... (v. 3, p. 162).

'Definition. Whereas up to now the image (imago) has been an entity of reason (ens rationalis), the shapes (figurae) of things really present on the paper, or on any other screen, will be called pictures (picturae)' (p. 174). To demonstrate the focusing of the picture in the eye he used in proposition xxiii the simplified model of a spherical globe of water (a) placed inside the aperture (ef) of a camera obscura (Fig. 3), but he argued that the radiation entering the eye was refracted by the crystallinus not alone but in combination with the cornea and the aqueous humour. His phrase 'within the limit of the intersections of the parallels' meant within the caustic of refraction formed by a spherical lens refracting parallel rays (cf. props, xv-xvi, xx). He explained how rays from each point (i) on the visible object (hi) were brought together through their intersections in the width mn to form in this model a somewhat indistinct reversed picture on the screen placed at kl. When a screen with a small window is placed in front of the globe within the limit of the intersections of the parallels, and the window is smaller than the globe, a picture of the visible hemisphere is projected onto the paper, formed by most of the rays brought together behind the globe at the limit of the last intersection of the rays from a luminous point. The picture is inverted, but purest and most distinct in the middle. So great is the uncertainty in this matter and indeed such its novelty that, unless we take the greatest care, it may easily become confused. Indeed I was held up myself for a long time, until I convinced myself that all the different effects had the same explanation.

'Thus' he added in a note, 'we may seek some light from method', for there was one 'form of refraction through a globe by which vision is deceived by imagining to itself simulacra which are not real (we called them imagines)' (cf. props, vii, xvii-xviii), and another 'by which real pictures of things are formed' (cf. props, xix-xxii and xxiii). He concluded with the corollary: 'Here is seen the function of the pupil (foramen uveae) in the eye; also why the sides of the retina are nearer the crystallinus than the bottom' (prop, xxiii, pp. 177-178). In the next proposition he used his knowledge of conic sections, citing Apollonius, to

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demonstrate the operation of his model lens, concluding with the corollary: Thus is seen the design of nature concerning the posterior surface of the crystalline humour in the eye. She wants all the rays entering the pupil from a visible object to come together at one point on the retina, both so that each point of the picture will be so much the clearer, and so that the other points of the picture will not be accidentally confused with other, unfocused or focused rays. It is also seen that the dilation of the pupil has no other purpose than that which I said above, nor does it confuse the picture but only makes it clearer' (prop, xxiv, pp. 178-179), He went on to face the question of visual perception: The sensation (passio) of vision follows the action of illumination, in measure (modus) and proportion. The retina is illuminated distinctly point by point from individual points of objects, and most strongly so at its individual points. Therefore in the retina, and nowhere else, can distinct and clear vision come about. This is so much the more evident because distortion of the proportions of the picture leads to faults of vision, as has been demonstrated. And I do not know whether Democritus was celebrating with his name idolum rather this picture, by which vision happens, than that mirroring ... But 'the inversion of my picture can be brought against me, which Witelo with great assiduity dodged — And I really tortured myself for a long time in order to show that the cones, having turned right into left in the entrance of the pupil, are made to intersect again behind the crystallinus in the middle of the vitreous humour, so that another inversion is brought about, and what were made left again become right, before they reach the retina'. But he gave up 'this useless trouble'. And so if you are bothered by the inversion of this picture and fear that this would lead to inverted vision, I ask you to consider the following. Just as vision is not an action (actio), simply because illumination is an action, but contrary to an action an affection (passio), so also, in order that the positions may correspond, the capacity for affection (patientia) must be in a direction opposite to the agents. Now the positions are perfectly opposite when all the lines connecting opposite points run through the same centre, which would not have been so if the picture had been erect. And so in the inverted picture, although right and left are interchanged everywhere and with respect to any common line, nonetheless with respect to themselves the right-hand parts of the object are perfectly opposed to the right-hand parts of the picture, and the upper parts of the object to the upper parts of the picture, as a hollow to a hollow . . . Therefore with the picture inverted none of that absurdity is committed from which Witelo so much ran away, and in which lessen followed . . . (v.4, pp. 184-186). In this somewhat contrived way Kepler was saying that so long as the parts of the image retained with respect to themselves the order found in the visible object, the reversal and inversion of their orientation did not matter. The question nevertheless still puzzled contemporaries like Johann Brengger.

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Kepler never found a satisfactory way of answering this question which he rightly placed outside optics in natural philosophy, or more specifically in what became sensory physiology and psychology, but without being able to conceive in any fresh way what happened to the image beyond the retina. He made his next and final contribution to optics in his Dioptrice (1611), written in response to Galileo's Sidereus nuncius as a theoretical, mathematical analysis of how images were formed by lenses singly and in combination. One result was his new astronomical telescope. At the same time he developed his theory of light and vision. Intromission and extromission were for certain purposes interchangeable he wrote, but 'if we are concerned with the nature of luminous things, it is an advantage to express ourselves clearly and to insist on having nothing but the emissions of rays from luminous points' (Praefatio; GW iv, 341). Again he preceded his discussion of vision with an account of the camera obscura: To paint visible things on a white screen with a convex lens (lens)' (problema xliii); The picture with the lens is inverted' through the pairs of cones sharing a common base on the lens (prop, xliv); Tor the sake of instruction we shall call each of such pairs a paint-brush (penicillum)''; these painted the picture on the retina when 'all the paint-brushes of all the points come together on the lens as on the common base of the cones' and pass through inverted to it (definitio xlv; GW\\, 367-368). Kepler seems to have left no doubt of the provenance of his ocular model in the visual arts.12 But when he came to what happened next in vision he could only remain puzzled: Vision is the sensation (sensio) of the affected (affectd) retina filled with visual spirit; or, to see is to sense the affected retina to the extent that it is affected. The retina is painted with the coloured rays of visible things. This picture or representation (pictura seu illustratio) is a kind of affection (passio), but not superficiary,13 as when chalk is rubbed on a wall or light shines on it, but a qualitative affection penetrating the spirits . . . But this picture does not complete the whole of vision unless the image (species) on the retina, capable in this way of affection (patiens), passes through the continuity of the spirits to the brain and is there delivered to the threshold of the faculty of the soul . . . But inside within the brain is something, whatever it may be, which is called the sensus communis, on which is impressed the image of the instrument of the affected vision, that is painted by the light of the visible thing ... But this impression is hidden from our understanding . . . (prop. Ixi, pp. 372-373).

Some years later in 1620 the English diplomat Henry Wotton described to Francis Bacon a moving visit he had made to Kepler at Linz. This 'famous man in the sciences', to whom Wotton proposed to bring one of Bacon's books, was using a camera obscura as an aid to painting a scene just as Daniele Barbaro had advised. Kepler had in his study a landscape which he said that l2 Cf. dedicatory letter, Ges. Werke, iv, 331, and Dissertatio cum Nuncio Sidereo (1610), ibid. 293 on Porta's 'perspicilla'; Straker (1971: above note 1), 467-479, with M. Caspar und F. Hammer, 'Nachbericht' in Kepler, ibid, iv (1941) 415^21. "The term superficiaria in Roman law meant situated on another man's land

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he had done himself, 'non tanquam pictor, sed tanquam mathematicus'. He described how he set up a little black tent with a small hole in it 'to which he applies a long perspective-trunke... through which the visible radiations of all the objects without are intromitted, falling upon a paper, which is accommodated to receive them, and so he traceth them with his pen in their natural appearance, turning his little tent round by degrees till he hath designed the whole aspect of the field' (GW xviii, 42).u Just after this Jean Leurechon published in his popular Recreation mathematique (1624) an account of the camera obscura, for artists as an aid to painting, and 'for philosophers, it is a fine secret to explaine the organ of the sight, for the hollow of the eye is taken as the close chamber, the balle of the aple of the eye, for the hole of the chamber, the crystalline humour for the lens of glasse (respond ... a la lentille de verre), and the bottome of the eye, for the wall, or leafe of paper' (probleme ii).15 Kepler's intellectual behaviour when investigating the operation of the eye conforms exactly to the precept and practice of his investigation of the operation of the celestial system. He would not remain satisfied with anodyne indecision but drove his analysis of each problem to its end in either an acceptable solution or an acknowledged defeat. This he did by attending strictly to quantitative details. He insisted in the Mysterium cosmographicum (1596) that while the Ptolemaic and Copernican hypotheses were observationally equivalent, the reason for this must itself be investigated, and one could not remain undecided for there were important phenomena for which the former could provide no causes whereas in Copernicus their relations were 'so beautifully apparent, there must be some inherent cause of all these things' (c.l; GW i, 15-16). He made the discovery of that cause his research programme. Likewise he refused to retreat from the problem of the camera obscura either with Witelo and Pecham into ignorance of the obscure nature of light or with Mastlin into the unavoidable inaccuracy of all human observation. Again he insisted in his astronomy both that 'an hypothesis is built upon and confirmed by observations' and that he was looking for 'physical causes', so that he could show that 'the celestial machine' was like 'not a divine living thing' but 'a clockwork' in which 'manifold movements' came from a simple 'corporeal force', which could 'be determined by numbers and geometry'.16 This was his approach to the operation of vision. The key to his success in both of his principal inquiries was that in each he set out by heroic analytical labours to identify the essential scientific questions belonging to the subject-matter, to '"Wootton to Bacon 1620, in Kepler, Ges. Werke, xvii, 42; cf. Straker (1976: above note 6). ''French edition published under the pseudonym Henri Van Etten (Pont-a-Mousson, 1624), English transl. as Mathematical Researches (London, 1633) with the 'for the lens of glasse' substituted for a mistranslation of the bracketed French. l6 Kepler to David Fabricius 4.vii.l603, Ges. Werke, xiv, 412, and to Herwart von Hohenburg 10.ii.1605, ibid, xv, 146.

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distinguish these according to their categories, and to answer them in the appropriate order. This involved the extraction and separation of the quite different questions confused in the received presentation of the subject, and the recognition that despite the ancient tradition of both astronomy and optics within the mathematical sciences and natural philosophy, both contained essential questions that remained still open. Thus in astronomy the primary question was to establish the geometry of the planetary orbits, after which came the question of how these were caused. In the optics of the eye and the camera obscura the primary question was to establish the geometry of the rays that formed the image, after which came the question of how this enabled us to see with the eye as we do. In both subject-matters he broke with received commitments: in astronomy with the circularity imposed by ancient metaphysical beliefs; in ocular physiology with the ancient supposition that since the eye was a living sentient organ, any account of its operation must provide an immediate explanation of our visual perception. Kepler rethought the geometry and more fundamentally the essential commitments of both subjects from as near to the beginning as he could get. Kepler's new theory made possible a precise geometrical analysis, led by himself in his Dioptrice, of the functions of the different parts of the eye in focusing and controlling the picture on the retina. By his decision to solve first this geometrical problem of vision, isolating the operation of the eye as an optical device from whatever might follow from it, he opened the way to formulating purely physiologically or physically numerous further problems of accommodation, myopia and hypermetropia, astigmatism, cataract, binocular vision, the design of spectacles to correct visual defects, and the design of optical instruments. It was the mathematicians who pursued these lines of inquiry, and from them that the medical profession came eventually to grasp the new ocular physiology and its medical applications. Influential in this were Vopiscus Fortunatus Plempius with his Ophthalmographia (1632, 1648) who as professor of medicine at Louvain began to promote Descartes's physiological programme; Descartes himself; and later Isaac Newton's physician friend William Briggs with his Ophthalmographia (1676, 1686).17 Kepler's methods were notably exploited by Christopher Scheiner at the Collegio Romano. Scheiner in his Oculus (1619) published for the first time a vertical section of the eye showing the optic nerve entering the eyeball to one side (Fig. 6; i.1.9, p. 17). He made a study of refraction through the different parts of the eye and its fluids which he put into glass ampullae (ii.1.5-12, pp. 61-73; ii.2.1-16, pp. 77122) and described a model of the whole eye which consisted of a camera obscura with a cornea and lens, a spherical glass retina, and aqueous and "Cf. J. Hirschberg, Geschichte der Augenheilkunde, iii.l (Leipzig, 1908); G. Ovio, Storia deU'oculistica (Cuneo, 1950-1952); H. M. Koelbing, 'Ocular physiology in the seventeenth century and its acceptance by the medical profession', Analecta medico-historica 3 (1968), 219-224.

346 Ar
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Naiur*,TuI>i

ct

Oculj,

in

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ioUritj

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con&nfuf'.

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Fig. 4. from Schemer, Rosa ursina, ii. 23 (Bracciani, 1630): illustrating his comparison between the eye and a camera obscura with a lens system, and the effects on each of using further lenses.

vitreous humours enclosed in two glass chambers (iii.1.1-11, pp. 123-161). Beginning with the heading 'Applicatio dictorum ad oculum' (iii.1.12, pp. 161163), he applied his model to show that in the eye a reversed and inverted image or picture of the visible object was thrown onto the retina (iii. 1.12-26, pp. 161-193), and that this and not the lens was the sensitive organ (iii.1.27-34, pp. 193-216). Later in his Rosa ursina (1626-1630) he described experiments carried out in Rome in 1625, in which the formation of the image on the retina was observed directly. This he wrote 'I saw most clearly in the human eye here in Rome in the Jubilee year, where, after the sclerotic had been scraped off the bottom of the eye, the light of a candle sent in through the pupil, the rays having intersected, fell upon the retina; something that has often been proved by experiment in the eyes of many animals' (ii.23, pp. 110-112). He went on to

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exemplify 'the admirable agreement of nature and art' (ii.23-33, pp. 106-136) in a detailed comparison between the eye and a camera obscura containing a system of lenses, studying the effects on each of adding further lenses as with spectacles and in the telescope, helioscope and microscope (cf. Fig. 4).18 Scheiner helped to establish the camera obscura as a model of the eye. Thus Johann Christoph Kohlhans in his Tractatus opticus (1663) cited Schemer's two books for his account: 'Of the application of the camera to the eye' (ii.2.3, p. 257); 'The agreement of art and nature is wonderful: thus as the eye is a natural camera obscura, so is the camera obscura an artificial eye' (p. 501). Likewise Johann Christoph Sturm in his Collegium Experimentale (1676) asserted 'the eye to be nothing other than a little camera obscura' (ii, p.7).19 More original was Christiaan Huygens's demonstration in his Dioptrica (prop, xxxi; 1703), written probably during 1667-1691, of the optical system of a simplified eye reduced to a single spherical refracting surface and of a model constructed as a camera obscura with a cornea, a lens and a diaphragm corresponding to the iris.20 But the new theory was by no means evidently true even to everybody competent to understand it. The Jesuit mathematician Francois Aguilon in his Opticorum libri (i.l, 27, 1613, pp. 2-6, 26-27), a work covering the whole range of optical science from ocular physiology and perception through physics to perspective and geometrical projection, argued that the sensitive organ was the lens capsule (aranea), which he believed to be an extension of the retina and the optic nerve.21 Edme Mariotte provoked a long controversy, centred in the Academic Royale des Sciences and involving especially Jean Pequet and Claude Perrault, with Jean Mery and Philippe de La Hire, by questioning whether his discovery of the blind spot at the entry of the optic nerve still allowed the retina to be regarded as the sensitive organ of vision.22 If Kepler himself provided an exemplary model for the analysis of the composite problem of vision into its parts, so that his solution of ocular optics allowed the further psychological and philosophical questions of vision to be reintroduced on that scientific foundation, he still left these questions largely "Cf. M. von Rohr, 'Ausgewahlte Stiicke aus Christoph Scheiners Augenbuch', Zeitschrift fur opthalmologische Optik 7 (1919), 35^4, 53-64, 76-91, 101-113, 121-133, 'Zur Wurdigung von Scheiners Augenstudien', Archiv fur Augenheilktinde 86 (1920), 247-263; Crombie (1967: above note 1). "Cf. also Johann Andrea Volland, Oculus (Altdorf, 1679) on the eye as a camera obscura; and Johann Gabriel Doppelmayr, Dissertatio visionis sensum (1699), published Gottingen (1748), 169, on Schemer's experiments removing the back of the eye. 20 Huygens, Dioptrica in Opera posthuma (Louvain, 1703), 112-116; cf. J. P. C. Southall, 'The beginnings of optical science1, and 'Early pioneers in physiological optics', Journal of the Optical Society of America 6 (1922), 292-311, 827-842. 21 Cf. M. von Rohr, 'Auswahl aus der Behandlung des Horopters bei Fr. Aguilonius um 1613', Zeitschrift fur opthalmologische Optik 11 (1923), 41-59. 22 Cf. M. D. Grmek, 'Un debat scientifique exemplaire: Mariotte, Pecquet et Perrault a la recherche du siege de la perception visuelle', History and Philosophy of the Life Sciences 7 (1985), 217-255.

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unformulated, let alone answered. There were such psychophysiological problems as the relations between direct and indirect vision and between the visual fields of the two eyes. There was the perennial philosophical problem of the relation between physical stimuli of any kind and unphysical sensations. It was Descartes who explicitly clarified the analysis of vision into its component problems, with full acknowledgement to Kepler.23 In doing so he showed how to use the modelling of nature by art as an instrument not simply of technical, but more generally of logical and conceptual analysis and exploration. Following Kepler's convincing lead, the mathematicians from Scheiner and Descartes down to Huygens and Newton who investigated the technical frontiers of visual physiology came to see in the precise relating of perceiver to perceived a central problem of the scientific movement. Descartes shared with all concerned the ancient ambition to improve nature by art, for he opened La dioptrique (i, 1637; Oeuvres, vi): 'The whole conduct of our life depends on our senses, among which vision being the noblest and most universal, there can be no doubt that inventions serving to increase its power are the most useful there can possibly be'. It would be difficult to find a better example than the telescope, but 'to the shame of our sciences this invention, so useful and so admirable, was found first only by experiment and chance' by someone without mathematical knowledge. He proposed to develop a true science of optics. His more general contribution to scientific thinking was to show that by liberating systematically from each other the different kinds of question and frontier involved in the traditional formulation of vision, each could then be explored without confusion from the others. Descartes, with Marin Mersenne, approached the question left by Kepler of how the retinal image could give us sensations and perceptions by distinguishing, on more "Descartes to Mersenne 31.iii.1638, Oeuvres, eds C. Adam and P. Tannery, 12 vols (Paris, 18971913), ii, 86; cf. for Descartes's optics J. Pucelle, 'La theorie de la perception exterieure chez Descartes', Revue d'histoire des sciences 12 (1935), 297-339, M. H. Pirenne, 'Descartes and the body-mind problem in physiology', The British Journal for the Philosophy of Science 1 (1950), 4359, Vision and the Eye, 2nd edn (London, 1967), G. Leisegang, Descartes Dioptrik (Meisenheim am Glan, 1954), R. L. Gregory, Eye and Brain (London, 1966), The Intelligent Eye (London, 1970), Crombie (1967: above note 1), N. Pastore, Selective History of Theories of Visual Perception: 16501950 (New York, 1971), W. Van Hoorn, As Images Unwind: Ancient and modern theories of visual perception (Amsterdam, 1972), G. Simon, 'On the theory of visual perception of Kepler and Descartes' in A. Beer and P. Beer (eds), Kepler: Four Hundred Years (Vistas in Astronomy 18; Oxford, 1975), G. C. Hatfield and W. Epstein, The sensory core and the medieval foundations of early modern perceptual theory', Isis 70 (1979), 363-383, A. M. Smith, Descartes' Theory of Light and Refraction. (Transactions of the American Philosophical Society, 77) 3; (Philadelphia, Pa., 1987); and for the discovery of the sine law of refraction J. W. Shirley, 'An early experimental demonstration of Snell's law', American Journal of Physics 19 (1951), 507-508, E. Rosen 'Harriot's science: the intellectual background', in J. W. Shirley (ed.), Thomas Harriot: Renaissance Scientist (Oxford, 1974), pp. 2-4, J. A. Lohne, 'Zur Geschichte der Brechungsgesetzes', Sudhoffs Archiv 47 (1963), 152-172, D. J. Struik, 'Snel, Willebrord (1580-1626)', in Dictionary of Scientific Biography 12 (1975), 499-502, P. Costabel, Demarches originates de Descartes savant (Paris, 1982), pp. 63-76. After the announcement of the sine law by Descartes to Marin Mersenne in June 1632, it was the latter who published it for the first time in his Harmonie universelle, Traitez de la nature des sons ...', i, prop, xxix (Paris, 1636), 65-66, cf. Correspondance, ed. C. De Waard, 2nd edn, iii (Paris, 1969), pp. 316, 318-319.

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general philosophical grounds, the case of men from that of animals acting simply as natural automata made by God, responding to physical stimuli from which God had given them no capacity to receive sensations. The image formed in the eyes of animals was purely physiological. In the animal machine he could push Kepler's optical analysis to the limit by asking what purely physiological motions followed from this physiological image and passed through the body. Thus he could complete the technical isolation of the formation of the image from the logical or ontological problem (recognized since Plato) of how any physical image or motion could cause sensation and perception, effects in a different category, in a sentient body. La dioptrique is an essay at once in mathematical and experimental science and in the use of hypothetical models, the most elegant and the most successful of his scientific writings. In it he disposed of certain technical advantages over his predecessors, in particular by his knowledge of the sine law of refraction, discovered independently long before by Thomas Harriot and Willebrord Snel and perhaps also independently by himself. He surpassed them all in presenting a new science of vision within the context of a new science of the senses in general. By this time he had developed several different and not wholly reconcilable hypothetical physical models for light and its effects in vision. He would begin his account of vision with 'the explanation of light and its rays' but, since he was concerned here only with how it entered and was refracted through the eye, 'there is no need for me to undertake to say what truly is its nature'. Our embodied soul could know external objects only through the motions which these produced in our nerves. We were in a position like that when we found our way about in the dark with a stick, or that of men born blind who had found their way about by touch all their lives so that 'one could almost say that they see with the hands'. Now we could suppose that light is nothing but 'a certain movement, or a very rapid and very lively action' that passed through transparent media into our eyes, just as the movement or resistance encountered by the stick passed into the hands of the blind man (i). The operation of the senses in animals was purely physical and physiological. But in man 'we know already well enough that it is the soul that senses, and not the body . . . And we know that it is not properly speaking because it is in the members that serve as organs of the external senses that it senses, but because it is in the brain, where it exercises that faculty called the common sense . . . Finally we know that it is through the nerves that the impressions that objects make on the external members reach the soul in the brain'. But we must take care not to suppose that, in order to sense, the soul needs to look at images which may be sent by the objects as far as the brain, as our philosophers commonly do; or, at least, we must conceive the nature of these images quite otherwise than they do. For . . . they do not consider in them anything else except that they must

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have a resemblance to the objects with they represent... instead of considering that there are several other things besides images that can stimulate our thought; as for example signs and words, which do not resemble in any way the things which they signify. And if, in order to separate ourselves as little as possible from the opinions already received, we prefer to acknowledge that the objects which we sense really send their images as far as the interior of our brain, we must at least note that there are no images which must resemble in everything the objects which they represent.

Just as Kepler had used the experience of painting to form his conception of the retinal picture, so Descartes did likewise to replace this simple conception by the sophisticated conception of symbolic representation of an object by sensory clues: Just as you see that engravings, made only of a bit of ink put here and there on a piece of paper, represent to us forests, towns, men and even battles and storms, even though, from the infinity of diverse qualities which they make us conceive in these objects, there may be none but the shape alone to which they have properly a resemblance; and even then it is a very imperfect resemblance, seeing that they represent on an entirely flat surface bodies elevated and sunk and that even, following the rules of perspective, they often represent circles better by ovals than by other circles, and squares by lozenges than by other squares, and likewise with all the other shapes: so that often, in order to be perfect as images, and to represent an object better, they must not resemble it. Now we must think in just the same way of the images that are formed in our brain, and we must note that it is only a question of knowing how they can furnish the soul with the means of sensing all the diverse qualities of objects to which they correspond, and not at all how in themselves they resemble them. Just as, when the blind man of whom we have spoken above touches some bodies with his stick, it is certain that those bodies do not send anything else to him except that, by making his stick move diversely according to the diverse qualities that are in them, they move by this means the nerves of his hand and then the places in his brain from which these nerves come; this is what gives occasion to his soul to sense as many of the diverse qualities in these bodies as there are varieties in the movements that are caused by them in his brain (La dioptrique iv).

'You see well enough then that, in order to sense, the soul does not need to look at any images similar to the things which it senses; but that does not stop it being true that the objects which we look at imprint quite perfect images in the bottom of our eyes'. This 'some people have already very ingeniously explained by comparison with what happens in a chamber', a camera obscura: 'For they say that this chamber represents the eye' with all its essential parts. One could demonstrate this by 'taking the eye of a man freshly dead, or failing that of an ox or some other large animal', cutting away the back and replacing it with a translucent white body such as a piece of paper or eggshell, and putting the eye into a hole in a dark room with its pupil facing a sunlit scene outside (Fig. 2). Then 'if you look at the white body RST you will see, not perhaps without admiration and pleasure, a painting which will represent very naturally in perspective all the objects that are outside towards VXY, proportioned to their distance, at least if you make sure that this eye keeps its natural

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Fig. 5. From Descartes, La dioptrique, v (Leiden, 1637): illustrating the transmission of light from the object (VXY) to form a visual image in each eye (RST, rst), and then of these images through the optic nerves to form corresponding patterns (789) in the cerebral cavities.

shape'. Now, 'having seen this painting in the eye of a dead animal, and having considered its causes, one cannot doubt that an entirely similar painting is formed in that of a living man, on the internal skin, in the place of which we have substituted the white body RST . . . Moreover, the images of objects are not only formed at the bottom of the eye, but they also pass beyond as far as the brain, as you can easily understand if you suppose that, for example, the rays that come into the eye from the object V (Fig. 5) touch at the point R the extremity of one of the little threads of the optic nerve which takes its origin at the place 7 on the interior surface of the brain 789'. Similarly for the other objects X and Y. 'From which it is clear that once more a painting 789 is formed, sufficiently similar to the objects V, X, Y, on the interior surface of the brain facing its cavities' (La dioptrique v). Thus 'although this painting, in passing thus as far as the inside of our head, always retains something of a resemblance to the objects from which it proceeds', vet it is not 'bv means of

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this resemblance that it makes us sense them . . . but rather . . . it is the movements by which it is composed that, acting immediately upon our soul in as much as it is united to our body, are instituted by nature to make it have such sensations'. And 'because it is the soul that sees, and not the eye, and because it sees immediately only by the intervention of the brain' (vi), any disturbance in the brain or the nerves must produce corresponding disturbances and illusions of vision. Descartes remained committed to his attempt to understand how the soul was related to the body, but by his line of analysis he, like the more sceptical Mersenne, turned the inquiry towards more immediately answerable questions. Stepping aside from the ontological question of how physical motions of any kind could cause sensations, events belonging to different categories, they directed attention to the physical and physiological clues that determined different sensations and perceptions. Together they pioneered, in the two major senses of vision and hearing, the empirical and experimental exploration of the correlation of sensations and perceptions with states both of the external world and of the nervous system, as these were observed and conceived in current physical and physiological theory. In this way they launched in the 17th century a new programme for the science of the special senses and more generally of the mediation of sensory information and its coordination in the behaviour of the animal body and in the perceptions of the human soul. It was in this context that consideration of other senses finally dissolved the visual model of the representative image, for if the pictorial resemblance of the retinal image to its object was merely accidental to the essential information received through the eye, an image of sound could more obviously mean likewise only an ordered correspondence of its motions with its source. Just as Mersenne did in his quantitative analyses of both musical and optical sensations, Descartes in L'Homme and in La dioptrique vi explored quantitatively how different visual clues and their relations gave us perceptions of the position, distance, size and shape of objects. He tried to show not only how our different sensations and perceptions were correlated with different physiological states of our nervous system, but also that if a particular physiological state were postulated, then particular sensations or perceptions must follow.24 The new empirical programme for the science of the senses was endorsed and developed by philosophers, physiologists and mathematicians alike, despite some considerable disagreements on both fundamental and more particular issues. Thomas Hobbes and Pierre Gassendi in somewhat different 24

Cf. Descartes, L'Homme (Oeuvres, xi), pp. 143-144, 174-177 and Meditationes de prima philosophiae, ii, vi (1641), Principia philosophiae, ii. 1-2, iv. 189 (1644), Les passions de I'dme, arts. 23, 36 (1649); A. C. Crombie (1967: above note 1), The study of the senses in Renaissance science', in Actes du X' Congres International d'Histoire des Sciences: 1962 (Paris, 1964), pp. 93-114, 'Mathematics, music and medical science', Actes du XIf Congres ... 1968 (Paris, 1971), pp. 295310, 'Marin Mersenne and the seventeenth-century problem of scientific acceptability', Physis 17 (1975), 186-204, Marin Mersenne (forthcoming).

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Xr

£ Fig. 6. From Schemer, Oculus, /. /. 9 (Oeniponti, 1619): showing the structure of the eye, with the refracting media of the cornea (E) and lens (MN), and the optic nerve (O) entering the eyeball to one side of the point of central vision on the retina (D).

ways met Descartes's stark division of the created world into extended unthinking body and unextended thinking mind by offering other accounts of the mediation and coordination of the information received through the senses. Hobbes elaborated especially in his optical writings a purely corporeal, mechanistic psychology.25 Gassendi set out from the Greek atomists to devise another conjectural model.26 Both agreed with Descartes that objects in the external world were represented symbolically in the motions they produced through the senses; both attempted to formulate clearly the problems of correlating sensory with physiological states; and both made valuable observations on this subject. A basic principle of the whole programme, however often it was breached, was that the speculative models designed to explore these problems should lead to solutions testable by observation. This opened two interesting questions. One concerned the differentation of the senses. Descartes had argued in La dioptrique and L'Homme that while the special sense organs were so designed that they were normally stimulated only by specific kinds of physical motion (as light, sound or pressure), the kinds of sensation that resulted were determined not by those kinds of external motion but by the part of the brain to which they were conducted. Against this Thomas Willis, influenced by Gassendi, maintained that it was the different kinds of external motion or particle that determined the specificity of the senses, and that those 'proportionate to one sensory are incommunicable to most others'.27 It was not technically possible to settle this dispute, but the second question proved easier. Descartes had assumed that the coordination of the information received through the different senses had been included in the inherited design of the animate body, so that a blind man groping about with two sticks would form a conception of the geometry of space exactly as did a sighted man. "Hobbes, 'Opticae', first published by Mersenne, Universae geometricae, mixtae mathematicae synopsis (Paris, 1644), pp. 567-589, and in Objectiones iii to Descartes, Meditationes ii. 26 Gassendi, Syntagma philosophicum, Physica, iii.2.2.1-4, vi.2, viii.2-4 in Opera, ii (Lyon, 1658), 237 sqq., 338 sqq., 402 sqq., and in Obj. v to Descartes, Meditationes ii, vi. "Willis, De anima brutorum, i.10 (Oxford, 1672), p. 159.

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Nicolas Malebranche on the contrary argued that coordination was a question for empirical research,28 and this was to be formulated precisely in the famous problem put by William Molyneux to John Locke: whether a man born blind and given sight would be able at once to recognize with his eyes differences in shape which he had already learned by touch with his hands.29 Molyneux and Locke thought not, and with this George Berkeley agreed for particular reasons. He argued that physiological theory could not determine what the man would see, and that in general we learnt by experience to judge shape, distance, size and so on for each sense separately and also by experience how the diffferent senses were coordinated. Results of operations for congenital cataract were to confirm this argument.30 Berkeley thus pointed to an explicitly autonomous empirical psychology of perception able to explore its subjectmatter independently of current physics and physiology. Alhazen, Kepler and Descartes were three supreme virtuosi who by creating expectations and commanding assent each dominated their subject for long periods. All were masters of the art of theoretical modelling. Kepler displaced the Greek commitment to an immediate explanation of visual appearances accepted by Alhazen, by accepting a different commitment making demonstrated physical principles apply as strictly to the animate organ modelled as to the inanimate model itself. Descartes succeeded in addressing afresh the problems of the cerebral physiology of perception left standing by Kepler, by pushing the mechanistic analysis still farther and asking what purely physical motions followed the focusing of the image on the retina, so reducing the whole physiological process involved in vision and sensation in general to one of purely physical coordination within an animal machine. Thus he could define physiology, and liberate the distinct physiological, psychological and ontological questions encountered in the animate and sentient body all from each other. 'The nature of things, hidden in darkness', Marcello Malpighi wrote a little before Leibniz's remarks on the subject, 'is revealed only by analogizing. This is achieved in such a way that by means of simpler machines, more easily accessible to the senses, we lay bare the more intricate'.31 It would be ill-advised to think that 'the human mind has uncovered all the secrets of nature', but it could 'uncover a good part of its artifices'. An inquirer examining the parts of the body "Malebranche, De la recherche de la verite, i (Paris, 1674), text established by G. Lewis (Paris, 1946). M Locke, Essay Concerning Humane Understanding, ii.9 (London, 1690). "Berkeley, Essay toward a New Theory of Vision (Dublin, 1709) and The Theory of Vision, or Visual Language ... Vindicated (London, 1733); cf. M. von Senden, Space and Sight: The Perception of Space and Shape in the Congenially Blind Before and After Operation (London; 1960). "Malpighi, Anatomes plantarum idea (1675), in Opera omnia (Louvain, 1687), p. 1 cf. Leibniz, Elementa Physica, ii. (c. 1682-4) in Philosophical Papers and Letters, translated and edited by L.E. Loemker, 2nd edn. (Dordrecht, 1969), p. 284.

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and so proceeding a priori has come to form models (moduli, modelli) and figures (typi) of them, with which he places before the eyes the causes of these effects and gives the reason for them a priori and, aided by their rational sequence, understanding the mode of operation of nature, he constructs physiology and pathology and then the art of medicine. A clear experimental proof of this is the optical camera, in which the mathematician produces all the effects that are observed in vision in the state of health and disease in animals, demonstrating a priori the necessity of those effects that follow from variation in the shape of the lens and from the too great distance or nearness of the parts; so that the mode of operation (ratio modo) and the defects of vision are demonstrated from knowledge of the mechanism made by man analogous to the eye.32

"Malpighi, Opera posthuma (Amsterdam, 1698), pp. 276, 289-290: completed 1687; in Latin and Italian.

And so, joining mathematical demonstrations with the uncertainty of chance, and reconciling what seemed contraries, taking its name from both, it justly arrogates to itself this stupendous title: the geometry of chance. (Pascal, Adresse a I'Academie Parisienne)

17 Contingent Expectation and Uncertain Choice: Historical Contexts of Arguments from Probabilities1 i

T

HE STORY of Aristomenes in the Roman novel Metamorphoses or The Golden Ass of Apuleius offers a peculiar view of chance and luck in the ancient world. Apuleius was writing in the second century A.D. His character Aristomenes finds on a journey a long lost friend miserably reduced to half-starvation in filthy rags. His friend responds to his greeting by urging him to keep away and let Fortune do what she would with him as long as she pleases. Instead Aristomenes takes him to the baths, scrubs him down, and gives him fresh clothes, a good meal, and a bed at the inn. But his friend's warning was just. Bad luck is catching, and soon Aristomenes becomes himself likewise afflicted, forced into exile, never again to return to home or happiness. We are here in a different moral cosmology from that of the Good Samaritan. We are in a different world also from that of Aristotle's ethics and of Greek medicine, let alone astronomy, for we are in an arbitrary world of chance whose consequences might be feared but were essentially unpredictable. We are in a region which Aristotle had placed for that reason essentially outside rational knowledge, yet it was part of the total world in which some people saw themselves living. That total world is something we should always i. This paper is based on corresponding chapters of my book Styles of Scientific Thinking in the European Tradition (London: Gerald Duckworth and Co., 1994), which contains full documentation both of original sources and of my considerable debt to other scholars. An earlier version was published as "Pari sur le hazard et choix dans 1'incertain", in Medicine et probabilities: Actes de la journ&e d'etudes du 15 decembie 1979, 6d. A. Fagot (Paris, 1982), pp. 1-42,. Basic information about most of the persons discussed will be found in the Dictionary of Scientific Biography, ed. C. C. Gillispie (New York, 1970-80; 16 vols.)

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keep in mind when we try to penetrate into the more scientific thinking of any period, meaning by that the thinking that solved problems and made discoveries which we can recognize as continuing features of nature and of human knowledge. The subject of contingent expectation and uncertain choice is the world of experience identified by Aristotle as being usually and for the most part consistent and regular, but not invariably or necessarily so. Hence arguments, demonstrations and conclusions about it could be only probable in varying degrees, never certain as in geometry. This was recognized by Plato and Aristotle and other Greek thinkers as the common experience of medical diagnosis and prognosis, of legal judgements, of weather prediction, of expectations from planting to harvest, of navigation, of outcomes of battles, and so on. To deal with this kind of experience a characteristic style of thinking came to be developed with a common form of argument for the variety of contingent situations and subject-matters in which it was met, a form distinct from that developed for such a subject as geometry and its applications for example in astronomy and optics. We can define what I call a scientific style by three characteristics: (i) its form of argument: its methods of discovery and demonstration,- (2) its conception of nature: beliefs about what there is in existence to be discovered; and (3) habits of mind: especially the expectations of and responses to innovation and change, the dispositions of a society and of individuals within it. The sources of an intellectual style of this kind must obviously be looked for not simply in natural science, but much more generally in the intellectual and moral commitments and history of a culture or society, commitments antecedent to any specific science. Commitments to a style may have a long gestation, and likewise a tenacious life. But a style may also be imposed by the subject-matter. The common problem in all contingent and uncertain subjects and situations was that those concerned, facing a succession of uncertain outcomes, might be obliged to make a decision, but on insufficient grounds: the march of events might force a decision, but the grounds available could make it only to some degree likely to be proved correct. The problem had a similar form equally for theoretical and for practical choice whenever the subject-matter

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could not be reduced to a simple logical or mathematical or dogmatic certainty. An experimenter exploring a complex subjectmatter could assent to a scientific hypothesis only contingently on the evidence obtained so far, just as a physician or judge or a navigator or a military commander or a merchant or a gamester must decide at the moment of action only on a contingent expectation from the choice which he judged the most likely to gain his ends. The history of Western thinking in probabilities on this kind of subject-matter has had then two main concerns, ( i ) It has been a search for dependable criteria of judgement that would reduce uncertain expectation to as exact a probability as the subject-matter would allow. We can ask historically then: On what grounds did people give, or not give, assent to evidence, explanations, theories, courses of action? (2) At the same time Western thinking has been an exploration of nature and its expectations, of the relation of expectations available to us to expectations embodied in nature, hence of possible conceptions of nature and its knowability. On what grounds then did people of a particular period expect that future events would happen, and that past events had happened, in any context? It is illuminating, indeed essential, to look at these issues comparatively in different historical contexts. Thereby we can see how some questions came to be asked (while others remained unasked) which came to establish the intellectual character of an age. I can best illustrate the comparative history of thinking in probabilities by pointing briefly to its central focus in examples from suitably different historical circumstances: ancient, medieval, and early modern, with a final glance at the theory of natural selection as a general theory of decision applied to human and natural choice alike. In each of these periods problems appeared under its own distinctive vision and in each the attempts to reduce uncertainty to probability were made within the limitations imposed both by that vision and by the subject-matter: persuasive when they could not be demonstrative, qualitative in antiquity, and quantified in early modern Europe by bringing the contingent and variable within the realm of mathematical order. Each through the survival of texts made its distinctive contribution to its successors.

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The Greeks developed thinking in probability with great originality in medicine and law. Focusing on the different types of argument appropriate to different subject-matters, they provided a classification in which to place probable judgement of the uncertain situations both of nature and of practical human life. Let me illustrate this with a brief collage of quotations. First the Hippocratic Prognostic: "I hold that it is an excellent thing for a physician to practice forecasting. For if he discovers and declares unaided at the side of his patients the present, the past and the future, and fills in the gaps in the account given by the sick, he will be believed to understand the cases, so that men will confidently entrust themselves to him for treatment. Furthermore he will carry out the treatment best if he knows beforehand from the present symptoms what will take place later." But some diseases did kill: "it is necessary therefore to learn the nature of such diseases, how much they exceed the strength of men's bodies, and to learn how to forecast them. . . . For the longer you plan to meet each emergency, the greater your power to save those who have a chance of recovery . . . " (c. i). Hippocratic diagnosis and prognosis was an inference, from collections of symptoms usually present, to their probable antecedents and consequences. Thus the famous signs of death (c. 2). The possibility of predicting the course of a disease was based on a classification both of patients and of diseases, so that patients of a type would all react alike to the same disease, and diseases of a type would always run the same course, within the same general environmental conditions. But Hippocratic authors also noted considerable differences in the predictability of different ailments. Some authors were more impressed by the essential natural uniformity of human beings, indeed of men with animals, of kinds of disease, and of comparable environmental conditions. Others were more impressed by the irreducible uncertainty introduced by a variability so great, both in the human body and in external conditions, as to make each individual case virtually unique. Individual bodies differed so much in general, as well as according to sex and age and type, that except in specific ailments such as lesions prognosis seemed virtually impossible. In all cases it was essential

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to follow adequate procedures for evaluating information got from patients, and for detecting what they might consciously or unconsciously misrepresent or conceal. Most authors held that despite the uncertainty of the evidence medical prognosis was both possible and useful, just as it was possible within limits to forecast weather from likewise variable signs. For, taking due account of environmental conditions, "in every year and in every land" good and bad signs remained uniform in their indications, and proved "to have the same significance in Libya, in Delos, and in Scythia". Hence "it is not strange that one should be right in the vast majority of instances, if one learns them well and knows how to estimate and appreciate them properly". One need not trouble oneself about "the name of any disease. For it is by the same symptoms in all cases that you will know the diseases that come to a crisis at the times stated" (c. 25). We have here the recognition of a science of usual though not invariable, and not necessary, connections or regularities of events when observed in adequate numbers. It offered objective descriptive knowledge that could be established inductively, without having to know their causes, by observing and recording these stable contingent regularities. The empirical probability so established, that sequences of events already observed would likewise be observed in the future, yielded then a rational expectation. Thus on medical correlations the Hippocratic Aphorisms: "Those who are constitutionally very fat are more apt to die quickly than those who are thin" (ii.44); "Those with an impediment in their speech are very likely to be attacked by protracted diarrhoea" (vi. 32). Similarly the Aristotelian Problemata: "Why is it that the plague alone among diseases infects particularly persons who come into contact with those under treatment for it?" (i.y); "Why are people more liable to fall ill in the summer, while those who are ill are more liable to die in the winter?" (i.2,$); "Why are boys and women less liable to white leprosy than men, and middle aged women more than young?" (x.4J; "Why is it that fair men and white horses usually have grey eyes?" (x.n). Greek thinkers recognized probability essentially within the context of a search for certainty and a qualitative analysis of degrees of certainty in different subject-matters. Thus the Greek physicians might match the astronomers in aspiring to infer both

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antecedents and consequences from any present state of affairs, making past and future in effect a property of that present, but with an essential difference. The past and future expected from the mathematical postulates of the astronomers were necessary could not be otherwise, and presented no choices for decision on their outcome. But the contingent expectations from the stable but not invariable regularities found in the complex subject-matter of medicine presented a continual series of uncertain choices both about the nature of the medical situation and about appropriate action. The physicians then, ancient and modern, facing successive stages of a process of uncertain outcome, might be obliged to make a decision only to some degree likely to be proved correct. It was the same with law, but with a practical difference. Thus Plato: "in the law courts nobody cares for truth (dAnOeia, veritas) . . . but only about persuasion (neiOco, persuasio) and that is concerned with what is likely (eiKoq, verisimile)"; for "the people get their notion of the probable [piobabile] from its likeness (ouoioinc;, similitude) to truth, and . . . these likenesses can always be best discovered by someone who knows the truth" (Phaedrus 272.DE, 273D). Likeliness or probability were then to be measured against demonstration and necessity (dn68ei^iq, dvdyKq), and the force of argument had to be appropriate: "If a mathematician . . . elected to argue from probability in geometry, he would not be worth anything". Mathematical questions could not be settled by "appeals to plausibility (mOavoAoyia, piobabile}" (Theaetetus i62E), but by contrast in the sciences of nature we had to be content with something less than mathematical demonstration: "We must be content then if we can furnish accounts no less probable (probabiles) than any other, remembering that I who speak and you my judges are only human, so that it is enough that in these matters we should accept the likely story (eiKoxa uu6ov, probabilia dicentur) and look for nothing further" (Timaeus ipCD). Here Plato seems to be assimilating natural science to legal persuasion, a point of great historical interest when we remember the essential part played by persuasion in the acceptance or rejection by any community of scientific as of other novelties. The whole enterprise of persuasion in ancient legal and moral and political life, the subject of Aristotle's Rhetoric and Topics and Sophistic! Elenchi, which should always be set beside the demonstrative logic of the

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Analytics and the scientific and ethical works in any account of his scientific method, was a rich and natural field for the analysis of probable arguments, of the credibility of evidence, and of the matching possibility of error. Aristotle's development of this classification was to resonate through history, just as the Latin versions of his words were to provide much of our philosophical terminology. Aristotle offered an exemplary analysis of scientific arguments appropriate to "things that come about by necessity and always, or for the most part", from which he excluded "a third class of events" attributed to chance. For "chance is supposed to belong to the class of the indeterminate and to be inscrutable to man" (Physics ii.s, ip6b 12-14), but really "chance obscure to human calculation is a cause by accident and in the unqualified sense a cause of nothing" (Metaphysics xi.8,10653 33-5). Hence: "There is no understandin through demonstration of what holds by chance. For what holds by chance is neither necessary, nor for the most part, but what comes about apart from these,- and demonstration is of one or other of these. For every deduction is either through necessary or through for the most part propositions; and if the propositions are necessary, the conclusion is necessary too; and if for the most part, the conclusion too is such" (Posterior Analytics i.3O, 8yb 18-25, trans. Barnes, 1975). He identified probability then as a descriptive regularity observable in his second class of events: those which "nature produces for the most part" lying between what nature produced "without exception" and the accidents of "fortune" which were "beyond expectation", as in the good luck of receiving some benefit or of "escaping some evil that might reasonably be expected" (Magna moralia ii.8, iO26b 38-73 4,30-33). Within reasonable expectation: "Most of the things about which we make decisions, and into which therefore we inquire, present us with alternative possibilities. . . . A probability (eiKo<;, verisimile) is something that usually happens, but only if it belongs to the class of the contingent or variable" (Rhetoric i.2, 13573 34-7). Also: "A probability is something generally approved" (ev8o^oq, piobabilis): what men know to happen or not to happen, to be or not to be, for the most p a r t . . . , for example the envious hate, the beloved show affection". The argument might use signs: "for anything such that when it is found another thing is found, or when it has come into

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being the other has come into being before or after, is a sign of the other's being or having come into being" (Prior Analytics ii.27, /oa 3-9). Signs might be infallible as a woman's "giving milk is a sign that she has lately borne a child", or fallible as "that a man breathes fast is a sign that a man has a fever" (Rhet. i.2, 13573 2 3~37/ b3, 15, 18) but he might do so without a fever. But "no particular probability is universally probable. . . . For what is improbable does happen, and therefore it is probable that improbable things will happen" (ibid, ii.24, 104239-12). Central to Aristotle's whole treatment of probability was his insistence that human beings could initiate choice both in their opinions and in their actions. Within the subject-matter of mathematical and natural necessity "understanding is universal and through necessities, and what is necessary cannot be otherwise"; whereas "opinion is about what is true but can also be otherwise" (Post.An.al. 1.33, 88b 30-8934), and was as unstable as its object. Hence in dealing with human behaviour above all "we must be content..., in speaking about things that are only for the most part true and with premises of the same kind, to reach conclusions that are no better...; for it is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits. It is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs" (Nicomachean Ethics i. 3, io94b 19-27). Opinion was open to persuasion, and persuasion could likewise be turned simply to winning a case, for: "If you have no witnesses on your side, you will argue that the judges must decide from what is probable. . . . If you have witnesses and the other man has not, you will argue that probabilities cannot be put on their trial" (Rhet. i, 15, 13763 18-22). By contrast with the pragmatic motives of politicians and lawyers aiming rather at effect than truth, the first aim of persuasion in ancient philosophy was to persuade oneself. Some diverse examples will illustrate the drive of ancient as of later analysis to stabilize the uncertain by defining the limits and degrees of its probability in comparison with the certain. Of particular interest were the criteria offered by the Greek sceptic Carneades of Gyrene by which to distinguish, in between the clearly true and the clearly false, the limits and degrees of what could be known only as more

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or less probable. Carneades accepted the Pyrrhonic questioning of all theoretical knowledge so that the only dependable guide in life was the success or failure of previous experience. He aimed to make this precise by a critical analysis of the presentation of sensible evidence to our judgement. Presentations could be true, or false, or at once both true and false to what they presented, but since we had no means of knowing this object, to us as "the subject experiencing the presentation" they could be only "apparently true" or "apparently false". Our judgements could be only more or less "probable" likewise, "for neither that which itself appears false, nor that which though true does not appear so to us, is naturally convincing to us". The presentation that was "of such a nature as to persuade us ... to assent" was "that which appears true" clearly. This was the first "criterion of truth" (Sextus Empiricus, Against the Logicians, i. 169-73) which ensured "that both our judgements and our actions are regulated by the standards of the general rule"; but "since no presentation is ever simple in form but, like links in a chain, one hangs from another", it had to be supported by further inquiry. The second criterion was then that a presentation had to be supported by other circumstantial evidence: "just as some physicians do not deduce that something is a true cause of fever from only one symptom, such as too quick a pulse or a very high temperature, but from a syndrome, such as that of a high temperature with a rapid pulse and soreness to the touch and flushing and thirst and analogous symptoms". Then when nothing "in the syndrome provokes in him a suspicion of its falsity, he asserts that the impression is true" (ibid. i. 175-9). The third and most trustworthy criterion was that the presentation should be not only circumstantially uncontradicted but also thoroughly tested. Thus "we scrutinize attentively each of the presentations in the syndrome", just as an aspirant to judicial office was scrutinized before appointment. The scrutiny in natural inquiries would cover observer, medium and observed: vision and mental capacity, illumination and distance, size and arrangement, and so on. Likewise just as in the trivial affairs of life a single witness might be questioned, in the more important several witnesses, and in still more important "we cross-question each of the witnesses on the testimony of the others" (ibid. i. 182-4), so also in natural inquiry. For these reasons such philosophers as Car-

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neades would "prefer the probable and tested to the simply probable, and to both of these the presentation that is probable and tested and uncontradicted" (Sextus Empiricus, Outlines of Pyrrhonism, 1.2.29). They "use probability as the guide of life" (ibid, i. 231); and they held that in all natural inquiries it was by expert observation that false arguments were detected: for "it is not the dialectician who will expose them, but the experts in each particular art who grasp the connection of the facts" (ibid. 11.236). For Carneades then as for most other ancient philosophers the need for a method of probable argument arose from the uncertainty not of natural causation but of our knowledge of it. It was only the Epicurean "swerve" of atoms from their course "at quite uncertain times and uncertain places" (Lucretius, Dererumnatura, ii. 218-9) that introduced a systematic intrinsic indetermination into Greek conceptions of the nature of things. Thus the Stoics in their debates with the sceptics resolved the evident contradiction between the possible and the determined by agreeing that to designate a realm of the possible implied no objective contingency, but designated only what seemed possible to us. Hence the meaning of chance was simply "that chance is a specific relation of men towards cause, and thus the same event appears to one as chance and to another not, depending on whether or not one knows the cause" (Alexander of Aphrodisias, De anima ii, "De fortuna": Scripta minora, ed. Bruns, 1892, p. 179). It was in the practical contexts of medicine and law that ancient writers developed their criteria of probable judgement in most detail. Cicero in his programme of making Greek philosophy available in Latin established probabalis as the technical term best expressing the range of meanings in its Greek equivalents. No one "could conduct his life without decisions". Hence the wise man, when he could not have certainty, "employs probabilities (Academica ii: Lucullus, 34.109-11). Then: "That is probable (probabile) which for the most part comes to pass, or which is part of the ordinary beliefs of mankind" (De inventions, i. 19.46). Arguments for probability came from signs, credibility, previous judgements, and comparability: "some principle of similarity running through diverse materials" (ibid. i. 20.48). A powerful argument used in both law and medicine was the convergence of evidence. Faced with indications of murder "some one or two of these things

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can by chance have happened in such a way as to throw suspicion upon this defendant". But if he were known to have quarrelled with the victim, had been seen making preparations before the crime, at the appropriate place contrary to his usual habits when it occurred, with blood on his clothes afterwards, and so on: "for everything to coincide from first to last he must have been a participant in the crime. This cannot have happened by chance" (pseudo-Cicero, Rhetorica ad Heiennium, ^.41.53). Quintilian in his well known account of forms of legal proof and evidence elaborated this argument from convergence on the model of Aristotle's commensurate universal, aiming at an enumeration of signs or indications that would uniquely define the event, so that "what was only suspected may appear certain" (Institutio oratoria, v.p.i11). Short of certainty he distinguished degrees of credibility, ranging from that of what usually happened to that of which there was nothing contradictory in its happening. Law then and medicine established the essential forms of ancient arguments for probability. Their criterion of the convergence of as wide as possible a rang of evidence, accompanied by the insistence that assent was to be given only to propositions supported by all the relevant evidence available, was to have a crucial function in the whole development of scientific argument in every subject-matter. Ill

The whole complex question of reasonable assent and expectation, of estimating the possible and the probable, of apportioning probabilities from incomplete or uncertain evidence, and of divine and human knowledge of the future, was to be given a new existential context by the presuppositions of the theology, and later by their secularization in the economy and philosophy, of the new society of Western Christendom. The providential theology of the creation of the world revealed in the Hebrew scriptures presupposed a transcendently divine creator, whose omnipotent freedom and inscrutability made all events and their connections ultimately contingent from the human point of view. But within that contingency conjectures about possible connections and their probable consequences had a basis in the assurance of a uniform causal-

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ity in nature. The theology of creation presupposed also a new conception of time as a linear dimension. This was quite different from any conception of time found in antiquity. The Western vision of time and of man's place in history was sharply and enduringly refocused by St. Augustine (De civitate Dei xi.io, xii. 10-22,, xxii.26; De Trinitate 111.9, xv.is).2 He attacked especially the Stoic theory of cyclical dissolutions and regenerations of the world and the human race in an endless determined repetition without responsibility or hope, and he attacked likewise the Epicurean reduction of the origins and history of all that exists to meaningless chance. He established a specifically Christian conception of time as a linear dimension along which the world and mankind could fulfill an unique historical purpose and each person could act with individually responsible initiative. With these Christian expectations came a reorientation of Western thinking about both past and future. Mankind was seen with an eternal destiny, to be fulfilled through the advances and retreats of historical trial, but always with hope. The conception of the natural world as the product of a rational and benevolent Creator, and of rationally responsible man made in his image to fulfill a providential purpose, offered a standing invitation to use the gifts of reason and the senses to discover, as Kepler was to put it, God's thoughts in the creation (Kepler to Herwart von Hohenburg, 9/10. iv. 1599, in Gesammelte Weike, hrg. Dyck, Caspar et al., XIII, 1965, p. 309). It was also an invitation to discover the benefits placed there for mankind. If we are looking for those large sociological commitments that send a whole culture in one direction rather than another, we could argue that this kind of hope for human purpose and human intelligence could provide at least a strong predisposition towards an active rational drive to scientific thinking and technical invention. 2. Cf. L. Spitzer, "Classical and Christian ideas of world harmony", Tiadito, 2 (1944), 409-64, 3 (1945), 307-64; J. E Callahan, Four Views of Time in Ancient Philosophy (Cambridge, MA, 1948); T. E. Mommsen, "St. Augustine and the Christian idea of progress: the background of the City of God", Journal of the History of Ideas, 12 (1951), 346-74; C. A. Patrides, The Phoenix and the Ladder: The rise and decline of the Christian view of history (Berkeley & Los Angeles, 1964); A. C. Crombie, "Some attitudes to scientific progress: ancient, medieval and early modern", History of Science, 13 (1975), 213-30; R. Sorabji, Time, Creation and the Continuum: Theories in antiquity and the early middle ages (London, 1983).

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In any case medieval philosophers and mathematicians, taking up ancient problems in this new context, identified and explored further areas of contingent possibility and probability in a variety of uncertain situations. I shall discuss two such explorations, one concerned with judgement and assent and the other with expectation. Both had a profound influence on Western intellectual and social life. Assent: From the twelfth century, philosophical theologians, educated in the newly recovered texts of Euclid and of Aristotle's logic, set out to incorporate all the products of reason and revelation alike into a single logically structured theology and metaphysics. The resulting tension forced some necessity for choice and also an attitude to the nature of error, both within Christendom and in relation to Islam and Judaism and paganism outside. Given the dual source of human knowledge in the divine gifts of true reason and undeniable revelation, the whole enterprise then made an urgent issue of the possibility of error in good faith, of the treatment to be given to unpersuadable heretics and infidels, and generally of the commitments and expectations involved in disagreement as well as agreement. The crucial question of assent concerned the acceptability and credibility of evidence for events and for beliefs that could not be clearly and infallibly demonstrated. The probability of an alleged event was then said to depend on the frequency with which it usually occurred, together with the credibility or authority of whoever alleged it. Thus in the twelfth century John of Salisbury: "Something is probable if it seems obvious to a person of judgement, and if it occurs in a given way in all instances or in some other way only in very few. Something that is always or usually so either is or seems probable, even though it could possibly be otherwise" (Metalogicon 11.14). But probable arguments were also included with a somewhat different purpose in dialectic and rhetoric: "for the dialectician and the orator, the one trying to persuade an adversary and the other a judge, are not too much concerned about the truth or falsity of their arguments, provided only that they have likelihood". Even worse "sophistry, which is seeming rather than real wisdom, merely wears the guise of probability or necessity" (ibid. ii.3J. Alexander Neckam exemplified "the power of persuasion" with a story of a cleric at the end of the

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twelfth century who asserted on his deathbed that "he would never believe in a future resurrection unless he was persuaded of it with probability" (De naturis rerum . . . ii.i73, ed. T. Wright, 1863^.297). He was persuaded that he could not lose by believing in his resurrection, because if it were true he would not have put his salvation at risk by unbelief, and if it were not he would never know. Between sophistry and persuasion there was a wavy line. Central to the question of assent was that of the degree of certainty of knowledge possible in different subject matters. Starting from the Aristotelian maxim "the mode of knowledge must correspond to the matter" (cited by Aquinas), philosophical logicians during the thirteenth and fourteenth centuries made a sophisticated analysis and classification of logical procedures for the control of argument and evidence that deeply affected the development of the natural sciences along with other theoretical and practical disciplines. It is important to note once more how common forms of argument could be applied to diverse subjects which could be treated as formally the same, even if materially different. This was central to the intellectual movement of which sciences of nature were an integral part. Thomas Aquinas for example distinguished what he called three modes of "rational procedure in the sciences". The first was the pure rationality possible in abstract mathematics, where scientific demonstration starting from self-evident first principles could yield absolutely certain conclusions. The sciences of nature, starting from assumed rather than self-evident principles, could not aspire to that degree of certainty, but they could nevertheless achieve reliable knowledge by following the regular and uniform causal processes of things. Least certain of all were the moral and practical sciences, with far from uniform subject-matters. For "the closer any science conies to singulars, as in operative sciences like medicine and alchemy and ethics, the less certainty they can have because of the multitude of singulars that have to be considered", for "error follows if any are omitted", and also "because of their variability" (Expositio super librum Boethii De Trinitate . . . q.6, art.i, rec. Decker, 1959, pp. 205, 207, 209). But even if in these sciences, as in human affairs in general, it was not possible to have "demonstrative and infallible proof", but possible to have only "a certain conjectural probability", this was nevertheless genuine

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knowledge. So for example "although it may be possible for two or three witnesses to agree in a lie, yet it is neither easy nor probable that they will agree. Hence their testimony is accepted as true, especially if they do not waver in it, and if they have not been suspected on other occasions" (Summa theologiae, ii.i, q.ios, art. 2 ad 8). From this elaborate analysis of the diverse possibilities open to human inquiries carried out by the philosophical community of the universities came then a highly sophisticated control of argument and evidence to decide a question, including decision in the sciences of nature by observation, experiment and calculation. The different intellectual disciplines acquired specific identities defined by their subject-matters and forms of argument.3 The 3. Cf. T. Schiitz, Thomas-Lexicon, 2 ter Aufl. (Paderborn, 1895); A. Gardeil, "La certitude probable", Revue des sciences philosophiques et theologiques, 5 (1911), 237-68.441-85; T. Richard, Leprobabilisme morale et laphilosophie (Paris, 1922); T. Deman, "Notes de lexicographic philosophique m6die>ale: Probabilis", Revue des sciences philosophiques et theologiques, 22 (1933), 260-90, and "Probabilisme" in Dictionnaire de theologie catholique (Paris, 1936), vol. XIII.i, 417619,- V. Cioffari, Fortune and Fate from Democritus to St. Thomas Aquinas (New York, 1935), The Conception of Fortune and Fate in the Works of Dante (London, 1941), Fortune in Dante's i4th Century Commentators (Cambridge, MA, 1944); W. S. Howell, The Rhetoric of Alcuin and Charlemagne (Princeton, 1941); R. McKeon, "Rhetoric in the middle ages", Speculum, 17 (1942), 1-32; M. J. Junkersfeld, The Aristotelian-Thomistic Concept of Chance (Notre Dame, IN, 1945); R. I. Defferari, M. I. Barry and L. McGuiness, A Lexicon of St. Thomas Aquinas (Washington, DC, 1948): "Certitude", "Probabilis", "Probabilitas", etc.,- A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science 1100-1700 (Oxford, 1953; revised reprint 1971), Augustine to Galileo: Medieval and Early Modern Science, revised 2nd ed., reprinted with further revisions (London & Cambridge, MA, 1979,- 2 vols.), and Styles of Scientific Thinking, ,chs. 7-8 (note i above); .E. R. Curtius, European Literature in the Latin Middle Ages, trans. W. Tras (New York, 1953); G. Preti, "Dialettica terministica e probabilisimo nel pensiero medievale", in Le crisi dell'uso dogmatico della ragione, a cura di A. Banfi (Roma & Milano, 1953), pp. 61-97; M. D. Chenu, La theologie comme science au xiiie siecle, 36 6d. (Paris, 1957), La theologie au xii siecle, 2e 6d. (Paris, 1976); J. R. Weinberg, Abstraction, Relation and Induction: Three essays in the history of thought (Madison, Wl, 1968); E. F. Byrne, Probability and Opinion: A study in the medieval presuppositions of post-medieval theories of probability (The Hague, 1968); J. E. Murdoch, "Mathesis in philosophiam scholasticam introducta: the rise and development of application of mathematics in fourteenth-century philosophy and theology", in Arts liberaux et philosophie au moyen age (Montreal & Paris, 1969), pp. 215-54, "The development of a critical temper: new approaches and modes of analysis in fourteenth-century philosophy, science, and theology", in Medieval and Renaissance Studies, ed. S. Wenzel (Chapel Hill, NC, 1976); P. Michaud-Quantin avec . .. M. Lemoine, Etudes sur le vocabulaire philosophique

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occasions were distinguished on which it was appropriate to use demonstration or persuasion, and to appeal to the senses, reason, faith, authority, tradition, usage and so on. The central area of probability was that where an exiguous demand for action required decision that could not in the circumstances be certain. A practical problem in dealing for example with heresy and unbelief was to diagnose states of mind and to establish rules for a doubting conscience. A humane rule was to act on the most probable judgement with an inherent likelihood.4 The problem was parallel in the diagnosis of diseases, of witchcraft and magic, of the perpetrators of crimes, and so forth. The identification of a state of things depended in all such cases on antecedent assumptions about what existed and what was possible. Accepting such assumptions, theologians, lawyers, physicians and philosophers responding to a variety of practical demands developed a certain systematic precision in collecting and weighing evidence: for example in dealing with heresy and spiritual error (a basic practical question in view of their accepted consequences both for the individual person and for the order of society),5 and in dealing with leprosy, smallpox, du moyen age (Roma, 1970); A. Maieru, Terminologia logica della tarda scolastica (Roma; 1972); J.}. Murphy, Rhetoric in the Middle Ages (Berkeley & Los Angeles, 1974); The Cultural Context of Medieval Learning, ed. J. E. Murdoch and E. D. Sylla (Boston Studies in the Philosophy of Science, vol. XXVI; Dordrecht & Boston, MA, 1975); Lexikon des Mittelalters, hrg. von L. Lutz et al. (Aachen, 1977-85; 3 vols.); G. R. Evans, Old Arts and New Theology: The beginnings of theology as an academic discipline (Oxford, 1980); F. Oakley, Omnipotence, Covenant and Order: An excursion into the history of ideas from Abelard to Leibniz (Ithaca, NY, 1984). 4. Cf. Deman, "Probabilisme" (1936; note 3 above), pp. 418 ff, 431 ff, 442 ff. 5. Cf. Deman, ibid.; H. C. Lea, The Inquisition in the Middle Ages: Its organization and operation (London, 1963); J. B. Russell, Dissent and Reform in the Early Middle Ages (Berkeley & Los Angeles, 1965), Religious Dissent in the Middle Ages (New York, 1971), Witchcraft in the Middle Ages (Ithaca, NY, 1972), A History of Witchcraft: Sorcerers, heretics and pagans (London, , 1980), and J. B. Russell and C. T. Berkhout, Medieval Heresies: A bibliography (Toronto, 1981); G. Leff, Heresy in the Middle Ages (Manchester, 1967,- 2 vols.); Heresies et societes dans 1'Europe pre-industrielle (ne-i8e siecles) (Paris, 1968); H. C. E. Midelfort, Witch Hunting in Southwestern Germany, 1562-1684: The social and intellectual foundations (Stanford, CA, 1972); E. LeRoy Ladurie, Montaillou, village occitan de 1294 a 1324 (Paris, 1975); R. Kieckhefer, European Witch Trials: Their foundations in popular and learned culture (Berkeley & Los Angeles, 1976); M. Lambert, Medieval Heresy (London, 1977); G. Schormann, Hexenprozesse in Nordwestdeutschland (Hildesheim, 1977); E. M. Peters, The Magician, the Witch and the Law (Hassocks, Sussex, 1978); Heresy and Authority in Medieval Europe: Documents in transla-

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plague, and venereal and other diseases,6 and with usury.7 Rules were developed likewise for the exegesis of the Scriptural revelation.8 In all these diverse contexts the search for grounds for tion, ed. E. M. Peters (Philadelphia, 1980); G. Henningsen, The Witches'Advocates: Basque witchcraft and the Spanish Inquisition, 1609-1614 (SanRemo, NV, 1980). 6. Cf. the sections by M. McVaugh on methods of diagnosis etc. in A Source Book in Medieval Science, ed. E. Grant (Cambridge, MA, 1974), pp. 745-808, and also the preceding sections on medical theory, pp. 700 ff ; K. Sudhoff, "Pestschriften aus den ersten 150 Jahren nach der Epidemic des Schwarzen Todes 1348", Archivfur Geschichte der Medizin, 2-17 (1909-1925), Aus der Friihgeschichte der Syphilis (Studien zur Geschichte der Medizin, vol. IX; Leipzig, 1912); M. Neuburger, Geschichte der Medizin (Stuttgart, 1911), vol. II; A. C. Klebs et E. Droz, Remedes contre la peste: Facsimiles, notes et liste bibliographique des incunables sur la peste (Paris, 1925); A. M. Campbell, The Black Death and Men of Learning (New York, 1931); D. P. Lockwood, Ugo Benzi: Medieval philosopher and physician, 1376-1439 (Chicago, 1951); P. Richards, The Medieval Leper and his Northern Heirs (Cambridge, 1977); G. Baader und G. Keil, "Mittelalterliche Diagnostik: ein Bericht", in Medizinische Diagnostik in Geschichte und Gegenwart, hrg, C. Habrich, E Marguthund J. H. Wolf (Munchen, 1978), pp. 135 ff.; J. AgrimieC. Crisciani, Malato, medico e medicina nel medioevo (Torino, 1980); L. E. Demaitre, Doctor Bernard of Gordon: Professor and practitioner (Toronto, 1980); S. Jarcho, The Concept of Heart Failure from Avicenna to Albertini (Cambridge, MA, 1980); N. G. Siraisi, Taddeo Alderotti and his Pupils: Two generations of Italian medical learning (Princeton, 1981), and the next article in this volume; D. Palazzotto, The Black Death and Medicine: A report and analysis of the tractates written between 1348 and 13 so (Ann Arbor, MI, 1980); D. Williman, The Black Death: The impact of the fourteenth-century plague (Binghamton, NY, 1982). 7. Cf.}. T. Noonan, The Scholastic Analysis of Usury (Cambridge, MA, 1957),- J. W. Baldwin, The Medieval Theories of the fust Price: Romanists, canonists, and theologians in the twelfth and thirteenth centuries (Transactions of the American Philosophical Society, n.s. 49, part 4; Philadelphia, 1959); J. Gilchrist, The Church and Economic Activity in the Middle Ages (London, 1969); B. Nelson, The Idea of Usury, 2nd ed. (Chicago, 1969); R. de Roover, La pensee economique des scolastiques: doctrines et methodes (Montreal, 1971), "The scholastic attitude toward trade and entrepreneurship", in Business, Banking, and Economic Thought in Late Medieval and Early Modern Europe: Selected studies, ed. J. Kirschner (Chicago, J 974)/ PP- 336-45; J. Le Goff, Marchands et banquiers du moyen age, 2e e"d. (Paris, 1972); L. K. Little, Religious Poverty and the Profit Economy in Medieval Europe (London, 1978). 8. Cf. H. Caplan, "The four senses of scriptural interpretation and the medieval theory of preaching", Speculum, 4, part 2 (1929), 282-90; B. Spicq, Esquisse d'une histoire de 1'exegese latine au moyen age (Paris, 1944); B. Smalley, The Study of the Bible in the Middle Ages, 2nd ed. (Oxford, 1952); R. M. Grant, A Short History of the Interpretation of the Bible, revised ed. (London, 1965); R. E. McNally, "Exegesis, medieval", in New Catholic Encyclopedia (New York, 1967), vol. V, 707-12; G. W. H. Lampe, J. Leclercq, B. Smalley, E. I. J. Rosenthal, "The exposition and exegesis of Scripture", in Cambridge History of the Bible, ed. P. R. Ackroyd et al. (Cambridge, 1969), vol. II, 155-279,- The Bible and Western Culture, ed. W. Lourdaux and D. Verbalist (Louvain, 1970).

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reasoned assent or dissent, and for distinguishing the kinds of argument and authority with power to convince, were part of the style of the whole intellectual culture. Expectation: Ancient insights into probability were qualitative. For whatever reason, the Greeks never developed either the conceptions or the techniques for a mathematical mastery of chance and uncertainty in any subject-matter. The treatment of assent in the main contexts discussed by medieval philosophers was again essentially qualitative. The need to stabilize uncertain choice by quantitative measures of probable expectations was something grasped in the different practical circumstances of the commercial expansion of late medieval Europe. Moral philosophers exploring the moral context of the new enterprises met the objection that profit gained by interest on the investment of money as a loan was usury, by arguing that profit was justified by risk. Gilles of Lessines for example described, at the end of the thirteenth century, a mentality of expectation in which a business partner or a lender or an insurer could calculate a just rate of profit or interest in proportion to the risk on capital outlay assumed (De usuris... c.6, J 593/ fols. i4iv-2r). Such calculations became established practice notably in fourteenth-century Italian marine insurance, with graded premiums, estimated from accumulated experience, for distance and season and dangers from storms and pirates.9 The 9. Cf. F. E. de Roover, "Early examples of marine insurance", Journal of Economic History, 5 (1945), 175-200, R. S. Lopez and I. W. Raymond, Medieval Trade in the Mediterranean World (New York, 1955); G. Stefani, Insurance in Venice from the Origins to the End of the Serenissima (Trieste, 1958; 2 vols.); with E Hendricks, "Contributions to the history of insurance, etc.", Assurance Magazine, 2 (1852), 121-50, 222-58, 393-5, 3 (1853), 93-120, cf. 10(1863), 205-19; E. Bensa, IIcontratto di assicurazione nel medio evo (Genova, 1884); A. Chaufton, Les assurances (Paris, 1884), vol. I,- W. Gow, "Marine insurance" in Encyclopedia Britannica, nth ed. (Cambridge, 1910-1911); C. T. Lewis and T. A. Ingram, "Insurance" in ibid.,- C. E Trenerry, The Origin and Early History of Insurance (London, 1926); G. Valeri, "I primordi dell' assicurazione attraverso il documento del 1329", Rivista del diritto commerciale, 26, part i (1928), 600-41; A. Checchini, "I precedenti e lo sviluppo storico del contratto d' assicurazione", Atti dell'Istituto Nazionale delle Assicurazione (Roma, 1931), vol. Ill; T. O'Donnell, History of Life Insurance in its Formative Years (Chicago, 1936); E. Besta, Le obbligazioni nella storia del duetto italiano (Padova, 1937); I- Heers, "Le prix de 1'assurance a la fin du moyen age", Revue d'histoire economique et sociale, 37 (1959), 7-19; A. Tenenti, Naufrages, corsaires et assurance maritime d Venise 1592-1609 (Paris, 1959); H. Braun, Geschichte der Lebensversicherung und der Lebensverischerungstechnik, 2te Aufl. (Berlin, 1963); L. A. Boiteux, La fortune de mei; le besoin de securite et les debuts

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rational pursuit of profit from any of its sources required thus both personal enterprise and the habit of quantitative order, assisted technically by the new commercial arithmetic and the new financial methods of double-entry bookkeeping and the bill of exchange.10 Bernardino of Siena in the fifteenth century advised merchants, in a sermon, that if they were not assiduous in "subtly estimating risks and opportunities, they are certainly not fit for this business" (Sermo 33: "De mercationibus et artificibus . ..", art.i,c.i,i427: Opera omnia, IV, 1956, p. 142). Merchants he insisted should be honest, should sell unadulterated goods with correct weights and measures; and partners should settle up honestly at least once a year, and then go to confession (p. 143, cf. i6i-2).u A merchant wrote his younger contemporary Benedetto Cotrugli must above all estimate the future expectations guiding his actions from a systematic record of past gains or losses, for: "Mercantile records are means to remember all that a man does, from whom he must take and to whom he must give, the costs of wares, the profits and the losses, and every other transaction on which a merchant is dependent. It should be noted that knowing how to keep good and orderly records teaches one how to draw up contracts, how to do business, and how to make a profit. A merchant should not rely on memory, for that has led to many misde 1'assurance maritime (Paris, 1968); F. Melis, Origini e sviluppi delle assicurazioni in Italia (secoli XIV-XVI) (Roma, 1975), vol. i. 10. Cf. A. P. Usher, "The origins of banking: the primitive bank deposit (12001600)", Economic History Review, 4 (1932-34), 399-428, The Early History of Deposit Banking in Mediterranean Europe (Cambridge, MA, 1943); R. de Roover, "Aux origines d'une technique intellectuelle: la formation et 1'expansion de la compatabilite' £ partie double", Annales d'histoire economique et sociale, 9 (1937), 171-93, 270-98, Involution de la lettre de change (Paris, 1953), "The development of accounting prior to Luca Pacioli according to the account books of medieval merchants", in Business, Banking ... (note 7 above), pp. 119-79; E. Peragallo, The Origin and Evolution of Double-Entry Bookkeeping: A study of Italian practice from the fourteenth century (New York, 1938); F. Melis, Storia della ragioneria (Bologna, 1950); R. S. Lopez, The Three Ages of the Italian Renaissance (Charlottesville, VA, 1970), The Commercial Revolution of the Middle Ages, 950-1350 (Englewood Cliffs, NJ, 1971); Lopez and Raymond, Medieval Trade... (note 9 above), PP- 359ffn. Cf. R. de Roover, San Bernardino of Siena and Sant'Antonio of Florence: Two great economic thinkers of the middle ages (Boston, MA, 1967), especially pp. 13-14, "The scholastic attitude . .." (note 7 above), pp. 343-4; cf. M. G. Kendall, "The beginnings of a probability calculus", Biometrika, 43 (1956), 1-14 for his sermon on games of chance.

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takes" (Delia meicatum et del mercante perfetto, i. 13, 1573, fols. 37r-38r: written I458).12 All this matched the rational habit of foresighted design in the mathematical arts and sciences, in perspective painting and in engineering and architecture, and the systematic recording of techniques and results in an experimental investigation. It is surely no accident that it was in this same practical ambience that appeared the numerical estimation both of future expectations a posteriori, from the numerical regularities of past experience, and of expectations a priori, arising from the theoretical concept of an exhaustive division into equally possible outcomes in games of chance.13 Luca Pacioli14 in the fifteenth century and 12. Trans, modified from Lopez and Raymond, Medieval Trade (note 9 above), pp. 360, 375-7, cf. 416-8. 13. Cf. for the history of probability theory and statistics G. Libri, Histoire des sciences mathematiques en Italie, depuis la renaissance des lettres jusqu' a la fin du dix-septieme siecle (Paris, 1838-41; 4 vols.), II, 188 ff.; I. Todhunter, History of the Mathematical Theory of Probability (Cambridge & London, 1865); V. John, Geschichte der Statistik (Stuttgart, 1884); F. E. A. Meitzen, Theorie und Technik dei Statistik (Berlin, 1886); M. Cantor, Vorlesungen iiber Geschichte der Mathematik, 2te Aufl. (Leipzig, 1894-1901,- 3 vols.), I, 522, II 327 ff. ; The History of Statistics: Their development and progress in many countries, ed. J. Koren (New York, 1918); H. M. Walker, Studies in the History of Statistical Method (Baltimore, MD, 1929); H. Westergaard, Contributions to the History of Statistics (London, 1932); A. Wolf, A History of Science, Technology and Philosophy in the Sixteenth, Seventeenth and Eighteenth Centuries, new ed. by D. McKie (London, 1951-52; 2 vols.); M. Kline, Mathematics in Western Culture (New York, 1953); F. N. David, "Dicing and gaming (a note on the history of probability)", Biometrika, 42 (1955), 1-15, Games, Gods and Gambling: The origins and history of probability and statistical ideas from the earliest times to the Newtonian era (London, 1962); M. G. Kendall, "The beginnings of a probability calculus" (note 11 above), "Where did the history of statistics begin?", Biometrika, 47 (1960), 447-9; O. Ore, "Pascal and the invention of probability theory", American Mathematical Monthly, 67 (1960), 409-19; E. Coumet, "Leprobleme des parisavant Pascal", Archives Internationales d'histoire des sciences, 18 (1965), 245-72, "La the"orie du hasard-est elle nee par hasard?", Annales ESC, 25 (1970), 574-98; Studies in the History of Statistics and Probability, ed. E. S. Pearson, M. G. Kendall and R. L. Plackett (London & High Wycombe, 1970-77; 2 vols.); L. E. Maistrov, Probability Theory: A historical sketch, trans, from the Russian and ed. S. Kotz (New York, 1976); O. B. Sheynin, "On the prehistory of the theory of probability", Archive for History of Exact Sciences 12 (1974), 97-141, "Early history of the theory of probability", ibid., 17 (1977), 201-59, "On the history of the statistical method in biology", ibid., 22 (1980) 323-71; I. Schneider, Die Entwicklung des Wahrscheinlichkeitsbegriffs in der Mathematik von Pascal bis Laplace (Habilitationsschrift Universitat Munchen, 1972), "Die mathematisierung der Vorhersage kiinftiger Ereignisse in der Wahrscheinlichkeitstheorie von 17. bis zum 19. Jahrhundert", Berichte zur Wissenschaftsgeschichte, 2 (1979), 101-12, "Mathematisierung des Wahrscheinlichen

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Girolamo Cardano in the sixteenth dealt with both questions within the context of writings on commercial arithmetic. At any moment of time, they argued, a partner who had invested a certain amount in a company was in the same position as a player who had gained a certain number of points in a game of chance. What was the value of their investment or stake at that moment? Cardano offered a solution making the fundamental principle that of fair expectations: that there should be for all partners or players equal possible outcomes under equal conditions: "The most fundamental principle of all in a game of chance is the equality whether of players, of bystanders, of money, of situation, of the dice box, of the dice itself. To the extent that you depart from that equality, if you do so in your own favour you are unjust, if in that of your opponent you are a fool" (Liber de ludo aleae, c.6, Opera, I, und Anwendung auf Massenphanomene im 17. und 18. Jahrhundert", in Statistik und Staatsbeschieibung in derNeuzeit vornehmlich i6.-i8. Jahrhundert, hrg. von M. Rassen und J. Stagl (Paderbom, 1980), pp. 5 3-73,1. Schneider und K. Reich, "Die wirtschaftliche Entwicklung des Mittelalters im Spiegel der arithemetischen Aufgabensammlungen und ihrer Nachfolger, der Rechenbucher des 15. und 16. Jahrhunderts", Aus dew. Antiquariat, no. 52 (1978), 217-29; I. Hacking, The Emergence of Probability: A philosophical study of early ideas about probability, induction and statistical inference, covering the period 1650 to 1795 (Cambridge, I 975); I- van Brakel, "Some remarks on the prehistory of the concept of statistical probability", Archive for History of Exact Sciences, 16 (1976), 119-36; M. Ferriani, "Stori e 'prehistoria' del concetto di probabilita nell' eta moderna", Rivista di filosofta, 10 (1978), 129-53; A. Fagot, L'explication causale de la mort (Universite de Paris, these de doctoral non publiee, 1978), "Probabilities and causes: on life tables, causes of death, and etiological diagnoses", in Probabilistic Thinking, Thermodynamics, and the Interaction of the History and Philosophy of Science, ed. J. Himtikka, D. Gruender and E. Agazzi (Dordrecht & Boston, MA, 1981), pp. 41-104; K. Pearson, The History of Statistics in the ijth and i8th Centuries against the changing background of intellectual, scientific and religious thought: Lectures... 1921-33, ed. E. S. Pearson (London & High Wycombe, 1978); L. J. Cohen, "Some historical reflections on the Baconian conception of probability", Journal of the History of Ideas, 41 (1980), 219-32; D. L. Patey, Probability and Form: Philosophic theory and literary practice in the Augustan age (Cambridge, 1984); A. C. Crombie, Styles of Scientific Thinking, chs 17-20 (note 1 above). 14. Cf. Lucas de Burgo (Luca Pacioli), Summa de arithemetica, geometria et proportionalita, ix, tract. 1-2 (rules for companies), 4-6 (exchange and money), 7 (division of gains and losses), 10 (games of chance), 11 (double-entry bookkeeping) (Venice, 1494); L. Olschki, Geschichte der neusprachlichen wissenschaftlichen Literatur (Heidelberg, 1919), vol. 1,151 ff.; R. E. Taylor, No Royal Road: Luca Pacioli and his times (Chapel Hill, NC, 1942); David, "Dicing . . .", Games . . . (note 13 above), pp. 36 ff.; Coumet, "Le probleme de paris ..." (note 13 above), pp. 248 ff. ; Schneider und Reich, "Die wirtschaftliche Entwicklung ..." (note 13 above).

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1663, p. 263).15 The same applied by general agreement among all commercial and moral writers to business. Then the instantaneous saleable value of a stake whether in a business or in a game was the amount that should be risked on its future expectations of gain or loss. Thus as the Jesuit Leonard Leys (Lessius) was to put it: "The uncertain risk on capital outlay must be reduced to a price that is certain" ("Periculum sortis incertum debet reduci ad certum pretium", in De iustitia et iure... ii.iii, "De contractibus", c. 25, dubitatio 2, and c. 16, i6o6).16 Interesting attempts were made to establish the equivalence in value of an investment of money by one partner and of work by another. Moral philosophers tried also to make the equality of possible outcomes under equal conditions an explicit principle of jurisprudence for fair trial by law17 IV

In these various ways a calculus of expectation and choice was already by the sixteenth century transferring the whole experience of contingency and variability and chance from a context either of purely qualitative probability, or of irrational hazard or accident or personal luck, into one of the rational mathematical order. Mathematical expectation stabilized the future outside the uncertainty of time, by rationalizing risk and hope as a proportion of the possibilities present at every stage of any enterprise. Then an 15. Trans, modified from S. H. Gould in O. Ore, Cardano: The gambling scholar (Princeton, 1953), pp. 189 ff; cf. A. Bellini, Girolamo Caidano e il suo tempo (Milano, 1947); C. Gini, "Gerolamo Cardano e i fondamenti del calcolo della probabilita", Metron, 2* 11958), 78-96; David, Games . . . (note 13 above), pp. 55 ff.; Coumet, "Le problime des paris..." (note 13 above), 26off. ; M. Fierz, Girolamo Cardano (1501- '$76): Artz, Naturphilosoph, Mathematiker, Astronom und Traumdeutei (liasel & Stuttgart, 1977). 16. Cf Coumet, "La th^orie du hasard . . ." (note 13 above); C. Sommervogel, Bibhotheque de la Compagnie de Jesus, nouvelle ed. (Bruxelles & Paris, 1893), vol. IV, cols. 1726-51. 17. Cf. Domingo de Soto, Libri decem de iustitia et iure, iv. q.5, art. 2: "Utrum per ludum dominium transferatur", vi, q.i: "De usuris", q.6: "De contractu societatis", q.y: "De contractu assecurationis" (Lyon, 1559); Petrus a Navarra, De ablatorum restitutione in foro conscientiae, iii: "De laedente in rebus fortunae", c.2: "De restitutione rei alienae ex contractu", pars 3: "De restitutione rei alienae ex contractu societatis adquisitae"; A. Palau y Dulcet, Manuel del librero Hispano Americano (Barcelona & Oxford, 1957), vol. X, 428.

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uncertain future, and likewise an uncertain past, could be reduced to a probable expectation that was a measurable property of every present. This was the programme to be established with a new elegance and power in one aspect above all by Blaise Pascal, Christiaan Huygens, Antoine Arnauld and Pierre Nicole, Gottfried Withelm Leibniz and Jakob Bernoulli, and in another by John Graunt, Jan de Witt, William Petty and Edmund Halley. The context of this programme was a fresh awareness of the similarity in form of a variety of theoretical and practical situations requiring decision: in religion and morality, in law and politics, in gambling and commerce, in medicine and natural science. A re-examination of dependable knowledge was required first by the renewed challenge of scepticism initiated from the sixteenth century editions of Sextus Empiricus and its other Greek sources principally by Michel de Montaigne, and then by the expansion of scientific experience.18 The significant response to sceptical assertions of the undecidability of important questions, whether of just or effective action or of religious or scientific belief, was the development of a systematic new logic for the uncertain area lying between the traditional bimodality of simply true or simply false, a new logic by which the uncertainty could be stabilized in kinds and degrees of assent or of expectation appropriate to the material. Thus Francis Bacon explained that the principle of his new method of inquiry was "that we should establish degrees of certainty (cei18. Cf. H. G. Van Leeuwin, The Problem of Certainty in English Thought 16301690 (The Hague, 1963); D. C. Allen, Doubts Boundless Sea: Skepticism and faith in the Renaissance (Baltimore, MD, 1964); C. Vasoli, La dialettica e la retorica dell' Umanesimo (Milano, 1968); P. France, Rhetoric and Truth in France: Descartes to Diderot (Oxford, 1972); C. B. Schmitt, Cicero Scepticus: A study of the influence of the Academica in the Renaissance (The Hague, 1972), "The recovery and assimilation of ancient scepticism in the Renaissance", Rivista critica di storia della ftlosofia, 27 (1972,), 363-86; L. A. Jardine, Francis Bacon: Discovery of the art of discourse (Cambridge, 1974), "Lorenzo Valla and the intellectual origins of Humanist dialectic", Journal of the History of Philosophy, 15 (1977), 143-64,- C. J. R. Armstrong, "The dialectical road to truth: the dialogue", in French Renaissance Studies: 1540-70: Humanism and the Encyclopaedia, ed. p. Sharratt (Edinburgh, I 976), pp. 36-51; N. Jardine, "The forging of modern realism: Clavius and Kepler against the sceptics", Studies in History and Philosophy of Science, 10 (1979), 141-73; R. H. Popkin, The History of Scepticism from Erasmus to Spinoza, 3rd ed. (Berkeley & Los Angeles, 1979); B. J. Shapiro, Probability and Certainty in Seventeenth-Century England (Princeton, 1983); Patey, Probability and Literary Form (note 13 above); and Crombie, Styles of Scientific Thinking (note i above) for detailed discussions of what follows with bibliographical references.

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titudinis gradus}" in our knowledge of nature (Novum organum, Preface, 1620, Works, ed. Spedding et al., I, 1857, p. 151). Religious writers argued that if belief could be made neither apodeictic like mathematics or metaphysics, nor certifiable by the senses like physics, it could be given nevertheless a moral certainty beyond reasonable doubt by the accumulation of reliable testimony. The whole question provided an occasion to investigate the grounds for reasonable assent, and for distinguishing degrees of assent, both to the reliability of the evidence and to the credibility of the events and beliefs concerned. Hence Herbert of Cherbury's scale: "Of Truth, so far as it is distinguished from revelation, from probability, from possibility, and from falsehood" (De veritate . . . , 1624). Also Hugo Grotius: "so are there divers wayes of proving or manifesting the truth. Thus there is one way in mathematics, another in physics, a third in ethics, and lastly another kinde when a matter of fact is in question: wherein verily wee must rest content with such testimonies as are free from all suspicion of untruth: otherwise downe goes all the frame and use of history, and a great part of the art of physicke, together with all dutifulness that ought to be between parents and children: for matters of practice can no way else be knowne but by testimonies" (De veritate . . . ii. 24, 1633; English trans., 1632, p. 148). William Chillingworth offered the reasonable rule that we should not "expect mathematical demonstrations . . . in matters plainly incapable of them, such as are to be believed, and if we speak properly, cannot be known". It would be equally unreasonable for anyone to demand "a stronger assent to his conclusions than his arguments deserve" and to want "stronger arguments for a conclusion than the matter will bear" (Religion of Protestants, Preface to the Author, 1638). We had to be "content . . . with a morall certainty of the things" we "believe" which "are only highly credible, and not infallible" (ibid. ii. 154, p. 112). So our "judges are not infallible in their judgements, yet are they certain enough, that they judge aright, and that they proceed according to the evidence given" (ibid. iii. 26, p. 140). Something short of "truths, as certain and infallible as the very common principles of geometry and metaphysics", with "an adherence to them as certain as that of sense or science", were and had to be sufficient in many circumstances for reasonable calculated risk and prudent

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action. For "the evidence of the thing assented to, be it more or lesse, is the reason and cause of the assent in the understanding (ibid. vi. 51, p. 371). So then: "Do you think that there is such a city as Rome or Constantinople?" Properly speaking "I could not say that I knew it, but that I did as undoubtedly believe it, as those things which I did know". For while in their testimony "every particular man may deceive or be deceived, it is not impossible, though exceedingly improbable, that all men should conspire to do so". Hence with sufficient witnesses already, "my own seeing these cities would make no accession, add no degree to the strength and firmness of my faith concerning this matter, only it would change the kind of my assent, and make me know that which formerly I did but believe" ("An answer to some passages in Rushworth's Dialogues", Works, Additional Discourses ix, 1704, P. 47)In all our judgements what "we call experience", according to Thomas Hobbes, "is nothing else but remembrance of what antecedents have been followed by what consequents", in many particular observations or experiments whether natural or contrived: "Thus after a man hath been accustomed to see like antecedents followed by like consequents, whensoever he seeth the like come to pass to any thing he had seen before, he looks there should follow it the same that followed them". So "consequent upon that which is present, men call future; and thus we make remembrance to be the prevision of things to come, or expectation or presumption of the future". Conversely there was a "conjecture of the past, or presumption of the fact", when a man who "seeth the consequent, maketh account there hath been the like antecedent; then he calleth both the antecedent and the consequent, signs one of another, as clouds are signs of rain to come, and rain of clouds past". But "the signs are but conjectural; and according as they have often or seldom failed, so their assurance is more or less; but never full and evident. . . . If the signs hit twenty times for one missing, a man may lay a wager of twenty to one of the event; but may not conclude it for truth" (Humane Nature, ch. 4. 6-10, 1640, English Works, ed. Molesworth, IV, 1840, pp. 16-18). It was by reducing present judgement to an exactly calculated expectation of the future that Pascal and Huygens provided the essential mathematical model for the successive decisions that

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must be made through the uncertainties of all terrestrial existence, whether by nature or by men. This model was their calculation of expectations a priori among the closed possible outcomes of a game of dice. Thus, wrote Pascal, "what was rebellious to experience has not been able to escape from the dominion of reason. Indeed we have reduced it by geometry with so much security to an exact art, that it participates in its certainty and now boldly progresses. And so, joining mathematical demonstrations with the uncertainty of chance, . . . it justly arrogates to itself this stupendous title: the geometry of chance (aleae geometria)" ("Adresse a 1'Academie Parisienne", 1654, Oeuvres, pub. par Brunschvicg et al., Ill, 1908, pp. 307-8; presentation de Lafuma, 1963, pp. 102-3). They showed then how to calculate the present value of a stake in a game from the proportion of favourable to possible expectations exhaustively enumerated. This measured the mathematical expectation at every stage, a central principle defined by Huygens: "One's hazard or expectation (sors seu expectatio] to gain any thing, is worth so much, as, if he had it, he could purchase the like hazard or expectation again in a just and equal game" ("De ratiociniis in ludo aleae" in Schooten, Exercit. math., I 657 / pp. 52,1-2,; English trans. Arbuthnot, Of the Laws of Chance, 1692, p. 3). It was likewise to stabilize decision under uncertainty that Arnauld and Nicole at Port-Royal incorporated these insights into their analysis of judgement a posteriori among the open possible outcomes of experience. Hence their title: La logique ou Tart de penser, contenant outre les regies communes plusieurs observations nouvelles propre a former le judgement (1662). Here they delineated for the whole period the question of how to estimate the objective probability alike of historical and legal evidence for the past, and of predictions leading to action for the future. The absolute rule of impartial objectivity was that we must discount all personal motives and interests in "what we desire should be true. Nor is there any other truth than this, that ought to be found in the thing itself independent from our desires, which ought to prevail over us" (La logique . . . iii. 20.1, 5e ed., 1683; English trans., 1685 revised). When presented with accounts of two possible events: "How then shall we resolve to believe the one rather than the other, if we judge them both possible?" The rule here was that an event "must not

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be considered nakedly, and in itself, like a proposition in geometry; but all the circumstances that accompany it, as well internal as external, are to be weighed with the same consideration. I call internal circumstances such as belong to the fact itself, and external those that relate to the persons, whose testimonies induce as to believe it". Then "if all the circumstances are such that it never or very rarely happens, that the same circumstances are accompanyed with falsehood", we were persuaded to believe it as a "moral certainty", and conversely (ibid., iv. 13). With this rule La logique located the developing critique of the external reliability of evidence for historical events within the conception of their internal credibility determined by current scientific knowledge. It epitomized the common intellectual commitments alike of the rationally critical history of mankind envisaged by Jean Bodin and Francis Bacon and the rationally critical natural science of Galileo and Marin Mersenne and Descartes. Critical estimates of historical evidence, and frequencies of associations of events, yielded degrees of probability within a world of physical law eliminating myth and magic. In all reports of events "we must examine them by their particular circumstances, and by the credit and knowledge of the reporters". Hence "circumstances are to be compared and considered together, not considered apart. For it often happens, that a fact which is not very probable in one circumstance, which is ordinarily a mark of falsehood, ought to be esteemed certain, according to other circumstances", and the other way round (ibid, iv. 14). Likewise: "These rules that serve us to judge of things past, may be applied to things to come. For as we probably judge a thing to have come to pass, when the circumstances which we know are usually joined to the fact, we may as probably believe that such a thing will happen, when the present circumstances are such as are usually attended by such an effect. Thus it is that the physicians can judge of the good or bad success of diseases, captains of the future events of war, and that we judge in the world of the most part of contingent affairs". But in all cases "for that we may judge what is fit to be done, to obtain the good and avoid the evil, we ought not only to consider the good and that evil in itself, but also the probability whether it may happen or no,- and geometrically to consider the proportion which all the things hold together" (ibid, iv. 16).

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That scientific treatment of contingent expectation and uncertain choice had been transformed in concept and technique together by Pascal's aleae geometria, by Huygens's mathematical expectatio, by the measure given in La logique of "la probabilite qu'il arrive ou n'arrive pas" of an event as "geometriquement la proportion que toutes ces choses ont ensemble"; and also by the contemporary analysis in England and the Netherlands of life expectancy was noted by the historically observant Leibniz. From that viewpoint of explicit scientific recognition; the antecedent and subsequent history alike of the calculus of expectation and choice, both a priori and a posteriori, could be brought into intellectual perspective. Leibniz himself had looked independently for a logic of degrees of probability for the contingent and the uncertain first on the model of Roman jurisprudence. Turning then to mathematics he came to look for a general calculus of inquiry giving degrees of certainty according to the subject-matter, from an ars combinatoria such as Ramon Lull had invented and more recently Mersenne had used to calculate the possible combinations of a set of elements from which there could be realizations in fact, whether of musical tunes or languages or natural events. He seems to have brought together these two lines of inquiry only after he had studied, in Paris during 1672-76, the treatment of mathematical expectations a priori in games of chance by Pascal and Huygens, and a posteriori in life insurances by Jan Hudde and Jan de Witt and again by Huygens, himself then in Paris. Leibniz aimed to develop an ample scheme of human knowledge in which provision would be made for "a new logic for knowing degrees of probability", an exact "art of weighing probabilities" (Leibniz to Jean Frederic 1679, in Werke, hrg. Klopp, IV, 1865, pp. 422-23) applicable to law and politics and medicine and the study of history and so on, "where one must come to a decision and take a part even when there is no assurance" ("Nouvelles ouvertures", Opuscules, par Couturat, 1903, pp. 225-27). Technical mastery of this new style of scientific thinking was brought to its first maturity by Jakob Bernoulli in his Ars conjectandi (1713), concluding in Part iv by "setting forth the use and application of the preceding principles in civil, moral and economic affairs". In these and similar matters which we could not strictly know for certain, we had to conjecture, and: "To conjecture about something is to measure

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its probability; and therefore the art of conjecturing or the stochastic art (ars conjectandi sive stochastice) is defined by us as the art of measuring as exactly as possible the probabilities of things with this end in mind: that in our decisions or actions we may be able always to choose or to follow what has been perceived as being better, more advantageous, safer or better considered; in this alone lies all the wisdom of the philosopher and all the prudence of the statesman" (ibid. iv. 2). In this truly seminal work Jakob Bernoulli identified problems and offered solutions that were to guide inquiry for a century. The new mathematical grasp of the regularities of numerical frequencies present in adequately numerous populations gave a mastery of rational expectation and consequential action, within the limits of errors both of events and of estimations, that was to be diversified thereafter into the varied subject-matters of nature and of human society. Philosophical mathematicians and naturalists, in their search for stable knowledge and reasoned decision, established through their insights, at once into the conception and into the techniques of probable and statistical inference, both new methods of scientific exploration and in the end a new economy of nature. The term statistics appeared in this period in the traditional context of "civile, politica, statistica e militare scienza" (Ghilini, Annali di Alessandria, "A'lettori lo stampatore", 1666) as a comparative description of states, and the term was to retain also that essentially descriptive meaning after it had been applied as "statistik" as well to the numerical condition and the inferred prospects of a society (Achenwall, Abriss dei neusten Staatswissenschaft. . ., 1749). It was under the different name of "political arithemetick", supplied by William Petty (Political Arithmetick, Dedication, 1690), that the new "application of mathematics to economico-political matters" (Leibniz to Thomas Burnet i/n. ii. 1697, in Die Philosophischen Schriften, hrg. Gerhardt, III, 1887, p. 190) brought with it the first systematic collection of numerical data made explicitly for the calculation of rates of change and probabilities a posteriori, on which to base decision and action.19 From the numerical frequencies so discovered was then to come the calculation, for any given moment, both of the individual 19. Cf. W. L. Letwin, The Origins of Scientific Economics: English economic thought 1660-1776 (London, 1963).

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probability of an event such as the death of a particular individual or the loss of a particular ship, and of the statistical probability of such an event occurring in the population. This kind of calculation was given a new model especially by English and Dutch writers on vital statistics and demography, who provided thereby an immediate application to social and medical policy. John Graunt in his pioneering Natural and Political Observations ... made upon the Bills of Mortality (1662,) set out explicitly the fundamental discovery that statistical regularities appeared in large numbers which were lost in small numbers. Graunt's scientific method established a new dimension of experimental medicine. From the records of births and of deaths with their symptoms kept for London for over half a century, he initiated inquiries based on the insight that stable mortality rates and sexratios and so on could be translated immediately into approximate probabilities a posteriori. This then provided for inferences in two directions: directly to the likelihood of a possible event coming about, and conversely to the likely causes of events already brought about. He insisted that records should include consistent and regular information about all diseases and other calamities, environmental and social conditions, ages and longevities, and so forth; and that account should be taken only of symptoms and other observable facts and not of opinions. In this way he made an analysis of the proportions of deaths in the population to be attributed to different causes. For example he attributed chronic diseases providing a constant proportion of the total deaths to constant conditions of the environment, and epidemic diseases providing fluctuating proportions to fluctuations in those conditions. Accepting the theory that these diseases came from alterations in the air, then: "as the proportion of acute and epidemical diseases shews the aptness of the air to suddain and vehement impressions, so the chronical diseases shew the ordinary temper of the place, so that upon the proportion of chronical diseases seems to hang the judgement of the fitness of the country for long life". Thus he observed in his numerical data for London that "among the several casualities some bear a constant proportion unto the whole number of burials; such are chronical diseases, and the diseases, whereunto the city is most subject; as for example, consumptions, dropsies, jaundice" and so on; and "some accidents, as grief,

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drowning, men's making away themselves, and being kiPd by several accidents, etc. do the like, whereas epidemical, and malignent diseases, as the plague, purples, spotted-feaver, small-pox, and measles do not keep that equality, so as in some years, or moneths, there died ten times as many as in others" (Natural and Political Observations . . . ch. 2, pp. 13-18). Among the epidemic diseases he made a detailed analysis of the supposed causes of plague by the method of comparing their "greater or less degrees" (Aristotle, Topics ii.io, ii4b 37~sa6; cf. Bacon, Novum organum, ii. 13) and eliminating those that did not match the phenomena (Natural and Political Observations... ch. 4, pp. 33-36). His rather English conclusion was that only the weather matched the plague in its sudden fluctuations. Graunt seems to have initiated here the analysis of inverse probability to be developed by Jakob Bernoulli, Abraham de Moivre and above all by Thomas Bayes, Pierre-Simon Laplace and Antoine-Augustin Cournot. Likewise his "inference from the numbers and proportions we finde in our Bills" (ibid, c.3, pp. 22-3) to the likelihood of dying from various particular diseases initiated the direct analysis of expectations developed especially by Huygens, de Witt and Halley as well as by Jakob Bernoulli. Halley provided a model for the calculation of statistical expectations a posteriori by taking Breslau, an isolated town where virtually all who died had been born, as a pure sample of mankind for pricing life annuities. The data for Breslau gave "a more just idea of the state and condition of mankind, than any thing yet extant that I know of", because virtually the whole population lived out their lives there without immigration or emigration. He showed that "the purchaser ought to pay for only such a part of the value of the annuity, as he has chances that he is living; and this ought to be computed yearly, and the sum of all those yearly values being added together, will amount to the value of the annuity for the life of the person proposed". Thus "the sum of all the present values of those chances is the true value of the annuity" ("An estimate of the degrees of mortality of mankind . . .", Philosophical Transactions, 17, 1693, pp. 600-3). The theory of decision implied here was to be elaborated by Buffon and Daniel Bernoulli into a theory of moral advantage or utility, based on the real value for our way of life of our expectations at particular times

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and in particular circumstances. Thus Daniel Bernoulli wrote: "Ever since geometricians first began to study the measurement of risks (sortes], everyone has affirmed that the value of an expectation is obtained by multiplying the values of each expected particular by the number of chances by which they can be obtained, and then dividing the aggregate of these products by the total number of chances". The chances to be considered must be "equally possible (aeque proclives)", and the "value should be estimated not from the price of a thing, but from the utility (emolumentum) which each takes therefrom. The price is estimated for the thing itself and is the same for everyone, the utility from the circumstances of the person" ("Specimen theoriae novae de mensura sortis", 1730-31, trans. Sommer, 1965). Likewise Buffon: "The mathematician in his calculation estimates money by its quantity; but the moral man must estimate it otherwise . . . ; and since the value of money in relation to the moral man is not proportional to its quantity, but rather to the advantages which money procures, it is obvious that this man ought to take a risk only in proportion to the expectation of these advantages" ("Essai d'arithmetique morale", §16,1730, Histoirenatuielle, Supplement IV, 1777, p. 80). Meanwhile from these statistical methods was to come a new statistical conception of an economy of nature generated through time by a sequence of decisions on instantaneous real values, by natural necessity as by human choice. V

An alternative to the economy of nature produced either by chance as proposed by the Greek atomists and Lucretius, or by the providential design of each separate creature preadapted to its circumstances within the whole creation, was developed by PierreLouis Moreau de Maupertuis in three essays begun before 1741 with his Essai de cosmologie and concluding with his Systeme de la nature published in 1751.20 Beyond alike those who believed 20. Cf. P. Brunei, Maupertuis (Paris, 1929; 2 vols.); E. Guyenot, Les sciences de la vie aux xviie et xviiie siecles: 1'idee de 1'evolution (Paris, 1941); A. C. Crombie, "P.L.M. de Maupertuis, F.R.S. (1698-1759), precurseur du transformisme", Revue de synthese, 78 (1957), 35-56; B. Glass, "Maupertuis, pioneer of genetics and

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that a blind mechanism could have produced all the wonderful adaptations to needs daily visible in organized bodies, and those who believed too readily that they had grasped providence in every contradictory detail, Maupertuis looked for a unifying principle truly characteristic of the Creator: a principle to be found "in phenomena of which the simplicity and universality suffered no exception and left no equivocation" (Essai de cosmologie, "Avantpropos", Oeuvres, i, 1756, p. xi). He found what he sought in his principle of least action. From this principle he claimed to deduce the general laws of all movement and change, which "being found precisely the same as those observed in nature, we can admire its application to all phenomena, in the movement of animals, in the vegetation of plants, in the revolution of the stars: and the spectacle of the universe becomes so much greater, so much more beautiful, so much more worthy of its Author. . . . These laws, so beautiful and so simple, are perhaps the only ones that the Creator and Ruler of things has established in matter in order to effect all the phenomena of this visible world" (ibid. pp. 42-45). Maupertuis approached the whole argument through the calculus of probability, applied to the political arithmetic of nature. Newton had thought that it was impossible that "a blind destiny" could have made the planets all move in the same direction in almost concentric orbits almost in the same plane. But if one supposed this "as the effect of chance", while very improbable "some probability nevertheless remains", so that one could not say that it must be the "effect of a choice" by the Creator. Likewise The argument drawn from the adaptation of the different parts of animals to their needs. . . . Does not all this indicate an intelligence and a design which presided over their construction? This argument struck the ancients as it struck Newton: and in vain the greatest enemy of providence replies to it that use has not been the goal at all, that it has been the consequence of the construction of the parts of animals; that chance having formed the eyes, the ears, the tongue, they have been used for sense, for speaking. But could it not be said that in the fortuitous combination of the productions of nature, since it would be only those that had certain adaptive relations (rapports de convenance) that could survive, it is not surprising that this adaptation is found in all the species that exist? evolution", in Forerunners of Darwin, ed. B. Glass, O. Temkin and W. L. Strauss, Jr. (Baltimore, MD, 1959), with other relevant papers therein; J. Roger, Les sciences de la vie dans la pensee fianfaise du xviiie siecle (Paris, 1963).

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Chance, it could be said, had produced an innumerable multitude of individuals; a small number were so constructed that the parts of the animal could satisfy its needs; in another infinitely greater number there was neither adapation nor order. All these latter have perished: animals without mouths could not live, others without reproduction organs could not perpetuate themselves. Only those have remained in which there was order and adaptation, and these species, which we see today, are only the smallest part of those which a blind destiny had produced (ibid. pp. 7-12; cf. Lucretius i. 1021-51, ii. 573-6, iv. 833-5, v. 56-7, 519-31, 837-77, and Empedocles in Aristotle, Departibus animalium, i. i, 6403 17-25).

Yet this could prove the perfection of providence: for "everything would be so ordered that a blind and necessary mathematics executes what the most enlightened and free intelligence prescribed" (Maupertuis, ibid. p. 2,5). Thus, extending the Cartesian mechanistic model from the biology of the individual organism to the biology of populations, Maupertuis saw in the numerical proportions and the adaptations of living species to their needs and environments, no longer the immediate operation of providence, but the necessary generation of order out of chance and chaos by the blind statistics of the least quantities required: varied birth and selective survival. The economy of nature was not then a perpetual pre-established harmony, but a shifting balance of perpetual trial for survival or exclusion. The history of living things on the Earth was a succession of states of dynamic equilibrium which had generated through time the adaptive diversity that we now observed. This simple statistical principle he combined next with a genetical hypothesis, giving to his "sketch of a system which we have proposed to explain the formation of animals . . . only the degree of assent that it deserves" (Venus physique, ii. 8, 1745, Oeuvres, II, 130-1). Then: Could we not explain by that how from only two individuals the multiplication of the most dissimilar species could have followed? They would have owed their first origin only to some fortuitous productions in which elementary particles would not have kept the order which they had in the father or mother animals; each degree of error would have made a new species; and by means of repeated deviations would have come the infinite diversity of animals that we see today: which will perhaps go on increasing with time, but to which perhaps the sequence of centuries will bring only imperceptible increments (Systeme de la nature, § xlv, Oeuvres, II, 148*49*)-

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"But should the system we propose be confined to animals?... Have not plants, minerals, and even metals a similar origin? Does not their production lead us to the production of other more organized bodies?" (ibid. § xlvii, p. 150*). All this concerned "what man has in common with the beasts, the plants, and in some way with all organized creatures". Man has in addition a principle by which he could "know God, and in which he finds moral ideas of his duties", and by which he could abstract from particular physical perceptions and "rise to this knowledge of a wholly different order" (§ Ivii, p. 160*). "To make natural history a true science", Maupertuis wrote in his Lettre sur le piogres des sciences (1752), "we must apply ourselves to researches that make us know not the particular shape of this or that animal, but the general processes of nature in its production and its preservation" (Oeuvres, II, 386). He rescued design in the history of nature, from a vision projected unmistakably from Lucretius and Empedocles, and he avoided the embarrassment of having to attribute misadaptations and adaptations alike to the individual attention of providence, by looking for the simplest and most universal principle through which, in animate as in inanimate matter: "A blind and necessary mechanics follows the designs of the most enlightened and free Intelligence" ("Accord de differentes loix de la nature", 1744, Oeuvres, IV, 21). From his approach through probabilities, Maupertuis looked, like Aristotle and like Descartes, for a world that could not be otherwise. By his highly original identification of varied birth and selective survival as the least quantities from which a blind statistics must generate progressively divergent adaptation, he brought the origination of species then within the calculus of the probability of success or failure at every stage of the process. Thus he could postulate that without any other cause progressive order, progressive genetic diversification with adaptation to variations of the environment, progressive complexity and novelty, must be generated in time with automatic necessity from unordered inherited variations (some fortuitous, some initiated by the environment) by the purely statistical process of different rates of survival. Maupertuis's speculative originality was to identify this necessary statistical process of the vectorial transformation of species by the accumulation of random changes through survivals and exclusions.

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In this whole intellectual context we can surely see in the conception of an instantaneous real value developed from Halley to Daniel Bernoulli and Buffon, with its immediate relevance to economic life, a description likewise of the situation of a biological species. It was Maupertuis who suggested to Daniel Bernoulli that he should calculate the real advantage for mankind of inoculation against smallpox. Considering the "total quantity of life" of a sample born at the same time until the death of the last individual, or the "average life" of each newborn child, Bernoulli offered a theorem by which "we should decide whether to reject or to introduce inoculation for newborn children, in so far as we wished to adopt the principle of the greatest utility for all mankind" ("Essai d'une nouvelle analyse de la mortalite causee par la petite verole, et des advantages de 1'inoculation pour la prevenir", §§12, 14, 1760, pp. 27, 33, trans. Bradley, 1971, with changes). But the relative advantage for individuals had to be weighed against the risk at every age, so that as d'Alembert pointed out "the interest of the state and that of the individual should be calculated separately" ("Sur 1'application du calcul des probabilities a 1'inoculation de la petite verole", 1761, p. 38). Again Adam Smith saw in economic society a statistical mechanism designed for an end which followed from "the order, the regular and harmonious movement of the system, the machine or economy by means of which it is produced" (Theory of Moral Sentiments, iv. i, 1759, p. 348). Businesses in competition faced the options of survival in various degrees or exclusion through the statistical accumulation of gains or losses, or of transformation to meet new circumstances. Competition stimulated structural and technical innovation and expansion into new markets : for "increase in demand" for goods "encourages production, and thereby increases the competition of the producers, who, in order to undersell one another, have recourse to new divisions of labour and new improvements of art, which they might never otherwise have thought of" (Wealth of Nations, 1776, ed. Campbell et al., V.i.e. 26, 1976, p. 748). For individual or business or state, for part or whole, advantage or disadvantage however marginal must accumulate with repetition and so with time must generate divergence. Laplace showed that regularities hidden by the complexity of phenomena could be

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revealed by the analysis of adequate numbers (Th&orie analytique des probability, ii.s, 1812). Seemingly echoing Thomas Malthus, he wrote that it was "principally by the lack of subsistence that the progressive march of the population is arrested. In all the species of animals and plants, nature tends without ceasing to augment the number of individuals until they are at the level of the means of subsistence" (Essaiphilosophique swlesprobabilites, 3e ed., 1816, p. 171). He continued: "By the repetition of an advantageous event, simple or compound, the real benefit becomes more and more probable and increases without ceasing : it becomes certain in the hypothesis of an infinite number of repetitions". Dividing it by the total number of events, "the mean benefit of each event is the mathematical expectation itself, or the advantage relative to the event. It is the same with a loss which becomes certain in the long run, however little the event may be disadvantageous". This theorem with others like it "proves that regularity ends by establishing itself in the very things most subordinated to what we call chance. When events are in large numbers, analysis gives again a very simple expression of the probability that the benefit will be confined within determined limits". The same went for loss. On the truth of this theorem "depends the stability of institutions based upon probabilities. But in order that it can be applied to them, it is necessary that these institutions should multiply the advantageous events by means of numerous transactions" (ibid. pp. 174-75). They must also base their decisions on the real value for a way of life of expectations at particular times and in particular circumstances. The real advantage expected of any event in sufficient numbers could be calculated then, for all participants alike, as a proportion of the possibilities present at every stage of any enterprise, whether the participants were biological species or varieties or commercial enterprises or players in a game, each competing for limited resources or hazardous outcomes. Thus the uncertain future could be stabilized for all alike in mathematical regularity by computing the probable expectation of gain or loss, growth or decline, as a measurable property of each participant at every instant. We know that Charles Darwin, in developing his theory of natural selection, became at some stage aware of the analysis by Malthus of the ratios of births to survivals. Perhaps the account

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given by Adam Smith of transformation as an alternative to the exclusion of a business by competition might have suggested the same for species. With natural selection Darwin in effect applied to the economy of nature the economic principle of net marginal advantage applied by Laplace to human commerce.21 He wrote in 21. Darwin referred in his "Notebooks on Transformation of Species" (transcribed by P. H. Barret in H. E. Gruber, Darwin on Man, London, 1974) to Mai thus (D 134 6-135 e, £3:1838), and to Adam Smith (M 108, 155: 1838, and N 184), and later he gave full credit to Malthus in his Autobiography, ed. N. Barlow (London, 1958), p. 120; cf. on Malthus also C. Darwin and A. R. Wallace, Evolution by Natural Selection, ed. G. R. de Beer (Cambridge, 1958), pp. 7-8 (Wallace, 1858), 46-68 (Darwin 1842), 116-9 (1844), 259 (1858), 273-9 (Wallace 1858); and on Adam Smith the reference in Darwin, Natural Selection . . . written from 1856 to 1858, ch. 6, ed. R. Stauffer (Cambridge, 1975), p. 233. Darwin wrote in the 3rd ed. of The Origin of Species, ch. 14 (London, 1861), pp. 517-8, in discussing whether life originated with one or many creations, that "Maupertuis' philosophical axiom of 'least action' leads the mind more willingly to admit the smaller number"; cf. his Variation of Animals and Plants Under Domestication, Introduction (London, 1868), pp. 12-13. He never referred to Laplace but the entomologist William Kirby (whose work Darwin knew) in the seventh of the Bridgewater Treatises, On the Power, Wisdom and Goodness of God as Manifested in the Creation of Animals and in their History, Habits and Instincts, Introduction (London, 1835), vol. I, pp. xxiv ff., xxxii ff., xl ff., accused both Laplace and Lamarck of trying "to ascribe all the works of creation to second causes; .. . without the intervention of a first" (p. xxiv). He adapted Adam Smith to argue that the Malthusian struggle brought about by the growth of populations to the limits of subsistence was the means used by the Creator to maintain the order and harmony of the system as a whole (ch. 3, vol. I, 141-4, ch. 18, vol. II, 243-4). Karl Marx wrote to Friedrich Engles on 18. vi. 1862: "It is remarkable how Darwin recognises among beasts and plants his English society with its division of labour, competition, opening up of new markets, 'inventions', and the Malthusian 'struggle for existence'. It is Hobbes's bellum omnium contra omnes . . . " (Selected Correspondence, Moscow & London, 1956, pp. 156-7). Engles commented to P. L. Lavrov on 12-17. ix. 1875: "The whole Darwinist teaching of the struggle for existence is simply a transference from society to nature of Hobbes's doctrine of bellum omnium contra omnes and of the bourgeois-economic doctrine of competition, together with Malthus's theory of population. When this conjurer's trick has been performed . . . , the same theories are transferred back again from organic nature to history and it is now claimed that their validity as eternal laws of human society has been proved" (ibid., pp. 367-8). Cf. T. Cowles, "Malthus, Darwin, and Bagehot: a study in the transference of a concept", Isis, 26 (1936), 341-8; A. Sandow, "Social factors in the origin of Darwinism", Quarterly Review of Biology, 13 (1938), 315-26; A. C. Crombie, "Darwin's scientific method", in Actes due IX e Congres International d'Histoire des Sciences: Barcelona-Madrid 1959 (Barcelona & Paris, 1960), pp. 354-62,- R. M. Young, "Malthus and the evolutionists: the common context of biological and social theory", Past and Present, no. 43 (1969), 109-45, "Darwin's metaphor: does nature select?", TheMonist, 55 (1971), 442-503; M. Ruse, The Darwinian Revolution: Science red in tooth and claw (Chicago, 1979); R. G. Mazzolini, "Stato e organismo, individui e cellule nell' opera di Rudolf Virchow negli anni 1845-1860", Annali dell'Istituto storico italo-germanico in Trento, 9 (1983), 153-293.

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his "Notebooks on Transmutation of Species" opened in July 1837 after his return in the previous year from his long voyage in the Beagle: "Seeing the beautiful seed of a bull rush I thought, surely no 'fortuitous' growth could have produced these innumerable seeds, yet if a seed were produced with an infinitesimal advantage it would have better chance of being propagated" ("Notebooks...," E 137, 1839, in Gruber, Darwin on Man, 1974, p. 460). Five year later in his Essay of 1844 he wrote that in the struggle for existence "less than a grain in the balance will determine which individuals shall live and which perish". In changing conditions "there is a most powerful means of selection, tending to preserve even the slightest variation, which aided the subsistence or defence of those organic beings, during any part of their whole existence, whose organization had been rendered plastic "(in Evolution by Natural Selection, ed. de Beer, 1958, p. 24i).22 Darwin, like Maupertuis, was making a point about the survival of even marginal advantage quite different from anything found in ancient atomism, for he was reducing the uncertain expectations of the fortuitous beloved by the atomists to the exact necessity of a statistical law. He wrote in the long manuscript of Natural Selection (18 5 7) of which On the Origin of Species (1859) was published as an abstract: "mere fluctuating variability, or any direct effect of external conditions . . . are wholly inadequate to explain the infinitude of exquisitely correlated structures, which we see on all sides of us The most credulous believer in the 'fortuitous concourse of atoms' will surely be baffled when he thinks of those innumerable and complicated yet manifest correlations". Hence: "No theory of the derivation of groups of species from a common parent can be thought satisfactory until it can be shown how these wondrous correlations of structure can arise. I believe that such means do exist in nature, analogous, but incomparably superior, to those by which man selects and adds up trifling changes" in cultivating domesticated animals and plants. This "means of selection" in nature was "that severe, though not continuous struggle for existence, to which... all organic beings are subjected, and which would give to any individual with the slightest variation of service to it (at any period of its life) a better chance of surviving, and which would almost 22. Cf. R. A. Fisher, The Genetical Theory of Natural Selection (Oxford, 1930); A. C. Crombie, "Interspecific competition", The Journal of Animal Ecology, 16 (1947), 44-73-

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ensure the destruction of an individual varying in the slightest degree in the opposite direction. I can see no limit to the perfection of this means of selection" (Natural Selection, ch. 5, ed. Stauffer, I 975> PP- 1 74~5)- Hence the fundamental efficacy of the "Principle of Divergence. . . . For in any country, a far greater number of individuals descended from the same parents can be supported, when greatly modified in different ways, in habits, constitution and structure, so as to fill as many places, as possible, in the polity of nature, than when not at all or only slightly modified". More generally "a greater absolute amount of life can be supported in any country or on the globe, when life is developed under many and widely different forms, than when under a few and allied forms". Divergence into new varieties and species was then a necessary consequence of the unlimited accumulation of marginal advantages opened into the economy of organisms by "the greatest amount of their diversification", which doctrine is in fact that of 'the division of labour'" (ibid. ch. 6, pp. 227-8, 233). With something of Adam Smith as the author of this doctrine Darwin had been familiar for many years (cf. "Notebooks . . ." M 108, 155, 1838, and N 184 in Gruber, ibid. pp. 286, 296, 351, 390). It is difficult to tell how far Darwin himself was aware of the ideas crystallized by Laplace, or of the form of argument used by Maupertuis in his identification of varied birth and selective survival or exclusion as the least statistical quantities from which the adaptive transformation of species must necessarily and automatically be generated.23 Like them both he envisaged a form of argument in which the consequences of statistical postulates followed with the certainty of a physical law, and like Maupertuis he saw in this a truer conception of the Creator than that of a series of independent creations: "how much more simple and sublime power: let attraction act according to certain law; such are inevitable consequences. Let animal be created, then by fixed laws of generation, such will be their successors . . . " ("Notebooks . . . " B= II101-2, 1837, ed. de Beer et al., 1960, p. 53). In this form he looked from the start for "laws of change, which would then be main object of study, to guide our speculations with respect to past and future" (ibid. B = II 228-9, p. 69). Like Laplace he estimated 23. See note 20 above.

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the probability of a theory by its range of predictions: "these speculations, even if partly true, they are of the greatest service towards the end of science, namely prediction; till facts are grouped and called there can be no prediction. The only advantage of discovering laws is to foretell what will happen and to see bearing of scattered facts" (ibid. D = IV 67, p. 137). For, he wrote long afterwards: "In scientific investigations it is permitted to invent any hypothesis, and if it explains various large and independent classes of facts it rises to the rank of a well-grounded theory" (Variation . . . , 1868, p. 9). He cited "the greater simplicity of the view of a few forms or of only one form having been originally created, instead of innumerable miraculous creations having been necessary at innumerable periods"; and "this more simple view accords well with Maupertuis's philosophical axiom of 'least action' " (ibid. pp. 12-13). Darwin laid out the argument of the Origin of Species itself with legal advocacy, showing why its premises should be accepted and what followed from them, stating the difficulties of his theory and demolishing them one by one: "For I am well aware that scarcely a single point is discussed in this volume on which facts cannot be adduced, often apparently leading to conclusions directly opposite to those at which I have arrived. A fair result can be obtained only by fully stating and balancing the facts and arguments on both sides of each question" (Origin, ch. i, 1859, p. 2). He had to prove that the visible order of nature was the result of an historical process, brought about by stable statistical probabilities discoverable only by careful analysis beneath the immediately observable surface of things: "Throw up a handful of feathers, and all must fall to the ground according to definite laws; but how simple is this problem compared to the action and reaction of the innumerable plants and animals which have determined, in the course of centuries, the proportional numbers and kinds" found anywhere upon the Earth (ibid. ch. 3, p. 75). He concluded: "I cannot believe that a false theory would explain, as it seems to me that the theory of natural selection does explain, the several large classes of facts above specified" (ibid., 2nd ed., ch. 14, 1860, pp. 480-1). "To my mind" Darwin wrote finally, "it accords better with what we know of the laws impressed on matter by the Creator, that the production and extinction of the past and present inhabit-

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ants of the world should have been due to secondary causes. . . . Thus, from war in nature, from famine and death, the most exalted object which we are capable of conceiving, namely the production of the higher animals, directly follows. There is grandeur in this view of life, with its powers, having been originally breathed into a few forms or into one,- and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved" (ibid., ch. 14, 1859, pp. 488, 490). But this evolution of living things, brought about by the statistical probability at every moving point of time that the decision would be success or failure, had no general direction. It was propelled only by the necessity for survival that advantage should be taken of every available opportunity: a kind of statistical principle of plentitude with in itself no evident purpose except to generate adaptive diversity and hence increase the total quantity of life. "I cannot think that the world, as we see it, is the result of chance" Darwin repeated; "and yet I cannot look at each separate thing as the result of design" (Darwin to Asa Gray 26. xi. 1860, in Life and Letters, ed. F. Darwin, II, 1887, p. 353). Each separate thing was rather the product of general laws, but the problem for him remained whether "the existence of so-called natural laws implies purpose. I cannot see this" (Darwin to W. Graham 3.vii. 1881, in ibid, i, 315). The Duke of Argyll recorded the aging Darwin's response to his remark that it was impossible to look at the many "wonderful contrivances for certain purposes in nature" discovered by Darwin himself "without seeing that they were the effect and the expression of mind". Darwin replied: "Well, that often conies over me with overwhelming force; but at other times . . . it seems to go away" (ibid. p. 316). Thomas Henry Huxley in his treatment of Evolution and Ethics (1893) placed the question of design and purpose firmly within the horizon of human responsibility. He described "attempts to apply the analogy of cosmic order to society" (CollectedEssays, IX, 1894, p. 82) as simply "reasoned savagery" (ibid. p. 115): "The history of civilization details the steps by which men have succeeded in building up an artificial world within the cosmos. Fragile reed as he may be, man, as Pascal says, is a thinking reed" (ibid. p. 83;

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Pascal, Pensees 2oo^Lafuma =347 Brunschvicg). That was his true expectation. Surely all this points to the fundamental logic of evolutionary and of moral expectation and choice alike. For we can place the biological theory of the evolutionary transformation of living organisms by varied birth and selective survival, that is by natural selection, within a theory of decision, whether made impersonally in nature or voluntarily by man, in its most general form. This was a distant outcome of the analogy of economic expectation and of choice according to real value and their quantification. The quantified concept of future things, formed in the mind from numerical data collected in rational anticipation of action, introduced into business and games, as it was to do into politics and war, the style of a mathematical rational art. The mathematical science of statistics, developed with the calculus of probabilities in the seventeenth and eighteenth centuries, offered something beyond the traditional descriptions of the natural and human resources of states. It was transposed, especially in eighteenth-century France and Britain, into a new statistical economy at once of human society and of nature. The essential concept of the instantaneous real value of a stake in a game or a commercial enterprise, measured by the amount that should be risked on its future expectations of gain or loss, was transferred to the formally identical situation of a biological species. We may see then a formal identity between the economic concept of net marginal advantage, which Laplace showed must with repetition generate an ever increasing divergence between enterprises or states, and Charles Darwin's biological concept of natural selection generating an evolution of species. The measure of the instantaneous value of a variety or species as a contributor to the total quantity of life, like that of a commercial enterprise or of a player for stakes, was its expectations in the circumstances of that instant. The same applies to a decision fittest for the occasion, whether in a choice of action or a choice of theory. The difference is that men in their decisions may be free and responsible, may by free choices accelerate or retard or reverse a process of gain, whether in things or in knowledge, and may beyond the quantity choose the quality of life. The conformity of logical style so discovered in scientific think-

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ing, through different historical periods and over a wide variety of subject matters, provides an illuminating insight into very deep characteristics of our intellectual culture. It also raises the question of the limits of a scientific style, and of the motivation of scientific change. It is an insight that can come only from a comparative historical analysis. It is only through such philosophical history that we can see how problems and their solutions came to be formulated, promoted, and accepted or rejected. As historians of a movement through the past we can only interpret the signs we have now in the present, and the signs seem to indicate that what I call the intellectual and moral commitments of any major culture have a very tenacious life. In that sense we may conclude indeed: Veritas ftlia temporis.

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Antoine Arnauld et Pierre Nicole, La logique ou I'art de penser, contenant outre les regies communes plusieurs observations nouvelles propres a former le jugement (Paris, 1662); 5 e ed. revue et de nouveau augmentee (1683), ed. critique de P. Clair et R Girbal (Paris, 1965). , Logic; or, The Art of Thinking: in which, besides the common, are contain 'd many excellent new rules, very profitable for directing of reason, and acquiring of judgement, in things as well relating to the instruction of man's self, as of others . . . translated into English by several hands (London, 1685). Divi Aurelii Augustini Hipponensis Episcopi, Opera (Venetiis, 1584; 10 vols.). , De civetate Dei in Opera, curaverunt B. Dombart et A. Kalb (Corpus Christianorum, ser. Lat., vols. XLVII-XVLIII; Turnholti, 1955). , Concerning the City of God against the Pagans (De civetate Dei], trans. H. Bettenson (Harmondsworth, Middlesex, 1972). Frances Bacon, Works, ed. J. Spedding, R. L. Ellis and D. D. Heath (London, 1857-59; 7 vols.).

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S. Bernardinus Sienensis, O.F.M., Opera omnia . . . studio et cura PP. Colegii S. Bonaventurae (Firenze, 1950-56; 5 vols.). Daniel Bernoulli, "Specimen theoriae novae de mensura sortis", Commentarii Academiae Imperialis Petropolitanae (Petropoli, 1738), vol. V ad annos 1730 et 1731, pp. 175-92. , "Exposition of a new theory on the measurement of risk" (1730-31}, trans. L. Sommer, Econometrica, 22 (1954), 2,3-36. , "Essai d'une nouvelle analyse de la mortalite causee par la petite verole, et des avantages de 1'inoculation pour la prevenir", Memories de mathematiques et de physique, dree des registres de 1'Academie Royal des Sciences, de 1'annee 1760 (Paris 1766), 1-45 (avec Histoire delAcademie Royale des Sciences, annee 1760; Paris, 1766). Jacob Bernoulli, Ars conjectandi, opus posthumum (Basileae, 1713) (James Bernoulli), Part Four of the Art of Conjecturing, and Correspondence between Leibniz and Bernoulh, trans. Bing Sung, Harvard University Department is Statistics Technical Report no. 2 (1966: duplicated). (Jakob Bernoulli), Die Werke, hrg. von J. O. Fleckenstein, O. Spiess, B. L. van der Waerden, der Naturforschenden Gellsellschaft in Basel (Basel, 1969-75; 3 vols.). L. Bradley, Smallpox Inoculation: An eighteenth-century mathematical controversy (Nottingham, 1971). Georges-Louis Leclerc, Comte de Buffon, Histoire naturelle, generale et particuliere (Paris, 1749-89,- 36 vols.). Hieronymi Cardani Mediolanensis, Opera omnia ..., cura Caroli Sponii (Lugduni, 1663; lovols.). William Chillingworth, The Religion of Protestants, a Safe way to Salvation, or An Answer to a booke entitled Mercy and Truth, or, Chanty maintain'd by Catholiques, which pretends to prove the contrary (Oxford, 1638). , Works . . . with . . . his nine Additional Discourses (London, 1704). Cicero, Academica, with English trans, by H. Rackham (London & New York, 1933). Pseudo-Cicero, Ad C. Herennium de ratione dicendi {Rhetorica ad Herennium], with English trans, by H. Caplan (London & Cambridge, MA, 1956). Benedetto Cotrugli Rugeo, Delia mercatura et del mercante perfetto, libri quattro (Vinegia, 1573). Charles Darwin, On the Origin of Species by means of Natural Selection, or the preservation of favoured races in the struggle f or hfe (London, 1859). , The Variation of Animals and Plants under Domestication (London, 1868; 2 vols.). , The Life and Letters, ed. F. Darwin (London, 1887; 3 vols.). , More Letters, ed. F. Darwin and A. C. Seward (London, 1903 ; 2 vols.).

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, The Autobiography: with original omissions restored, ed. with appendix and notes by N. Barlow (London, 1958). Charles Darwin and Alfred Russel Wallace, Evolution by Natural Selection, ed. with a foreword by Sir Gavin de Beer (Cambridge, 1958). Charles Darwin, "A transcription of Darwin's first Notebook on Transmutation of Species'", ed. P. H. Barrett, Bulletin of the Museum of Comparative Zoology at Harvard College, 122 (1960), 247-96. , "Darwin's Notebooks on Transmutation of Species", ed. with introd. and notes by Sir Gavin de Beer, M. J. Rowlands and B. M. Shramovsky, Bulletin of the British Museum (Natural History): Historical series, 2 (196061), 25-200, 3 (1967), 131-76 (here Notebooks B-D are numbered I-IV: see Barrett and Gruber). , Natural Selection: Being the second part of his big species book written from 1856 to 1858, ed. from the MS by R. Stauffer (Cambridge, 1975). Girolamo Ghilini, Annali di Alessandria, overo le cose accadute in essa cittd nel suo, e circonvicino territorio dall' anno dell' origine sua sino al MDCLIX (Milano, 1666). Gilles de Lessines, De usuris in communi, et de usurarum contractibus, in Divi Thomae Aquinatis . . . Opera omnia (Venetiis, 1593), xvii.2, opusculum 73, fols. i39v-47v. John Graunt, Natural and Political Observations Mentioned in a following Index, and made upon the Bills of Mortality (London, 1662); 5th ed. (1676) reprinted in Petty, Economic Writings, ed. Hull, (1899), vol. II, 314-431. Hugo Grotius, De veritate religionis Christianae, ed. 3a (Lugduni Batavorum, 1633; isted. 1627). , True Religion explained and defended. . . Of the Truth of Christian Religion (London, 1632). H. E. Gruber, Darwin on Man: A psychological study of scientific creativity, together with Darwin's Early and Unpublished Notebooks, transcribed and annotated by P. H. Barrett (London, 1974). Edmund Halley, "An estimate of the degrees of the mortality of mankind, drawn from curious tables of the births and funerals at the City of Breslau", and "Some further considerations on the Breslau Bills of Mortality", Philosophical Transactions, 17 (1693), 596-610, 654-6 bis. Edouard Herbert, Baron de Cherbury, De la verite en tant qu'elle est distincte de la revelation, du vray-semblable, du possible et du faux,... revue et argumente par le mesme auteur, 3e 6d. (Paris, 1639). Hippocrates, Oeuvres completes, traduction nouvelle avec le text grec en regard,... par E, Littre (Paris, 1839-61; 10 vols.; reprinted 1961-62). , with an English trans, by W. H. S. Jones and E. T. Withington (London & Cambridge, MA, 1923-31; 4 vols.).

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Hippocrate, texte etabli et traduit par R. Joly (Paris, 1967- ; 3 vols. to date). Thomas Hobbes of Malmsbury, Humane Nature: or, The fundamental elements ofpolicie . . . (London, 1650): Epistle Dedicatory 1640. , Engish Works, ed. Sir William Molesworth (London, 1839-45; n vols.). Thomas H. Huxley, Collected Essays (London, 1893-1925; 9 vols.). Christiaan Huygens, "De ratiociniis in ludo aleae" in Latin trans, by Franciscus a Schooten, Exercitationum mathematicarum libri quinque (Lugduni Batavorum, 1657), pp. 517-34. , Oeuvres completes, publiees par la Societe Hollandaise des Sciences (La Haye, 1888-1950; 22 vols.). loannis Saresberaensis Episcopi Carnotensis, Metalogicon libri iv, recognovit. . . C. C. J. Webb (Oxford, 1929). John of Salisbury, The Metalogicon: A twelfth century defense of the verbal and logical arts of the trivium, trans. D. D. McGarry (Berkeley & Los Angeles, 1955). Johannes Kepler, Gesammelte Werke, hrg. . . . unter der Leitung von W. von Dyck und M. Caspar . . . F. Hammer (Miinchen, 1937-59,- 18 vols.). The Rev. William Kirby, On the Power, Wisdom and Goodness of God as Manifested in the Creation of Animals and in their History, Habits and Instincts (London, 1835,- 2 vols.). Pierre-Simon de Laplace, Theorie analytique des probabilites (Paris, 1812). , Essai philosophique sur les probabilites, 3e ed., revue et augmentee par 1'auteur (Paris, 1816); first published as preface to the Theorie analytique . . ., 2e ed. (Paris, 1814). , Oeuvres completes (Paris, 1878-1912; 14 vols.). Gottfried Wilhelm Leibniz, Die Werke . . . hrg. O. Klopp (Hannover, 1864-84; ii vols.). , Die Philosophischen Schriften, hrg. von C.I. Gerhardt (Berlin, 187590; 7 vols.). , Opuscules et fragments inedits, extraits des manuscrits de la Bibliotheque royale de Hanouvre par L. Couturat (Paris, 1903). , Samtliche Schriften undBriefe, hrg. von der Preussischen/Deutschen Akademie der Wissenschaften zu Berlin (Darmstadt, Liepzig & Berlin, 1923-; Hildensheim, 1970-; 6 vols. to date). Leonardus Lessius, e Societate lesu S. Theol. in Academia Lovaniensi professore, De iustitia et iure caeterisque virtutibus cardinalibus hbri iv (Parisiis, 1606; ist ed. Lovanii, 1605). T. R. Malthus, An Essay on the Principle of Population as it affects the future improvement of society. . . (London, 1798,- 2nd ed. 1803). Karl Marx and Friedrich Engels, Selected Correspondence (Moscow & London, 1956).

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Pierre-Louis Moreau de Maupertuis, Oeuvres^ nouvelle ed. corrig6e et augmentee (Lyon, 1756; 4 vols.). Petri Navarra Toletani theologi, De ablatorum restitutione in foio conscientaelibriquatuor, 2 a ed. (Lugduni, 1593; isted.Toleti, 1585; 2 vols.). Alexandri Neckam, De naturis rerum libri duo . . . ed. T. Wright (London, 1863). Luca Pacioli: Prater Lucas de Burgo Sancti Sepulcri Ordinis Minorum, Summa de arithemetrica, geometiia et proportionalita (Venetiis, 1494). Blaise Pascal, Oeuvres, publiees suivant 1'ordre chronologique avec documents et notes, par L. Brunschvicg et P. Boutroux et F. Glazier (Paris, 1904-14; 14 vols.). , Oeuvres completes, presentation et notes de L. Lafuma (Paris, 1963). , Oeuvies completes, texte etabli, presente et annote par }. Mesnard (Paris, 1964-70; 2 vols.). Sir William Petty, Five Essays in Political Arithmetick (London, 1687). , Political Arithmetick (London, 1690). , The Economic Writings, together with the Observations upon the Bills of Mortality more probably by Captain John Graunt, ed. C. H. Hull (Cambridge, 1899; 2 vols.). Divin Platonis, Operum a Marsilio Ficino tralatorum tomi quinque . . . (Lugduni, 1550). Quintilian, Instituto rhetorica, with English trans, by H. E. Butler (London & Cambridge, MA, 1921-22; 4 vols.). Sextus Empiricus, with an English trans, by R. G. Bury (London &. Cambridge, MA, 1939-49; 4 vols.). Adam Smith, The Theory of Moral Sentiments (London, 1759). , The Theory of Moral Sentiments, 6th ed. enlarged (London, 1790), ed. D. D. Raphael and A. L. Macfie (Oxford, 1976). , An Inquiry into the Nature and Causes of the Wealth of Nations (London, 1776); 3rd ed. (1784) ed. R. H. Campbell and A. S. Skinner, textual ed. W. B. Todd (Oxford, 1976; 2 vols.). Fratris Dominici Soto Segobiensis, theologi, Ordinis Praedicatorum, . . . Salamantini professoris, Libri decem de iustitia et iure (Antwerpiae, 1568; isted. Lugduni, 1559).

Everything would be so ordered that a blind and necessary mathematics executes what the most enlightened and free intelligence prescribed. (Maupertuis, Essai de Cosmologie i)

18 P.-L. Moreau de Maupertuis, F.R.S. (1698-1759). Precurseur du Transformisme I

Pierre-Louis Moreau de Maupertuis, fils de Ren6 Moreau, seigneur de Maupertuis, naquit a Saint-Malo en 1698; mort a Bale en 1759, il est bien connu comme un des grands mathematicians francais de la premiere moitie du xvme siecle et comme Fauteur du principe physique qui porte le nom de principe de moindre action. II est important aussi dans Phistoire de la science comme le premier protagoniste en France des idees newtoniennes, et comme le createur effectif et le premier president de 1'Academic de Frederic le Grand a Berlin. Un aspect de son ceuvre scientifique qui n'est certainement pas moins important que ceux susmentionn^s, aspect qui, jusqu'ici, n'a pas attire beaucoup 1'attention, c'est sa contribution a la th£orie du transformisme organique. II est, en effet, 1'auteur du premier essai systematique en vue de formuler une th6orie des causes du transformisme, et c'est cette contribution qui forme le sujet de cet expose. Maupertuis etait, en effet, comme le demontra feu Pierre Brunet par son etude eclaire1© et interessante J, une personne de vitalite etonnante. Avant de discuter le probleme de 1'origine des especes selon les ide"es de ses contemporains, et la solution qu'il y proposa, je devrai dire quelques mots de sa vie. Cette vie ne manque certainement pas d'interet, tenant en effet quelque chose de ce caractere bizarre du si 1. P. BRUNET, Maupertuis, Paris, 1929, 2 parties Cf. [J.-H.-S. FORMEY], «Eloge de M. de Maupertuis», Histoire de I'Academie royale des Sciences, annee 1759, Berlin, 1766, pp. 464-512; see A. C. Crombie, Styles of Scientific Thinking in the European Tradition, ch. 20 (London, 1994) for up to date bibliography.

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souvent a des incidents qui surviennent a des personnes de bonne volonte et d'intelligences perspicaces, mais qui ne sont pas entierement affermies par le bon sens. On dit que la mere de Maupertuis Fidolatrait plutot qu'elle ne Faimait; enfant, il semble bien avoir 6t6 quelque peii gate et pendant toute sa vie il continua de manifester son esprit independant dans la plupart des circonstances. Jeune homme, 11 passa deux ans a Farmee comme officier de cavalerie. Puis, apres avoir acquis en France un certain renom comme mathematicien, le premier grand tournant dans sa vie — tournant dans lequel il entraina bientot la science fran^aise tout entiere — fut sa visite a Londres en 1728, Fannee qui suivit la mort de Newton. II passa six niois a Londres, et fit la connaissance de Samuel Clarke — partisan de Leibniz dans la polemique celebre a propos de la conception de Newton sur Pespace absolu et de la theologie naturelle — et celle d'autres membres eminents de la Royal Society. Peu de temps apres, le contraste entre la physique cartesienne et celle de Newton se trouva caracterise d'une facon spirituelle par Voltaire dans cette lettre bien connue, numero 14 des Lettres philosophiques (1734), qui dit 2 : « Un Fran^ais qui arrive a Londres trouve les choses bien changees en philosophic comme dans tout le reste. II a laisse le monde plein, il le trouve vide. A Paris on voit FUnivers compose de tourbillons de matiere subtile; a Londres on ne voit rien de cela. Chez nous c'est la pression de la lune qui cause le flux de la mer; chez les Anglais c'est la mer qui gravite vers la lune... Chez nos Cartesiens tout se fait par une impulsion qu'on ne comprend guere; chez M. Newton, c'est par une attraction dont on ne connait pas mieux la cause. A Paris vous vous figurez la terre faite comme un melon; a Londres, elle est aplatie des deux cotes. La lumiere, pour un Carte'sien, existe dans Fair; pour un newtonien, elle vient du soleil en six minutes et demie... Voila de serieuses contrarietes! » Maupertuis etait convaincu que le point de vue de Newton sur ces questions etait correct et celui de Descartes faux, et des son retour a Paris, il se mit a encourager un mouvement en faveur du systeme newtonien. C'est lui qui persuada Voltaire de la valeur scientifique de la theorie, avancee par Newton, de Fattraction universelle — nous verrons comment 2. VOLTAIRE, (Euvres completes, «d. Beuchot, Paris, 1879, XXII, 127-8.

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il adapta cette derniere a sa propre th6orie g^neiique — et de I'lnferiorite de tout systeme rival de la physique et de la cosmologie de Newton. Comme dit d'Alembert au sujet de Maupertuis, « le premier qui ait os^ parmi nous se declarer ouvertement newtonien », dans son Discours preliminaire a I'Encycloptdie 3 : « Maupertuis a cru qu'on pouvoit etre bon citoyen, sans adopter aveuglement la physique de son pays [le cart^sianisme]; et pour attaquer cette physique, il a eu besoin d'un courage dont on doit lui savoir gre\ » Par un des premiers et des plus heureux essais de vulgarisation scientifique, Voltaire introduisit dans le grand public en France le systeme newtonien. Apres quelques annees passees a 1'etude de Fastronomie, Maupertuis attira Tattention du public par un voyage audacieux, en 1736-1737, en Laponie, destine a resoudre la question de la forme de la terre en mesurant un arc de m^ridien situ£ le plus au nord possible. On avait fait en 1735 des mesures semblables vers le sud, au Perou. Maupertuis ecrivit une description du voyage a travers les montagnes et les forets; la gene epouvantable causee par les mouches, qu'on ne pouvait pas ^carter meme en s'entourant d'une £paisse fum^e; les cataractes qu'il fallait franchir sur les bateaux tres lagers des Lapons. Par son sang-froid, sa bonne humeur, sa tenacite, il semble avoir maintenu I'unit6 de Texp^dition. Ses Observa~ tions... faites par ordre du Roy au Cercle Polaire 4, qui d^crit leurs aventures, est un des livres de voyages les plus captivants. En 1738, peu apres son retour, Voltaire — ami aussi bon que-pouvait 1'etre une personne toujours disposed k sacrifier 1'amitie a la vanite et a Fambition personnelle — recommanda a Frederic de Prusse d'appeler Maupertuis pour former a Berlin une Academic des Sciences, ecole newtonienne qui d^passerait en importance 1'Academic de Paris. En 1740, 1'annee de son accession au trdne, Fre"d6ric invita Maupertuis a Berlin pour mettre ce projet a execution; mais il fut bientot arr^te, temporairement, par un incident bizarre. Au moment de Tarriv^e de Maupertuis a Berlin, la Prusse etaft en eiat de guerre avec TAutriche, pour la possession de la Sil&sie. En Janvier 1741, Maupertuis ecrivit a Frederic, 3. D'ALEMBERT, (Enures philosophiques, historiques et litteraires, Paris, 1805, I, 281. Cf< R. DUGAS, La m&canique OB XVII" sietle* Nettchitel, 1954, pp. 586-92. 4. (Euvres de M. de Maupertuis, Lyon, 1756, III, 69 sqq.

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lui demandant la permission de venir au camp royal pour lui soumettre des plans pour 1'Academic. Frederic envoya cette reponse laconique : « Venez ici, Ton vous attend avec impatience » 5. Mais le tableau charmant des conversations sur le front entre le Roi-Philosophe et son philosophe particulier n'allait pas durer. Quelques jours apres son arrivee, Maupertuis se trouva pris dans la bataille de Molwitz; son cheval s'emballa et Fentraina derriere les lignes de 1'ennemi. Pendant quelques jours, on crut au camp prussien qu'il etait mort. « Nous en sommes touches aux larmes », £crivit Voltaire, en apprenant les nouvelles; « Mon Dieu! Quelle fatale destinee! » 6. Mais un peu plus tard, Voltaire re$ut de nouveaux details. « J'apprends dans le moment, ecrivit-il, que Maupertuis est a Vienne, en bonne sante. II fut depouill£ par les paysans dans cette maudite Foret-Noire, ou il etait comme Don Quichotte faisant penitence. On le mit tout nu; quelques housards, dont un parlait franc.ais, eurent pitie de lui, chose peu ordinaire aux housards. On lui donna une chemise sale, et on le mena au comte Neipperg [Neuperg]. Tout cela se passa deux jours avant la bataille. Le comte lui preta cinquante louis avec quoi il prit sur-le-champ le chemin de Vienne, comme prisonnier sur sa parole : car on ne voulut pas qu'il retournat vers le roi, apres avoir vu 1'armee ennemie, et on craignit le compte qu'en pouvait rendre un geometre... » 7 On permit a Maupertuis d'aller de Vienne a Paris, ou le roi attendit qu'il retournat a Berlin. Mais Frederic, comme Voltaire, avait traite 1'afFaire avec un manque de serieux qui offusqua Maupertuis, et ce n'est, en effet, qu'en 1745 qu'il oublia definitivement son ressentiment et s'etablit a Berlin, ou il se fixa vite par son mariage avec une Prussienne. L'arrivee de Maupertuis a 1'Academie de Berlin fut un vrai succes; il y attira Euler, Meckel, Condillac, La Mettrie, Lalande, et d'autres savants et ecrivains distingues8. Tout alia a merveille jusqu'a ce que Voltaire, dont Maupertuis trouvait deja quelque peu ennuyeux les sarcasmes per^ants, decidat en 1750 que lui aussi se fixerait a Berlin. Une querelle 5. BRUNET, op. cit., I, 90. 6. VOLTAIRE, Lettre A M. l'Abt>6 de Valori, 2 mai 1741. (Euvres completes, 70 vol. (Paris, 1785-89), XXXVI, 46. Cf. ibid., I, 20; BRUNET, op. cit., I, 91. 7. VOLTAIRE, (Euvres, XXXVI, 46-47. 8. BHUNET, op. eft., I, 110, 123, 137.

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eclata entre les deux philosophes, ostensiblement au sujet de ce que Voltaire qualifia de tentative ridicule de la part de Maupertuis, c'est-a-dire de son essai de se servir du principe de moindre action comme argument pour prouver 1'existence de Dieu 9, mais querelle envenimee par une hostility personnelle de plus en plus profonde. Voltaire y parait sous un jour des plus defavorables. Maupertuis essaya de s'en tenir au fait; le but de Voltaire, c'eiait de gagner dans cet echange de polemique et de faire paraltre son ennemi a la fois cretin et canaille. Pour ce qui est de ses ecrits, il y reussit. Dans sa Diatribe du Docteur Akakia (1752), il repr^sente Maupertuis comme « un homme qui aurait, par exemple, douze cents ducats de pension pour avoir parle1 de mathematique et de metaphysique, pour avoir disseque deux crapauds, et s'etre fait peindre avec un bonnet fourr6 » 10. (On avait peint le portrait de Maupertuis en costume lapon.) II dit aussi qu'il etait un « ignorant » ayant « en recompense une imagination singuliere », et un « Arlequin d^guise en archeveque » u. Le roi fut choque de ces critiques sur le president de son Academic, et Voltaire dut quitter la Prusse, rendant son Ordre de Merite et sa clef de Chambellan, selon sa propre expression : « au Salomon du Nord, pour ses etrennes, les grelots et la marotte » 12. Voltaire ne pardonna jamais a Maupertuis; de sa nouvelle demeure en Alsace, il continua de Tattaquer13 et, dans L'Homme aux quarante 4cus, il le ridiculisa meme apres sa mort en 1759. L'interet que Maupertuis prit a la biologic date des premiers temps de sa carriere scientifique. Dans une des premieres conferences 14 qu'il soumit a 1'Academic des Sciences, en 1727, il fit crouler la vieille croyance que les salamandres etaient spontanement combustibles — sujet singulier de recherches a cette epoque; mais la conference contient aussi une description d'experiences prouvant que la salamandre est ovovivipare (c'est-a-dire que les oeufs peuvent 6clore dans 9. Ibid., I, 128-58. Cf. E. MACH, La Mecanique, traduction fran^aise, Paris, 1925, IV, § 2, p. 425 sqq. 10. VOLTAIRE, CEuvres, XXIII, 562; BHUNET, op. cit., I, 148. 11. VOLTAIRE, (Euvres, XXIII, 563, 565. Cf. « Vie de Voltaire par Condorcet », ibid., I, 231 sqq. 12. BRUNBT, op. cit., I, 152. 13. Dans Histoire du Docteur Akakia et du natifde Saint-Malo (1753). 14. Histoire de I'Acadtmie royale des Sciences, annte 1727, Mtmoires, pp. 27-32.

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et hors de la mere). En 1731, il publia un autre article excellent sur les differentes especes de scorpions15. II £tait, en effet, naturaliste de pure race, chose rare pour un math^maticien. Un ami decrivit sa maison a Berlin comme etant « une veritable menagerie, remplie d'animaux de toute espece, qui n'y entretenaient pas la proprete. Dans les appartements, troupes de chiens et de chats, perroquets, perruches, etc. II fit venir une fois de Hambourg une cargaison de poules rares avec leur coq. II etait dangereux quelquefois de passer a travers la plupart de ces animaux, par lesquels on etait attaque... M. de Maupertuis se divertissait surtout a creer de nouvelles especes par 1'accouplement de differentes races; et il montrait avec complaisance les produits de ces accouplements, qui participaient aux qualites des males et des femelles qui les avaient engendres. J'aimais mieux voir les oiseaux, et surtout les perruches qui etaient charmantes » 16. Le meme ecrivain a decrit aussi comment « M. de Maupertuis rassemblait avec beaucoup de peine et a grands frais des animaux etrangers ou singuliers, pour observer leurs allures et etudier en quelque sorte leur caractere ». II

Maupertuis ecrivit sa premiere oeuvre importante sur la production de nouvelles especes pendant le sejour qu'il fit a Paris pour reprendre des forces, apres le malheureux incident de Molwitz; d'autres ceuvres suivirent, a Berlin. Avant d'en parler, il faut etudier en raccourci 1'etat du probleme de 1'origine des especes a cette epoque, c'est-a-dire 1'etude dans toute son ampleur de la raison pour laquelle tous les animaux et toutes les plantes connus en sont venus a assumer leurs formes actuelles. II est utile de distinguer deux aspects de la question gen6rale. Par exemple, quand on donnait des explications dans le sens du transformisme, deux problemes principaux se trouvaient engages : 1° la preuve, d'apres la morphologic comparative, la paleontologie et les experiences de reproduction, qu'un processus historique de transformisme avait, en effet, eii lieu; 2° les theories sur les causes de ce processus, une s6rie de lois a 1'aide desquelles on pouvait d&luire, et 15. Tbid., 1731, pp. 223-9. 16. BRUNET, op. cit., I, 179-80.

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ainsi expliquer a la maniere classique, le processus evolutionniste, de meme que Ton explique les mouvements des planetes par la mecanique newtdnienne. En effet, pendant un siecle environ, avant que, dans la deuxieme moitie du xixe siecle, la theorie du transformisme ne soit generalement acceptee, beaucoup de biologistes se rendirent compte que bien des elements militaient en faveur du processus historique, mais ils n'etaient pas satisfaits des essais contemporains faits pour 1'expliquer17. Dans un sens tres general, sans application particuliere a la biologic, les explications evolutionnistes sont parmi les plus anciennement connues de la science. Les premiers cosmologistes grecs ont cherche a montrer que toute la complexite du monde que nous observons derivait d'un etat plus simple. Mais, pour une raison ou pour une autre, de telles explications avaient passe de mode et une grande partie de 1'evidence de base par laquelle la theorie du transformisme organique s'etait renouvelee au xvnr siecle, fut, en effet, rassemblee par des biologistes qui ne la consideraient aucunement en termes de transformisme. Au xvn* siecle et aux premieres annees du xviii", le probleme le plus important pour les botanistes et pour les zoologistes, c'6tait d'elaborer un systeme efficace de classification. Cela occupa tout biologiste d'importance (a part les physiologistes), depuis Belon et Cesalpino au xvi' siecle, en passant par John Ray, Tournefort, Tyson et d'autres, jusqu'k Linne, dont le Systema Naturae en 1735 resuma toute la serie des essais anterieurs 18. Dans le Syst&me de Linne, les lignes principales de la classification moderne des plantes avec la nomenclature binome se trouvaient etablies; la classification zoologique de Linn6 reussit moins bien et il fallut la modifier considerablement plus tard. Mais ce qui nous concerne le plus, ce sont les principes. Linne montra comment mettre precisement en rapport logique avec tous les autres, chaque espece, genre, ordre et classe, et comment identifier un organisme inconnu, lui donner un nom, et le mettre dans le Systeme de la Nature. 17. Cf. E. GtrrfNor, Les Sciences de la vie aux XVII" et XVIII" siecles, Paris, 1941; P. G, FOTHERGILL, Historical Aspects of Organic Evolution, Londres, 1952; et pour1 une bibliographic excellente voir C.-C. GILUSPIE, Genesis and Geology, Cambridge, Mass^ 1951, pp. 23 sqq. Cf. aussi J.-T. MERZ, A History of European Thought in the Nineteenth Century, Loadres, 1903, II, et E.-S. RUSSEL, Form and Function, Londres, 1916. 18. Cf. H. DAUDIN, Etudes d'histoire des sciences naturelles, Paris. 1926, I.

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Le but immediat des tentatives de Linne, c'etait de resoudre le probleme pratique de ramener £ 1'ordre un monde divers et chaotique; mais, comme ses contemporains, il pretendait que la classification devait montrer non settlement un ordre commode, mais le vrai ordre de rapports entre les individus. C'est-a-dire que la classification devait etre non settlement un systeme artificiel, mais aussi ce qu'on appelait un systeme « naturel », qui exprimat ce que Linne appelait « 1'ordre souverain de la Nature » 19. Get « ordre souverain de la Nature », selon les conceptions du xvn* et du xviii" siecle, possedait plusieurs caracteristiques qui sont importantes, car elles formaient Farriere-plan des theories evolutionnistes du xvme siecle. D'abord, c'etait un ordre essentiellement immuable, dans lequel toute chose et toute substance dans 1'univers, les astres et les planetes dans leurs mouvements, les elements chimiques, les etres vivants, avaient chacun leur place et leur role definis. Galilee et Descartes avaient detruit la conception particuliere de 1'ordre naturel derivee d'Aristote, mais la croyance qu'il y avait un ordre stable dans 1'univers physique, ordre qui etait reste sans changement depuis la creation, persistait largement. De notre point de vue, la chose la plus importante en rapport avec cet ordre fixe de la nature, c'est qu'on considerait que les especes biologiques etaient fixes et avaient des limites definies. L'opinion de Linne etait que toutes les especes d'organismes avaient et6 creees par Dieu des le commencement, et n'etaient pas susceptibles de changement sauf en des deiails non essentiels20; a son avis, cette th^orie se trouvait appuyee par roeuvre de Harvey, de Redi et de Swammerdam, d^montrant que des organismes se reproduisaient par des reufs. Dans la reproduction, c'etait la nature specifique qui etait transmise : toute difference remarquee entre parent et rejeton devait etre accidentelle et temporaire 21. Un deuxieme trait de « 1'ordre souverain de la Nature » de Linne, c'etait qu'il estimait que les organismes formaient une echelle, s'etendant de 1'etre vivant le plus primitif, a peine 19. Caroli LINNAEI, Systema naturae, 13s ed., Vienne, 1767, I, 13. 20. Plus tard, comme resultat d'experiences avec 1'hybridation, Lannd admit la possibilite de mutations limit^es des especes dans nn genre particulier, qui avait ele cree par Dieu. Sur toute cette question, ses disciples Etaient beaucoup plus dogmatiques que Linne m£me., 21. Caroli LINNAEI, Philosophia botanica, Stockholm, 1751, p. 99. Cf. DAUDIN, op. cit., I, 65. Cf. ARISTOTE, De generatione animalium, I, 21-22; II, 1, 731 b 33-35; III, 3-4.

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susceptible de se distinguer de la matiere inorganique, au degr£ le plus bas de 1'gchelle, en passant par les plantes, les zoophytes (Sponges, etc.), les animaux, jusqu'a 1'homme, au degr£ le plus £lev&22. Cette idee d'une £chelle de la nature organique derivait, en premier lieu, d'Aristote 23. Tout d'abord, on supposa l'6chelle lineaire; puis, lorsqu'on connut mieux le probleme, on assigna aux plantes et aux betes des rameaux diffgrents, y ajoutant des groupes subordonn^s ou des rameaux plus petits, et ainsi de suite, tout comme s'il s'agissait d'Un arbre24. Get arbre devint les « donn£es > que les theories de transformisme devaient expliquer. Cela peut se voir dans la notion de « gradation » traitSe par 1'anatomiste anglais, Edward Tyson, en 1699, dans son e"tude bien connue du chimpanzS. Tyson dit qu'en faisant « une elude comparative de cet animal et d'un singe, une guenon et un homme..., on peut mieux observer les gradations de la nature dans la formation des corps animaux, et les transitions faites entre un animal et un autre » 25. Une troisieme caracteristique de 1'ordre de la Nature, c'elait la croyance qu'il y avait dans 1'univers une harmonic. On supposait qu'il y avait adaptation parfaite des parties d'un organisme avec son ensemble, et aussi des organismes avec leur milieu physique et de 1'un a 1'autre : par exemple, que les plantes s'alimentaient du sol, les insectes des plantes, les oiseaux des insectes, les oiseaux plus grands des oiseaux plus petits, et ainsi de suite, le tout maintenant un gquilibre parfait de population26. Tous les savants se trouverent impressionne's par cette harmonic; Newton regarda la structure de 1'ceil de la mouche comme extant une preuve th^ologique sMeuse; John Ray d^crivit « la sagesse de Dieu, manifested dans les CEuvres de la creation » 27; la soi-disante preuve des 22. Cf. A.-O. LOVEJOY, The Great Chain of Being, Cambridge, Mass., 1936. 23. Cf. ARISTOTE, Historia animalium, VIII, 1, 588 b 4; De gen. animal, II, 1, 733 b 1-17. 24. Cf. DAUDIN, op. cit., I, 159-73. 25. Edward TYSON, Orang-Outang, sive Homo Sglvestris, Londres, 1699, preface, p. vn. Cf. M.-F. Ashley MONTAGU, « Edward Tyson, M.D., FJR.S., 1650-1708, and the rise of human and comparative anatomy in England » (Memoirs of the American Philosophical Society, XX). Philadelphia, 1943, pp. 240-1. 26. LINN£, Systema naturae, 6d. cit, I, 10-11, 17-18, 535. Cf. DAUDIN, op. cit., pp. 174-5. 27. The Wisdom of God manifested in the Works of the Creation, Londres, 1691.

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causes finales, raisonnant de la montre a 1'Horloger Divin, devint un des lieux communs de la thSologie naturelle, comrae, par exemple, dans I'Analogy of Religion de Bishop Butler, et dans les ecrits de Paley. Les moralistes du xvur siecle firent appel a rharnionie de 1'univers physique pour appuyer leurs vues sur la « gouvernance » morale du monde. Une voix dissidente fut celle du docteur Johnson, martyre de la goutte, qui ne trouvait aucune explication rationnelle de la douleur physique. Cette conception de 1'ordre, de Pharmonie dans le monde biologique devint un probleme important pour les protagonistes d'explications evolutionnistes, car ils essayaient essentiellement de demontrer comment du chaos pourrait sortir Pordre. Avant que Maupertuis et d'autres evolutionnistes eussent mis a jour leurs idees, on trouvait cela impossible. Cela se voit clairement dans le fameux « discours de degr^s », prononce par Ulysse dans le Troilus and Cressida de Shakespeare. Apres avoir decrit comment « The heavens themselves, the planets and this centre « Observe degree, priority and place » et ainsi de suite, en descendant par Pordre naturel et social tout entier, Ulysse dit : « Take but degree away, untune that string, « And, hark, what discord follows! each thing meets « In mere oppugnancy. » 28 S'il n'y avait pas un ordre exterieur a observer, la vie se trouverait reduite a un chaos de lutte entre les individus. On verra de quelle maniere Maupertuis, dans sa theorie du transformisme, se servait d'une telle lutte comme moyen pour developper Pordre. Cette comparaison entre les mondes social et naturel vient bien a propos, car, a partir de la fin du xvne siecle, Popinion sur la question d'un ordre fixe commencait a donner partout des signes de modification. II est impossible d'examiner ici le developpement de Pidee de progres historique, mais on peut citer quelques evenements significatifs 29. La controverse entre « les Anciens et les Modernes > ouvrit toute la question 28. Troilus and Cressida, I, 3. 29. Cf. F. BRUNETI&RE, « La formation de 1'idSe de progres au xviiie siecle », Etudes critiques sur I'histoire de la litterature frangaise, 5« serie, 2« ed., Paris, 1896, pp. 183-350; J.-B. BURY, Th« Idea of Progress, Londres, 1920; R.-F. JONES, « Ancients and Moderns » (Washington

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de savoir si la pense'e et la civilisation s'etaient ameliorees; et, en grande partie grace aux triomphes de la science, elle se termina par une victoire retentissante pour les Modernes. L'opinion elait an changement historique. Ceux qui e"crivaient sur 1'histoire — les « sociologues », comme on les appelle aujourd'hui — eherchaient a formuler les lois du developpement social inspire'es directement par le modele des lois de la meeanique de Newton. Us prenaient en consideration 1'influenee de P ambiance, de la nourriture, de la geographic, des etudes, et ainsi de suite. Les ecrivains les plus influents en matiere de progres historique et de transformisme biologique se connaissaient tous tres bien; en effet, la plupart d'entre eux dtaient des Francais. Voltaire, qui par son Siecle de Louis XIV (1752) et son Essai sur les mceurs et I'esprit des nations (1756), produisit les premiers essais valables dans le domaine de Fanalyse des causes de 1'histoire, « histoire philosophique » comme il la nommait, connaissait particulierement Maupertuis (comme nous 1'avons vu) et aussi Buffon 30. Diderot, qui traita de la sociologie et de la biologic, engagea une controverse contre Maupertuis31. Le developpement parallele des idees de progres social et de transformisme biologique est un des aspects les plus se*duisants de toute 1'affaire et fournit en me'ine temps un exemple frappant de Tinfluence dans plusieurs spheres differentes d'une forme particuliere de la pensee ou de la maniere de regarder les choses, a un moment donne. Pour ce qui regardait la biologic, en meme temps que Linne pr^parait son tableau magnifique d'un « ordre souverain de la Nature » immuable, d'autres biologistes rassemblaient en differents endroits les faits evidents qui s'opposaient a cette conception des choses, surtout a 1'idee que toutes les especes connues avaient et4 creees a la fois et que jamais aucuii changement ne s'etait produit. Par exemple, la vraie nature des fossiles dtait connue de certains ecrivains depuis Fepoque University Studies, N. S., Language and Literature, VI), Saint-Louis, 1936; W. K. FERGUSON, The Renaissance in Historical Thought, Boston, Mass., 1948, pp. 68-112. 30. Cf. Thomas PENNANT, Tour on the Continent 1765, 6d. G. R. de Beer, Londres, 1948, pp. 38-39 : « Madame de Buffon told me that Voltaire was worth 113.000 livres a year and 700.000 in cash, that he traded in cattle, insured ships, etc.; that his original estate was only 500 £ pr Annum. » 31. Cf. MAUPERTUIS, (Enures II, 169-84, Cf. A. VARTANIAN, Diderot and Descartes, Princeton, 1953.

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classique &*, et Robert Hooke, ail xvir siecle, avait signal^ que 1'histoire des fossiles montrait, selon son expression, « qu'il y a eu aux epoques anterieures beaucoup d'autres especes de creatures, dont nous ne pouvons trouver aucun exemple actuellement; et il se peut qu'il y ait actuellement beaucoup de nouvelles especes, qui n'existaient pas au commencement » S3. Buff on donna un premier compte rendu de la succession de formes differentes dans les couches geologiques, dans son Histoire de la Terre (1744), et une description plus etendue, dans les Epoques de la Nature (1778). L'evidence experimentale que des changements he're'ditaires pouvaient avoir lieu dans 1'organisnie eiait attested par les horticulteurs, en particulier par ceux qui cultivaient la fraise et la tulipe (1'industrie des oignons hollandais commenc,ait a. se developper), et par les eleveurs de pigeons et de chiens, comme aussi par les anomalies humaines, telles que 1'albinisme chez les negres (un cas fut cite par Tyson34) et la polydactylie. Se basant sur tout cela, Buff on, en 1753, dans 1'article bien connu de son Histoire Naturelle au sujet de « L'Ane », donnait un aper^u brillant d'une conception ^volutionniste de 1'origine d'une meme souche de tous les animaux. Linne avait classe le cheval (Equus cauda undique setosd) et 1'ane (Equus cauda extreme setosa) comme deux especes du meme genre (ou famille); pour Buff on, cela impliquait qu'ils devraient avoir le meme parentage. Car, « si Ton admet une fois qu'il y ait des families dans les plantes et dans les animaux •», ecrivit-il, « que 1'ane soit de la famille du cheval, et qu'il n'en differe que parce qu'il a degdnere, on pourra dire egalement que le singe est de la famille de 1'homme, que c'est un homme degenere, que l'homme et le singe ont eu une origine commune comme le cheval et 1'ane, que chaque famille, tant dans les animaux que dans les vegetaux, n'a eu qu'une seule souche, et meme que tous les animaux sont venus d'un seul animal, qui, dans la succession des temps, a produit en se 32. Cf. P. DUHEM, Etudes sur Ldonard de Vinci, II, Paris, 1909, pp. 289, 307-8, 316-7, 323-4, 336-9; A.-C. CROMBIE, « Avicenna's influence on the medieval scientific tradition », dans Avicenna: scientist and philosopher, 6d. G. M. Wickens, Londres, 1952, pp. 97-99. 33. Robert HOOKE, « A Discourse of Earthquake », Posthumous Works, ed. R. Walter, Londres, 1705, p. 291. 34. Ashley MONTAGU, Edward Tyson, pp. 212-3.

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perfectionnant et en ddg£n6rant, toutes les races des autres animaux » 35. Si tous les organismes sent ainsi censes tirer leur origine d'ancStres communs, et avoir subi des modifications dues au climat, & 1'alimentation, etc., au cours de 1'histoire gSologique, ceci expliquerait le fait, sur lequel se basalt la classification, que, par exemple, un groupe comme les vertelwe's £tait une s6rie de variations sur un plan de base commun. De ce point de vue, conclut Buffon, on peut regarder tous les animaux comme appartenant a la meme famille, ce qui n'empeche pas que « dans cette grande et nombreuse famille, que Dieu seul a con^ue et tirSe du ndant, il y ait d'autres petites families projete"es par la Nature et produites par le temps... ». De par ces passages tire's hors du contexte, « L'Ane » se trouve souvent citd en t&moignage de I'Svolutionnisme de Buffon. Mais a lire 1'article tout entier, il est evident que, quelles que fussent ses ide~es plus tard M, tout le but de la discussion dans « L'Ane », c'elait d'attaquer la conception de families d'ou suivaient ces consequences radicales. En effet il ne pr6sente la possibility du transformisme que pour la detruire. Quant aux families de Linn6 — premier objet de son attaque37 — il ecrivit : « Ces families sont notre ouvrage ... la Nature ... ne connait point ces pr^tendues families, et ne contient en effet que des individus. » Le seul terme de classification qui r^pondait a quelque chose de r^el, c'6tait 1'espece, la succession d'individus susceptibles de se reproduire par croisement, engendrant ainsi un rejeton fecond. L'usage d'expressions telles que « la famille » pour toute autre chose que la commodity leur emploi pour signifier une parente de descendance, etait reprehensible. Malgr§ la presence chez les plantes, les animaux et les hommes, de variations hereditaires, il n'y avait aucune Evidence, declarait Buffon, pour que ces dernieres aboutissent a de nouvelles especes, tandis qu'il y avait des difficultes considerables a supposer que tel e"tait le cas, par exemple, le fait que la plupart des variations observers etaient des monstruosites, 1'absence d'especes intermMiaires, et I'lmprobabilite qu'une variation se produisit chez des individus de 1'autre sexe de 35. Histoire naturelle, Paris, 1753, IV, 381-2. 36. Cf. « De la degeneration des animaux », ibid., 1766, XJV, 311-74. 37. Ibid., IV, 378; cf. « Maniere d'eludier et de trailer 1'histoire naturelle », ibid., 1749, 1-20 sqq.

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sorte qu'elle put se reproduire38. « Quoiqu'on ne puisse pas demontrer que la production d'une espece par la degeneration soit une chose impossible a la Nature, conclut-il, le nombre des probabilites contraires est si enorme, que philosophiquement meme on n'en peut guere douter. » « L'Ane » occupe ainsi une position curieuse dans 1'histoire de la theorie du transformisme, car quoique Buffon avance la theorie expres pour 1'attaquer, il donne neanmoins la le premier apercu systematique de la possibility qu'un procede historique du transformisme ait pu avoir lieu. Mais ce n'est pas a Buffon qu'il faut attribuer 1'honneur d'avoir ete a 1'origine de la theorie moderne du transformisme, c'est plutot a Maupertuis, que cite Buffon et dont les vues sur ]a variation genetique se trouvaient indubitablement le but d'attaque par Buffon dans « L'Ane ». Maupertuis semble avoir ete le premier qui trouva I'idee que tous les organismes tirent leur origine, avec modification, d'ancetres communs; on trouve cela dans son Essai de Cosmologie, ecrit avant 1741 quoique public seulement en 1750. II avait public entre temps un autre livre a ce sujet, avec le titre charmant, pour un traite scientifique, de Venus physique (1745). Dans ces O3uvres, Maupertuis presenta le premier une explication - systematique et causative du processus transformiste. Maupertuis abordait le probleme de 1'origine des especes entierement du cote de la genetique, et il ecrivit la Venus physique en premier lieu pour donner Fexplication d'un phenomene specifique, et ensuite, en generalisant, de tout phenomene semblable. Le phenomene specifique, c'etait un garcon negre, albinos, amene a Paris de TAmerique du Sud, qu'il avait vu dans le salon d'une dame a la fois elegante et intellectuelle, en 1744. Vu que 1'ambiance dans laquelle la curiosite intellectuelle s'exprime est aussi importante a 1'histoire de la science qu'a 1'histoire de la pensee en general, il vaut la peine de rappeler qu'a cette epoque la science naturelle etait tres a la mode dans la haute societe frangaise. Voltaire a decrit cette periode comme une epoque ou tout honnete homme devait etre philosophe, ou une dame pouvait 38. Ces difficultes sont tout a fait suffisantes pour expliquer le rejet, de la part de Buffon, dans « L'Ane », du transformisme. On ne devrait pas attribuer trop d'influence, comme par exemple le fait Guyenot (op. cit., p. 397), a son exclamation : « Mais non, il est certain, par la revelation, que tous les animaux ont egalement participe a la grace de la creation.... »

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oser 1'etre sans ambages. II existe une histoire de deux dames qui contracterent la passion de Peiude de 1'anatomie, ce qu'on regardait comme extravagant, me'me en ces temps de pensee avanc6e. Une certaine dame gardait dans son boudoir un cadavre qu'elle disse'quait pendant ses heures de loisir; tandis qu'une autre avait un dispositif special, fixe dans sa voiture, de fagon a pouvoir diss&juer tin cadavre pendant de longs voyages, tout comme d'autres dames d'un gout plus conventionnel auraient pu s'adonner k la lecture. Maupertuis donna dans sa Vdnus physique une description du petit negre, qui commence, en temoignant d'une sympathie tout humaine : « J'oublierais volontiers ici le phenomene que j'ai entrepris d'expliquer : j'aimerais bien mieux m'occuper du reveil d'Iris, que de parler du petit monstre dont il faut que je vous fasse 1'histoire. » 39 II continue : « C'est un enfant de 4 ou 5 ans qui a tous les traits des negres, et dont une peau tres blanche et blafarde ne fait qu'augmenter la laidenr. Sa tMe est couverte d'une laine blanche tirant sur le roux : ses yeux d'un bleu clair paraissent blesses de I'^clat du jour : ses mains grosses et nial faites resscmblent plutot aux pattes d'un animal qu'aux mains d'un homme. II est n6, a ce qu'on assure, de pere et mere africains, et tres noirs. » 11 fait ensuite mention de m^moires au sujet d'autres negres albinos, de ralbinisme parmi les merles, les corbeaux et les poules, et d'autres changements hereditaires dans les plantes acclimatees et chez les animaux apprivoises 40. Son but immediat est, done, de trouver une theorie de Theredite susceptible d'expliquer ces ph6nomenes, tout aussi bien que 1'heredite normale 41. Pendant la premiere moitie du xvnr siecle la theorie dominante de la generation et de 1'heredite 42, c'etait celle de la « pr^formation », qui existait sous deux formes : dans 1'une, on supposait rembryon derive entierement de 1'ceuf, la fonc39. MAUPERTUIS, (Euvres, II, 115-6. 40. Ibid., pp. 118-9. 41. Gf. C. ZIRKLE, « The early history of the idea of the inheritance of acquired characters and of pangenesis », Transactions of the American Philosophical Society, Philadelphia, XXXV (1946), 139-40, 131. 42. Cf. GuvfiNOT, op. cit., pp. 208-312 ? E.-J. Ck)LE, Early Theories of Sexual Generation, Oxford, 1980.

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tion du male n'etant que de stimuler 1'ceuf a commencer a se developper; dans 1'autre, avancee apres la decouverte par Hartsoeker et Leeuwenhoek, en 1674-1677, du spermatozoide — resultat direct du nouveau microscope — c'etait le germe male seulement qui se transformait en embryon, la femelle se bornant a fournir la nourriture 43. La theorie de 1'heredite etait la meme, quelle que fut la forme de « preformation » qu'on preferat. Considerons 1' « ovisme », comme s'appelait la premiere. On soutenait que chaque partie de 1'adulte contribuait a 1'ceuf par une particule, 1'oeuf etant ainsi un adulte en miniature; pendant le developpement embryologique, les particules ne faisaient que se dilater jusqu'a devenir des parties a dimensions adultes. On supposait le premier individu de chaque serie — la femelle — avoir ete cr£e avec toutes les generations subsequentes dedans, 1'une a I'int^rieur de 1'autre, telle une boite chinoise; dans le cours du temps, les generations ne faisaient qu'eclore et se developper, 1'une apres 1'autre. Selon 1' «ovisme », les males de chaque generation ne faisaient naitre aucun autre individu. L'autre forme de !a theorie preformationiste, connue sous le nom de « animalculisme », etait exactement pareille, sauf que le germe male etait I'element operateur. Maupertuis fit remarquer que ni 1'une ni 1'autre des formes de la theorie preformationiste ne pouvait expliquer certaines observations : la ressemblance avec les deux parents, ou avec des ancetres eloignes mais pas avec les ancetres immediats, les hybrides, et les nouvelles caracteristiques qui se montraient de temps en temps dans des plantes, des animaux et des hommes44. Pour expliquer ces phe"nomenes, il dit, en premier lieu, qu'il fallait supposer que 1'embryon se formait de 1'union des germes des deux parents, le male et la femelle 43. A cette epoque-la, le role des cellules dans la repro43. Cf. MAUPERTUIS, (Euvres, II, 21-24. 44. Ibid., pp. 64-71, 80-85, 93, 109-10. Cf. Lettres, XIV, ibid., pp. 267-82; Lettre sur le progr&s des sciences, ibid., pp. 385-90. Cf. B. GLASS, « Maupertuis and the beginnings of genetics », Quarterly Reviews of Biology, Baltimore, XXII (1947), 196-210; P. OSTOYA, Maupertuis et la biologic », Revue d'Histoire des Sciences, VII (1954), 60-78. 45. « II me semble, ecrivit-il, que Pidee que nous proposons sur la formation du foetus satisfairoit mieux qu'aucune autre aux phenomenes de la generation; a la ressemblance de 1'enfant, tant au pere qu'a la mere; aux animaux mixtes qui naissent des deux especes differentes; aux monstres, tant par exces que par defaut : enfln cette idee paroit la seule qui puisse subsister avec les observations de Harvey. » MAUPERTUIS, (Euvres, II, 93. Sur Harvey, cf. pp. 36-50.

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duction etait mal connu, et il supposait que le germe etait un produit fluide. II dit que chaque liquide seminal se composait de particules, chacune desquelles derivant d'une partie donnee du parent. Par 1'union entre les parents, les deux liquides se melangeaient et les particules se combinaient en paires, une de chaque parent; la serie entiere de paires faisait naitre 1'embryon. II y avait beaucoup plus de particules qu'il n'etait necessaire pour former 1'embryon, par consequent, il y avait un degre de largeur considerable dans la serie particuliere de caracteristiques actuellement heritee par le rejeton. Maupertuis soutenait que c'etaient les membres normaux de 1'espece, dans un leger degre de variation, qui se reproduisaient, parce que chaque particule avait « un plus grand rapport d'union » avec les particules habituellement voisines, qu'avec d'autres. Ces « rapports d'union », dit-il, pouvaient s'expliquer en supposant qu'il y avait une force d'attraction qui fonctionnait entre eux, force analogue £ la gravitation de Newton et a I'attraction suggeree comme explication de la combinaison chimique 46. Mais on ne peut pas concevoir cette attraction comme etant simplement une force physique. II y a un instinct des animaux, dit-il, « qui leur fait rechercher ce qui leur convient, et fuir ce qui leur nuit », et « n'appartient-il point aux plus petites parties dont 1'animal est forme? Get instinct, ... ne suffit-il pas cependant pour faire les unions necessaires entre ces parties? » 47. Plus tard, dans son Systeme de la Nature (1751), Maupertuis etait encore plus net. « Les elements propres a former le foetus, dit-il, nagent dans les semences des animaux pere et mere : mais chacun extrait de la partie semblable a celle qu'il doit former, conserve une espece de souvenir de son ancienne situation; et 1'ira reprendre toutes les fois qu'il le pourra, pour former dans le foetus la meme partie. » 48 S'il se produit un defaut d'attraction, de sorte que des combinaisons anormales de particules se fassent, le resultat dans ces circonstances est une variation ou un monstre en quelque sorte. D'abord, les particules venant d'ancetres normaux, avec le plus d'affinite pour 1'union normale, sont plus nombreuses, dans le fluide seminal de la variele, que celles 46. Ibid., pp. 88-92; cf. pp. 139-41. Cf. NEWTON, Opticks, 4e ed. 1730. Query, 31. 47. MAUPERTUIS, GRuvres, II, 31. 48. Ibid., pp. 158-9.

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de la disposition nouvelle, de sorte qu'apres quelques generations, la variete peut retourner au type normal49. Mais si les facteurs qui produisent la variety continuent a f onctionner pendant plusieurs generations, alors les particules donnant de nouveaux assemblages, avec des souvenirs des nouvelles situations, en viennent peu a peu a surpasser en nombre celles propres a faire les traits originaires, de fa^on que la variete soit etablie. Maupertuis suggera qu'on pouvait verifier cette theorie par 1'experience simple de trancher la queue a des souris pendant plusieurs generations, pour voir s'il serait possible de produire une race de souris sans queue. Les particules de queue dans les liquides seminaux seraient peu a peu reduits en nombre et finiraient par disparaitre. Selon Maupertuis, les causes de ces nouvelles dispositions de particules sont de deux sortes. D'abord, il y a des recombinaisons dans les liquides seininaux, produites par « le hasard », c'est-a-dire par certaines circonstances inconnues fonctionnant dans les fluides m£mes, « dans lesquelles les parties elementaires n'auroient pas retenu 1'ordre qu'elles tenoient dans les animaux peres et meres » 50. D'autre part, des changements peuvent se produire du fait du milieu, par exemple, par le climat, la nourriture, la mutilation. Etant donn6 la theorie de Maupertuis, les variationsvenant de ces deux causes seraient heritees. Parce que des enfants negres nes de parents blancs se trouvaient incomparablement plus rares que des negres albinos, Maupertuis soutenait que le blane etait la couleur humaine primitive, et que la chaleur de la zone torride fomenta « les parties qui rendent la peau noire » 51. Un negre albinos etait ainsi un retour au type primitif. Cette theorie tout entiere soulevait toutes les difficult^s qu'il pouvait y avoir a accepter le recit de la Genese sur la descendance de toute la race humaine £ partir de deux parents originaux52. Dans son Essai de Cosmologie et son Syst&me de la Nature, Maupertuis se servit de cette theorie de Theredit^ pour donner une explication generale de 1'origine des especes. Fai&ant la supposition que de nouvelles dispositions des particules elementaires avaient eu lieu par le pass6 sans interruption, alors dit-il : « Chaque degr£ d'erreur aurait fait une nouvelle 49. 50. 51. 52.

Ibid., Ibid., Ibid., Ibid.,

pp. 119-21. p. 148*. p. 123. p. 128.

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espece : et a force d'ecarts repetes, seroit venue ia diversity infinie #es anhaaux que nous Toyons aujourdlrai. » *• Mais comment les nouvelles Tarietes s'adaptaient-eHes mi miheu? Maupertuis n'etait plus a meme d'accepter la vieille notion que Diea avail cre£ les organismes en adaptation parfaite a leurs conditions et a leurs besoms, et de plus, il dit que Ton avait beaueoup abuse de la preuve des causes finales. II y avait dans la nature une Evidence considerable de gaspillage et de mal-adaptation; et, tout en admettant que la gouvernance des choses se trouve eventuellement sous la gouverne de la Providence, les causes qu'on est a meme d'observer immediatement semblent etre de pur hasard. I/explication de 1'adaptation de Torganisme est a la fois une anticipation remarquable de la theorie de la selection naturelle de Charles Darwin, et la reflexion de Finfluence d^Empedocle et de Lucrece. 4 Mais ne pourroit-on pas dire, ecrit-il, que dans la combinaison fortuite des productions de la Nature, comme il n'y avoit que celles ou se trouvoient certains rapports de convenance, qui pussent subsister, il n'est pas merveilleux que cette convenance se trouve dans toutes les especes qui actuellement existent? Le hazard, diroit-on, avoit produit une multitude innonabrable d'individus; un petit nombre se trouvoit construit de maniere que les parties de ranimal pouvoient satisfaire a ses besoins; dans un autre infiniment plus grand, il n'y auroit ni convenance, ni ordre; tous ces derniers ont peri; des animaux sans bouche ne pouvoient pas vivre, d'autres qui mamquoient d'organes pour la generation ne pouvoient pas se peipetuer : les seuls qui soient restes sont ceux ou se trouvoient Fordre et la convenance; et ces especes, que nous voyons aujourd*hui, ne sont que la plus petite partie de ce qu*un destin aveugle avoit produit. » M En faisant valoir cette explication de la diversification des organismes comme un processus qui avait eu lieu dans le temps, Maupertuis tourna sens dessus dessous tout le probleme de Tadaptation. Ray et Linne" avaient essaye1 de pr6senter une image du monde organique tel qu'il avait et6 cree par Daeu dans un etat d'harmonie autoregulatrice, chaque creature s'adaptant parfaitement a son mode de vie; ceci entraina la consequence que des cas de mal-adaptation cons53. Ibid., p. 148 *. 54. Esscri de Cosmologie, (Euvres, I, 11-12.

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tituaient un embarras theologique et biologique considerable. Pour Maupertuis, au contraire, Tadaptation ne s'achevait que par un processus de lutte et d'elimination, en comme^ant par un monde en chaos, quand, comme dans le discours d'Ulysse, « each thing meets in mere oppugnancy ». L'ordre fut retabli par la loi de la jungle. Un autre probleme que Maupertuis devait confronter, c'etait d'expliquer 1'apparition d'innovations pendant le processus du transformisme dans le temps, de telle fa^on que les organismes montrassent non seulement une diversification dans des milieux differents, mais formassent aussi une Echelle de perfection ou d'amelioration. Tel est le sujet principal de son Systeme de la Nature. Maupertuis s'interessait particulierement a 1'emergence de nouvelles facultes intellectuelles que Ton pouvait observer en montant I'^chelle, depuis les creatures tres modestes telles que les vers, jusqu'au chien, au singe et a rhomme. Son probleme 6tait d'expliquer Emergence de facultes intellectuelles en termes de sa th^orie de 1'heredite, a Taide de nouvelles combinaisons de particules elementaires. II decida tout de suite qu'il etait possible de faire deriver des qualites telles que la m^moire, rintelligence ou le desir, d'une conception de particules, et de forces telles que 1'attraction, destined seulement a manier la matiere inorganique; des caracteres intellectuels de ce genre ne trouvaient absolument aucune place dans cette conception 55. Sa solution du probleme suivit les lignes ^tablies par Leibniz 56. 11 fit remarquer que Descartes avait rendu insoluble le probleme, en etablissant une separation absolue entre les intelligences qui pensent et les corps qui s'etendent dans 1'espace. Mais 1'existence d'animaux et d'hommes demontrait que la pensee et 1'etendue pourraient etre toutes les deux des qualites de la meme substance de base. Les phenomenes intellectuels observes dans certains organismes pouvaient s'expliquer, dit-il, en dotant les particules elementaires d'un degre de « perception » — selon son expression57. Ensuite, tout comme de nouvelles combinaisons des particules memes produisirent de nouveaux organes et fonctions du corps, de meme les nouvelles combinaisons concomitantes de perceptions Elementaires donnerent lieu a de nouvelles facultes intellects. (F.uvres, II, 152-5. 58. Cf. BRUNET, Maupertuis, II, 391-408. 57. MAUPERTUIS, (Euures, II, 155M61; Cf. pp. 147-9, 157-49*.

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tuelles, car toutes etaient unies dans une seule et nouvelle perception, qui etait quelque chose d'autre que la totality de ses parties. En faisant usage de cette theorie, Maupertuis chercha a expliquer le caractere hereditaire de qualites intellectuelles, telles que le talent pour les mathematiques dans la famille Bernoulli et pour la musique chez les flls de J.-S. Bach. II chercha aussi a expliquer I'origine d'organismes (la vie) venant des combinaisons de la categorie la plus simple de particules elementaires en des molecules plus complexes, et 1'evolution de 1'intelligence depuis les creatures les plus humbles jusqu'a rhomme. La seule exception qu'il fait au processus general, c'est chez 1'homme la connaissance de Dieu, le sens du devoir moral, et le raisonnement abstrait, tous, a son avis, d'un ordre different de « 1'intelligence qui resulte des perceptions reunies des Elements » 58. II n'offrit pas d'expliquer 1'origine chez rhomme de ces facultes superieures, mais se contenta de faire remarquer leur existence. II serait absurde d'exiger de la theorie de Maupertuis qu'elle soit plus qu'une analyse formelle remarquable de quelquesuns des problemes de base par rapport au transformisme. Si Ton compare la richesse d'observations et d'exemples qu'on trouve dans VOrigine des Especes de Charles Darwin, aux ecrits de Maupertuis, ceux-ci paraissent bien na'ifs et un peu minces. Mais dans 1'histoire du probleme, son travail est de la plus haute importance. II n'est nullement exagere de dire qu'il reorienta toute la question de I'origine, de la diversification, de 1'adaptation, et du transformisme emergeant des etres vivants. Ses idees furent le point de depart des discussions de Buff on et de Bonnet sur ces problemes; elles influencerent Lamarck59, quelques-uines meme d'entre elles se retrouveront, ayant sans doute parcouru une route indirecte, dans la theorie genetique de pangenese de Charles Darwin, et dans sa theorie de la selection naturelle, comme dans la theorie de rhereditS par le souvenir, de Samuel Butler. En dehors de la sphere immediate de la biologie, sa notion d'ordre sortant du chaos et ses contributions a la « theologie naturelle » du transformisme, se trouvaient discutees avec acharnement par Voltaire, Diderot et d'autres 6crivains associes a 58. Ibid., p. 160*. 59. Cf. BRUNET, op. cit., pp. 166, 288-9, 326-36, et « La notion d'6volution dans la science moderne avant Lamarck », Archewn, Rome, XIX (1937), 37-43.

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1'Encyclopedic franchise 60. Des questions semblables devaient ressusciter lors de la potemique sur le darwinisme, an xix" siecle. Certes, Maupertuis ne trouva pas la solution du probleme, il ne decouvrit pas une th^orie satisfaisante du transformisme. II fallait toutes les preuves detaille'es de Charles Darwin pour convaincre les biologistes de 1'operation de la selection naturelle; et il fallait Mendel et la geneiique moderne pour eviter les difficult^ de Buffon et pour montrer comment les variations h&reditaires — les mutations — pouvaient etre preserves dans la race, et ne pas etre fusionnees de nouveau dans le type normal. Et on ne peut pas dire d'ailleurs que nous ayons encore trouve la solution de tous les problemes suscites par Maupertuis. Done, si nous pouvons retenir une des insultes de Voltaire, et admettre la description qu'il fait de son ancien ami comme « un vieux capitaine de cavalerie travesti en philosophe » 61, nous pouvons aussi voir le Philosophe du Roi, maintenant le chef de la cohorte evolutionniste, chevauchant avec une volonte plus tenace, et d'une maniere plus Elegante, que lors de Tattaque malencontreuse qu'il fit seul a la bataille de Molwitz.

60. La pens^e de Maupertuis sur la theologie naturelle arrivait a exercer une influence importante. Dans son Examen de la preuve de I'existence de Dieu employee dans I'Essai de Cosmologie (Histoire de I'Academic des Sciences, Mtmoires Ann6e 1756, Berlin, 1758, pp.389-424), Maupertuis avait discute le caractere relatif des assertions mathe"-* matiques et metaphysiques, et avait refuse" k ces dernieres tout caractere de necessite. En consequence de ce m^moire, les Acaddmiciens de Berlin mirent au concours le probleme : « Les rente's metaphysiques sont-elles susceptibles de la m£me Evidence que les rente's mathematiques, et quelle est la nature de leur certitude? » Le prix alia a Moi'se Mendelsohn et Kant eut un accessit. C'est dans ce me"moire, ou 1'influence de Maupertuis apparait nettement, que Kant faisait pour la premiere fois sa distinction entre analyse et synthese, et il en resta toujours au point de vue critique y adopte. Voir MOSES MENDELSOHN, Abhandlung fiber die Evidenz in metaphysischen Wissenschaften..., Berlin, 1764. Le memoire de Kant suit, sans no,m d'auteur, pp. 67-99 : Untersuchungen iiber die Dentlichkeit der Grundsatze der naturlichen Theologie und der Moral, zur Beantwortung der Frage welche die Konigl. Akademie der Wissenschaften zu Berlin auf das Jahr i763 aufgegeben hat. Cf. Kant, Sammtliche Werke, &d. G. Hartenstein, Leipzig, 1867, II, pp. vii-vm, 281-309. 61. L'Art de Men argumenter en philosophic reduit en pratique par un vienx capitaine de cavalerie travesti en philosophe (1753), dans VOLTAIRE, (Euvres, XXIII, 581; cf. BRUNET, op. cit., I, 153.

19

The Public and Private Faces of Charles Darwin When Charles Darwin's elder brother Erasmus read The Origin of Species, he wrote off a letter of congratulations saying : «the d priori reasoning is so entirely satisfactory to me that if the facts won't fit in, why so much the worse for the facts is my feelings.1 Charles's response to this compliment is not recorded, but he must have been surprised. He had tried in his book to overwhelm the reader with facts. But his unscientific brother had been struck by one characteristic that indeed gave power to Darwin's argument : its highly theoretical form. A second characteristic that now strikes us ishe kind of explanation used. This cut through all the qualitative diversity that was making biological theory so unmanageable and aimed to be strictly quantitative and mechanistic. The fact that The Origin of Species succeeded in making evolution accepted while previous writers on the subject had failed has raised a problem for historians of science. Neither the idea of evolution nor the theory of natural selection to explain it was original with Darwin. How did he alone manage to convince his contemporaries? Some unsympathetic critics, in the nineteenth as well as the twentieth century, have looked for the answer in external circumstances. They have said that Darwin was lucky with his timing, that his book appeared just at the moment when his fellow scientists and the public were ready to accept it. They have also accused Darwin of playing up to public opinion, and of being unfair to precursors who had anticipated all his main ideas. To these unsympathetic explanations of his success Darwin himself made the obvious and just reply that scientists had been persuaded to accept evolution for good reasons and that it was in the main he who had persuaded them. He had spent over twenty years, virtually since his return to England in the «Beagle» in 1836, collecting evidence to test his theories. His organisation i. The Life and Letters of Charles Darwin, ed. Francis Darwin, London, 1887, ii. 234; see A.C. Crombie, Styles of Scientific Thinking in the European Tradition, ch. 24 (London, 1994).

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of the evidence was immensely superior to that of any of his precursors. He might have added that the history of science is littered with precursors — including many of those that became attached to himself — who became interesting only when someone after them succeeded where they failed. He could also have said thad effective originality consists not only in having ideas but also in knowing how to exploit their scientific consequences to the full. Darwin is one of the most interesting of all scientific authors for the modern reader because, in addition to his pleasant style, he was himself intensely interested in all these questions of scientific method and scientific originality that were involved in his work. For example he wrote to one of his sons in 1871 that he had been speculating about «what makes a man a discoverer of undiscovered things, and a most perplexing problem it is». He went on : aMany men who are very clever — much cleverer than discoverers —, never originate anything. As far as I can conjecture, the art consists in habitually searching for causes or meaning of everything which occurs. This implies sharp observation and requires as much knowledge as possible of the subject investigated*.2 Darwin did not formulate any systematic philosophy of science, any more than Newton did. Practising scientists rarely do. But both left a trail of informal evidence, especially when forced to justify particular scientific conclusions, showing how they actually used ideas and why they believed their explanations to be scientifically satisfactory and the alternatives unsatisfactory. The materials for studying these questions in Darwin's case are all available in his correspondence, note books and diaries as well as his published works. They throw considerable light not only on how his mind in fact worked, but also on how he came to make evolution scientifically acceptable. One of Darwin's main criticisms of his predecessors — not an entirely just one — was that they had relied too much on indirect evidence simply for the occurrence of evolution, without looking for an adequate explanation. So their conclusions remained superficial. He proposed a different approach : first to look for an adequate cause of evolution, and then to see whether this was able to account for the various different phenomina concerned. In the introduction to the Origin he made public a description of how 2. The Autobiography of Charles Darwin, ed. Nora Barlow, London, 1958, p. 164

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he ad set about this process of discovery. This leads us into the central problems of his intellectual biography and scientific method. In the famous opening paragraph of the Origin, Darwin presented himself as a thinker not at all corresponding to his brother's praise, but, on the contrary, slow to use ideas until forced to do so by patiently accumulated facts. He described how he ad been struck while on the «Beagle» by the geographical distribution of related animals in South America and the relation of living to fossil forms ; how he thought these facts might throw light on the origin of differences between species ; how, when he got home, he collected still more facts. Eventually, he wrote, «"After five years" work I allowed myself to speculate on the subject*. He added : «I have not been hasty in coming to a decision*. The picture built up is repeated elsewhere. «I worked on true Baconian principles*, he wrote in the Autobiography, «and without any theory collected facts on a wholesale scale*.8 To Joseph Hooker he wrote in 1844 that he was «determined to collect blindly every sort of fact* bearing on the problem. But, he admitted, «At last gleams of light have come, and I am at last convinced (quite contrary to the opinion I started with) that species are not (it is like confessing a murder), immutable*.* Now this was written in the same year that Darwin wrote the long Essay on evolution by natural selection of which part was to be read at the Linnean Society in 1858 together with A. R. Wallace's paper on the same subject. The Essay was based on an even earlier sketch. In many ways it is the clearest and most attractive presentation of Darwin's ideas. The Origin follows its argument closely, simply adding much more supporting evidence. So when Darwin wrote disingenuously to his friend Hooker about «gleams of light* having come, he had in fact already worked out his theory in full detail. No doubt Darwin chose to present this picture of his progress as a shield against the accusation that evolution was merely speculative. Certainly this was the usual current view of the idea. His published self-portrait also fitted in with some contemporary ideas on scientific method, especially those of J. S. Mill. It was a picture of a great discoverer that gave public satisfaction. But it 3. Ibfd., p. 119.

4. Life and Letters, ii. 23.

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was largely false. In his private thoughts Darwin was a very different character. Darwin's correspondence is notorious for the number of contradictory statements it contains. But from his letters together with the other evidence it is possible to build up a well-documented intellectual biography. One thing becomes immediately certain. ((Collecting facts to give us ideas*, as Buffon had once put it, was the reverse of Darwin's method. «How odd it is*, he wrote to a correspondent in 1861, «that anyone should not see that all observation must be for or against some view if it is to be of any service!*5 In 1857 he wrote to Wallace: «I am a firm believer that without speculation there are no good and original observations*.8 «Let theory guide your observations*, he wrote with pleasant candour to another correspondent, «but till your reputation is well established, be sparing in publishing theory. It makes persons doubt your observations*.7 His son Francis, who worked as his assistant during his last years, confirms this picture. He wrote that his father «often said that no one could be a good observer unless he was an active theoriser. This brings me back to what I said about his instinct for arresting exceptions : it was as though he was charged with theorising power ready to flow into any channel on the slightest disturbance, so that no fact, however small, could avoid releasing a stream of theory, and thus the fact became magnified into importance. In this way it naturally happened that many untenable theories occurred to him ; but fortunately his richness of imagination was equalled by his power of judging and condemning the thoughts that occurred to him*.8 To be overflowing with ideas is surely the basis of all great originality, whether in the sciences or the arts. Darwin's main problem was not to get ideas, but to give his ideas effective scientific form in which they could be tested. The autobiography of Darwin's discoveries shows that he was driven to them all by his gifts for active speculation. Without those gifts he might have remained simply an inspired naturalist, a collector of unexplained information. He describes in his Autobiography his intense satisfaction as a boy with Euclid's clear 5. More Letters of Charles Darwin, ed. Francis Darwin and A. C. Seward, I/ondon, 1903, i. 195. 6. Life and Letters, ii. 108. 7. More Letters, ii. 323.

8. Life and Letters, i. 149,

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geometrical proofs and later with the logical form of Paley's Evidences for Christianity. Shortly before he sailed in the «Beagle» he was much struck by an incident with Adam Sedgwick, Professor of Geology at Cambridge, with whom he went on a geological investigation in North Wales. A labourer at Shrewsbury had shown Darwin a typically tropical shell found in a local gravel pit. He told Sedgwick, but Sedgwick merely said that someone must have thrown it there. He added that if it really did belong to the area «it would be the greatest misfortune to geology, as it would overthrow all we know about the superficial deposits in the midland counties*.9 Nothing before, Darwin wrote, had ever made him so thoroughly realise that science consists of a structure of laws and generalisations. Another experience on the same trip struck him later. Sedgwick was looking for fossils. Neither of them noticed the evidence of glaciation that is so characteristic of the area — a striking instance, as he said, of how easy it is to overlook phenomena, however conspicuous, if you don't expect them. It was in geology that Darwin first learnt to be a scientist. When he sailed in the «Beagle» in December 1831 he had had no proper formal training in any scientific discipline. This was not unusual at the time but it was at first a considerable disadvantage. The piles of papers he brought back describing rough dissections made on the voyage were almost useless. But he describes how having to work out the geology of an unknown area taught him the necessity of reasoning in advance and using predictions to guide his observations. He worked out his whole theory of coral reefs, which cleared up the whole question, on the west coast of South America before he had ever seen a true coral reef. Only when the «B eagle* crossed the Pacific was he able to test the theory by examining actual reefs. Darwin's note books show that his work on evolution began in the same highly speculative spirit. Like many great innovators, like Kepler and Galileo with the new cosmology, he became convinced himself long before he had enough evidence to convince others. He first considered the question at the very beginning of his serious work as a biologist, when the «Beagle» called at the g. Autobiography, pp. 69-70. 10. Charles Darwin and the Voyage of the Beagle, ed. Nora Barlow, London, 1945, pp. 246-7.

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Galapagos Islands in 1835." He was then twenty six. His attention, as he said later, was aroused by the way the animals and plants varied slighttly from island to island of this group. In 1837 he opened his first note book on atransmutation of species*,11 and wrote that the Galapagos species and the South American succession of fossils related to living forms were the origin of all his views. In this note book he speculated optimistically on the unexplained phenomena evolution would be able to explain, and described the form of theory that would give the explanatory power he was seeking. He shows that he was looking for a theory in which the whole production of all past and present organic forms could be shown to follow from given laws on the model of Newton's theory of gravitation. This was before he had any clear idea of what the laws of evolution might be. Thus he wrote : «let attraction act according to certain law, such are inevitable consequences — let animals be created, then by the fixed laws of generation such will be their successors*.12 These «laws of change* would then become «the main object of study, to guide our speculations*. Again and again in his writings he was to take Newtonian mechanics as the model for a scientific explanation. He had already by 1837 connected the problem of extinction with that of adaptation. Then in 1838 he read Malthus on the pressure of population against the means of subsistence. So, he concluded a famous autobiographical passage, «it at once struck me that under these circumstances favourable variations would tend to be preserved, and unfavourable ones to be destroyed. The result would be the formation of a new species. Here, then, I had at last got a theory with which to work*.13 For the public he was writing at this time, in the Journal of Researches, in terms of old concepts such as the uniformity of action of the «creative power* in producing similar organisms in a given area.14 The prodigious labours in collecting facts to which Darwin dedicated the rest of his life all stemmed from this new theoretical source. Far from working ablindly*, «without any theory* — as 11. Life and Letters, ii. 5-8, i. 276; CHARLES DARWIN, Journal of Researches, London, 1839, pp. 474-5; Autobiography, p. 118; CHARLES DARWIN and A. R. Wallace, Evolution by Natural Selection, ed. Sir. Gavin de Beer, Cambridge, 1958, pp. 5-6, 25-26. 12. Life and Letters, ii. 9. 13. Autobiography, p. 120. 14. Journal of Researches, pp. 212, 469, 474,

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if that were possible! — all his observations bore on very precise questions. The whole point of the vast labour he undertook in collecting facts about the selection of domesticated varieties of animals and plants by breeders was in order to explore the hypothesis that tnatural selection* had produced natural species and evolution by an extension of the same process. As he wrote : tl assume that species arise like our domestic varieties with much extinction ; and then test this hypothesis bv comparison with as many general and pretty well-established propositions as I can find made out — in geographical distribution, geological history, affinities, etc. ...».15 And «this seems to me the only fair and legitimate manner of considering the question — by trying whether it explains several large and independent classes of facts*.1" Far from being the classical example of a «Baconian» he tried to paint himself, Darwin appears as an almost extreme exponent of speculative thinking. In modern jargon the form of his thought might be called «hypthetico-deductive» or «retrodictive». He became puzzled by various observations and always used hypotheses to probe the question with further observations. The test of his hypothesis of evolution by natural selection was its range of application. He laid it out in the Origin like a legal argument, showing why its premisses must be acceped and what followed from them, stating the difficulties of the theory and demolishing them one by one. He concluded that a theory that explained so much could not be false. Besides the form of Darwin's argument, the second characteristic that strikes the modern reader is liis conception of the kind of material explanation of evolution that would de scientifically satisfactory. This aspect of his discussion of evolution was a contribution to biological thought as important as natural selection itself. Biology at that time was a field of confused issues. Natural theology and untestable ad hoc notions about innate organic drives towards improvement were mixed up with testable, analytical science. Darwin, and Wallace independently, made explicit the criteria of scientific explanation by which they judged all attempts to account for the facts. They took their stand on the model of physics and aimed to be strictly mechanistic. In contrast with 15. Life and Letters, ii. 78-9. 16. CHARLES DARWIN, Variation of Animals and Plants under Domestication, and ed., London, 1875, i, 9.

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biology, physics consisted of theories and laws that were testable, allowed no discontinuities in their field of explanation, and eliminated mysteries. Darwin comparied his treatment of natural selection with contemporary physicists' treatment of theories of gravitation, light and the ether. The theory of evolution by natural selection required two sets of laws : laws of heredity and variation, and laws of survival. Darwin and Wallace contributed the second, and for their law of natural selection they took an idea from the social sciences and organised it on the phvsical model. Natural selection was a statistical law of the redistribution of matter and energy among competing consumers. It showed how increasing order would be automatically generated from unordered variations by the operation of purely mechanistic principles. Wallace compared its action to that of the governor of a steam engine. Thus the built-in responses of a Cartesian mechanism would lead it to multiply, evolve and inhabit the earth. Darwin and Wallace each argued that natural selection, like a physical law, offered a sufficient and testable explanation of all the facts. Thus if it were confirmed no other kind of explanation would be necessary. Darwin has recently been criticised because in face of one large difficulty, concerning the first set of laws required by his theory of evolution, he later retreated from this position. According to the views on heredity and the best reasoning then available the mathematical odds against successful variations being transmitted were overwhelming. He felt himself forced to admit that hereditary variations might be produced by the direct action of the environment, thus giving evolution a direction independent of natural selection. Perhaps it was weak of him to make this retreat. But it is asking a lot to expect him to have guessed that the theoretical solution to his problem lay behind an innocent-looking title in the Royal Society Catalogue of Scientific Papers : «Experiments in Plant Hybridization» by Gregor Mendel. When we remember the state of biological theory, in the first half of the nineteenth century, it is easy to appreciate the force of Darwin's remark that the chief obstacle to the new ideas was that «of looking at whole classes of facts from a new point of view». Yet he also admitted that biologists were waiting for a theory in which all the diverse facts that were being accumulated would fall into place. oLooking backs, he wrote to Sir Charles Lyell on reading the last proof sheet of the Origin, «I think it was more

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difficult to see what the problems were than to solve them». 17 The problem as he saw it was to make evolutionary theory quantitative and predictive. Natural selection is still supported by far less direct evidence than most contemporary physical theories. But few biologists would deny its potential explanatory power. Not the least part of Darwin's intellectual success was that he knew what he was doing. Perhaps the most deceptive thing about his intellectual biography is that he reached his main conclusions so early. He was fifty when the Origin was published, but he knew the kind of evolutionary theory he wanted by the age of twenty-eight and wrote out his first sketch of it at thirty-three.

17. Life and Letters, ii. 170,

The best part of human language, properly so called, is derived from reflection on the acts of the mind itself. (Coleridge, Biographia literaria xvii)

20

The Language of Science

May I say first how honoured I am to be invited to participate in this Forum, and at the same time how alarmed I feel at doing so 'dans 1'espace francophone', with all the accompanying hazards for someone whose native tongue is English. I should like to say also that I am, as for myself, entirely in sympathy with the aim of the Forum 'de montrer la vitalite de la science dans 1'espace francophone', except that I should put the question differently. The vitality of scientific thought in French is after all evident to all the world. The practical problem is rather that of maintaining the language as a medium of communication in a world increasingly, and it seems unstoppably, dominated by English. This has great dangers for English itself, which risks becoming disintegrated into a diversity of dialects scattered round the globe, as classical Latin was disintegrated after the fall of the Roman empire into the different Romance languages of Europe. The beauty and sophistication achieved by these languages, pioneered by Italian and reaching a new dominance with French, may seem to offer some hope for a disintegrated English; but only after many, many generations. I hope that at least in Europe we will find a different solution which will maintain our languages more or less as they are. I believe that a monoglot Europe would be a cultural disaster, and that thought of all kinds, including scientific, would be enormously impoverished by having effectively only one language. A language after all embodies and expresses a way of thinking, the perspective of a whole cultural experience. To translate that perspective from one language into another requires far more than knowledge simply of the languages themselves, as anyone who tries to translate even between English and French very soon discovers. There are of course great practical problems, in the world as it is becoming, both for French and for English and indeed for other major languages. Events tend to go the way of least resistance. We must keep our nerve. Concerning more specifically the subject of this Table ronde, I shall comment briefly, and inevitably impressionistically, on some historical relations between language and scientific thinking and their changes. History illuminates the present and no doubt the future, and we must take a long view. When we speak today of natural science we mean a specific vision, created within Western culture, at once of knowledge and of its object, at once of

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science and of nature. We can trace this vision to the commitment of the ancient Greek philosophers, mathematicians and physicians, for whatever reason, to the decision of questions by argument and evidence as distinct from custom, edict, authority, revelation, rule-of-thumb or whatever else. In this way they developed the notion of a problem as distinct from a doctrine, and they initiated the history of science as the history of argument in a search for principles at once of nature and of argument itself. They discovered two fundamental principles from which the essential style of Western scientific thinking has followed: those of exclusive natural causality, and matching that of formal proof. The marvellous and fascinating scholarship which during recent decades has so much enriched our knowledge of other major ancient cultures has not, so far as I can see, revealed there a grasp of these principles, whether in Babylon or Egypt, India or China, or Central America. They had impressively ingenious and inventive technologies, including highly original mathematical technologies as in Babylonian arithmetic and astronomy, in an ambience of myths scarcely related to technical knowledge. In Western terms they had no system of rational science. The idea that the style of thinking arises from the intellectual and moral commitments which provide the expectations, dispositions and memories of a culture in an invitation to treat the history of science as a kind of comparative historical anthropology of scientific thinking. This must be concerned before all with people and their vision; we must learn to look at once with and into the eye of the beholder. Styles of thinking and making decisions, established with the commitments with which they began, habitually endure as long as these remain. Hence the structural differences between different civilisations and societies and the persistence in each of a specific identity, continuing through all sorts of changes. It is an important question, as we look at the westernisation of the globe, to ask at what levels general moral and intellectual commitments are altered, and what remains the same. Restricting the question to an historical anthropology only of Western science, language is an indispensable guide both to theoretical ideas and to real actions. Any language embodies a theory of meaning, a logic, a classification of experience, a conception of perceiver, knower and agent and their objects, and an apprehension of existence in space and time. We need to ask how language conditioned scientific thinking and was in turn altered by it. We may distinguish three levels: those of the structure of a language itself, of general conceptions of the nature of things expressed in it, and of particular theories. The language of causality for example is closely related to conceptions of causality. It is hard to say which came first, but there is an obvious structural conformity between the grammar of subject and predicate found in all European languages, and the ontology of substance and attribute developed most systematically by Aristotle. Aristotle's logic imposed on Western science for many centuries a form of demonstration, relating cause to effect as premise to conclusion, expressing this grammar and ontology of subject-predicate, substance-attribute. His conception of causality was structural and non-

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temporal and was focused on the definition, which explained both the behaviour and the existence of something by its defining attributes. Parallel to this the Greek mathematicians exploited the speculative power of geometry by imposing upon the phenomena at once its deductive logic and an appropriate geometrical model delineating for each its form in space. Thus they reduced the phenomena of visual perspective to the properties of the straight line and the angle, of astronomy to the properties of the sphere, of mechanics to the relations of weights determined by the properties of the straight line and the circle. They could then develop their immediate research into the phenomena purely theoretically within the model itself. The geometrical conception of causality was again structural and nontemporal, focused on space and place, not on the sequence of events in time. These conceptions, and specifically Aristotle's logic of subject and predicate, were to become a major obstacle to the medieval and early modern natural philosophers and mathematicians of Latin Christendom who, in a different intellectual context, came to develop a new conception of causality based not on static structure by on rates of change. They came to express causality in the language not of subject and predicate but of algebraic functions, and they devised a new Latin terminology to express such fundamental quantities as velocity, acceleration, instantaneous velocity, and so on. These quantities were defined in the fourteenth century by mathematicians in Paris and Oxford, and their terminology was to be used by Galileo and Newton. This new functional causality of classical physics related events as sequences in time brought about only by contact or through a medium or field; the disputed choice between these was based on wider ontological beliefs. Starting with Roger Bacon causality came to incorporate a theology of laws of nature laid down by the Creator: for as Dante put it 'dove Dio senza mezzo governa, la legge natural nulla rileva (where God governs without intermediate the natural law has no relevance)' (Paradiso xxx. 122-3). Created law reestablished the stable predictability of nature within Hebrew-Christian doctrine. Newton was to combine this theology with Euclid in calling his fundamental dynamical principles 'axioms, or laws of motion' (Principia mathematica). Such language clearly arises not from the interior of natural science but from its intellectual context. Must science in different linguistic cultures always acquire differences of logical form, and must a language always impose its ontological presuppositions on the science developing within it? The technical language of science has often been developed partly to escape from just such impositions, and to detach a specific scientific meaning from misleading analogies coming from its source in common vocabulary. The word current', wrote Michael Faraday, 'is so expressive in common language that, when applied in the consideration of electrical phenomena, we can hardly divest it sufficiently of its meaning, or prevent our minds from being prejudiced by it' (Experimental Researches in Electricity, i, London, 1839, p. 515). With the aid of William Whewell he devised a new terminology to fit the exact context of electro-chemistry, for

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example replacing the word 'pole', inconveniently suggesting attraction, with the neutral 'electrode'. From the fourteenth century radically new technical languages were gradually built up, precisely symbolised first for mathematics and music. From the end of the fifteenth century the mathematical symbols +, — , x, -f-, > , < , , / , = etc. came into use to represent operations or relations previously written out in words. Later in the seventeenth century Francois Viete began to systemise the essential general principle of modern algebra by designating quantities by letters, distinguishing knowns, unknowns, powers and so on. Thus was launched the universal numerical language of mathematics, and during the same period that of music, both transcending all national boundaries and transparently comprehensible within their explicit limits. Their message was precision and economy, but of course precision alone is useless without content, which comes from scientific or artistic imagination. This depends on vision beyond such limits, and it is vision controlled by a precise critique that establishes, usually in advance of any particular research, the kind of world that is supposed to exist. This in turn established the kind of explanation in science, and presentation in art, that will give satisfaction because the supposedly discoverable has been discovered. But all this needs to be expressed in our natural languages, and that leaves our problem there just as I indicated at the beginning of these brief comments. Note: see my Styles of Scientific Thinking in the European Tradition (London, 1994).

21

Some Historical Questions about Disease

Under this very general title I want to talk briefly about the relations between medical science, the medical art of healing, and conceptions of disease. But first it may be helpful to put this question within a much larger context of what we may call a comparative historical anthropology of science and medicine, focusing on people and their vision, and their circumstances both human and physical.* The central history of science as I see it is the history of argument: an argument initiated in the West by ancient Greek philosophers, mathematicians and physicians in their search for principles at once of nature and of argument itself. Of its essence have been periodic re-assessments, varying considerably in different historical contexts, of its presuppositions about the nature of what exists, about scientific cogency and validity, and about the intellectual, practical and moral justification of the whole enterprise. Of its essence also have been its genuine continuity, even after long breaks, based on education and the study by any generation of texts written by its predecessors; and its genuine progress both in scientific knowledge and in the analysis of scientific argument with its various logical, experimental and mathematical techniques. It has been a subtle historical question to assess what has continued through different periods and societies and what has changed. We can characterise the vision and the circumstances of people at different times and places by what we may call their commitments. It is their intellectual and moral commitments, involving their expectations, dispositions and memories, that give to people their vision and their style of thinking and of making decisions. We can distinguish two kinds of intellectual commitment in the history of science: 1 Commitments to conceptions of nature and its knowability to man, within the context of general beliefs about the nature of existence, and of man in See A.C. Crombie, Styles of Scientific Thinking in the European Tradition (London, 1994) with 'Historical Commitments of biology', The British Journal for the History of Science, iii (1966) 97-108, 'Historical Commitments of European Science', Annali dell'Istituto e Museo di Storia delta Scienza di Firenze, vii. 2 (1982) 29-51, 'Pari sur le hasard et choix dans 1'incertain' in Medecine et probabilities, ed. A. Fagot (Paris, 1982) 3-41; and for various questions indicated below Hippocrates, ed. W.H.S. Jones, i (London and New-York, 1923), P. Lain Entralgo , Mind and Body: Psychosomatic Pathology (London, 1955), La Historia Clinica, 2nd ed. (Barcelona, 1961), O. Temkin, 'The Scientific Approach to Disease: Specific Entity and Individual Sickness' in

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mental and bodily health or disease: such conceptions tend to be strongly conditioned by language. 2 Commitments to conceptions of science, that is of scientific methods of argument, inquiry and explanation. From the interaction of these two intellectual commitments come the perception of problems, as distinct from doctrines; conceptions of acceptable questions to put to a subject-matter as well as of acceptable answers; and to a considerable extent the direction of attention and inquiry towards certain types of problems and of solution and away from others. They establish in advance the kinds of problem that will be seen and so they foster certain kinds of discovery, and at the same time they establish the kinds of explanation that will give satisfaction because the supposedly discoverable has been discovered. Scientific change comes from a combination of scientific experience, especially of failure, with rethinking of basic principles, again with a deep involvement of language. Any language itself embodies a theory of meaning, a logic, a classification of experience in names, a set of presuppositions about exists or seems to exist behind experience. Language mediates man's experience of nature and of himself; hence philology, both of traditional languages and of the technical languages of the sciences and arts (given precision in symbols first in mathematics and music), can be an indispensable guide to theoretical ideas and real actions. 3 A third kind of commitment giving people their vision is to conceptions of what is desirable and possible, in view of evaluations of the nature, purpose and circumstances of human life. Such commitments concern right human action, what should and can be done, both morally, and scientifically and technically in the sense of being capable of achieving their ends. To this kind of commitment are linked dispositions, both of individuals and of societies, generating habitual responses to events: dispositions to expect to master or to be mastered by events, to change or to resist change both in ideas and in practices, to accept or to reject the possibility of truth within supposed error and hence to integrate within reasoned argument both agreement and disagreement. Here education and experience can furnish options for the choice of a different future. 4 Besides these three kinds of intellectual and moral commitment giving people their vision there is a fourth kind of commitment involving their circumstances. This is the commitment to the physical and biological environment in which they find themselves: they may try to change it, but first it is given. A comprehensive comparative historical anthropology of science and medicine would address itself to questions at the different levels indicated by Scientific Change, ed. A.C. Crombie (London, 1963) 629-58, T. McKeown, The Rise of Modern Population (London, 1976), W.H. McNeill, Plagues and Peoples, (Oxford, 1977), M.D. Grmek,

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these commitments, some given by nature, some made by man. Thus at the level of nature there is historical ecology: the reconstruction of the physical and bio-medical environment and of what people made of it, from both written records and physical remains, as in striking recent work on palaeopathology, palaeodemography, palaeobotany, and the history of climate. Reconstruction at the levels of people and their vision requires the exegesis of evidence including in its scope religion, law, politics and so on far beyond simply scientific thought. At all levels historical questions demand in the historian exact scientific and linguistic knowledge (as well as much else of the intellectual, visual and other sorts of culture that mediate human experience) to enable him to control the view of any present recorded through the eyes and language of those who experience it. It does not have to be demonstrated here that the road to understanding of our human condition at any time, including the present, lies as much through the study of history as through that of the nature and people immediately in front of us. This is as true of scientific and medical thinking and practice as it is of any other of our activities and habits. Styles and forms of thinking and behaving become established with the commitments with which these began and they persist as long as they remain. Hence the structural differences between different civilisations, cultures and societies. Of course there is development, change and occasionally revolution, but more often than not retaining a structural similarity throughout from habit and education. One may cite the persistent differences between China and Europe, and the persistent similarities between Russia before and after 1917. Hence the need for an historical dimension for a true perception of ourselves as human beings in all our cultural diversity, and for an educated understanding of change itself. This, like most human behaviour, begins in the mind. I come now to medical science, medical art, and conceptions of disease. We may start with the definition of medicine given in the Hippocratic Epidemics (i. 11): The art consists of three things: the disease, the patient and the physician. The physician is the servant of the art. The patient must help the physician to combat the disease'. The historian must study all three. They present the subtle question of the relation of medical science to medical art, with goals that are different, but intricately tied together. Medical science aims through the analysis of its subject-matter at theoretical understanding to be expressed in general statements. Since antiquity it has been concerned with two main activities: (1) the observation and recording of regularities of symptoms and their course through the duration of diseases: this is found in the case-histories developed by Egyptian and Babylonian physicians; but the whole method was transformed by (2) the search for causes, introduced by the Greeks under the name of Hippocrates. The Greek

Les Maladies a I'aube de la civilisation occidentale (Paris, 1983), A. Fagot-Largeault, L'homme bio-tthique (Paris, 1985).

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physicians, in accordance with their general habit of mind, madephysiologia, knowledge of nature, essential to the science and art of medicine. There was really no general conception of nature before the Greeks, anyhow in the Western ancient world. There was an often detailed discernment of empirical connections and regularities, in medicine as in astronomy (which involved sophisticated mathematical predictions), but no conception of nature as a system of exclusive natural causality, and no associated form of argument for demonstrating causal connections by an explicit logic. 'Each disease has a natural cause' wrote the author of the Hippocratic Airs, Waters, Places (§ 22), 'and nothing happens without a natural cause'. With the Greek search for causes in medicine came the concept of the natural norm (e.g. the balance of the four Galenic humours), after all an abstraction, and of disease as deviation from that norm. Causes of disease came to be conceived of as of two kinds: (1) physiological disturbances of the body or psychological disturbance of the soul arising from within; and (2) effects on the patient of external agents. Conceptions of these two kinds of cause, whether of internal disturbances or of agents that may invade the body as specific entities, have provided the substantial programme for Western medicine ever since. Diseases are identified and distinguished by the regular appearance of specific symptoms, given names, and allocated causes within current medical theory. This raises historical questions of its own in the identification of diseases recorded from the past. Some like Thucydides's plague of Athens correspond in symptoms to no known current disease, while others like diptheria, bubonic plague and smallpox have persisted through the centuries with recognisably the same diagnostic symptoms, which became attributed to persisting specific microbial pathogenic agents. Medical art by contrast with science aims not at generalities by at restoring and preserving the health of particular individuals. To do that of course it has used the results of medical science, but it cannot treat an individual patient as simply an example of general phenomenon. It is concerned with an individual person who is unique and irreplaceable by any other person. It shares this concern rather with the traditional religions than with analytical science. Where it differs is in the means. Its relation to medical science is like that of other practical arts, aiming at the composition of an effect, to their corresponding sciences: of painting for example to optics, or of the gaining of political ends to the analysis of rhetorical manipulative skills. Here the complexities begin. A politician acting with no regard to truth may still provide for the public good; a physician acting on his best understanding of scientific theory may propel his patients to disaster; while desired effects may be produced with what may seem to be no real understanding of causes, as for example by traditional Chinese or Indian medical practices and by Western psychiatry. Theories of disease have obviously affected treatment and are not neutral or innocent, whether physicians looked like Thomas Sydenham for specific drugs to act on specific diseases as Cinchona acts on malaria or for specific remedies as did Edward Jenner and Louis Pasteur, or they insisted as

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did others like Francois Broussais and some modern physicians dealing with degenerative disorders and neuroses that diseases are abstractions and that it is the patient who has to be treated. It is the perception of the unique and responsible human individual that has given rise to the ethical questions of Western medicine. People who saw their lives within at once a physical and a moral cosmology took corresponding attitudes to disease and calamity and choice of all kinds, stressing natural causation or moral responsibility according to their beliefs. Job saw his ailments within an entirely moral context and complained because, as a just man, he should be so unjustly afflicted. In the ancient world there was an immediate contrast between Greek medical thinking, which might reduce sin to sickness, and Hebrew moral thinking reducing sickness to sin. This contrast continued through the Christian middle ages, and it persists in some legal attitudes to crime, and in the whole conception of diminished responsibility as a pathological as distinct from a moral phenomenon. Boundaries have been drawn differently in different periods and circumstances between the normal and the abnormal: for example deaf-mutes were classified as imbeciles until it was discovered by science in the seventeenth century that they were dumb because they could not hear. Again personal attitudes to suffering and death through illness, as to hard decisions like that of Thomas More which could lead only to martyrdom, have differed fundamentally according to general beliefs about human existence and its purpose. It made a difference whether the prospect was Christian hope or simply extinction, and whether ultimate death was of the body or of the soul. It was through the form of argument and procedure developed through the Hippocratic case-history, then the recognition of statistical regularities, and eventually the clinical trial, that medical art and science found a way to come together to relate individual illnesses to the general explanations reached by scientific analysis. The Greeks remained purely qualitative in the regularities they observed and the prognoses made from them. It was in the different practical circumstances of the commercial expansion of late medieval Europe that mainly Italian mathematicians began to grasp the idea of quantitative expectation for such purposes as insurance and the division of profits. In the seventeenth century Blaise Pascal, Christiaan Huygens and Jakob Bernoulli showed with great mathematical sophistication how, from the regular numerical frequencies present in adequate numbers of things, to stabilise uncertain expectations as probabilities. This offered a new mastery of rational choice and action in a whole range of subject-matters, from the sciences of nature to commerce and politics. In medicine John Graunt in his Natural and Political Observations . . . made upon the Bills of Mortality (1662) set out explicitly the fundamental discovery that statistical regularities appeared in large numbers of things which were lost in small numbers. This was a phenomenon new to science whose recognition came to transform scientific thinking. Starting from the records of births and of deaths with their symptoms kept for London for over half a century, Graunt arranged for a further regular recording of

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information about all diseases and related data in the area, insisting that his helpers should record only observed symptoms and other facts and should ignore opinions, medical or otherwise. He saw that stable mortality rates, sexratios etc. could be translated immediately into approximate probabilities a posteriori. This then provided for inferences in two directions: directly to the probability of a possible event coming about, and conversely to the probable causes of events already brought about. In this way he made an analysis of the proportions of deaths in a population to be attributed to different causes, distinguishing chronic or endemic diseases from epidemic diseases, and so on. The next century and a half witnessed through the work of Buff on, Daniel Bernoulli, Thomas Bayes, Laplace and many others an elaboration and sophistication of statistical analysis and theory of probability without which the quantitative study of disease would scarcely have been possible. This began seriously with the institutional facilities provided by the modern hospitals of the nineteenth and twentieth centuries. Here, by means of new techniques of medical examination, quantitative data were accumulated for describing individual illnesses in new and precise detail; by observing many cases of the same disease standards and limits of normality were established; clinical symptoms were related to physiology and pathology; a scientific taxonomy of disease was developed. All this followed from a statistical approach to the normal and the abnormal, and it led eventually to an experimental approach to clinical science. The science and art of medicine would scarcely be what they are now without the controlled therapeutic trial for exploring the actions of drugs, and the statistical methods that have revealed such hitherto obscure connections as that between smoking and cancer. The essential scientific insight came here from R.A. Fisher's book The Design of Experiments (1935). I will conclude with three final historical questions. (1) The appearance of disease as recorded historically must always depend on the eye of the beholder: we must then examine the credentials, beliefs and methods of observation of the witnesses who describe and identify diseases, as well as the symptoms they describe. Likewise we must examine the eye of the modern historian: we are inevitably alerted to phenomena of the past by current interests, and that also we must monitor critically. The same applies to high modern technology: could quantitative epidemiology itself invent diseases existing only it its own results? (2) Our enthusiasm for medical science, with its fascinating intellectual problems, can blind us to more mundane aspects of medical history. For example the death rate in England, where full records have been kept from the beginning of the eighteenth century, declined steadily from that time, but the discoveries of causes of disease and the therapies introduced over two centuries had no general effect on that steady decline before the general use of sulphur drugs and antibiotics about fifty years ago. The cause of the decline was not medical science but hygiene (town drains, water supply), improved general nourishment, and public health. This might have some bearing on some developing countries and groups in industrialised

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counties now afflicted with AIDS. Like most aspect of human behaviour, the problem begins in the mind. There is a case for making intensive studies both of the historical ecology and of the historical anthropology of Africa, which presents special problems for historical investigation because of the relative lack of documentary evidence. (3) Lastly this: the self-critical European tradition, which includes science and is unique among the cultures of the world, has generated a capacity, albeit often uncertain, to see Western values through alien eyes and all in comparison with each other. Hence Western anthropology, and historiography of thought of many kinds and in many contexts and periods. To do this is of course an immensely difficult exercise in critical imagination, empathy and reasoning. We may the more easily grasp other mentalities by exploring the scientific origins and development of our own from the Greek search for principles at once of a subject-matter and of argument about it. A true comparative intellectual anthropology must look not only with, but also into the eye of the beholder.

The choice: to be conscious participants in, or victims of, historical tradition.

22

Historians and the Scientific Revolution

To a generation made more aware than any previous one of the division between science and the humanities, there is a particular interest in the treatment of the ' Scientific Revolution' by the earliest modern historians who discussed the history of science!. As observers living during or just after the event, writers of ' philosophical history' from Francis Bacon to Voltaire set out to give a systematic account of the meaning, for an educated person, of the scientific movement as a revolution in ideas, methods and attitudes. They had inherited the techniques and conceptions of the historical discipline that had been developed by scholars since the fifteenth century, contemporaneously with modern science itself, and they used them to show how science had emerged in the history of civilization. In doing so, they gave analyses both of the nature of scientific thought itself, as they saw it, and also of the conditions that favoured or discouraged its progress, that have left their mark on subsequent conceptions of the history of science down to the present day. The writer who summed up the whole of this early conception of the scientific revolution as an historical event was Voltaire2. A product of the 1 An earlier version of this paper was published in «Endeavour», xix (1960) 9-13. On the historiography of science, cf. also O. Temkin, An essay on tbt usefulness of medical history for medicine, ^Bulletin of the History of Medicine*, xix (1946) 9-47, The study of the history of medicine, «Bulletin of the Johns Hopkins Hospital*, civ (1959) 99-106, and Scitntfic medicine and historical research, ^Perspectives in Biology and Medicine*, iii (1959) 70-85; F. N. L. Poynter, below, n. 28; H. Butterfield, below, n. 20; A. C. Crombie, Science, Optics and Music in Medieval and Early Modern Thought, chs. 1-2 (London, 1990) and Styles of Scientific Thinking in the European Tradition, chs. 1-2, 22 (London, 1994). 2 Cf. J. H. Brumfitt, Voltaire Historian (Oxford, 1958); G. Lanson, Voltaire, 5eme ed. (Paris, 1924).

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age in which both modern science and modern historiography reached maturity, Voltaire was not only the first systematic historian of civilization and the first to make extensive use of the comparative method, but also the first historian to treat the history of science systematically as part of the history of civilization. In this, his conception of history stands in striking contrast with that of nineteenth-century historians, who concentrated their attention almost entirely on political and constitutional events, a limitation from which historians have by no means yet entirely freed themselves. Voltaire became known on the Continent as the most influential popularizer of Newtonian physics and of English empirical philosophy. He interpreted the scientific movement to educated Europe and projected it in a conception of history that, in spite of criticisms to which it is open both in general and in particular, still forms a recognizable part of the historical outlook of a large part of the educated Western world. The view of the scientific movement that Voltaire incorporated into his systematic reconstruction of history came in the first place largely from the publicists of contemporary science, especially Francis Bacon and Fontenelle, and from the great scientists themselves. But he also made use of a view of history that had originated with the humanist historians of fifteenth-century Italy and had become modified by science, during the seventeenth century, in the controversy between the Ancients and Moderns. Voltaire presents a picture of the historical consciousness of an age in which all educated people shared a common background in the humanities and in which the ' new philosophy', of experimental and mathematical science, had recently become established as an essential part of general culture. He gave expression to what many thought, or were ready to think. The view of history into which all the early modern historians fitted the origins of modern science was based on a specific conception of a great revival in European civilization between the fifteenth and the seventeenth centuries. This conception not only established a periodization of history, into Ancient, Medieval and Modern, that has become conventional; it made value judgements and offered explanations of the course of events that carried with them formulae for future advance. By Voltaire's time the conception had gone through three main stages of development: humanist, religious, and scientific. The concept of a renaissance in the fifteenth century, after a thousand years of ' dark ages' following the fall of Rome, was developed during the period of the Renaissance itself3. In the fourteenth century Petrarch, 3 See W. K. Ferguson, The Renaissance in Historical Thought: Five centuries of interpretation (Cambridge, Mass., 1948); H. Baron, The Crisis of the Early Italian Renaissance, 2nd ed., i (Princeton, 1966).

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inspired by a romantic admiration for pagan Latin literature, the city of ancient Rome, and the ideal of republican virtue, had divided history into 'ancient' (antiqua) — before Constantine's adoption of Christianity, and ' modern ' (nova) — the long succeeding period of barbarism and ' darkness ' (tenebrae) that had continued to his own time. From the end of the fourteenth century, humanist historians of art and of the Italian city states, especially of Florence, added to this periodization the notion of a recent revival, the beginning of which they often placed in the thirteenth century. The term ' middle age' (media tempestas) was introduced in the fifteenth century in Germany in reference to Nicholas of Cusa4. From the first, this conception of antiquity, a middle period of barbarism, and a recent revival was far from merely descriptive; it made an historical judgement that influenced contemporary action. For example, the fifteenth-century Florentine historian Leonardo Bruni, who first explicitly used this periodization in political history, made the recent political progress of his city an explicit revival of the model of republican Rome. In 1483 Flavio Biondo, a papal secretary and student of the monuments of ancient Rome, defined the chronological boundaries of world history, with A.D. 410 to A.D. 1410 as a period different from those preceding and following it. Other Italian historians, especially Machiavelli, were even more precise in their use of history for contemporary political purposes. Similarly, historians of the arts, in presenting the contemporary development of painting, sculpture and literature as a revival of classical models, wrote to encourage the new styles. They knew little and cared less about medieval Latin literature and the Gothic art beyond the Alps. For example Filippo Villani, writing at the end of the fourteenth century, mentions no poets for nine centuries before Dante and no artists before Cimabue, who recalled art to nature, and Giotto, «who not only can be compared with the illustrious painters of antiquity but surpassed them in skill and genius» 5 . Practising artists like Ghiberti and Alberti were content to accept this account of their relation to the past, and in the sixteenth century it became finally established in Vasari's phrase for the new style, la rinascita. The whole movement was crowned, he wrote, by «that excellence which, by surpassing the achievements of the ancients, has rendered this modern age so glorious» 6 . The humanist historians made the conception of a revival, leading on to new conquests, an explicit part of their historical thinking, but half4 P. Lehmann, Vom Mittelalter und von der lateinischen Pbilologie des Mittelalters, «Quellen und Untersuchungen z. lateinischen Philologie des Mittelalters», v. i (1914); G. Gordon, Medium Aevum and the Middle Age (Society for Pure English Tract No. xix; Oxford, 1925); M. L. McLaughlin, «Humanist concepts of renaissance and middle ages in the tre- and quattrocento*, Renaissance Studies, ii (1988) 131-42; Crombie, Styles. . . Ch. i above n. i. For Petrarch see Ferguson, op. cit., p. 8. 5 Quoted by Ferguson, op. cit., p. 21; see pp. 9-21. 6 Ferguson, op. cit., p. 64; see pp. 59-67.

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consciously it had for long been an element in the restless mentality of the ' barbarians' who had entered into the lands and heritage of the western Roman Empire. It began to find expression by writers in the twelfth and thirteenth centuries who could observe the effects on intellectual life of the translations being made, from the Greek and Arabic into Latin, of scientific and philosophical works, and who were witnessing also a modest technical revolution in the development of machinery for harnessing the power of wind, water, and draught animals, and in building, glassmaking, metallurgy, warfare, .surgery, navigation and other activities. According to John of Salisbury, in the twelfth century, the French scholar «Bernard of Chartres used to compare us to dwarfs perched on the shoulders of giants, so that we see more and farther than they can, not because we have keener vision or greater height, but because we are lifted up and borne aloft on their gigantic stature» 7 . A century later, Roger Bacon could assert the progress of knowledge more confidently : « We of later ages should supply what the ancient lacked, since we have entered into their labours, by which, unless we are asses, we can be aroused to better things; because it is most miserable always to use old discoveries and never to be on the track of new ones Christians should ... complete the paths of the unbelieving philosophers, not only because we are of a later age and should add to their works, but so that we may bend their labours to our own ends » 8.

The activist attitude that is essential to the research mentality, prepared not simply to contemplate knowledge gained from past writers but to use it as a base for further advance, can already be seen in formation in the writings of scholastic natural philosophers and mathematicians such as Robert Grosseteste, Roger Bacon, Albertus Magnus, Thomas Bradwardine or Nicole Oresme. It was the motive behind the numerous proposals for scientific method already characteristic of the thirteenth and fourteenth centuries, as they were to become more abundantly of the seventeenth. Moreover, Roger Bacon anticipated (with differences) his namesake Francis in offering an analysis of the «causes of error» 9 and of the stagnation of science in contemporary Christendom, including among the most important the neglect of mathematics and «experimental science» 10 and the under-valuation of true learning. The low opinion of 7 loannes Saresberaensis; Metalogicon libri iv, iii-4, recognovit... C. C. J. Webb (Oxford, 1929). The same remark is quoted by Alexander Neckam, De naturis rerum libri duo, i. 78, ed. T. Wright (London, 1863); cf. R. Klibansky, Standing on the shoulders of giants, « Isis », xxvi (1936) 147-98 Roger Bacon, Opus Majus, ii. 15, ed. J.H. Bridges, iii (London, 1900) 69-70. » Ibid., i. 10 Opus Majus, vi, « De scientia experimental!», ed. Bridges, ii. On this cf. A. C. Crombic, The relevance of the middle ages to the scientific movement, in « Perspectives in Medieval History », ed. K. F. Drew and F. S. Lear (Chicago, 1963) 35-57, and with }. D. North, Bacon, Roger, in « Dictionary of Scientific Biography » (New York, in press); M Schramm, Aristotelianism • basis and obstacle to scientific progress in the middle ages, « History of Science », ii (1963) 104-9.

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medieval culture held by the humanists was based on literature and Gothic art rather than on science and philosophy, in which at first they took little interest. But both the scholastic and the humanist reformers applied the same activist formula to history, taking an attitude to the past determined by the needs and aspirations of the present and providing a programme for future action. Such an attitude seems to be a deeply persistent element in modern European historical thinking. To the humanist doctrine of the Renaissance, the religious controversies of the sixteenth century added a new interpretation that was to become a second important element in later accounts of the rise of modern science. To justify their own position, both humanist and Protestant writers agreed in seeing the immediate past as a revolting spectacle of ignorance, superstition and corruption, polluting the pure stream of style or doctrine that had existed in an earlier, ideal period of their choice. «Throughout the first two centuries of Protestant historiography», Wallace K. Ferguson has written in his recent study, The Renaissance in Historical Thought11, a medieval culture meant scholasticism, and scholasticism meant a peculiarly pernicious state of ignorance». The Catholic Erasmus attacked medieval education, to which he attributed the decline. The English Protestant Bishop John Bale, in 1548 described the great scholastic writers as «that obscure and ignoble breed of sordid writers of sentences and summulae, the mere recording of whose names should move generous and well-born minds to nausea» 12 . Ferguson continues: «Taking over the Erasmian conception of the close causal relation between the revival of learning and that of religion... the Protestant historians blandly assumed that any improvement in learning must have led to a clearer perception of truth and therefore must have aided the acceptance of Protestant doctrine» 13 . The connection between humanism, Protestantism, and the rise of modern science became established in historical doctrine at the end of the seventeenth century, when each movement was seen as part of a common revolt against authority — the authority of scholastic education which still dominated the universities, the authority of Aristotle and Galen. In each case the reformers appealed from authority accepted in the immediate past, to an earlier state of things which they held belonged to a tradition that had been broken. The humanists turned from the ' dog' Latin and barbarous jargon of the scholastics to the pure style of classical literature, especially of Cicero. The Protestants appealed from the institutionalized sacerdotal guidance of the medieval Church to the 11 12

P. 51.

Quoted by Ferguson, ibid., p. 51 " Ibid., p. 54.

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plain text of Scripture and private judgement of its meaning, such as they held had existed in the primitive Church. The humanist-trained scientific reformers appealed first from medieval ' corruptions' to the pure Greek text of Aristotle, Galen or Ptolemy, and later from these texts to direct observation of nature such as had been practised in Greek times. The complete doctrine was succinctly expressed by the American writer Cotton Mather in his American Tears upon the Ruines of Greek Churches published in Boston in 1701: «Incredible darkness was upon the Western parts of Europe, two hundred years ago: learning was wholly swallowed up on barbarity. But when the Turks made their descent so far upon the Greek churches as to drive all before them, very many learned Greeks, with their manuscripts, and monuments, fled into Italy, and other parts of Europe. This occasioned the revival of letters there, which prepared the world for the Reformation of Religion too; and for the advances of the sciences ever since» 14 . The same form of the doctrine making a close connection between the literary revival, the Reformation, and the rationalism of modern science is found in Pierre Bayle's Dictionary, published in 1697 and a source of many of Voltaire's historical opinions. The need of the innovating parties in the literary and religious controversies to define their position in relation to the immediate past affected the historiography of science rather by their general attitude to the past than by an special interest they had in science. Humanist editors of Archimedes, Hippocrates or Aristotle were more interested in establishing a good Greek text or making a good Latin translation than in the mathematics or biology the texts contained. There are cases of literary scholars such as Conrad Gesner being led by by the text to the study of nature, and in Gesner's case to becoming a first-rate observer and naturalist. Similarly, the sixteenth-century reconstructions of the original text of Archimedes required mathematical as well as linguistic skill, and in this tradition the young Galileo himself was led to reconstruct Archimedes' methods before extending them to new scientific problems15. But humanist interest in Greek science, as in other aspects of ancient literature, had its origin in a backwards-looking admiration for antiquity; before it looked forwards it had to become something more than merely literary. Early in the seventeenth century, a new group of scientific commentators upon history arose with a completely different outlook upon the past and the future. These writers, Campanella, Francis Bacon, Descartes and their followers, mark the third major stage in the conception 14 15

Pp. 42-3; Ferguson, op. cit., p. 55. Galileo Galilei, La Bilancetta (1586), « Opere » ed. naz., i (Firenze, 1890) 211-6.

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of history that was to find full expression in Voltaire. They combined a full measure of contempt for the medieval past with an entirely new estimation of the importance of the scientific revival. Like their predecessors, they made their interpretation of history in the interests of a contemporary movement of which they were spokesmen. But, except in so far as these had prepared the ground for science, they were in general unsympathetic towards the humanist and religious reformers, whose controversies they were inclined to find either uninteresting or unintelligible. They turned their eyes to the future and saw a favourable prospect. They held that the new science was something essentially different from anything found in classical antiquity, let alone the barbarous middle ages; something which they themselves were adding to civilized life. Their attitude was similar to that taken by some sixteenth-century artists to the relation of their own work to classical models. Writing more and more in the vernacular, the new scientific propagandists stressed the material benefits brought by science and rational technology, most famously by the invention of printing, gunpowder, and the mariner's compass16, and by the general advance of industry, commerce, geographical discovery and medicine. The source of power over nature, as Francis Bacon was most emphatic in pointing out, was knowledge. The age began to bristle with works on scientific method and with schemes for scientific Utopias such as Campanella's City of the Sun (1623) and Bacon's New Atlantis (1627). Explanations of the past stagnation and present progress of science were used to provide the formulae for future advance. Common to them all was the stress laid, in varying degrees, on experiment, mathematics, and the usefulness of science. All were optimistic about the success that could be expected from the right organization and methods. This optimism about the progress of humanity through natural knowledge was accompanied by a renewed hope in nature itself. In its light the sixteenth-century doctrine that the powers of nature and mankind were in decay was rejected, later to be replaced by the eighteenth-century belief in their limitless perfectibility17. The most influential of the early seventeenth-century analyses of the history of science and of contemporary science were undoubtedly those by Francis Bacon and Descartes. Their accounts were comple16

Cf. R. F. Jones, Ancients and Moderns, and ed. (St. Louis, 1961). See J. B. Bury, The Idea of Progress (London, 1920); Jones, op. cit.; H. Baron, Towards a more positive evaluation of the fijteenthcentury renaissance, « Journal of the History of Ideas », iv (1943) 21-49, The ' Querelle ' of the Ancients and Moderns as a problem for renaissance scholarship, « ibid. », xx (1959) 3-22; V. I. Harris, All Coherence Gone (Chicago, 1949). Cf. G. Hakewill, An Apologie of the Power and Providence of God in the Government of the World, or An examination and censure of the common errour touching natures perpetuall and universall decay, 3rd ed., revised and augmented (Oxford, 1635). 17

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mentary and comprehensive, and they became the starting points for disagreement as well as for development. Bacon stressed experiment and utility; Descartes stressed mathematics and utility. This combination provided the standard two-fold formula for future progress. Both writers used history, according to the commonplace repeated in Sir Walter Ralegh's phrase, «to teach by examples of times past, such wisdom as may guide our desires and activities» 18 . In both, the key to their conceptions of scientific method can be found in their view of the history of science. In his peremptory references to the history of philosophy, Descartes described how he found that only in mathematics, pure and applied, had there been any grasp of truth 19 . His analysis of scientific method was aimed at realizing the ideal of a «universal mathematics» embracing all the sciences. Bacon went into the history of science much more thoroughly than Descartes and offered the first detailed modern sociological and historical analysis of the conditions for, and causes of, scientific progress and decline. In the Advancement of Learning (1605) Bacon divided the study of human history into three kinds, civil, ecclesiastical, and literary, each with its own sources and problems. In his discussion of the third kind, he set out a remarkable design for an intellectual history that would not only include the origin and development of scientific thought in different societies, but would also relate scientific progress and decay to the disposition of the people and their laws, religion and institutions. Bacon had called for something which he found lacking in his time, a history of «the general state of learning to be described and represented from age to age, as many have done the works of nature and the state civil and ecclesiastical; without which the history of the world seemeth to me to be as the statua of Polyphemus with his eye out; that part being wanting which doth shew the spirit and life of the person». He wanted something more than the « small memorials of the schools, authors, and books» in the « divers particular sciences» and «barren relations touching the invention of arts or usages». What he wanted from intellectual history, he wrote, was «a just story of learning containing the antiquities and originals of knowledges, and their sects; their inventions, their traditions; their diverse administrations and managings; their flourishings, their oppositions, decays, depressions, oblivions, removes; with the causes and occasions of them, and all other events concerning learning, throughout the ages of the world; I may truly affirm to be wanting. The use and end of which work I do not so much design for curiosity, or satisfaction of those that are the lovers of learning; but chiefly for a 18 19

History of the World, book ii, ch. xxi, § 6 (London, 1614) 537. Descartes, Regulae ad directionem tngfftii, iv; Discours de la methods, i.

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more serious and grave purpose, which is this in few words, that it will make learned men wise in the use and administration of learning» 20 . This was in effect a plea for the study of the history of science, and characteristically, its conclusions were to be applied in contemporary problems. Bacon complained in the preface to The Great Instauration that in the intellectual sciences there was no search for new knowledge. They «stand like statues, worshipped and celebrated, but not moved or advanced)). The mechanical arts had shown some progress, just because they were by their nature in close touch with experience and practice. Experiment, as he said famously, was essential for the a inquisition of nature» 21 ; it was the essential method of discovery; but in the past it had not been properly conceived. In the Novum Organum (1620) he described how, on the one hand, philosophers and men of learning had failed to test their theories critically by a comparison with systematic experiments and observations; whereas, on the other hand, the large number of experiments made in the course of technological practice provided few «of most use for the information of the understanding»22. Philosophers had spun out general systems with too little reference to facts, while «mechanics» were only interested in particular technical problems and did not search for causes. Bacon believed that they should combine their interests. His new experimental science was a method of acquiring knowledge of causes, tested by designed experiments, that would provide both explanations of nature and a rational basis for technology. Bacon's analysis, in the Advancement of Learning and the Novum Organum, of why science had not progressed in the past provided later historians in the seventeenth and eighteenth centuries with their basic views on the subject. He said that the sciences had fluorished during only three short periods of history: among the ancient Greeks, among the Romans, and, recently, among the nations of Western Europe. But even in those relatively favourable periods scientific progress had not been as great as it should have been. He gave several reasons for this. Besides the lack of understanding of the experimental method and of an effective approach to the ' inquisition of nature ', he emphasized the lack of opportunity for a proper scientific education, of a scientific profession commanding proper respect and position, and of government 20 Francis Bacon, Advancement of Learning, book ii. See P. Smith, A History of Modern Culture, i (London, 1930) 255-7; H. Butterfield, The history of science and the study of history, « Harvard Library Bulletin », xiii (1959) 329-47; P. Rossi, Francis Bacon: From magic to science (London, 1968). 21 Instauratio magna, in Francis Bacon, Worlds, collected and edited by J. Spedding, R. L. Ellis and D. D. Heath, i (London, 1864) 126, 132, iv (1860) 14, 20; cf. Novum organum, i. 98. 22 Novum organum, i. 99; see i. 78-105.

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interest in science. Scholars had concentrated their main attention on other disciplines, the Greeks and Romans on moral philosophy and the moderns on theology. There were no full-time scientists, except perhaps for «some monk studying in his cell, or some gentleman in his country house » 2 3 . In the universities « natural philosophy» was studied only at an elementary level as a preparation for some other profession; there was no proper scientific education, including the essential training in experiment, and there was no scientific profession in which men could specialize in particular sciences and earn a proper living. This state of affairs « hath not only had a malign aspect and influence upon the growth of sciences, but hath also been prejudicial to states and governments» 24 . In fact, Bacon's blunt appraisal remained largely applicable down to the university reforms and the development of a scientific profession in the nineteenth century. He said that the goal of natural science had not been appreciated: to enrich human life with new discoveries and powers. The right method of discovery had not been understood: designed experimentation, ordered in relation to «axioms». There had been too great a respect for « antiquity»: but true antiquity belonged to «our own times a 2 5 , with all the experience of earlier centuries behind them. There was too much complacency with existing knowledge and technical achievements, and too great a readiness to assume that nature was inscrutable and could not be mastered or understood. There was the fear that progress in science and philosophy would « end in assaults on religion » 2 6 . Above all there was a lack of rational optimism. Bacon's attitude to the history of science, his claim that his analysis had not only exposed the mistakes of the past but also provided the means of avoiding them in the future, above all his emphasis on the past neglect of experiment and the dangers of philosophical systems and his optimism for the future of scientific discovery and its applications, all deeply influenced the outlook of the founders of the Royal Society and contributed to the emotional energy behind their enterprise. They criticised Bacon for his neglect of mathematics, but they soon remedied that themselves; they also respected Descartes. The same combination of beliefs and attitudes can be found in the Academic royale des Sciences. In the literary war between the Ancients and Moderns, by the end of the seventeenth century the Moderns were able to use the recent progress of science to gain total victory over the humanist rearguard and to convince the educated public of the superiority of modern over ancient achieve23 24 25 26

Ibid., i. 80; see i. 78-79. Advancement of Learning, book ii; cf. book i, and Novum organum, i. 90-91. Nov. org., i. 84; cf. i. 80-81, 85, 103-5. Ibid., i. 89; cf. i. 92-94.

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ments in the arts and sciences. The scientific revolution was seen as the most important part of the recent revival of the West. «Is it not evident», John Dryden wrote in 1668, not in a scientific work but in his Essay of Dramatic Poesy, «in the last hundred years (when the study of philosophy has been the business of all the Virtuosi of Christendom), that almost a new Nature has been revealed to us? — that more errors of the school have been detected, more useful experiments in philosophy have been made, more noble secrets in optics, medicine, anatomy, astronomy, discovered, than in all those credulous and doting ages from Aristotle to us? — so true it is, that nothing spreads more fast than science, when rightly and generally cultivated»17. During the second half of the seventeenth century and the first half of the eighteenth, the new science radically changed the type of culture of educated Europeans. It had been demonstrated that experimental and mathematical analysis could solve interesting problems with useful applications. Theology and literary culture began to give way as dominant interests to a concern with the aims, methods, achievements, applications and consequences of science. Science began to develop as one of the learned professions, earning respect and sometimes reward, especially in France where the government gave direct support. Scientists acquired a new sense of solidarity among themselves. This is evident both in Thomas Sprat's History of the Royal Society, published in 1667 partly to justify the policy of the Society,- and in the Eloges, obituary biographies of great scientists of all nations, which Fontenelle wrote in the exercise of the office of permanent secretary of the Academie des Sciences, which he held from 1699 till 1741. Fontenelle popularized the scientific movement; books on botany were written for young ladies and on mathematics for the general public; Voltaire created literary events with his exposition of English empirical philosophy and science in his Lettres philosophiques, or Lettres sur les Anglais (1734), and with his exposition of Newton's natural philosophy. Leading writers on many subjects — Locke, Hume, Vico, Montesquieu, Rousseau, Diderot, Condorcet, Goethe —• studied science seriously and explored the possibility of extending its methods, the only sources of certain knowledge, to all aspects of human life, behaviour, and history. Just as science had discovered the fixed laws of nature, so they would try to discover those governing human behaviour and the progress and decline of civilizations. And just as scientific knowledge could be applied in technology, so they wrote history not simply to interpret society but also to change it. 27 See P. Smith, A History of Modern Culture, 2 vols. (London, 1930-34); L. M. Marsak, Bernard de Fontenelle: the idea of science in the French Enlightenment, « Transactions of the American Philosophical Society », n. s. xlix. 7 (1959); above n. 17. Cf. W. Wotton, Reflections upon Ancient and Modern Learning (London, 1694).

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It was these interests and attitudes that initiated the first detailed studies of the history of science, and of science as part of civilization. A history of medicine by Daniel Le Clerc published in 1696 is an early example of the Baconian analytical approach to intellectual history in a particular science. «There is», he wrote, «abundance of difference between a History of Physick, that is, a collection of all that relates to their persons, the titles, and number of their writings, and a History of Physick, that is, to set forth the opinions of the Physicians, their Systems, and Methods and to trace step by step all their discoveries.... This History ... is obliged to penetrate into the very soul of every age, and every Author; to relate faithfully and impartially the thoughts of all, and to maintain everyone in his right, not giving to the Moderns what belongs to the Antients, nor bestowing upon these latter what is due to the former; leaving every body at liberty to make reflections for himself upon the matters of Fact as they stand related"28. Leibniz followed Bacon in proposing the writing of a history that would include science, literature and religion as well as politics29. In 1751, in the Preliminary discourse of the Encyclopedic, D'Alembert wrote: «The metaphysical exposition of the origin and of the liaison of the sciences has been of great use to us in forming the encyclopaedic tree; the historical exposition of the order in which our sciences have followed one another will be no less advantageous in enlightening us on how to transmit these sciences to our readers» 30 . The next year, 1752, saw the publication of Voltaire's Siecle de Louis XIV, followed in 1756 by his Essai sur les moeurs et I'esprit des nations, written to convince his friend Madame du Chatelet, the translator of Newton's Principia into French, that the study of history could be as interesting as that of mathematics and natural science and could give rise to principles of equal importance31. In these works Voltaire set out to give an example of history written en philosophe, to discover the causes of progress and decline and to teach by the results. One of his greatest achievements was to replace the picture of world history guided by the hand of providence, as presented by Bossuet, by one in which events were explained by natural causes. His contemporaries Maupertuis and Buff on were doing the same 28 D. Le Clcrc, The History of Physic^, Author's preface (London, 1699); ist ed., Histoire de h medecine (Genevre, 1696). See F. N. L. Poynter, Medicine and the historian, « Bulletin of the History of Medicine », xxx (1956) 424; cf. W. Pagel, Aristotle and seventeenth-century biological thought, in « Science, Medicine and History », essays in honour of Charles Singer, i (Oxford, 1953) 509. 29 G. W. Leibniz, Sdmtliche Schriften, hrg. von der Preussischen Akademie der Wissenschaften, I Reihe, i (Darmstadt, 1923) 91, 103 (1670). 30 Cf. Smith, op. cit., ii, 250 sqq. 31 See Voltaire's introduction to the Siecle de Lotus XIV; his « La philosophic de 1'histoire », printed as an introduction to the Essai; and his « Remarques pour servir de supplement a 1'Essai », i-iii, xvii.

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for the history of nature, of the earth and its plant and animal inhabitants through geological time32. Voltaire's basic theme was a survey of European civilization from the time of Charlemagne to his own day, but in pursuing his analytical objective he cast the civilization of Europe against the background of world history. His account included a description of the history of the arts and sciences, religion, politics and commerce, populations and social structure, geography, climate and natural resources of ancient Egypt, Babylon, Greece and Rome, India and China, and of the life of savages, for comparison with the history of Europe. Science had provided him with a model of analytical and comparative methods of investigation; in return, he included in his comparative history of civilization a description of the history of science and technology. Other historians in the second half of the eighteenth century, notably Hume, Robertson, Gibbon and Condorcet, gave similar recognition, albeit sometimes peremptory, to the influence of science and technology in history. The same period saw the appearance of specialized histories of particular sciences. The publication of J. E. Montucla's great Histoire des mathematiques, in fact a history of the physical sciences, in 1758 was followed by other works of varying value including Joseph Priestley's histories of electricity and optics and J. S. Bailly's history of astronomy33. At the end of the century and in the early nineteenth century the succession continued with the historical writings of Laplace, Cuvier, Thomas Young, Delambre and, later, of Guglielmo Libri and William Whewell. Auguste Comte now succeeded Francis Bacon as the formative influence on the historiography of science34. But by this time the general character of historiography had changed: it had become more accurate, but also more restricted. The eighteenth-century historians whose outlook had been formed by the intellectual revolution of early modern times may have seen history in the mirror of their own aspirations. They drew from the new science their model of rational investigation; in repaying their debt, by making the history 32 See Bury, above n. 17; A. O. Lovejoy, The Great Chain of Being (Cambridge, Mass. 1936); A. C. Crombie, P. L. Moreau de Maupertius, F. R. S. (1698-1759), precurseur du transformisme, « Revue de synthese », Ixxviii (1957) 35-56; B. Glass, O. Temkin, W. L. Straus, jr. (editors), Forerunners of Darwin: 1745-1859 (Baltimore, 1959); J. Roger, Les sciences de la vie dans la pensee franfoise du XVIII* siecle (Paris, 1963). For the parallel interest in the history of nature and the history of mankind cf. R. Hooke, « A Discourse of Earthquakes », Posthumous Worfa, ed. R. Waller (London, 1705) 291, 334, 426-7, 433-6; Fontenelle, Histoire de I'AcadSmie Royale des Sciences, Annee 1710 (Paris, 1731) 22; Button, Les Epoques de la nature, ed. critique, par J. Roger (Paris, 1962); A. C. Crombie and M. A. Hoskin, The scientific movement and the diffusion of scientific ideas, in « New Cambridge Modern History », vi (Cambridge, 1969) 60-71. 33 Cf. Bailly, Lettres sur I'origine des sciences, et sur celles des peuples d'Asie, addresses a M. dt Voltaire (Londres et Paris, 1777). 34 Cf. A. Comte, Cours de philosophic positive, i, Premiere lec.on (Paris, 1830); W. Whewell, Philosophy of the Inductive Sciences, 2nd ed., ii (London, 1847) 320 sqq.; J. S. Mill, Auguste Comte and Positivism, 2nd ed. (London, 1866) 6-8; Bury, op. cit., ch. 16.

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of science and technology part of the history of civilization, they may have written polemically in order to extend the reign of ' reason' in their own day. The political and constitutional historians who dominated nineteenth-century historiography no longer felt that debt and they made history into the history of government. One reason for this may have been the influence of the classical seminar in German universities on the nineteenth-century conception of historical research. At the same time there was a hardening of the division in university education between science and the humanities. Classically trained historians excluded from their consideration all aspects of life not conventionally included among the 'humanities'. Also, during this formative period of nineteenth-century historiography, the general upset in the structure and concepts of government following the revolutionary wars in Europe, and the business of acquiring and governing empires, gave constitutional and political history an immediately topical and practical interest. Historiography must perhaps always reflect the problems of its own time. The character of life in our own day gives a new relevance to the eighteenth-century historians whose view included the whole of civilization. The present interest in social, intellectual and scientific history and in the comparative method are in a sense a return to the ideas with which mature modern historiography began in the age of Voltaire. Once more, historians in their analysis of human behaviour and human society are seeking enlightenment from all aspects of civilized life. Historiography is again becoming the study of civilization as a whole, with the potentiality of providing a bridge, instead or reflecting a division, between the scientific and humanistic sides of our education.

23

The Origins of Western Science'

The purpose of this book, according to the preface, seems to be to replace earlier accounts of ancient and medieval science, rather prominently for the latter my Augustine to Galileo, first published in 1952 but revised and greatly enlarged in 1959. Bruce Eastwood concludes in his generous but valedictory essay on my book and its influence in Isis (Ixxxiii, 1992, pp. 84-99): 'We can now reasonably hope for an up-to-date textbook on medieval science in David Lindberg's forthcoming survey'. Mine 'has completed its useful life' but as 'an old friend' it 'remains a connection to historical controversies and philosophical commitments of our disciplinary past'. Perhaps so, perhaps not, but it may be worth mentioning that the latest edition in English published by Harvard (1979) is still on the market and that of the eight editions in foreign languages, that in Italian (reprinted in 1982) remains especially active, and that in Spanish has been reprinted five times since its first publication in 1974. The Greek edition was handsomely reprinted in 1992, and others are in prospect. A book like The Beginnings of Western Science needs a vision of its subject, with the main lines of its perspective illustrated by telling details. Instead we have here a survey, written in an elementary style seemingly for a popular public knowing very little. 'My concern' Dr Lindberg writes, 'will be with the beginnings of scientific thought1 (p. 3), not with technology or methodology or anything else, but with the ideas and contents of science, or less ambiguously, natural philosophy. Some very brief indications or prehistoric attitudes to nature and of ancient Babylonian and Egyptian mathematics and medicine lead him to the true beginnings of scientific theory with the Greeks. The history of scientific thought, as I put it (History of Science, xxvi, 1988, pp. 1-12; above, ch. 1) is the history of a vision explored and controlled by argument. It is a vision and an argument initiated by ancient Greek philosophers, mathematicians and physicians in their search for principles at once of nature and of argument itself. By natural science we mean then a

David C. Lindberg, The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600 B.C. to A.D. 1450 (The University of Chicago Press, 1992).

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specific vision, created within Western culture, at once of knowledge and of the object of that knowledge, at once of natural science and of nature. We may trace the characteristically Western tradition of rational science and philosophy to the commitment of the ancient Greeks, for whatever reason, to the decision of questions by argument and evidence, as distinct from custom, edict, revelation, authority or whatever else. Of course all people as rational beings may decide questions by argument and evidence. It was the Greek style of rationality to make this explicit by the analysis of the reasoning involved, in the manner of Socrates. The Greeks developed thereby the conception of a problem as distinct from a doctrine. At the same time by deciding that, among the many possible worlds as envisaged in other cultures, the one existing world was a world of exclusively self-consistent and discoverable rational causality, they committed their scientific successors exclusively to this effective direction of thinking, and closed to them elsewhere still open visions of things. They introduced in this way the conception of nature, comprising a rational scientific system, in which formal reasoning matched natural causation, so that natural events and reasoned conclusions must equally follow exactly from true principles. Hence the two fundamental conceptions from which the characteristic style of all Western rational thinking has followed: causal demonstration and formal proof. The Western scientific movement has been concerned with man's relations with nature as perceiver, knower and agent. It can be identified most precisely among the great historical cultures as an approach to nature effectively competent not only to solve problems, but also to determine what counts as a solution, whether in particular cases or in general systems of theoretical explanation. Thus it offers rational control of subject-matters of all kinds, from mathematical to material, from ideas to things. A similar rational style is evident over the whole range of Western intellectual and practical enterprise, in ethics and metaphysics, in law, government and commerce, in drama and music, in the visual and constructive arts, and in technology and manufacturing. Of the essence of the scientific movement as a tradition have been its genuine continuity, even after long breaks, based on the study by any generation of texts written by its predecessors; its progress equally in scientific knowledge and in the analysis of scientific argument, for innovation is a product of continuity; and its recurrent critique of its practical and moral justifications. A subtle question then is what continued and what changed through different historical contexts, in the scientific argument and in the cultural vision through which experience is mediated, when education, experience and innovation could furnish options for a different future. The scientific argument comprises both the form and the subject-matter. It is obviously absurd, in analysing how a particular problem or phenomenon has been treated at a particular time, to consider the one without the other. But the same phenomenon may be treated in different forms or styles of argument, and a common form of argument may unite an assembly of diverse though cognate subject-matters. The Western scientific movement brought together

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within a common restriction to answerable questions a variety of forms or styles of scientific inquiry, demonstration and explanation, diversified by their subject-matters, by general conceptions of nature and the expectations they entail, by presuppositions about scientific cogency and validity, and by scientific experience of the interactions of creative thinking with testing, of programmes with their realisation, modification or rejection. The diversification and testing of these different forms of argument was the highly intellectualised product of many generations. A scientific style identifies certain regularities in the experience of nature which become its object of inquiry and define the questions put to the subject-matter within that style. The interactions between style and subject-matter then generate appropriate methods of inquiry and kinds of argument and evidence for finding acceptable answers. We can establish in the scientific movement a taxonomy of styles, distinguished by their objects of inquiry and forms of argument. Three were developed in the investigation of individual regularities, and three in the investigation of the regularities of populations ordered in space and time. The primary style invented by the Greeks was what I call postulation, in two different forms, mathematical and syllogistic. The former exploited the demonstrative power of geometry and arithmetic and eventually united all the mathematical sciences and dependent arts, from optics and music to mechanics, astronomy and cartography, under a common form of proof. The latter exploited the demonstrative power of logic as established by Aristotle in all the natural sciences as well as other subject-matters of philosophy. The second style I call the experimental argument, both to control postulation and to explore by observation and measurement the observable relations of more complex subject-matters in the search for their principles. Ptolemy used well designed experiments to control the postulations of optics and Galen did likewise to explore the operations of the ureters, the spinal cord, and other physiological phenomena. The experimental argument, in its various forms arid contexts, was logically designed to bring in experiment, with the necessary apparatus and instrumentation, at the relevant points of decision. The third style, hypothetical modelling, proceeds by exploiting the properties of a theoretical or physical artifact, which we know because we designed it ourselves, and with which we can simulate and thus explore and explain the phenomena of nature. Perhaps the most striking original model of all was Eudoxus's geometrical model of the cosmos, which transformed astronomy as developed with great arithmetical sophistication by the Babylonians into an entirely new style of scientific thinking. Hypothetical modelling was developed in a mature form by its transposition from art to science in early modern Europe: perspective painting was a perceptual model of the natural scene; Kepler solved the problem of the formation of the retinal image by using the camera obscura as a model of the eye; Descartes generalised the whole style. Taxonomy as the fourth style was again developed by the Greeks, notably Plato, Aristotle and Theophrastus, as a logical method of ordering variety in any subject-matter by comparison and difference, raising the question of

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discovering natural affinities. The fifth style, probabilistic analysis of contingent expectation and uncertain choice, was also broached qualitatively by Greek logicians and physicians and Roman lawyers faced with making decisions with incomplete but probable evidence, and it reappeared in medieval treatments of similar cases. It was quantified practically in the fifteen and sixteenth centuries in dealing with insurance and other commercial questions, and theoretically in its two forms, analytic and synthetic, in the seventeenth century. At the same time came the explicit discovery of a new kind of regularity, the statistical regularities in adequately numerous populations of economic, medical and other events. Lastly, the method of historical derivation, or the analysis and synthesis of genetic development, was again used first by the Greeks in application to human cultures and civilisations, before being appropriated in early modern Europe for the evolution of languages, of the Earth, and then later of living organisms. The subject-matter of historical derivation was defined by the diagnosis, from the common characteristics of diverse existing things, of a common source earlier in time, followed by the postulation of causes to account for the diversification from that source. Each style then defines the questions to be put to its subject-matter, and those questions yield answers within that style. A change of style changes the questions put to the same subject-matter, as the Aristotelian analysis of motion in a qualitative taxonomy of causes was replaced, from the fourteenth to the seventeenth century, by its analysis into quantitative functional relations. Thus each style of questioning can exclude others, a point made vigorously in this example by Galileo. But usually different styles are combined in any particular research. Each style introduces a specific conception of causality, and hence the fundamental differences in the physical worlds envisaged by geometrical postulation, but qualitative taxonomy, and by the quantified mechanistic and the probabilistic conceptions of nature. Each style again introduces new questions about the existence of its objects in nature as distinct from their being products of its methods of abstraction, classification, measurement, sampling and so on, or of its language. Lindberg's survey is very different from the kind of intellectual analysis just outlined. He begins his sketch of ancient science, occupying about a third of the book, with a rapid conventional run through Greek ideas from Homer and Hesiod to Plato and Aristotle. He rightly indicates that the fundamental questions for Greek philosophy were those of the nature of the identity persisting through change, causality, the structure of the cosmos and its relation to its first cause, and the nature and knowability of that cause. No sensible historian is likely to disagree with the statement that the 'proper measure of a philosophical system is not the degree to which it anticipated modern thought, but its degree of success in treating the philosophical problems of its own day.' (p. 67), but similar remarks dotted through the book seem to anticipate a fairly uneducated audience. Next come a brief account of Hellenistic natural philosophy with some interesting references to ancient

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schools and education, followed by a sketch of the Greek mathematical sciences, essentially of astronomy, optics, and the science of weights. He indicates correctly that both Euclid in his optics and Archimedes in his analysis of the balance exploit the demonstrative power of geometry to develop experimental sciences without experiments. An illustration of scientific style not mentioned is the Babylonian source of Ptolemy's tables correlating planetary positions, which became the model for those correlating angles of incidence and refraction. The science of optics was later substantially developed by astronomers. After this comes an account of Greek and Roman medicine, dealing with both clinical diagnosis and physiology from Hippocrates to Galen. The case histories and rational diagnostic procedures in the Hippocratic corpus (with their more primitive antecedents in the very different contexts of Egyptian and Babylonian medicine) matched the sophistication of the mathematical sciences, while the systematic physiological theory culminating the Galen matched in the microcosm of man the theory of the macrocosm. No mention is made of Galen's well designed experimental investigations which were to become a model for William Harvey. The narrative of ancient science concludes with the Roman popularisers and encyclopedists, most substantially Pliny, Latin translations and epitomes of Greek science notably by Calcidius with his version of the Timaeus, and Boethius, with a brief account of Roman and early Latin medieval education. There is no mention of the basic importance of Cicero as the author of the essential Latin philosophical terminology translated from the Greek, from which came that of modern European languages. It would have been useful also to include some account of the development of technical language and terminology, a subject pioneered in philosophy by Etienne Gilson and Alfonso Maieru and in science and mathematics notably by students of fourteenth-century kinematics and dynamics. No mention is made either of the development of vernaculars for science and philosophy, in which Dante, Geoffrey Chaucer and Nicole Oresme played so prominent a part. Another important omission, in a brief discussion of the role of Christianity, is the confrontation of Greek philosophy with the Hebrew and Christian theology of creation over the fundamental nature of God's relation to the world and to mankind. The confrontation began systematically in the first century B.C. with Philo Judeaus of Alexandria, the last great thinker in the line of Hellenised Jews. Directly and indirectly, through Lactantius, Augustine of Hippo, and other routes, Philo affected profoundly later Jewish, Christian and Moslem thought on this question and with it on natural philosophy. Philo accepted the Greek conception of the order of nature determined by unchanging causes, but the source of that order was not the Platonic god of the Timaeus, who made the world by a necessary act of his own perfection out of pre-existing matter, nor the eternal divine reason of Aristotle from which the world emanated as a necessary consequence of causes discoverable by human reason, nor the material divinity of the Stoics. The God of Abraham was in no way necessitated, but acted with an entirely free

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omnipotence to create ex nihilo a world entirely separate from himself, for reasons unknowable by man apart from divine revelation. Philo used the term logos for the principles on which God modelled his creation, like a city fashioned within the mind of an architect, from which followed with invariable regularity all the operations of this universe. But God could overrule these regularities just as he could have created another kind of universe had he so chosen. Philo saw in Scripture both literal and underlying meanings, from which he could apply the analogy of law to God's actions. In the Christian context the created world was then reduced to a mechanism operating according to a system of laws. Lactantius likened God's creation to Archimedes's modelling of the cosmos with his brass armillary sphere. Basil of Cappadocia likened it to a spinning top. The most pervasive route through which these ideas passed into Latin medieval thought was Augustine, for whom the naturales leges which God had ordained were the laws of measures, numbers and weights. He applied the concept of natural laws, or laws of nature, to the motions of the heavenly bodies, the generation of living things, and the development of the world itself pregnant with things to come. God could then be discovered in the great open book of nature, as well as in the revealed book of Holy Scripture. These ideas were to become fundamental principles of Western medieval and early modern natural philosophy. See my 'Infinite Power and the Laws of Nature: A Medieval Speculation' in L'infinito nella scienza, a cura di G. Toraldo di Francia (Roma, 1987) 223-43 (reprinted above, ch. 6); and with J.D. North, 'Univers' in Les caracteres originaux de I'Occident medieval, ed. J. Le Goff et J.-C. Schmitt (Paris, forthcoming). A brief and inadequate chapter on Byzantinum and Islam skips through Hellenistic commentaries on Aristotle, the translation of Greek science into Arabic, and the Islamic scientific achievement and decline, on which it raises some interesting questions but does little to explore them. No reference is made to the fundamental work of Roshdi Rashed and GUI Russell on Arabic optics and on the cultural situation of Islamic science in general. Next we have a standard account of the revival of learning in the West from the Carolingian reforms to the development of education in the schools of the eleventh and twelfth centuries, natural philosophy with its expansion through the translations from Greek and Arabic into Latin during the twelvth and thirteenth centuries, and the assimilation of this new learning in the universities. The confrontation of Aristotelian metaphysics with the Christian theology of creation again led to a vigorous defence of divine omnipotent freedom and human moral responsibility against determinist interpretations of Aristotle. On these central issues in the condemnations of 1270 and 1277 the recent work of Luca Bianchi (not cited here) has thrown new light. A chapter on the medieval cosmos summarises studies of Grosseteste, the terrestrial region with a brief sketch of cartography and of Jean Buridan and Nicole Oresme on the Earth's possible rotation, astronomy and its instrumentation, and astrology. This is all useful and the illustrations are excellent, but one misses any discussion of Richard of Wallingford or Chaucer and the profound and precise

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studies of them by John North. Also missing in a book making the claims of its subtitle is any reference to Dante. Coming to the physics of the sublunar region, after a few pages on matter and alchemy, Lindberg reaches the fundamental studies of his mentor, and his mentor's mentor, on the fundamental science of motion. This is well described in a few pages on the conception of motion in the thirteenth and fourteenth centuries, its mathematical representation, and dynamics and its quantification. Next comes the science of optics on which Lindberg himself has published good work, especially on the pinhole camera. The essential sources were Aristotle, Euclid, Ptolemy and Alhazen, with for the eye also Galen, and the essential medieval authors were Roger Bacon and Witelo. The study of the history of optics were pioneered by Vasco Ronchi, and that of medieval optics by myself, followed by A.I. Sabra, Lindberg, Stephen Straker with his fundamental Kepler's Optics (1971; Ann Arbor, Mich., 1980) and 'Kepler, Tycho, and the "Optical part of astronomy": The Genesis of Kepler's Theory of Pinhole Images' in Archive for History of Exact Sciences, xxiv (1981) 267-93, and later by others. Ronchi made his mistakes, as who does not, but he established the field in which we have all worked and put us all in his debt, just as Pierre Duhem did for medieval science in general. I note that Lindberg does not cite me in his section on medieval optics. This is a mistake, because my original monograph (1967) on the subject which he used is well known and is now readily available in my collection Science, Optics and Music in Medieval and Early Modern Science (London, 1990), and my more recent study, 'Expectation, Modelling and Assent in the History of Optics: i, Alhazen and the Medieval Tradition; ii, Kepler and Descartes', has a direct bearing on some of Lindberg's controversial opinions, especially on Kepler's relation to the medieval tradition. This long article was published in Studies in History and Philosophy of Science, xxi (1990) 605-32, xxii (1991) 89-115 and is reprinted above, ch. 16. The last chapter of any substance is an account of medieval medicine and natural history written under the guidance mainly of Nancy Siraisi and Michael McVaugh. On the latter subject a strange omission is the classic work of Agnes Arber on herbals, and more recently there are the original and indispensable studies of the manuscript tradition by Evelyn Hutchinson, Wilma George and, as further evidence of activity in the field, by the contributors to Die Kunst und das Studium der Natur vom 14. zum 16. Jahrhundert, herausgegeben von W. Prinz und A. Beyer (Weinheim, 1987). Lindberg has missed the opportunity offered by this book to develop a systematic historical study of important themes showing the character of scientific thinking in particular contexts and its changes. For example, his references to experiment are minimal, even though this is a subject of lively and serious discussion by medievalists such as myself, Jole Agrimi and Chiara Crisciani, and others. There is no reference at all to Pierre de Maricourt and his systematic experimental investigation of magnetism, to be respectfully acknowledged by William Gilbert. The well designed systematic experimental investigation of the rainbow by Theodoric of Freiberg, with a telling use of

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models, is mentioned in three lines without any indication of the experimentation but only as offering 'an explanation very close to the modern one' (p. 253; no reference in the attendant footnote to my basic analysis in my Robert Grosseteste and articles in Science, Optics and Music). This questionable judgement entirely misses the opportunity to point out the change of scientific style between Theodoric and Descartes. The change involved the fundamental structure of scientific thinking and in the object of scientific inquiry. Theodoric looked by an Aristotelian taxonomic analysis for the necessary and sufficient causal conditions defining a particular phenomenon. Descartes looked for a general quantitative law from which this and other such phenomena could be quantitatively deduced. Another example is the general question of quantification in medieval physics. Theodoric gave a false figure for the maximum elevation of the rainbow, which Roger Bacon had reported correctly from measurements with an astrolabe. There is no reason to doubt that Bacon's contemporary Witelo (only a passing reference by Lindberg) carried out original experiments which he described showing the production of colours by refraction through hexagonal crystals and spherical glass vessels filled with water, but there is every reason to doubt whether he made his alleged experimental measurements, like those of Ptolemy, correlating angles of incidence and refraction (as I pointed out in my Robert Grosseteste, pp. 223-5, and in my article of 1961 on quantification reprinted in Science, Optics and Music, p. 79). Why was there such manifest indifference to actual measurement? As I showed in this article, we must look at the context. Physics as developed from Aristotle in the universities, even the powerful procedures for representing qualitative change quantitatively leading to new sciences of kinematics and dynamics, required no reference to experiment or measurement in its internal logic, nor was this imposed by external professional or practical pressure. Experiments in the academic context were made in the mathematical scientiae mediae, notably optics, or in the realm of natural magic like magnetism. Accurate measurements were made when they were required by practical need as in astronomy. In my article I showed by comparing the treatment of three quantities, time, space and weight, in the academic context and in that of the practical arts, that it was practical demand that produced consistent measurement. The penetration of causal physics by the concepts of the mathematical scientiae mediae profoundly affected the whole structure and style of scientific thinking. This is evident in the influence of the Timaeus in the twelvth century; in the distinction by Grosseteste between the primary mathematical properties of matter and the secondary sensory qualities they produced in us; and in the conceptual shift in the fourteenth century that moved the object of inquiry away from the definition of natures to the discovery of relations between quantities expressible by what became algebraic functions. Corresponding to this was the use of the term laws of nature (leges naturae) by Roger Bacon in a scientific sense for the laws of reflection and refraction, with the notion of a universal nature constituted by such laws (Science, Optics and Music, pp. 68-9,

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77-8,148-50). In the end from Galileo onwards it was within the mathematical middle sciences that physical problems were formulated, so that the certification of their conclusions by measurement came to yield there, and not in the traditional conception of causes, the only true science of nature that could be discovered. It is a serious omission, both for understanding the scientific thinking and for relating it to its cultural context, to exclude from a book like this a discussion of the practical rational arts. The ingenious mechanism sketched in the thirteenth century by the architect Villard d'Honnecourt, the mechanical clock itself, the planetaria of Richard of Wallingford and Giovanni de' Dondi in the fourteenth century, and many other devices, were all rationally designed to facilitate the control of movements and the representation of quantities, the last two by academic men. Scientific instruments, notably in astronomy, were a product of the intercourse between theory and practice. Mechanisms also provided analogies for scientific theory, as they did for Jean Buridan and Nicole Oresme in likening the created world to a clock set going by God. At the end of the fourteenth century the universities went into decline and the leaders in original thought and action became a different group, largely outside them, of what Leonardo Olschki called artist-engineers. Their expertise lay in the rational control of materials, processes and practices of all kinds, from painting to music, from architecture to machinery, from cartography and navigation to accountancy. They brought about a general transformation of European intellectual life. An obvious example is the control of visual representation by means of the linear perspective invented by Filippo Brunelleschi at the beginning of the fifteenth century and explained by Leon Battista Alberti in his Depictura (1435). The analogy of artificial devices used to explain and apply perspective in painting came later to transform the science of vision. As I have shown in my article on Alhazen and Kepler (1990-91) mentioned above, using Straker's excellent account of the camera obscura, Alhazen in his brilliant geometrical model of ocular physiology did not make the reception of the forms of visible objects in the eye a purely geometrical inanimate process, as it was in inanimate transparent bodies, but a process modified geometrically by the sensive power in the receptor. Kepler, by taking the inanimate camera obscura as a true model of the eye, made ocular geometry a purely physical process and, by separating this from the questions of sensation and perception that had confused the issue since antiquity, demonstrated the formation of the image on the retina. Certainly, as Lindberg likes to insist, Kepler used his knowledge of existing optical theory in making his analysis: what else? His solution required a radical conceptual change, facilitated by the innovations and the innovative mentality of the rational arts. Aspects of this subject are well presented in three recent books: Science and the Arts in the Renaissance, edited by John Shirley and David Hoeniger (Washington, D.C., 1985), The Science of Art by Martin Kemp (Yale University Press, 1990), and The Heritage of Giotto's Geometry: Art and Science of the Eve of the Scientific Revolution by Samuel Y. Edgerton, Jr.

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(Cornell University Press, 1991). To conclude this litany of omissions, a book like this should address a further important aspect of the mentalities involved, the perception or otherwise of original progress by the natural philosophers building on the recovery of ancient learning: see my article 'Some Attitudes to Scientific Progress: Ancient, Medieval and Early Modern' (1975) reprinted in Science, Optics and Music. In my article 'Historical Commitments of European Science' (1982), also reprinted in Science, Optics and Music, I wrote: We may see the origins of modern science in the recovery, exegesis and elaboration of the Greek conceptions of rational decision and proof and of a rational system by medieval and early modern Europe. The recovery was made in a series of responses to ancient thought by a new society with some different mental and moral commitments and expectations, with a different view of nature and of man and his place in nature and his destiny, a different theology, a different economy and a different view of technology, but also with a vision of continuity. Much light can be thrown upon the intellectual orientations of European society, in making these responses, by attention to its apprehensions of continuity or discontinuity with the past and programmes projected therefrom. When philosophers pictured themselves in the twelfth century as dwarfs standing on the shoulders of giants, or looked in the fifteenth century for guidance from a Hermetic wisdom of supposedly Mosaic antiquity, or insisted in the seventeenth century that they were doing something entirely new, they were all making evaluations of the past which entailed programmes for future action. The same applied to the evaluative use of the historical terms middle ages, renaissance, reformation, scientific revolution, enlightenment and so on. These may tell us more about the periods in which they were invented than about those to which they refer. To characterise the process by which the science of nature developed its identity within the intellectual culture of medieval and early modern Europe is not easy. We may distinguish three broad stages of intellectual response and orientation brought about by the recovery and exploitation and then transcendence of ancient models. Each acquired a characteristic style of formulating and solving its problems. With the first intellectual impetus given by the recovery of ancient philosophical, scientific and mathematical texts in the twelfth and early thirteenth centuries came a primary intellectual achievement. This was the grasp and critical elaboration by the philosophical community of the medieval schools and universities of the construction of a demonstrative explanatory system on the models of Euclid's geometry and Aristotle's physics and metaphysics. Together with this came a critical elaboration of logical precision, from methods formalised by Aristotle, for the control of argument and evidence to decide a variety of questions, including decision by calculation and observation and experiment. I continued: The movement of intellectual orientation generated in Western Europe first then an organised capacity to act with rational intent in the control at once of argument and calculation. It generated at the same time an organised capacity to control a variety of materials and practices. We may distinguish this matching of logical control of argument by a likewise theoretically designed and measured control of matter as the second stage of European response to ancient

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models. . . . The painters, sculptors, architects, engineers, metalsmiths, assayers, surveyors, navigators, musicians, accountants and so forth comprising this group generated an effective context for seeing and solving the exemplary technical problems shared by the mathematical sciences with the visual, plastic, mechanical, musical, navigational and commercial arts. Training in the arts provided for both theory and practical skill. Their practitioners responding to a diversity of particular demands brought about a general transformation of European intellectual life by their search for precise understanding and control of materials in a variety of circumstances. . . . At the same time, for the philosophical and scientific community at large, the nature and range of the effects that might be anticipated still remained at the beginning of the seventeenth century in varying degrees open questions. There was by no means general agreement on the kind of world men thought themselves to inhabit, how they should investigate it and what kind of explanation should be accepted as satisfactory, how best to control it and to what ends control was most desirable. In this context the confident establishment during the seventeenth century of the rational experimenter and observer as the rational artist of scientific inquiry, designed first in the mind and proceeding by antecedent theoretical analysis before execution with the hands, marked the culmination of European orientation in response to ancient scientific sources in its third stage. The experimental philosopher as the rational artist might make his analysis by means of theory alone, quantified as the subject-matter allowed, or my modelling a theory with an artifact analytically imitating and extending the natural original. Both artist and philosopher could obtain the effect sought only as Galileo put it 'according to the necessary constitution of nature. . . . For if it were otherwise, it would be not only absurd but impossible. . .' (Le Opera, ed. naz., ii, 155,189). Art then could not cheat nature, but by discovering, obeying and manipulating natural laws, with increasing quantification and measurement, art was seen to deprive nature of its mysteries and to achieve a mastery exemplified by rational prediction, whether in the representation of a scene or the prognosis of a disease or the navigation of a ship. Galileo himself marks the connection and transition between two great European intellectual movements: from the world of the rational constructive artist to that of the rational experimental scientist. It was above all as the designer of an explicit scientific style, providing a philosophical strategy for the sciences of nature, that he illuminates the specific identity of natural science within the contemporary intellectual scene (pp. 9-17). This article is based on the historiographical introduction to my Styles of Scientific Thinking in the European Tradition: The History of Argument and Explanation Especially in the Mathematical and Biomedical Sciences and Arts, 3 vols. (London, 1994). The work offers an analysis of these questions, some of them discussed above, from antiquity to the nineteenth century. In my Augustine to Galileo, under the heading The continuity of medieval and seventeenth-century science', I summarised 'the original contributions made during the middle ages to the development of natural science in Europe' (1959, 1979, same pagination ii, 117-30). These I list as being in the logic of experimental argument, the application of mathematics to physics, theories of space and motion, the technical arts, descriptive medicine and natural history aided by naturalistic art, and conceptions of the purpose of natural science and of its knowability. I continued:

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But when all is considered, the science of Galileo, Harvey and Newton was not the same as that of Grosseteste, Albertus Magnus and Buridan. Not only were their aims sometimes subtly and sometimes obviously different and the achievements of the later science infinitely the greater; they were not in fact connected by an unbroken continuity of historical development. . . . Apart from anything else, the enormously greater achievements and confidence of the seventeenth-century scientists make it obvious that they were not simply carrying on the earlier methods though using them better. But if there is no need to insist on the historical fact of a Scientific Revolution in the seventeenth century, neither can there be any doubt about the existence of an original scientific movement in the thirteenth and fourteenth centuries. The problem concerns the relations between them.

One of the indispensable contributions made by medieval Western Europe was to provide in the universities a secure institutional context for learning and teaching over a wide range of subjects: the seven liberal arts, the three philosophies (natural, metaphysical and ethical), and medicine, law and theology. No such context was established in the ancient or Islamic worlds, and this certainly left the natural sciences in a much weaker position in those societies than was achieved in the West. One important cause of the discontinuity between fourteenth and sixteenth century science was the decline of the universities. I went on to consider briefly 'what the scientists of the sixteenth and seventeenth centuries in fact knew of the medieval work, and how the similarities and differences of their aims may be characterised'. The answer is that they knew quite a lot, as we might expect. The universities revived in the sixteenth century, especially in Italy, and scientific activity revived with them; learning in general also found new institutions in the new philosophical, literary, artistic and finally scientific academies. As for the differences of aims, I characterised this by saying that the 'main interest of scientists since Galileo has been in the ever-increasing range of concrete problems that science can solve', whereas the medieval natural philosophers were 'primarily philosophers' interested rather in clarifying the kinds of problems addressed by natural science than in solving them in particular. I added: 'It was a direction of interest that could have been fatal to Western science'. But the direction changed. This is all old stuff, so what is the point of Lindberg's somewhat bizarre presentation of what he calls 'the continuity debate', starting with Duhem, quoting from the unrevised edition of my Augustine to Galileo (1952) and out of context from my Robert Grosseteste (1953), citing my old friend Alexandre Koyre's criticism in a nevertheless flattering review, and so on? I find myself credited with a 'defense of the continuity thesis' (p. 361). I confess that I find this 'debate' as it has 'erupted' (p. 357) especially in the United States something less than rivetting. The question of what continued and what changed from one period to another, and what at any time was thought to have continued or changed, is a subtle one, not only from medieval to early modern and not only for scientific thought. It needs and deserves subtle and sophisticated treatment, and scholarly respect for the real thought that has

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been given to it, not a rhetorical travesty. Since I seem to figure prominently in this comedy, I have quoted some of my own continuing thoughts on the subject above. Koyre greatly illuminated our understanding of Galileo, and much else, by his brilliant demolition of the older image of Galileo as primarily rather a dedicated experimenter than a theoretician, but he was not himself much interested in experimental science and he misinterpreted Galileo's attitude to experiment. I have discussed this in my articles 'Galileo Galilei: A Philosophical Symbol' (1956) and 'Alexandre Koyre and Great Britain' (1987), reprinted above, chs. 12,13. The history of the historiography of any subject can be of profound and valuable interest for historians, and one of the most interesting perceptions of it can come from the intellectual and social contexts of knowledge and beliefs and prejudices within which the historical vision of scholars like Duhem and Koyre developed. But that is beyond the range here. Lindberg terminates his book with a list of medieval scientific achievements somewhat different from the one I published in Augustine to Galileo (1959), but coming to the same rather obvious conclusion: something continued, something changed. The truly dramatic cultural change brought about with the emergence of the new mentality of the Renaissance man of virtu, the rational artist designing the control of all his thoughts and actions, between the scholastic natural philosophers and the seventeenth century rational experimental and mathematical scientists, is not noticed. Is this a 'landmark book' as the publisher claims on the back cover? I hardly think so. It misses the lively innovative thought and research into the subject that has continued since Federigo Enriques, Marshall Clagett and I and others published our early books, and indeed to which some of us continue to contribute. But it is written by a distinguished scholar who is also an experienced teacher, and it will offer a valuable introduction to many interesting aspects of the beginnings of Western science. Postscript

H.F. Cohen, in his eccentric The Scientific Revolution (Chicago, 1994) 105-10, 153, manages to characterize me in a way similar to the above (p. 476), citing Koyre on me but not me on Koyre (as above chs. 12, 13, cf. also ch. 1), and referring to nothing published by me after 1963. This has some bizarre consequences. He writes that "in the early eighties, William Wallace (roughly simultaneously with Adriano Carugo and Alistaire Crombie) established a direct link between Galileo and previous thought on nature through the Jesuit Collegio Romano" (pp. 109-10; cf. 281-2, 573 n. 99). Everyone familiar with this subject knows that Carugo discovered this link first during 1969-71 through Pereira and Toletus, then in 1975 through Carbone, that I discovered in 1971 the link through Clavius, and that we gave this information to Wallace in 1972: see above ch. 9 and ch. 10, n. 11 with Appendix (a), and my Styles of Scientific Thinking . . . (1994) 549-51, 766 nn. 165-6, with for historiography Part I, pp. 3-89 of this work.

Oh, what a tangled web we weave, When first we practice to deceive! (Walter Scott, Marmion v.17)

Appendix to Chapter 10 (a)

Sources and Dates of Galileos Writings [with Adriano Carugo] The essential facts of the discovery by Adriano Carugo and myself that Galileo used, for his three sets of scholastic essays, sources connected with the Jesuit Collegio Romano, are outlined above in Chapter 10 on pp. 167-74 and in n. 11; see also ch. 9. Further details are set out in my review of W.A. Wallace's Galileo and his Sources (Princeton, 1984) in the Times Literary Supplement (22 November 1985, pp. 1319-20) and in subsequent correspondence (3 January 1986, pp. 13, 23,14 February p. 165, 25 July p. 815, and 29 August p. 939). In that review and correspondence I addressed two questions: Wallace's treatment of the authorship of our discoveries on which his book is based, and his treatment of those discoveries. I shall comment here only on his conception of evidence concerning Galileos logical Disputationes (MS Galileiano 27). The evidence is quite specific: the correspondence between Carbone's Additamenta published in 1597 and Galileo's MS 27. There is also the accusation published long afterwards by the Jesuit Paolo Delia Valle (Latinized as Paulus Vallius) in his Logica (1622) that someone identified with Carbone (naming the Additamenta) had plagiarized his lectures given at the Collegio Romano in 1587-88. No such lectures have been found, nor is there any mention of them in Jesuit records at present known. Moreover, supposing the Carbone had plagiarized Delia Valle's lectures, there is no evidence whatsoever, either from the contents of the Logica or from other sources, to connect them with Galileo. Undaunted by this Wallace imagined a connection: namely that Galileo had used for MS 27 a set of Delia Valle's alleged lecture notes, that these were obtained for him by Christoph Clavius on his request, that Carbone had plagiarized the same notes which Delia Valle allegedly distributed to his students, thus accounting for the correspondence between his and Galileo's texts, and that MS 27 must have been written by Galileo 'around 1590' when he was mathematical lecturer at Pisa (Galileo and his Sources, pp. 9, 89-94). For each and every one of these speculative assertions there is no evidence whatsoever: about Galileo's alleged request, about Delia Valle's ghostly lectures and their alleged distribution, about Carbone's alleged plagiarism, and for the date. Early in 1588 Galileo, after visiting Clavius in

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Rome at the end of the previous year, exchanged some letters with him about the demonstrations he had given in his theorems on centres of gravity (Opere, x, 22-30; cf. above n. 17). Clavius suspected in these quotpetitur principium, and perhaps also in Archimedes. Galileo explained more precisely. Clavius remained unconvinced. The correspondence was entirely mathematical, with no reference to logic or to Delia Valle or any other Jesuit, as was that contemporaneously on the same subject with Guidobaldo del Monte (x, 2536). There is no evidence for any discussion of logic. The petitio principii is evidently catching. Since our paper was published Carugo has made a thorough examination of the two massive volumes of Delia Valle's Logica and compared it with Carbone and Galileo. He has written to me with his new conclusions as follows: I found no evidence that either was in any way dependent on Delia Valle. Although similar questions were discussed by all three, as well as by many other contemporary authors both in print and in manuscript (contrary to what we believed in 1983; above p. 169), using the same stereotyped terminology, there is no textual correspondence between either Carbone or Galileo and Delia Valle. Beyond that there is positive evidence that Delia Valle could not have been the source for Galileo. Focusing on questions treated by both, in particular the praecognitiones, the species demonstrationis and the regressus, I found that Delia Valle drew extensively from, and actually plagiarized, Zabarella's logical tracts on these topics, frequently reprinted from 1586. For example: Zabarella, Opera omnia, (Venetiis 1600): 'Liber de speciebus demonstrationis',

Vallius, Logica, ii, (Lugduni 1622): Disput. 2, Pars 3: 'De speciebus demonstrationis',

Caput iii: 'De demonstratione a causa remota' (p. 302).

Quaest. 2, Caput iv: 'Qualis debeat esse demonstratio a causa remota etc.' (p. 305a).

Demonstrationem a causa remota docet Aristoteles negativam semper construi et in secunda figura in Camestres. Cuius ratio est, quoniam causa remota ut plurimum est amplior effectu: quare ea posita, non ponitur necessario effectus; proinde non potest effectus affirmative colligi ex ilia causa; ea vero ablata, effectus ex necessitate aufertur . . .

Quando vero est demonstratio a causa remota, docet Aristoteles necessario de bere esse in secunda

In omni demostratione tres terminos esse oportet . . . Termini igitur erunt causa, effectus et subiectum

In omni enim demonstratione tres terminos reperiri necesse est; quare in hac demonstratione tres erunt

figura et in Camestres, ac prohinde

conclusionem illius semper debere esse negativam . . . Cuius ratio est, quia causa remota ut plurimum solet esse universalior effectu: quare ea posita, non ponitur necessario effectus; ergo non potest ex huiusmodi causa colligi effectus affirmative; tamen ilia ablata, aufertur necessario effectus . . .

Appendix to Chapter 10 tertium, cui ambo insunt, sive a quo ambo negantur; et causa ipsa remota erit terminus medius, effectus maior extremitas, subiectum vero minor extremitas . . .

termini: nimirum causa, effectus et subietum, cui utrumqe inest, vel de quo utrumque negatur; et causa remota erit medius terminus, effectus maior extremitas, subiectum minor extremitas . . .

In propositione quidem maiore manifestum est poni medium terminum cum maiore extremitate, pro inde causam et effectum. Quare maiorem necesse est esse affirmativam, quoniam ex effectu et causa non potest nisi affirmativa enunciacio fieri: non enim hoc illius causa esset, si alterum de altero negaretur.

In maiore autem propositione ponitur maiore autem extremitas cum medio termino, consequenter causa cum effectu. Quare maior debet esse affirmativa, quia de causa affirmari debet effectus vel de effectu causa, non autem negari, si propositio vera est fututa.

At vero si ea maior debeat esse universalis, oportet causam de effectu predicari, non effectum de causa: quam effectus, non potest effectus de causa universaliter praedicari.

Maior autem debet esse universalis . . . ergo debet necessario praedicari causa de effectu, non autem effectus de causa, quia cum causa sit universalior effectu, non potest de illo universaliter praedicari.

"Liber de speciebus demonstrationis", Cap. xix: "In quo ostenditur etiam respectu nostri nullam demonstrationem notificare propter quid est, quin notificet etiam quod est." (p.333).

Disp. 2, Pars 3: "De specie bus demons rationis", Quaest.3, Caput ix: "Ostenditur non posse per demonstrationem cognosci propter quid, quin simul cognoscatur an sit" (p.321 a).

Ostendere possumus quod non modo naturam demonstrationis spectando, verum etiam nos ipsos demonstrantes respiciendo, omnis demonstratio notificans propter quid est notificat etiam quod est, et nobis tradit novam utriusque cognitionem quam ante demonstratio nem non habebamus.

Non solum naturam demonstrationis considerando, sed etiam si nostri et intellectus demonstrantis ratio habeatur, omnem demonstrationem perfectam ostendere propter quid et an sit rei, ita ut semper nobis per huiusmodi demonstrationem nova cognitio adveniat et ipsius propter quid et an sit ... etiam si antea habita sit cognitio aliqua ipsius an sit.

Aristoteles in 39. particula secundi libri Posteriorum, reddens rationem cur ille, qui rem esse cognoscit sine cognitione causae, non cognoscat quid ea sit, hanc rationem adducit: quia ille neque quod res ilia sit cognoscit, nisi leviter et ex accidenti:

Quod possumus colligere ex lib.2. Post. Text. 8 vel 9, qui reddens rationem cur ille, qui cognoscit rem esse sine cognitione causae, non cognoscat quid ilia res sit, ait hoc ideo contingere, quia ille neque quod res sit cognoscit, nisi leviter et

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quum enim res ita cognosci debeat uti est, ut autem sit habeat a sua causa, sequitur tune vere cognosci quod ea sit quando per causam per quam est cognoscitur.

ex accidenti; quia cum res eo modo, quo est, cognosci debeat, et esse habeat a sua causa, ideo tune vere et perfecte cognoscitur esse, quando cognoscitur causa prop ter quam est.

Zabarella's detailed and subtly argued analysis of the mental process called negotiatio intellectus or mentalis consideratio, by which the cause discovered through the first phase of the regressus (demonstratio quia) becomes known perfectly and precisely and can thus constitute the starting point of the second phase (demonstratiopropter quid), was closely followed and often copied almost word for word by Delia Valle: Zabarella 'Liber de regressu', Caput iv: 'In quo declaratur qualis sit in regressu primus processus etc.' (pp. 350351).

Vallius Quaest. 2: 'Quid sit regressus demonstrativus et quomodo fiat', Caput iii: 'Ostenditur qualis sit processus in demonstratione quia, quae est prima in regressu.' (pp. 344345).

Cognitio nostra duplex est, alteram confusam vocant, alteram vero distinctam; et utraque turn in causa, turn in effectu locum habet.

Cum duplex possit esse rerum cognitio, altera confusa, altera distincta; et utraque possit esse vel in causa vel in effectu.

Effectum confuse cogniscimus quando absque causae cognitione novimus ipsum esse, distincte vero quando per cognitionem causae; ilia quidem dicitur cognitio quod est, haec vero propter quid et simul etiam quid est.

Effectum quidem tune distincte cognoscere dicamus quando cognosciumus ilium per cognitionem causae, quando vero cognoscimus sine hoc, confuse; et haec cognitio confusa vocatur quod est, alia vero propter quid, in qua simul etiam cognoscimus quid est.

Causa vero quatenus causa est per causam sciri non potest, quia causam aliam non habet; si namque causam habet priorem, earn habet quatenus est effectus, non quatenus est causa.

Causa temen quatenus causa non potest cognosci per causam, quia non habet aliam causam; et si habet, sub hac ratione non est causa, sed effectus.

Datur tamen causae qui que cognitio turn confusa, turn distincta: confusa quidem, quando ipsum esse cognoscimus, sed quidnam sit ignoramus; distincta vero, quando cognoscimus etiam quid sit et ipsius naturam penetramus.

Datur tamen illius cognitio confusa et distincta eodem modo quo datur congnitio effectus; ita ut tune confuse causa cognoscatur, quando illius esse seu existentia cognoscitur; tune vero distincte, quando illiusnatura penetratur.

Appendix to Chapter 10 Exemplum aliquod nobis proponamus, in quo ipsam regressus naturam melius inspiciamus . . . Sumamus demonstrationem Arist. in lib. I Physicorum, qua ex generatione, quae substantiarum est, ostendit materiam primam dari ex effectu noto causam ignotam: generatio enim sensu nobis cognita est, subiecta vero materia maxime incognita.

Qualis sit regies us facile intelligemus: id quod otime explicat Zabarella exemplo desumpto ex Arist. in lib. I. Phys. ubi ex generatione, quae convenit substantiis, ostendit materiam primam dari. Ex effectu omnibus noto, qui est generatio, investigat existentiam materiae nobnis ignotissimae, quae est illius generationis causa.

Caput v: "Quod facto primo processu non statim regredi ad effectum possumus, sed mediam quandam considerationem interponi necesse sit" (p.351-354)

Caput iv: "Ostenditur post primam demonstrationem non sequi immediate deonstrationem propter quid, sed debere intercedere aliquid medium" (p.345-346)

Causa inventa, videtur statim ab ea regrediendum esse ad effectum demonstrandum propter quid: attamen hoc nondum facere possumus . . . Per regressum quaeramus cognitionem effecttus distinctam; hanc nobis causa confuse tantum cognita tradere non potest, sed earn prius distincte cognitam fieri oportet quam ab ea ad effectum regrediamur. Facto itaque primo processu, qui est ab effectu ad causam, antequam ab ea ad effectum retrocedamus, tertium quemdam medium laborem intercedere necesse est, quo ducamur in cognitinem distinctam illius causae . . .

Cum ergo in hoc primo discursu non habeamus cognitionem causae et effectus distinctam, neque cognoscamus causam et effectum formaliter . . . sed solum materialiter, et in premissis demonstrationis propter quid cognosci debeant causa et effectus formaliter . . ., non potest immediate post demonstrationem quia sequi demonstratio propter quid, sed debet intercedere aliquid morae . . . et illo tempore intermedio debeant aliqua considerari. . . quibus possimus cognoscere causam et effectum formaliter.

Hune aliqui vocarunt negotiationem intellectus, nos mentale ipsius causae examen appellare possumus seu mentalem considerationem . . .

Hanc intermediam intellectus considerationem aliqui vocant negotiationem intellectus, alii mentalem examen. . .

483

Zabarella goes on to explain what this mentalis consideratio is and how it takes place by examining in detail two examples of regressus taken from Aristotle. He claims that nobody else has ever explained it in the same way. Delia Valle also refers more briefly to the two Aristotelian examples of regressus examined by Zabarella and adds this remark: 'Quae duo exempla ex Aristotele desumpta explicat Zabarella Cap. 4, 5 et 6 de regressu, ubi audit se primum advertisse et explicasse artificum Aristotelis in his duobus locis et regressibus, ab aliis antea non animadversum' (p. 345). In Galileo's autograph the question 'An detur regressus demonstrativus' is discussed without mentioning either Zabarella or his explanation of the mentalis consideratio. Something corresponding to the latter is

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only briefly hinted as one of several requirements or 'conditiones regressus': 'ut facto primo progressu non statim incipiamus secundum, sed expectemus donee causam, quam cognoscimus materialiter, formaliter cognoscamus' (MS. Gal. 27, f. 31 v). Even if there was a purely theoretical possibility of a common source for Carbone and Galileo, this could not have been lectures given by Delia Valle. Since Carbone's text was published from 1597 in successive editions of Toletus's Commentaria, of which Galileo owned a copy (above p. 172, n. 10), it is reasonable to conclude that Galileo drew the excerpts with which he compiled his logical Disputationes either directly from Carbone as well as from other so far unidentified sources, or from some also unidentified existing compilation including these excerpts from Carbone. In either case Galileo's autograph of the Disputationes could not have been written on present evidence before 1597'.

Carugo's new work disposes of speculation that Delia Valle could have been a source of Galileo's MS 27. In 1988 Wallace published with the Universita di Padova a volume entitled ' Tractatio de praecognitionibus et praecognitis and Tractatio de demonstration, transcribed from the Latin autograph by William F. Edwards, with an introduction, notes and commentary by William A. Wallace' (Padua 1988). From his preface we learn that Edwards had made an incomplete transcription some years before which he had made available (see also Wallace in the Times Literary Supplement, 3 January 1986, p. 13). Before that Wallace had already used Carugo's transcription of MS 27 for his Galileo and his Sources. He had now in his possession one complete and one seemingly partial transcription. The relation between them will not be discussed here. It is regrettable that Wallace's wild conjectures, repeated here, should be mistaken for established facts by some, even if happily only very few, scholars unfamiliar with the documentary evidence, including that in the Edizio Nazionale, and with critical scholarship. Thus Anthony Grafton in his recent review in Isis (Ixxx iii, 1992, p. 656) of the 1988 volume writes uncritically that Wallace 'has redated' the logical essays in MS 27 'to the years 1589-1591', and 'identifies their ultimate source, convincingly, as a transcript or reportatio of one of the courses in logic held at the Collegio Romano', then 'pinpointing the course that Galileo probably used: that of Paulus Vallius'. Wallace's principal objective, since we informed him of Galileo's use of Jesuit textbooks for his scholastic essays on logic, cosmology and natural philosophy, seems to have been to show that Galileo's Jesuit sources were different from those which we have identified. Thus in his Prelude to Galileo he wrote (omitting any reference to our information) that, following his article 'Galileo and the Thomists', his own 'subsequent research . . . has revealed that the physical questions' (i.e. the Tractatus de alteratione et de elementis) 'are based . . . on reportationes of lectures given by Jesuit professors at the Collegio Romano around the year 1590' (p. 181). What Wallace has in fact shown is nothing of the kind about either the content or the date of Galileo's essays, but simply, in laborious detail, that these successions of lecture notes from the end of the 16th century have general similarities in content and organization among themselves and with Galileo's scholastic writings. This we might expect if they were all based on the same Jesuit textbooks. But there are no specific

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correspondences of Galileo's manuscripts with those of the reportationes such as we found with the printed textbooks, including corresponding lists of references to ancient and medieval authors. All of these are fully documented in the sections of our book which were sent to Wallace in 1973 (acknowledged in the preface of his Galileo's Early Notebooks, 1977). In Galileo and his Sources Wallace vacillated between claiming that there is a closer correspondence of Galileo's essays with the manuscript reports and lectures than with the printed books (with the possible exception of Clavius's) and admitting the contrary. Thus, after comparing parallel texts of the Jesuit Mutius Vitellesch's manuscript lectures with Pereira's printed book, he wrote that Galileo's composition is much closer to Pererius's than to Vitelleschi's (p. 87). The obvious conclusion would be that Galileo used Pereira's textbook, easily available in several editions, rather than taking notes from any unique and obscure manuscript containing Vitelleschi's lectures or any others. Nothing in Wallace's book, or in his Prelude to Galileo (pp. 200-17), or in Galileo's Early Notebooks, supports his later claim in the TLS (3 January 1986, p. 23) that this 'was presented by way of exception' to the many closer parallels alleged with Vitelleschi. But Wallace found 'more likely' an even more bizarre conclusion: that Galileo's source was Delia Valle's lectures on the same subject, 'that Valla had himself used Pererius when writing a revised version of his notes, and that Galileo appropriated these for his own use, thus basing himself on Pererius at second remove' (Galileo and his Sources, p. 87). This is absurd.1 Galileo is notorious for seizing the opportunities of the moment. When we attempt to evaluate what was written by so complex and contentious a person, and what was written about him, or may seem to have been connected with him, as evidence for his thoughts, intentions, discoveries or sources, we need to be critically wide awake, or just normally awake. We must be strictly guided by the critical criteria established in his own time, equally in classical textual scholarship and in experimental science, for deciding the boundaries between what, on the evidence, we know and what we do not know. Galileo habitually made claims unsupported by any known evidence and frequently refuted by it. When he heard of a discovery or contribution to science he would claim that he had made it himself, even many years before, as with Santorio's thermometer (Opere, xi, 350, 506), and Bonaventura Cavalieri's demonstration of the parabolic trajectory of a projectile (xiv, 386). Sometimes he would appropriate the work without acknowledgement, as perhaps with Francois Viete's treatise on mechanics (above p. 225) and with Mersenne's formulation of the law relating the frequency of a pendulum to its length (see below ch. 13). He would use every rhetorical device to misrepresent the scientific competence and arguments of opponents, as he did with the Jesuit mathematician and 1

Cf. Michael Sharratt, Galileo: Decisive innovator (Oxford: Blackwell, 1994) 47-60, 226-8, for a scholarly account of these questions, refreshingly contrasting with the neoscholastic axe-grinding, ideological posturing, and omissions currently plaguing too much of the Galileo industry.

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astronomer Orazio Grass! in their dispute over comets, while obstinately rushing himself into some wrong headed and untenable conclusion (see Pietro Redondi, Galileo eretico, Torino, 1983; below appendix b). He was capable of ignoring almost completely fundamental contemporary theoretical and experimental discoveries, as he did with Kepler's astronomy and optics. He would opportunistically present an opinion, or even change his own opinion, in order to cultivate some possible supporter or patron, as in his apparent conversion to Neoplatonic cosmology in his exegetical letter of 23 March 1615 to Piero Dini, meant for the eyes of Cardinal Bellarmino (Opere, v, 297-305, xii, 151-2). He could take up a succession of contrary positions in the same assertive style without any reference to any change, as in his treatment of Copernican cosmology. Should we accept literally his outline of work in progress, and claim to years of studying philosophy, in his letter to Vinta in 1610? (above p. 179). Self-promotion was usual with those wanting to impress a patron and gain a position, but Galileo's gladiatorial competitiveness and slipperiness seem to have been excessive even in his context (cf. Mario Biagiolo, Galileo Courtier, Chicago, 1993; below appendix c). Evidence of Galileo's engagement in astronomy and in philosophy has a direct bearing on the problem of dating his three sets of scholastic essays in MSS 46 and 27. According to the records of the University of Pisa he lectured during 1589-91 on Euclid and in 1591 on the 'caelestium motuum hipotheses', which was probably Sacroboscos Sphaera (C.B. Schmitt, The Faculty of Acts at Pisa at the time of Galileo', Physis, xiv, 1972, p. 262). He wrote to his father on 15 November 1590 to thank him for the Galen in '7 tomi' as well as 'la Sfera' which his father was sending and added that he was 'studying and having lessons with Signor Mazzoni, who sends you greetings' (Opere, x, 44-5). It was Galen the natural philosopher whom he cited in the Tractatus de elementis (cf. above ch. 9, pp. 156-8). When Galileo wrote from Padua in 1597 to congratulate Mazzoni on his book In Universam Platonis et Aristotelis (1597) and to refute his argument there against Copernicus (above pp. 176,196-8), he added warmly his 'satisfaction and consolation' at finding that his old mentor, 'in some of the questions which in the first years of our friendship we used to dispute together with such delight, inclined to the side that had seemed true to me and the opposite to you'. It would be hard to believe that these disputed questions did not include those to which Mazzoni had devoted his book: general questions such as the necessity of mathematics for physical demonstrations, and more particular questions of natural philosophy concerning relative gravity, the elements, Archimedes, Plato versus Aristotle, etc. Accepting that Galileo could have developed a serious interest in natural philosophy as well as in mathematics after his return to Pisa in 1589, nothing yet follows for the dating of his scholastic essays or of De motu gravium. A common feature in all these undated writings is his use of Jesuit publications. He continued over a long period to draw from Jesuit textbooks simplified accounts of traditional theories which he discussed in his original works. Thus he used Pereira's De communibus . . . for the Tractatio prima de mundo and

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Tractatus de elementis and also for falling bodies in De motu gravium (above pp. 220-3; and see Carugo, 'Les Jesuites et la philosophic naturelle de Galilee: Benedictus Pererius et le De motu gravium de Galilee', History and Technology, iv, 1987, pp. 321-33). He used Clavius's Sphaera for the Tractatio de caelo and again for his account of the 'horizontal plane' of the Earth in De motu gravium, a question recurring in the Dialogo (Opere, vii, 174 sqq.; above pp. 221-2, cf. 177-8,226-7). He used Clavius yet again and another work by Pereira for his dated Lettere a Madama Cristina (1615), and, as Carugo has informed me, he drew from Giovanni Giorgio Locher, Disquisitiones mathematicae de controversiis et novitatibus astronomicis (Ingolstadt, 1614), the formulation of traditional arguments against the motion of the Earth discussed in the Dialogo (1632). Galileo's changes back and forth between Copernican and traditional cosmology are an object lesson in the dangers of trying to link his undated with his dated writings. In 1597 he defended Copernicus against Mazzoni and claimed to Kepler, characteristically congratulating him for having avoided 'a perverted method of philosophizing', that he himself had come to accept Copernicus 'many years ago' but had not dared 'until now' to bring his arguments into the open. A few years later in 1604 he assumed the traditional cosmological arrangement to assert an explanation of the new star scarcely compatible with his mathematical refutation of Mazzoni. Again in his Trattato delta sfera, despite his reference to Copernicans, he assumed the old cosmology. In the undated Tractatio de caelo he explicitly refuted Copernicus, while in De motu gravium he cited him once on another subject but assumed the geocentric cosmology throughout and made it explicit in the final draft of the introduction (above pp. 176-8, 222-3). We cannot then draw any conclusions about dating from this series of contradictory opinions presented in the same assertive style, not even that Galileo could not have written De motu gravium during his public campaign for Copernicus which opened in 1610. It seems clear that he composed the parts forming this work over a long period, but for how long remains a problem. In several parts of De motu gravium (Opere, i, 254-7, 269-72, 350-2) he applies to the motion of falling bodies some theorems on floating bodies that he had first conceived early in 1612, when he reworked an account, drafted late in 1611, of an experimental and philosophical dispute on floating bodies into the mathematical, experimental and philosophical treatise published in the summer of 1612 as the Discorso (iv, 69). Again, as noted by Carugo, one of the writings De motu gravium (i, 297-8) contains a mathematical demonstration of the motion of bodies on inclined planes which was based on a theorem ascribed to Viete sent by Giovanni Battista Baliani to Galileo in 1615 (xii, 186-8; above pp. 224-5). Yet again, in these writings (ii, 261-6) there is a draft of the correct analysis and definition of the accelerated motion of falling bodies, which Galileo first published in the Discorsi (1638; viii, 197-8; cf. above pp. 226-7). Since there is no mention of this in the Dialogo (1632), where Galileo makes a point of informing the reader of his most interesting results concerning motion, should

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we date this draft after 1632? As already shown above (pp. 225-6), the Dialogo, planned in 1624-25, was linked with De motu gravium and the scholastic essays on cosmology and natural philosophy both through the fragmentary notes in MS 46 and through their common use of Jesuit sources. If we must accept that MS 27 was written after 1597, is it absolutely impossible that the essays in MS 46, with their links with Galileo's earlier interests at Pisa, were written before that date? What about the passages in MSS 27 and 46 for which no sources have come to light anywhere? Perhaps they all come from some undiscovered Jesuit compendium hidden in some library? 'Far from it being true that he spoke with scorn and little respect of the ancient philosophers, and particularly of Aristotle, as some of those who profess to be his followers foolishly and wrongly assert', wrote Niccolo Gherdardini, who had known him, 'he said only that this great man's way of philosophizing did not satisfy him, and that there were in it fallacies and errors' (Opere, xix, 645; see above ch. 9, p. 149). He defined his position in two letters to Fortunio Liceti shortly before his death. 'I believe . . .' he wrote on 15 September 1940 'that to be truly a Peripatetic, that is an Aristotelian philosopher, consists principally in philosophizing in conformity with Aristotelian teaching, proceeding with those methods and with those true suppositions and principles on which scientific reasoning (discorso) is based, supposing those general notions from which deviation would be the greatest flaw. Among these suppositions is everything that Aristotle taught in his Dialectics (i.e. Posterior Analytics), taking care to avoid fallacies of reasoning, directing and disciplining it to syllogize well and to deduce from the admitted premises the necessary conclusion; and such doctrine concerns the form of arguing directly. With regard to this part, I believe that I have learnt from innumerable advances in pure mathematics, never fallacious, such certainty in demonstration that, if not never, at least extremely rarely, have I in my arguments fallen into equivocation. Here then I am a Peripatetic' (xviii, 248). Galileo was confirming here his lifelong adherence to the conception of truly scientific demonstration set out by Aristotle in the Posterior Analytics and most perfectly examplified in mathematics (cf. above ch. 9, below ch. 13). He went on in a letter of January 1641 to insist that, concerning the content as distinct from the the form of natural philosophy, he was far from being a Peripatetic. Natural philosophy, as he had said so often before, was not 'what is contained in Aristotle's books', but rather 'I truly hold the book of philosophy to be that which stands perpetually open before our eyes; but because it is written in characters different from those of our alphabet, it cannot be read by everyone: and the characters of such a book are triangles, squares, circles, spheres, cones, pyramids and other mathematical figures, fittest for this sort of reading' (xviii, 295). As his old friend Mazzoni had declared and he had illustrated in all his mature investigations: 'Aristotle, from failure to apply mathematical demonstrations in the proper places, has widely departed from the true method of philosophizing' (above p. 197). Galileo himself failed to understand that the criterion of range of confirmation as the test of a theory, which he so brilliantly used, put an end to the possibility of reaching in natural philosophy Aristotle's epistemological goal of necessary apodeictic demonstration (cf. above ch. 9, p. 161).

(b)

Pietro Redondi, Galileo eretico (Torino, 1983) [with Adriano Canugo]

This fascinating and important book is a brilliantly perceptive and learned study of the cultural context of Galileo's Copernican disputes. Unfortunately it is flawed by an untenable specific thesis based on a document of dubious authorship. The following are comments by Adriano Carugo and myself published in the Times Literary Supplement on 28 October - 3 November 1988, p.1203: Sir, - Your reviewer of Pietro Redondi's Galileo: Heretic (September 23-29) correctly casts some doubts on the authorship of the document on which alone the entire argument of the book is based, but he seems none the less to agree with the argument itself: namely, that the first and main motive that started the sequence of events which led to Galileo's trial and recantation was his atomistic explanation in // Saggiatore of the sensory qualities and its heretical implications for the dogma of the Eucharistic transubstantiation; and that this motive was deliberately kept secret and never surfaced in the documents relating to the trial because Pope Urban VIII, an old friend of Galileo and the dedicatee of // Saggiatore, wanted to avoid the scandal of condemning him for heresy. Anyone familiar with the National Edition of Galileo's works and writings, which contains every document hitherto known concerning his life, is aware that the new document brought to light by Redondi has nothing to do with the trial, but is connected with a much less dramatic event already well known through the National Edition. The Jesuit Orazio Grassi, who had been violently attacked by Galileo in // Saggiatore, replied with a lengthy and detailed rebuttal in which he exploited every chance of paying back Galileo in the same coin of mockery and insinuation. When he came to discuss Galileo's digression on the cause of heat, Grassi, among many other things, expressed en passant 'some scruple' about the difficulty of reconciling Galileo's explanation of the sensory qualities as pure names with the miracle taking place in the Sacrament of the Eucharist, where the properties of bread and wine are preserved while the substance is transformed. At first Galileo dismissed such a scruple as nonsense. In his own copy of Grassi's work he annotated: 'I leave this scruple for you, since // Saggiatore was printed in Rome, with the permission of the superiors, and

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dedicated to the supreme head of the Church; it was revised by those who are responsible for the protection of true faith and who, by approving it, must also have thought of the way to remove such a scruple' (National Edition, Volume VI, page 486). On the other hand, Galileo was quick to point out, Grassi had encountered the opposition of the Jesuits themselves over having his own book printed in Rome and had to publish it abroad, in Paris, as Galileo wrote 'without his superiors' permission' ('senza licenza dei superiori'). Later on Galileo must have had some scruple himself, for in January 1628 he wrote to his Benedictine friend Benedetto Castelli in Rome to ask him to inquire of Padre Riccardi, Maestro del Sacro Palazzo, whether he was taking Grassi's objections seriously. Castelli assured Galileo that Padre Riccardi was on his side: 'He said that your opinions are not against the Faith, since they are merely philosophical . . . and he intends to help you if any trouble should be caused to you in the Tribunal of the Holy Office' (XIII, 393). The question was never raised again in Galileo's correspondence, nor is it mentioned in any other document in the National Edition. The new document found by Redondi, which is an anonymous assessment of Galileo's atomism in relation to the dogma of transubstantiation, and is addressed to an unnamed Padre (possibly Padre Riccardi himself), throws further light on this episode in Galileo's life. As such it constitutes an interesting and important addition to the National Edition, but that is all. As for 'Why the Church really quarrelled with Galileo', as announced on the front page of the TLS, the unique issue of Copernicanism is unequivocally documented in the records of the trial. There is no other doctrinal issue there, but there was a disciplinary issue concerning Galileo's behaviour in breaking his promise formally made in 1616 to Cardinal Bellarmine 'not to maintain, teach, or defend in any way, in words of writing', the Copernican opinion. Urban did not know of this promise, neither had Galileo informed him, when in 1630 he gave Galileo permission to publish a dialogue discussing nonconclusively the philosophical and physical arguments for and against both the Copernican and the Ptolemaic systems. This permission was given on condition that the book was published in Rome with the imprimatur of the Maestro del Sacro Palazzo. Because of the plague Galileo decided to have it printed in Florence, and in order to start this he asked Riccardi to send him a formal imprimatur on condition that he sent Riccardi the proofs sheet by sheet for final approval. Galileo did not send the proofs except for those of the preface and conclusion. The Dialogo sopra i due massimi sistemi del mondo was published in 1632 in Florence with Riccardi's imprimatur, which applied only in Rome, together with a second imprimatur from the Florentine Inquisitor. When the Pope received his copy he was furious. The documents do not state explicitly why. The first Commission which he appointed to examine the case discovered among the earlier records that of Galileo's promise to Bellarmine. The trial proceeded from there. It seems to us that, like many complex and influential historical events, the trigger was probably something accidental and even trivial, namely Urban's

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irritation at the apparently deceptive way in which Galileo had manipulated his permission to publish his book. Rivers of inky imagination have dramatized this event in ways that distort the real intellectual importance of its consequences. Recent writing on seventeenth-century history has been plagued, notoriously by the neo-puritan, neo-Marxist persuasion, with supposititious 'reasons of state' and other hidden motives behind the plain evidence of the documents. It would be a pity if Galileo studies were to go the same way.

(c)

Mario Biagioli, Galileo, Courtier: The Practice of Science in the Culture of Absolutism (Chicago, 1993); review published in the Washington Post; Book World, 12 December 1993, p. 9.

'It is in the royal interest to keep everybody suspended between fear and hope' (p.20). The author of the contemporary handbook on court manners under absolute princes quoted here went on to describe 'how the natural instability of favour is in the interest of the powerful' (p.325), how the successful competitor for 'the fruits of servitude' under princely patronage was permanently exposed to danger from mutations of princely interest of which he had neither intimate understanding nor control, and how on falling 'from the summit of favour one does not descend through the same steps which lead to the top. Often nothing stands between one's highest and lowest status' (p.327). The fallen favourite could not comprehend what he had done wrong; he found himself shunned by former friends at court; he did not just lose his privileges but had to be humiliated. The mythology of the system required that the princely patron possessed everything that he could possibly want. He received gifts, as he provided favours, by pure grace. Yet in fact both sides needed the other, the one for the benefits acquired, the other in order to manifest the honour and power on which his position rested. The problem for the ambitious client lay in the asymmetry of a relationship in which the prince alone had the power and could demand unlimited service and honour without any obligations. It is within a fascinating account of this courtly system that Mario Biagioli places the second and most celebrated half of Galileo's long scientific career. Galileo seems to have embarked in 1601 at the age of thirty-seven on the strategy that would enable him to escape from his position as a mathematical professor at Padua into an enhanced status at court. Along this social trajectory he constructed what Professor Biagioli calls 'a new socioprofessional identity for himself (p.5) as a philosopher creating at once a new natural philosophy and an audience for it. After some false starts with his military compass presented to the Gonzaga at Mantua, and an adroitly flattering emblematic play on the words cosmos and Cosimo II equating the attractive power of the ruling Grand Duke of Tuscany with that of William Gilbert's

Appendix to Chapter 10

493

great cosmic magnet, he hit upon the right formula with his discovery of Jupiter's four satellites early in 1610. By getting permission to call these the Medicean stars and to dedicate the Sidereus Nuncius describing them to the Grand Duke, he obliged this prince to endorse his discoveries. Since, he wrote in his preface, 'under Your auspices, Most Serene Cosimo, I discovered these stars unknown to all previous astronomers' (p. 132), they should rightly have his family name. His reward was his invitation back to Florence as the Grand Duke's chief mathematician and philosopher, a privileged entry into the world of the court. Galileo particularly requested that his title should include philosopher as well as mathematician, and this raises the interesting question of when and how he acquired his quite considerable knowledge of Aristotle. Certainly it was not as a student at Pisa, but some light may be thrown by the discovery some years ago by Adriano Carugo and myself that three unpublished essays in his hand on Aristotelian logic, physics and cosmology were based on well known textbooks written by, or associated with, Jesuit professors at the Collegio Romano. These (despite some unhappy American publications on the matter) cannot be dated by any known evidence, except that, as we have shown, the logical essay cannot have been written before 1597. Since Galileo's earlier interests were essentially in mathematics and its applications, it could be that his philosophical studies were part of his strategy of 'self-fashioning as a court philosopher' (p. 11). Besides this crucial move to the Florentine court, Biagioli gives detailed treatment on the same sociological lines of some further important episodes in Galileo's life: the dispute in 1611-13 over floating bodies which involved the fundamental difference between Aristotelian and mathematical (here Archimedean) physics; the transfer of his patronage focus to Rome; the dispute in 1619-28 with the distinguished Jesuit Orazio Grassi over comets to which Galileo contributed his brilliantly dialectical // Saggiatore (1623); and the publication of the Dialogo (1632) on cosmological systems, followed by his trial. The whole book makes interesting reading, despite its frequent repetitiveness, and it was a good and original idea to locate Galileo within the world of the courts, of which Biagioli gives so learned an account. Thus 'Galileo is presented not only as a rational manipulator of the patronage machinery, but also as somebody whose discourse, motivations, and intellectual choices were informed by the patronage culture in which he operated throughout his life' (p.4). He insists that Galileo's science was not 'determined by these concerns . . . Power does not censor or legitimate some body of knowledge that exists independently of it' (p.5). For all that he asserts repeatedly that Galileo's position and title as court philosopher was 'a crucial resource for the legitimation of Copernicanism and mathematical physics' (p.49); that this connection 'gave Galileo credibility' (p.58); that 'Galileo's strategy was aimed at legitimizing scientific theories by including them in the representation of his patron's power' (p. 125); that his recognition by the Medici 'allowed him to become even more credible and draw further assent to his discoveries from

494

Science, Art and Nature in Medieval and Modern Thought

others' (p. 133). Galileo certainly knew what he was doing in getting court patronage, both in Florence and in Rome, to support his scientific work and his personal career, but while he was a master of all the arts of rhetoric, persuasion and political manoeuvre, he certainly did not confuse the presentation and acceptance of his discoveries according to the manners of courtly culture with their credibility to his scientific peers. Court culture was irrelevant to scientific knowledge. Confirmation of the reliability of the telescope and of Galileo's discoveries made with it were requested by Cardinal Bellarmine from the competent Jesuit mathematicians at the Collegio Romano, and by the Emperor Rudolph II and the Medici ambassador from Kepler. They knew what they were doing. You cannot cheat nature was a favourite of Galileo's aphorisms, however much you may cheat your fellow men; and in the margin of the Dialogo: 'In the natural sciences the art of rhetoric is ineffective' (Opere, vii, 78; cf. below ch. 11). I had a sense in reading Professor Biagioli's reconstructions that Galileo and his contemporaries and disputes were being translated from 17th-century Italy into the world of 20th-century transatlantic sociology. Anthropological comparisons across cultures far apart in time and place may indicate certain constants of human behaviour, but may abstract these from recognizable distinctions of different cultures and from the individuality of real people. For all that the exercise can be illuminating, as in Biagioli's plausible, though not necessarily credible, interpretation of Galileo's fall from Papal favour. 'I do not hope for any relief, because I have not commited any crime', Galileo wrote on 21 January 1635 to Nicolas Fabri de Peiresc, who had been trying through the Pope's nephew Cardinal Francesco Barberini to get some relaxation of Galileo's house arrest at Arcetri. 'I could hope for and obtain mercy and pardon if I had erred, for faults are matters upon which a prince can exert mercies and dispensations, whereas upon someone who has been innocently condemned it is convenient to be rigorous, so that it seems that it has been done according to the law' (Opere, xvi, 215). Galileo certainly knew the score, even as a fallen favourite.

Corrections to Science, Optics and Music in Medieval and Early Modern Thought (1990)

p. vii, ch. 12: for Theory and Change read Theory Change. p. xvii: Science, Art and Nature 1995, Styles of Scientific Thinking 1994. p. 24, para. 3, line 9: "overweening". p. 29, para 3, line 3: "assertion". p. 55, Fig. 1 caption line 7: for "respectively; the rays" read "respectively, the rays". p. 117, line 2 from bottom: for "local" read "logical". p. 195, Fig. 17 caption line 4: after "ends" add "(labelled in reverse in MS)", and line 7: after "with" add "the". p. 228, Fig. 33 is printed upside down: see Fig. 49. p. 258, line 3 from bottom: for "(1986)" read "(1983)". p. 417: Further references were inadvertently omitted and will be found in the present volume at the ends of chapters 13 and 14.

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Index

(Sub-headings are in alphabetical order, except where chronological order is more helpful) Abano, Pietro d' 292 Abd al-Rahman ibn 'Umar al-Sufi (Asophus) 62 Abu Ma'shar 60 academies: —, Academia Fiorentina del Disegno 173 —, Academie Royale des Sciences 299, 347, 409, 411, 460, 461 —, see also colleges and universities acoustics see hearing; music; sound Adam 275, 276, 279 Adelard of Bath 16, 31, 32, 56, 59 Adrastus 293 Agricola 320 Agrimi, Jole 471 Aguilon, Francois 347 AIDS 449 Ailly, Cardinal Pierre d' 59, 62 Aix-en-Provence 271, 287 al-Battani 47, 62 al-Bitruji 58 al-Farabi, Abu Nasr 59, 79, 96 al-Farghani 59, 60 al-Kindi see Alkindi Albert of Saxony 80, 277 Alberti, Leon Battista 89, 98-9, 132, 453 —, and history of optics 319, 473 —, and origins of language 277 Albertus Magnus 47, 52, 126, 454 albinism 418, 421,424 alchemy 52, 54, 57, 63, 155 Aldobrandini, Ippolito see Clement VIII, Pope Alembert, Jean le Rond d' 392, 409, 462 Alexander of Aphrodisias 221 Alexander of Hales 52

Alexandria (city) 70 Alfarabi, Abu Nasr 59, 79, 96 Alhazen (Ibn al-Haytham) 55, 56, 132, 292, 336 —, critics 331, 333, 334 —, and history of optics 76, 305-17, 323, 326-7, 471, 473 —, —, model of eye 38 —, —, Optica 316, 319 —, visual theories 304, 325, 327-8, 329, 354-5 Alkindi (Al-Kindi) 55, 305 Alphonsine tables 62 Ambrosian Library of Milan 175, 187, 288 America see United Sates anatomical research 278, 320, 334 'Ancients and Moderns' 36, 453, 454, 460-1 Anglicus, Robertus 60 animals: —, and albinism 421 —, antelope 288 —, ass 418, 420 —, chickens 412, 421 —, dogs 418 —, monkeys 418 —, and origins of language 278, 280, 282 —, pigeons 418 —, salamander 411 —, scorpion 412 antelope 288 antibiotics 448 Apollonius 341-2 Apuleius, Lucius 357 Aquinas, St Thomas 77, 81, 126, 183-4, 228

498

Science, Art and Nature in Medieval and Modern Thought

—, and assent 370 —, and Galileo 189, 190, 193 Arabic texts 32-3 Aranzi, Giulio Cesare 324 Arber, Agnes 471 Arcetri (Italy) 24, 494 Archimedes 95, 102, 126, 129, 131 —, and the balance 208, 224, 469 —, and Galileo's undated writing 222, 223, 224, 225 —, and gravity 175 —, and mathematics 59, 151, 197 —, and scientific revolution 456 —, and theology 470 —, alluded to 149, 204, 486 architects/architecture 101, 103, 132, 212, 320 Archytus of Tarentum 9, 129, 219 argument, history of 12, 180-1, 357-400, 443-9, 467 Argyll, Duke of 398 Aristides Quintilianus 293 Aristotle 60, 190, 191, 192, 261 —, and acoustics 297-8 —, on art & nature 93-5 —, and causality 440-1 —, and Christian theology 22, 151, 470 —, on comets 177 —, and ethics 16 —, and expectation and choice 358, 3624, 367, 387, 390, 391 —, and false premise 182 —, and gravity 259, 260 —, as historian of science 37 —, and history of optics 325, 471 —, and influence on Galileo 149-61 —, and logic 51, 369, 440-1, 467 —, and mathematics 197, 198, 200 —, on mechanics 129 —, on morals 94 —, and music 292 —, and origins of language 275, 278 —, and philosophy 20, 21, 127 —, and physics 16 —, on politics 95 —, and primary & real properties 218, 219 —, and rhetoric 232, 236-40, 243, 247-8, 250-2, 362-3 —, and scientific revolution 456 —, and scientific style 159, 467, 468 —, and undated writing of Galileo 222, 226

—, alluded to 17-18, 40, 42, 43, 68, 71, 82-3, 87, 102, 121, 128, 132, 180, 183, 189, 206, 211, 357, 358, 414, 469, 470, 483,486, 488 Aristotelian/Thomist revival 166 Aristoxenus 131, 219, 292, 293, 295 arithmetic 59, 115, 178 —, commercial 377 —, political 385 Arnauld, Antoine 379, 382-4 artists, rational 89-114 art(s) 19 —, and geometry 99 —, and nature —, —, Aristotle on 93-5 —, —, Ficino on 100, 136 —, rational 473 Arundel, Lord (Thomas Howard) 288 Aselli, Gasparo 111 Ashmolean Museum 288 Asophus (Abd al-Rahman ibn 'Umar alSufi) 62 assent/judgement 367, 369-74, 380, 381 asses 418, 420 astrology 61, 115, 132, 136, 470 —, R. Bacon on 52, 54, 58, 60-1 —, Bonaventura on 52 —, Grosseteste on 47 —, and Possevino 132 —, Vieri on 136 astronomy 42, 181, 209, 257, 470, 471 —, Babylonian 86 —, and R. Bacon 54, 58, 61 —, and calendar reform 61 —, and camera obscura 320-3 —, and Clavius 155, 177, 178 —, clocks 82 —, and Copernicus 155, 209 —, education in 115, 117 —, and Galileo 178, 185, 209, 258, 486 —, Greek 86, 413, 441 —, Grosseteste on 40, 42, 46, 47 —, Hebrew tables 62 —, Leonardo da Vinci on 100-1 —, mathematical, & celestial motion 99, 155, 183 —, new star of 1604 177, 178 Atestinus, Cardinal 129 Athenaeus132 Athens, plague of 13 atomism 58, 71, 72, 157, 158, 490 atomists 68, 204 auditory perception 107-10, 291-9

Index Augustine, St (Augustine of Hippo) 69, 72, 127, 469, 470 —, and expectation and choice 368 —, and hearing 292 —, on laws of nature 69, 72-5, 77 —, and origins of language 276 —, and Platonism 139 —, and providential creation 27, 33 Augustine to Galileo (Crombie) 475-6 Avempace 153 Averroes 79, 126, 153, 189, 191 epicycles & eccentrics 181-2, 183 Avicenna (Ibn Sina) 56, 76, 79, 190 Avignon 125 Babel 109, 276, 279 Babylonian astronomy 86 Bach, J. S. 427 Bacon, Francis 211, 258, 387, 454 —, and expectation and choice 379-80, 383 —, and history of optics 343 —, and intellectual reform 17 —, and new science 35, 36, 279, 459 —, and scientific revolution 456, 457-60, 463 —, and universal language 278 Bacon, Roger 276, 278, 471 —, biography —, —, birth, date of 51 —, —, family background 51 —, —, education 51, 54 —, —, and Franciscan order 52, 53 —, —, imprisonment 53, 61 —, —, last written work 53 —, on alchemy 57, 63 —, analytical skills of 58 —, on astrology 52, 54, 58, 60-1 —, and astronomy 54, 58, 61 —, and benevolent destiny 27 —, and calendar reform 58, 61, 62, 63 —, and causality 441 —, on church reform 53 —, on experience 53-4 —, and geography 59 —, on geometry 58 —, and Grosseteste 39, 47, 52, 55, 56, 61 —, and language 51, 52, 56, 276 —, on mathematics 52, 54, 56, 60, 97 —, —, and logic 59 —, —, usefulness of 58 —, nature, and laws of 75-7, 472 —, optics 52, 54, 55, 56, 63, 292

499

—, —, history of 316, 317-19, 326 —, at Oxford 51, 52 —, at Paris 51, 52,58 —, on radius of earth 60 —, and rainbows 472 —, and reform 16-17, 33 —, and scientific revolution 454 —, scientific thought 53-63 —, on truth 53 —, written work 51, 52, 53, 57-8, 62-3 Bailly, J.S. 463 balance, theories of 208, 224, 469 Balduino, Girolamo 155 Bale, Bishop John 455 Baliani, Giovanni Battista 161, 208, 2245,487 Barbaro, Daniele 101, 132, 212 —, and history of optics 324, 327, 343 Barberini, Cardinal Francesco 272, 287, 494 Bardi, Count Giovanni 294, 295 Baronio, Cardinal Cesare 126 Barozzi, Francesco 117, 122, 131, 175, 194 —, and mathematics 195 Basel 324 Basil, St (of Cappadocia) 56, 127, 470 al-Battam 47, 62 Bayes, Thomas 387, 448 Bayle, Pierre 36, 456 'Beagle' voyages of Darwin 429, 431, 433 Beaulieu, Armand 287 Beeckman, Isaac 108, 296 The Beginnings of Western Science (Lindberg) 465, 468-74, 476-7 belief and doubt 166, 490 —, 'Bibliotheca selecta' (Possevino) 126 —, Christian 54, 61,68 —, Hebrew thought 68, 69 —, Islam 54, 61 —, Judaism 54 —, see also Catholicism; Creator; God; theology Bellarmine, Cardinal Robert 126, 184 186, 257, 258 —, Galileo's promise to 490 —, alluded to 185, 486, 494 Bellini, Lorenzo 118 Benedetti, Giovanni Battista 108, 132n, 219, 294, 296 —, and optics 327-8, 329 benevolent destiny, concept of 27 Berkeley, George 354

500

Science, Art and Nature in Medieval and Modern Thought

Berlin Academy of Frederick the Great 407, 410 —, see also colleges and universities Bernard of Chartres 31, 454 Bernardino of Siena 375 Bernoulli, Daniel 448 Bernoulli, Jakob 384-5, 387, 388, 392, 427 —, and expectation and choice 379, 384 —, and mathematics 447 Besson, Jacques 320 Biagioli, Mario 492-4 Bianchi, Luca 470 Biblioteca Nazionale Centrale di Firenze 167 Bibliotheca selecta (Possevino) 126-32 biology 21-2, 27, 106, 118, 435 Biondo, Flavio 453 al-Bitruji (Alpetragius) 58 Bodin, Jean 35, 383 Boethius, Anicius Manlius 18, 59, 219, 469 —, and music 42, 292, 293 Bologna 115, 117, 118, 139 Bonamico, Francesco 126, 158 Bonaventura, St 52 Bonnet, Charles Etienne 427 Borelli, Giovanni Alfonso 118 Borri, Girolamo 135, 139 Bossuet, Jaques Benigne 462 Bouchard, Jean-Jacques 272 Bourdelot, Pierre Michon 272 Boyle, The Hon. Robert 67, 84-5 Bradwardine, Thomas 59, 80, 454 Brahe, Tycho 177, 329-30, 331, 334, 471 Brengger, Johann 301, 342 Breslau (town) 387 Bresson, Agnes 287 Briggs, William 345 Britain 264, 399 —, see also England Broad, C.D. 263 Broussais, Francois 447 Brunelleschi, Filippo 319, 320, 473 Brunei, Pierre 407 Bruni, Leonardo 453 Bruno, Giordano, 166, 249 Brunschvicg, Leon 263 Brussels 264 Buff on, George-Louis Leclerc, Comte de 387, 388, 417, 418, 432 —, and classification of species 418, 427 —, on geology 418 —, and history of science 462

—, and statistical analysis 448 Bulver, Ezekial (fict) 28 bulverism 28 Buridan, Jean 80, 82, 470, 473 Burnet, Thomas 385 Burtt, Edwin 264 Butler, Bishop Joseph 416 Byzantinum 470 Caietanus, Thomas de Vio see Cajetan Cajetan (Thomas de Vio) 126, 155 Calcidius 69, 469 calendar reform 19, 47, 61, 62 —, and al-Battani 47, 62 —, R. Bacon on 58, 61, 62, 63 —, Gregorian 62, 125-6, 156 —, Grosseteste on 40, 47, 62 Cambridge 263, 433 camera obscura 340, 345-7, 350 —, in astronomy 320-3 —, experiments with 305, 310-11 —, as model of the eye 38, 105, 327, 329, 336-8 —, and ocular physiology 301 —, and painting 343 —, and screen image 326, 332 —, and solar eclipses 329-30, 332 —, Straker's account of 473 —, and visual theory 326 Campanella, Tommaso 80, 456, 457 Campanus of Novara 59 Carbone, Ludovico 169, 222, 270, 480 —, and correspondences with Galileo's texts 169-72, 479 —, and undated writing of Galileo 222 Carcavy, Pierre 208 Cardano, Girolamo 115, 126, 131, 132n —, and expectation and choice 377 —, and origins of language 284 —, and rhetoric 249 Carneades of Cyrene 364-6 Carrara, Bellino 165 cartography 19, 99, 106 Carugo, Adriano 155, 156, 158, 484, 489 —, and Galileo's Jesuit sources 269-70, 479-80, 486, 493 —, and Pinelli collection 175, 187 —, and sources of Galileo's scholastic essays 151, 153, 156, 167-9, 487 Casaubon, Isaac 289 Casserio, Giulio 298, 320 Cassirer, Ernst 194 Castelli, Benedetto 118, 209, 211, 272, 490

Index Catena, Pietro 117 Catholicism 135, 166 —, see also belief and doubt; Creator; God; theology causality 68, 71, 455, 459, 466-7 —, language of 440-1 cause and effect 86, 446 Cavalieri, Bonaventura 118, 226, 485 Ceredi, Guiseppe 102, 132, 212, 301, 302 Cesi, Frederico 223, 226 chance, games of 381, 382, 384 Charles, E. 51 Charles V, King, of France 82 Charron, Pierre 167 Chatelet-Lomont, Gabrielle Emilie, Marquise du 462 Chaucer, Geoffrey 81, 469, 470 Chiaramonti, Scipione 244, 245 chickens 412, 421 Children's Crusade 54 Chillingworth, William 380 Chinese medical practice 446 Chinese and origins of languages 278, 283 Christian moral theory 99 Christian theology 5, 72, 79, 99, 469 —, and Aristotle 22, 151, 470 Christianity and cosmology 27 church reform 36, 53, 456 —, see also belief and doubt Cicero, Marcus Tullius 51, 127, 455, 469 —, and expectation and choice 366-7 Cimabue, Giovanni 34, 453 Cimento, Academia del 118 —, see also colleges and universities Clagett, Marshall 477 Clarke, Samuel 408 classical languages 118 classification of species 413 Claudius Galius 129 Clavelin, Maurice 270 Clavius, Christopher 119, 122, 132n, 182 —, on astronomy 155, 177, 178 —, and calendar reform 62 —, Galileo visits 156, 175, 479 —, and influence on Galileo 176, 181, 194, 269-70 —, and influence on Possevino 128, 131 —, and mathematics 119-21, 122, 196, 198, 216 —, and MS Galileiana 27, 479, 480 —, and optics 326-7 —, and science 181-3, 184, 185, 187 —, and telescope 217

501

—, and undated writings of Galileo 2212, 224, 226, 227, 486-7 Clement of Alexandria, St 127 Clement IV, Pope 52, 53, 60 Clement VIII, Pope (formerly Ippolito Aldobrandini) 116n, 126, 139, 140 clepsydra 56 climate 43, 387 clinical trials 447 clock, mechanical 19, 473 clocks 60, 82 Goiter, Volcher 298 colleges and universities 115-40, 455 —, Academic Roy ale des Sciences 299, 347, 409, 411, 460, 461 —, 'Accademia della dottrina Platonica' 133 —, Basel 324 —, Berlin Academy of Frederick the Great 407, 410 —, Bologna 115, 117, 118, 139 —, Cambridge 433 —, Cimento, Academia del 118 —, Collegio Romano 132n, 153, 154, 165, 167, 168 —, —, and Carbone 172 —, —, and Clavius 217 —, —, founded 119 —, —, and Pereira 133, 270 —, —, and Rocco 186 —, —, and Scheiner 345 —, —, and Vallius 169 —, decline of 476 —, Ferrara 139, 140 —, Fiorentina del Disegno, Academia 103, 173 —, Florentine Academy 134 —, Gymnasium Patavium Societatis Jesu 126 —, Louvain 345 —, Messina 118 —, Padua 140, 172, 175, 177, 198, 484 —, —, and Galileo 178, 225, 227, 492 —, —, and mathematics 117, 118, 134 —, —, and philosophy 125, 133 —, —, and Possevino 126 —, Pavia 140 —, Pisa 116, 117, 118, 134-5, 139-140, 150, 486 —, Prague 334 —, Rome 133, 139, 140, 153 —, —, mathematics at 115, 116, 122 —, Venice 151, 294 Collingwood, R.G. 263

502

Science, Art and Nature in Medieval and Modern Thought

Colombe, Cristoforo delle 245-6 Colombo, Realdo 324, 325 colour and light 45 Columbus, Christopher 59 comets 43, 177, 178, 187, 211, 269, 485 —, Galileo v Grassi dispute 493 Commandino, Frederico 131 commerce/book-keeping methods 19 communism and truth 29 compass 175, 492 computer 90 Comte, Auguste 259, 260, 262, 463 Condillac, Etienne Bonnet de 410 Condorcet, Marie Jean Antoine Nicolas de Caritat, Marquis de 461, 463 Constantine I 453 Cooper, Lane 259 Copernicus 61, 131, 182, 187, 258 —, and astronomy 155, 209 —, and Galileo 153, 176, 177, 181, 186 —, —, and undated writings 222 —, and rhetoric 244 —, alluded to 344, 486, 487 coral reefs 433 Cosimo I, Grand Duke of Tuscany 117 Cosimo II, Grand Duke of Tuscany 179 cosmography see cosmology cosmology 22, 178, 228, 486 —, and Christianity 27 —, and Duhem 37 —, and Galileo 23, 80, 155, 167, 177, 487 —, and Grosseteste 470 —, and Kepler 433 —, and Maupertuis 420 Cotrugli, Benedetto 375 Council of Trent 136, 165, 166 Cournot, Antoine-Augustin 387 court manners 492 creation 27, 33, 67, 139 Creator 389, 396, 397, 441 —, benevolent 20, 22 —, eternal/onmnipotent 69, 72, 87, 113, 161 —, see also belief and doubt; Catholicism; God; theology Cremonini, Cesare 133 crime 372 Crisciani, Chiara 471 Crombie, Alistair C. 168, 172, 465-77, 471,472 Crowley, T. 51 Ctesibus 132 Cuvier, Georges 463

d'Abano, Pietro see Abano, Pietro d' d'Ailly, Cardinal Pierre see Ailly, Cardinal Pierre d' d'Alembert, Jean le Rond see Alembert Dalton, John 9 Dante, Alighieri 156 —, on origins of language 276, 441 —, and vernacular philosophy 469 —, and poetical revival 34 —, and Western science 471 Danti, Egnazio 132 Darwin, Charles —, and 'Beagle' voyages 429, 431, 433 —, and biology 21-2, 435 —, criticism of predecessors 430 —, and evolutionary theory 9, 38 —, and expectation and choice 393-8, 399 —, and letters 430, 432 —, and natural selection 425, 431, 435, 436, 437 —, rhetoric of 6 scientific method 429-37 —, and transmutation of species 434 —, see also evolution Darwin, Erasmus 429 Darwin, Francis Charles 432 de Honnecourt see Villard de Honnecourt de 1'Epee, Abbe Charles-Michel 285 De Morgan, Augustus 62 De motu gravium (Galileo) 201-5 deaf and dumb 109, 110, 276, 279, 283-4 Dee, John 48, 62, 63 Delambre, Jean Joseph 463 Delfino, Frederico 117 Delia Valle see Paulus Vallius Democritus 218 demography, population 385 Descartes, Rene 67, 83-4, 106, 408, 414 —, and expectation and choice 383, 391 —, and history of optics 345, 348-52, 353, 354 —, —, and camera obscura 350 —, and intellectual reform 17 —, on laws of nature 67, 83-4 —, and natural philosophy 228 —, and origins of language 282 —, and rainbow 38 —, and rhetoric 6 —, and scientific revolution 456, 457-8, 460 —, and scientific style 229, 270, 467, 472 —, and sound 296

Index d'Este, Cardinal Alessandro see Este, Cardinal Alessandro d' destiny, benevolent 27 determinism 22, 79 Dialogue (Galileo) 210-11 Diderot, Dennis 417, 427, 461 digestive system 111 Digges, Leonard 63 Dini, Piero 185 Diodati, Elie 271 —, and undated writing of Galileo 225 disease 372, 372-3, 443-9 —, AIDS 449 —, records 386, 386-7 —, smallpox 392 Disputationes (Galileo) 187-95 dissection 420, 433 dogs 418 Dominican order 53 Dondi, Giovanni de' 82, 473 Doni, Giovanni Battista 271, 272 Drake, Stillman 149, 161 Dryden, John 461 du Chatelet, Madam see ChateletLomont, Gabrielle Emilie, Marquise du du Laurens, Andre 298 Duhem, Pierre 37, 38, 132n, 257, 471 Duns Scotus, John 47 Diirer, Albrecht 99, 132, 320, 332 Duverney, Joseph Guichard 299 dynamics 180, 185 Earth, planet 160, 179 —, movement of 183, 184-5, 470, 487 —, orbit of 181 —, radius of 60 Eastwood, Bruce 465 eclipses 52, 329-30 ecology 7 economy 16, 22, 392 Edgerton, Samuel Y., Jr 473 education 115-40 —, arts/natural science 118 —, in astronomy 115, 117 —, classical languages 118 —, history 118 —, literature 118 —, logic 118 —, mathematics 118-40 —, metaphysics 118 —, moral science 118 —, oriental languages 118 —, physics 118

503

—, theology 118 —, see also colleges and universities Edwards, William F. 484 Elizabeth I, Queen of England 62 Empedocles 391 empiricism 262 Engels, Friedrich 394n engineering 23, 58, 96-7, 106, 320 England 35 —, and calendar reform 62 —, Peiresc travels to 286 —, see also Great Britain English philosophy 452 enlightenment 35 Enriques, Federigo 477 Epee, Charles Michel de L' 285 Epicurus 69 epicycles and eccentrics 181-2, 183, 184, 185 Erasmus 36, 455 Este, Cardinal Alessandro d' 254 ethics, Aristotelian 16 Ethiopia 288 Euclid 122, 123, 131, 132, 175, 486 —, on acoustics 96 —, and geometry 16, 17, 96, 217, 432-3, 469 —, and logic 369 —, and mathematics 96, 161, 196, 200 —, and music 18, 293, 295 —, and optics 55, 302-3, 305, 308, 471 —, —, and perspective 46, 137 —, —, treatise on 18 —, andProclus 101, 175 —, on ratios 58-9 —, and science, language of 441 —, and scientific argument 95 Eudoxus of Cnidus 68, 467 Euler, Leonhard 410 European groups and origins of languages 278 European interest in medieval history 37 ever-burning lamps 57 evolution 22, 398, 407, 412, 428, 429-37 —, see also Darwin, Charles; natural selection; transmutationof species evolution and the ass 418 expectation and choice 357-400 experience 53-4 experimental method 257 experimental philosophy 258, 262 experimental science 89-114, 467, 471 explosive powder 57 eyes 303-17, 319-28, 329, 333-42, 344-55

504

Science, Art and Nature in Medieval and Modern Thought

—, and camera obscura 38, 105, 327, 329, 336-8 —, see also under Alhazen; Ptolemy; see also optics Fabrici d'Acquapendente, Girolamo 126, 279 —, and language 278, 281, 282 —, and optics 320, 325, 334 falling bodies 104, 176, 208, 215-16, 268, 486, 487 Falloppio, Gabriele 126 false/true premise 182 falsification, method of 43 al-Farabi, Abu Nasr 59, 79, 96 Faraday, Michael 3, 441 al-Farghani 59, 60 Favaro 175, 205 —, and writings of Galileo 151, 156, 167, 222, 224 Ferdinand The Catholic' (Ferdinand II of Aragon) 59 Ferguson, Wallace K. 455 Ferrara 133, 139, 140 Ficino, Marsilio 19, 69, 95, 127 —, on art and nature 100, 136 —, and Catholicism 135 —, and music 293 —, and philosophy 166 —, and platonism 139 —, and rhetoric 249 —, and undated writings of Galileo 226 First Cause theory 22 First Council of Lyons (1245) 41 First Letter about the Sunspots (Galileo) 87, 150, 180, 186, 215, 216 Fisher, R.A. 448 Florence 156, 158, 159, 173, 271, 493-4 —, and Galileo's writings 224, 225, 490 —, and mathematics 118 —, Michelini returns to 272 Florence, Council of 125 Florentine Academy 134 —, see also colleges and universities Florentine Accademia del Disegno 103 Fludd, Robert 111 flying machines 33, 57 Fogliano, Lodovico 99 Fontenelle, Bernard le Bovier de 461 fossils 418, 433, 434 France 35, 125, 264, 287 —, deaf and dumb teaching 285 —, economy 399 —, and science 461

Francesca, Piero della see Piero della Francesea Francesco I, Grand Duke of Tuscany 134 Franciscan order 39, 52, 53, 59 Frederic, Jean 384 Frederick II, (the Great) King of Prussia 35, 276, 409-10, 411 Frisius, Gemma 323-4 Gaffurio, Franchino 99 Gagliardi, Achille 119, 125, 126, 133 Galapagos Islands 434 Galen (Claudius Galenus) 218, 305, 306, 456, 457, 471 —, atomist doctrine 157 —, and hearing 297 —, and micro/macrocosm 469 —, and optics 303, 307, 308, 309, 31516, 325 —, as philosopher 156 —, alluded to 102, 486 Galilei, Galileo see Galileo Galilei, Vincenzo 103, 108, 150, 156, 173, 486 —, and acoustics 174 —, and mathematics 198 —, and music 131, 151, 219 —, and sound 294-6 —, death 1591 295 Galileo 105, 260, 414 —, biography —, —, background 173 —, —, biographers 103-4, 149, 259 —, —, career —, —, —, at Padua 134, 492 —, —, —, at Pisa 117, 134, 198, 479 —, —, as court philosopher 493 —, —, critics 261 —, —, friends 24, 272 —, —, intellectual 168, 172, 173, 188 —, —, trial & house arrest 24, 489, 493, 494 —, and Aristotelian theories 149-61, 229, 259 —, and astronomy 178, 185, 209, 258 —, and causality 441 —, and Clavius 176, 181, 194, 270, 479 visits Clavius 156, 175, 479-80 —, on comets 177, 493 —, and Copernicus 153, 176, 177, 181, 186 commitment to 22, 177

Index —, and correspondences with Carbone's texts 169-72, 479 —, and cosmology 23, 80, 155, 167, 177 —, and court patronage 492-4 —, and dynamics 185 —, Earth, on motion of 184-5 —, on epicycles and eccentrics 185 —, and expectation and choice 383 —, and experimental enquiry 258, 262 —, and experimental physics 206-7 —, on gravity 104 —, on heat and light 219, 489 —, and Koyre's understanding of 26770, 477 —, letters 488 —, —, to Baliani 208 —, —, to Carcavy 208 —, —, to/from Castelli 211, 490 —, —, to Dini 185, 486 —, —, to father 198, 486 —, —, to/from Liceti 216-17, 229 —, —, to Mazzoni 198, 486 —, —, to Mazzoni/Kepler 176-7 —, —, to Vmta 179, 486 —, and light 215 —, and mathematics 118, 196, 197, 198, 212 —, —, his interest in 173, 217 —, Mazzoni, studies with 486 —, and mechanics 23, 103, 185, 212-13 —, and moon 106 —, and music 103, 219 —, and natural philosophy 23, 139-61, 167, 208, 213, 267 —, and new star of 1604 177 —, and optics 217, 343 —, meets Peiresc 286 —, on pendulum 179, 208, 279-3, 485 —, pendulum ratio, and discovery of 270-3 —, and philosophy 179, 257-62, 486 —, and properties/qualities 218 —, and Redondi's document 490 —, and rhetoric 6, 180-1, 216, 231-55, 494 —, and science 20, 35 —, science, and language of 441 —, on science and nature 165-229 —, and scientific revolution 456 —, and scientific style 270, 468 —, on sunspots 211 —, —, First Letter 87, 150, 180, 186, 215, 216 —, —, Second Letter 213

505

—, —, Third Letter 215 —, and telescope 106, 177, 185, 214 —, and theology 229 —, on tides 185-6 —, on truth 23, 24, 25 —, writings —, —, chronology/paper 155-8, 162-3 —, —, dating of 155, 165, 166n, 172-4n, 220-8, 487-8 —, —, dated 175 —, —, undated 172, 220-8, 486, 493 —, scholastic essays of 151-61, 168, 187 —, sources of 167-9, 221-2, 226-8, 26970, 486 —, —, scholastic essays 151, 155, 165, 221, 479-94 —, —, Carbone, Ludovico 169, 172, 269-70, 479, 484 —, —, Clavius, Christopher 153, 168, 269-70, 479 —, —, Paulus Vallius 479, 484 —, —, Pereira, Benito 153, 158, 168, 205, 269-70 —, —, Toledo, Francisco de 153, 158, 168, 205, 269-70 —, watermarks of paper 156, 157, 162-3 —, highest rates of citation 155, 194 The Galileo Prize 161, 167 Garin, Eugenio 158 Gassendi, Pierre 228, 229, 287, 352-3 Gaultier, Joseph 286-7 Gelenius, Sigismundus 277, 288 Geminus 131, 183 Gemistus 139 genetical disputes, Soviet 28 geography 59, 132 geology 22, 27, 418, 433 geometry 55, 58, 115, 131, 178, 441 —, analysis 45 —, and art 99 —, of Euclid 16, 17, 96, 217, 432-3, 469 —, of Greek mathematicians 4, 95-6 —, of Pascal 113 George, Wilma 471 Gerald of Wales 39, 42 Germany 37, 125, 271, 453, 464 Gesner, Conrad 278, 288, 456 Gessner see Gesner Gherardini, Niccolo 149 Ghetaldi, Marino 224 Ghiberti, Lorenzo 319, 453 Gibbon, Edward 463 Gilbert, William 35, 111, 210, 471, 492-3 Gilles of Lessines 374

506

Science, Art and Nature in Medieval and Modern Thought

Gilson, Etienne 263, 469 Giorgio, Francesco 131 Giotto 34-5, 453 God 33, 71, 72, 79-81,85, 182 —, omnipotent 71, 77, 79, 84, 85 —, see also belief and doubt; Catholicism; Creator; theology Goethe, Johann Wolfgang von 461 Gogava, Antonio 295 Gondisalvo, Domingo 96 Gorgias and rhetoric 234 Grafton, Anthony 484 Graham, W. 398 Grassi, Orazio 485, 489, 490, 493 Graunt, John 379, 386-7, 447-8 gravitational clocks 82 gravitational theories 117-18, 215-16, 259, 260, 434 —, and Archimedes 175 —, of Galileo 104, 480 Gray, Asa 398 Graz, solar eclipse at 330 Great Britain 264, 399 —, see also England Greek astronomy 86, 413, 441 Greek grammar 54 Greek language 68 Greek mathematics 4, 95-6, 265, 441 Greek optical theory 302-4, 315 Greek philosophy 16, 265, 456, 469 —, causal continuity 3-4 —, causality in medicine 446, 447 —, and natural science 1, 21, 440, 443 —, and probability 360-7 —, scepticism 71, 72, 167 —, and theology 70 Greek science 16, 265, 456 Greek texts 32-3 Gregorian calendar 62, 125-6, 156 Gregory III, Pope 125 Grienberger, Christopher 119, 217 Grosseteste, Robert 39-47, 472 —, background 39 —, career —, —, as bishop & statesman 40 —, —, clerk at Hereford 42 —, —, at Oxford 39 —, —, as scholar & teacher 40 —, ecclesiastical appointments 39, 41 —, Aristotle, influence of 42, 43 —, on astrology 47 —, and astronomy 40, 42, 46, 47 —, and R. Bacon 39, 52, 55, 56, 61 —, on calendar reform 40, 47, 62

—, and cosmology 470 —, and falsified conclusions 43 —, and Franciscans 39 —, and geometry 55 —, letters 39 —, on light 40, 41, 42-3, 44, 45 —, and mathematics 97 —, on methodology (4 essays on) 43-6 —, and music 42 —, and optics 316-17 —, philosophy of 40, 42-3 —, and scientific revolution 454 —, scientific writing 42 —, and sound 292 —, written work 40, 42, 43, 44, 45-6, 47-8 Grotius, Hugo 380 Guidi, Guido 298 Guiducci, Mario 215 Guy de Foulques, Cardinal see Clement IV, Pope Gymnasium Patavium Societatis Jesu of Padua 126 —, see also colleges and universities Halley Edmund 379, 387 Haly Ibn Sma 60 Harriot, Thomas 106, 349 Hartsoeker, Nicolaas 422 Harvey, William 111, 112, 414, 469 hearing 96, 107-10, 291-9 —, see also music; sound heat and light 219, 489 Hebrew. —, astronomical tables 62 —, doctrine 68, 69 —, grammar 54 —, language 275, 276, 277, 279 —, theology 27, 70, 469 Henry III, King of England 51 Herbert of Cherbury 380 Hereford 39, 42 heresy 372 Hermes Trismegistus 139 Hero of Alexandria 101, 102, 132 Herodotus 275 Hesiod 68 Hiero II, King of Synacuse, and undated writings of Galileo 223 hieroglyphics 289 Hipparchus 47, 153, 221 Hippocrates, and medical science 445 —, and rhetoric 235 —, and scientific revolution 456

Index 'Historical Commitments of European Science' (Crombie) 474-5 history —, of argument 12, 180-1, 357-400, 4439,467 —, human 458-9 —, Jesuit education 118 —, of science 451-64 Hobbes, Thomas 48, 63, 352-3, 381, 394n Hoeniger, David 473 Hohenburg, Hewart von 368 Holcot, Robert 81 Holy Scriptures 41, 53, 182, 470 Homer 68 Hook, Robert 418 Hooker, Joseph 431 Howard, Thomas, 2nd Earl of Arundel 288 Hudde, Jan 384 Hugh, Bishop of Lincoln 39 Hugh of St. Victor 33 humanists and scientific revolution 455 humankind, Western visions of 1-12 Humboldt, Alexander Baron von 59 Hume, David 258, 461, 463 Hunain (Hunayn) ibn Ishaq 56, 306 Hungary 125 Hutchinson, Evelyn 471 Huxley, Thomas Henry 398-9 Huygens, Christiaan 113, 347, 379, 3812,387 —, and expectation and choice 384 —, and mathematics 447 hydrostatic balance 224 hydrostatics 209, 211, 269 hypothesis 262, 467 Ibn al-Haytham see Alhazen Ibn Sfna (Avicenna) 56, 76, 79, 190 Ignatius see Loyola Indian medical practice 446 infinite power 67-88 inoculation 392 insurance 374, 384, 447 intellectual reform 16-17, 33 intellectual styles 2-6 Isabella of Castile 59 Islam 5, 54, 61, 470 isolated child, origins of language and 275, 276, 277, 280-1 Italian historians 453 Italian mathematicians 447

507

Italian universities, mathematics and Platonism in 115-40 Italy 35, 36, 82, 150, 452 —, Greeks flee to 456 —, Peiresc journey's to 286 —, spectacles invented in 317 Ivan IV, Czar (the Terrible) 125 Jandun, Jean de 176, 283-4 Japanese thinking 4 Javelli, Chrisostomo 126, 127 Jenner, Edward 446 Jerome, St 127 Jessen, Johannes 334, 342 The Jesuit 'Constitutions' (1556) 118, 121 Jesuits 134, 165-229 —, Aristotelian/Thomist revival 166 —, education —, —, arts/natural science 118 —, —, classical languages 118 —, —, history 118 —, —, literature 118 —, —, logic 118 —, —, mathematics 118-40 —, —, metaphysics 118 —, —, moral science 118 —, —, oriental languages 118 —, —, physics 118 —, —, theology 118 —, philosophy 132 —, as source of Galileo's writings 165, 167-9, 269-70, 493 —, and undated writing of Galileo 221, 222, 226, 227, 228 Jewish philosophy 72 Jews 127 Jews in Alexandria 70 John of Damascus 40 John of London 59 John (pupil of Roger Bacon) 53 John of Salisbury 369, 454 Johnson, Dr Samuel 416 Jordanus de Nemore 59 judgement/assent 369-74 Julian year 61, 62 Jupiter 185, 217 satellites 258, 287, 493 Justin, St (the Martyr) 139 Kant, Immanuel 260, 262 Kemp, Martin 473 Kepler, Johann 111, 176, 331, 334, 473 —, and astronomy 471, 485

508

Science, Art and Nature in Medieval and Modern Thought

—, and camera obscura 332, 336-8, 343 —, and cosmology 433 —, and expectation and choice 368 —, and history of optics 304-5, 329-45, 347-8, 350, 354-5, 485 —, and innovation 7 —, letters from Galileo 176, 487 —, and optical physiology 38 —, and planetary intervals 21 —, and retinal image 105 —, and solar eclipse 330 kinematics 180 Kirby, William 394n Kircher, Anthanasius 289 Kohlhans, Johann Christoph 347 Koyre, Alexandre 263-4, 267-70, 476, 477 La Galla, Giulio Cesare 215, 217 La Hire, Philippe de 347 La Mettrie, Julien Off ray de 410 Lactantius 469-70 Laertius, Diogenes 275 Lagrange, Joseph Louis de, Comte 258 Lalande, Joseph Jerome Le Francois de 410 Lamarck Jean-Baptiste Pierre Antoine de Monet de 394n language 54 —, of animals 278, 280, 282 —, Arabic 288 —, Babel 276 —, and R. Bacon 51, 52, 56, 276 —, of causality 440-1 —, Chinese groups 278 —, deaf and dumb 276, 277, 283-4 —, and electro-chemistry 441-2 —, English 91, 439 —, European groups 278, 288 —, French 439 —, German 288 —, Greek 68 —, Hebrew 275, 276, 277, 279, 288 —, history of 275-89 —, isolated child theory 275, 276, 277, 280-1 —, Italian 439 —, Latin 3, 68, 276, 439, 441, 453 —, of mathematics 442 —, of music 442 —, new terminology 3, 442 —, and the occult 276, 278, 279 —, origins of 275-85, 288-9 —, Persian 278, 288

—, philosophical 279 —, of science 3, 439-42 —, and Semitic groups 278 —, technical 442 —, universal 277, 278, 282 Laplace, Pierre-Simon, Marquis de 394, 396, 399, 448, 463 —, and analysis of numbers 392-3 —, and inverse probability 387 Larroque, Philippe Tamizey de 287 Latin language 3, 68, 276, 439, 441, 453 latitude/longitude 59, 60 laws of nature —, defined 86 —, St Augustine on 69, 72-5, 77 Le Clerc, Daniel 462 Leaning Tower of Pisa 259 least action, principal of 21, 389, 411 Lebegue, Raymond 287 Leeuwenhoek, Anton van 422 Leibniz, Gottfried Wilhelm 289, 408, 426, 462 —, and expectation and choice 379, 384, 385 —, and history of optics 301-2, 354 Leicester 39 Lenin, Vladimir Ilyich 28 Lenoble, Robert 263 lens 55, 56, 303, 304, 320, 343 Leo X, Pope 115 Leon, Pedro Ponce de 284 Leonardo da Vinci 19, 99, 100-1, 132n, 136, 252 —, and history of optics 320-3, 327, 334 1'Epee, Abbe Charles-Michel see Epee, Charles-Michel de L' Lessius (Leonard Leys) 378 letters, unidentified, of Galileo 187 Leurechon, Jean 344 Lewis, C.S. 28 Leys, Leonard (Lessius) 378 Libri, Guglielmo 463 Liceti, Fortunio 140, 216, 217, 229, 488 light 40, 42, 42-43, 44, 45, 215-6 Lincoln 39, 41 Lindberg, David C. The Beginnings of Western Science 465, 468-74, 476-7 linear scale 203 Linnaeus, Carolus (Carl von Linne) 41314, 414-15, 417, 418, 425 Linnean Society 431 Linz, Wotton 343 literature 118, 453, 455-6 Little, A.G. 51, 61, 62

Index Locher, Giovanni Giorgio 487 Locke, John 354, 461 logic 51, 118, 260, 369, 440-1, 467 London 264 —, population statistics 447 Louvain 345 Loyola, St. Ignatius 118-9, 121 Lucretius, Titus 56 —, and expectation and choice 366, 390, 391 —, nature, laws of 69-70, 388 —, and origins of language 275 Lull, Ramon 278, 384 Lavrov, P.L. 394n Lyell, Charles 6, 436 McCarthy, Senator Joseph 28 Mach, Ernst 260, 261 Machiavelli, Niccolo 35, 104, 453 macrocosm/microcosm 40 McVaugh, Michael 471 magic 57, 63, 278 Magiotti, Rafaello 272 magnetism 57, 59, 97, 111, 471, 493 magnification 55, 56, 316-17 Maieru, Alfonso 469 Malebranche, Nicolas 354 Malpighi, Marcello 118, 354 Malthus, Thomas 393, 434 Mantua 492 manual industry 97-8, 98, 100 Marciana library 288 Maricourt, Pierre de 57, 59, 97, 471 Mariotte, Edme 299, 347 Mars 185 Marseilles 288 Marsh, Adam 39, 52 Marsili, Cesare 226 Marsilius of Inghen 277 Martini, Francesco di Georgio 106, 320 Marx, Karl 394n Mastlin, Michael 330, 344 mathematics 57, 87, 97, 442 —, 16th century debate 21, 195-201 —, and Archimedes 59, 151, 197 —, and astronomy 99, 155, 183 —, and Bacon, R. 52, 54, 56, 60, 97 —, —, and logic 59 —, —, and usefulness of 58 —, at Bologna 115 —, and Clavius 119-21, 122, 196, 198, 216 —, and Euclid 96, 161, 196, 200 —, and Galileo 118, 196, 197, 198, 212, 488

509

—, —, his interest in 173, 217 —, Italian 447 —, in Jesuit education 118-40 —, and Platonism 115-40 —, and Possevino 128-31 —, at Rome 115 —, students 120-1 —, tutors 119-20 Mather, Cotton 456 Maupertuis, Pierre Louis Moreau de 407 —, biography/background 407, 410 —, —, Battle of Molwitz 410, 412, 428 —, and albinism 418, 421, 424 —, and animal studies 411-12 —, and cosmology 420 —, critics (Voltaire) 409, 410, 411, 417, 427 —, and expectation and choice 388-92, 394n, 395, 396 —, and history of science 462 —, least action, theory of 411 —, and probability 389-92 —, and salamander 411 —, and scorpion 412 Maurolico, Francesco 63, 119, 326-7, 330 Mazzoni, Jacopo 127 —, and Galileo 156, 176, 177, 198, 222, 486, 487, 488 —, —, letters from 176 —, and mathematics 196, 197, 198, 216 —, at Pisa 134, 139-40 —, and Platonism 139-40, 150 —, and Possevino 131 measurement and physical research 86-7 mechanical clock 60 mechanics —, clock 60 —, Guidobaldo del Monte and 212 —, Galileo and 23, 103, 185, 212-13 —, and scientific revolution 459 Meckel, Johann Friedrich 410 medical astrology 61 medical science 445-9 Medici, Cosimo de' 139 medicine, history of 462 medicine, university teaching of 115 Mediterranean Sea, measurement of 287 Mei, Girolamo 294 Mendel, Gregor 436 Mercurius Trismegistus 139 Mercury (planet) 185 Mersenne, Marin 132n, 186, 258, 286, 383, 384 —, and history of optics 348, 352

510

Science, Art and Nature in Medieval and Modern Thought

—, and Jesuits 228 —, on language 285 —, on mathematics 105-6 —, and music 107-10, 296, 297 —, and Neoplatonism 229 —, and origins of language 275-85 —, and pendulum ratio debate 270-3, 485 —, and sound 296, 297 —, and virtu 113 Mery, Jean 347 Messahala 60 Messina 118, 119 metaphysics 52, 54, 79, 118 Micanzio, Fulgenzio 271 Michelangelo 101, 101-2 Michelini, Famiano 272 microcosm/macrocosm 40 microscope 91 Milan 102 Mill, John Stuart 260, 431 Mirandola see Pico della Mirandola, Giovanni Moivre, Abraham de 387 Moleto, Gioseffe (Giuseppe) 117-18, 126, 134, 175 Molwitz 410, 412, 428 Molyneux, William 354 monkeys 418 Montaigne, Michel de 167, 184, 379 Monte, Cardinal Frances^.. Maria del 117 Monte, Guidobaldo del 102-3, 126, 132, 175-6 —, and mathematics 198 —, and mechanics 212 —, and undated writings of Galileo 225, 480 Montesquieu, Charles de Secondat, Baron de la Brede et de 461 Montpellier 286 Montucla, John Etienne 258, 463 moon 43, 47, 106, 177, 179, 186 —, mountains on 258 moral science in Jesuit education 118 morals 94, 99, 118 Morcillo, Sebastian Fox 127 More, Thomas 104, 447 mortality records 386-7 Moscow 125 Moses 139 Moslem philosophy 72 Moss, Jean Dietz 231-2 motion, inertial 38

Miiller, Adolph 165 Miiller, Johannes see Regiomontanus music 18, 96, 103, 174, 219 —, arithmetically quantified 99 —, and astronomy 42 —, fifth interval 263 —, and hearing 291-9 —, history of 291-9 —, new language of 442 —, and origins of language 282-3 —, pendulum ratio debate 270-3 —, science of 107-10 —, theories of 86 —, and vibration 219 —, see also hearing; sound musical academy of the Camerata 294 —, see also colleges and universities Muslim theology 79 mutation of species 418 National Edition of Galileo 489, 490 natural philosophy 20, 82, 149-61, 153, 228 —, and Galileo 23, 139-61, 167, 208, 213, 267 natural selection 425, 431, 435, 436, 437 —, see also Darwin, Charles; evolution; transmutation of species nature, laws of 67, 68, 69, 75-7, 470, 472 —, and St Augustine 69, 72-5, 77 —, and R. Bacon 75-7 —, Descartes on 83-4 —, designation of 86 —, and Lucretius 69-70, 388 —, medieval conceptions of 67-88 —, and Newton 67, 85, 186 —, and Philo Judaeus of Alexandria 70-2 —, and Suarez 83 —, and Bishop Etienne Tempier 80 —, and William of Ockham 77-8 nature, Western visions of 1-12 navigation/cartography 19 Neckham, Alexander 369 Neoplatonism and Catholicism 166 Nero 60 Netherlands 35, 286 Neuperg, Comte 410 new cosmology 177, 433 new philosophy see experimental philosophy New Star of 1604 177, 178, 487 Newton, Sir Isaac 408, 409, 415, 417, 430

Index —, and causality 441 —, and expectation and choice 389 —, and language of science 441 —, and laws of gravitation 434 —, on laws of nature 67, 85, 186 —, and mechanistic theory 434 —, and scientific revolution 461 —, translated by Madame du Chatelet 462 'Nicholas, Master' (teacher) 59 Nicholas (Nicolaus) of Cusa 61, 62, 99, 453 Nicole, Pierre 379, 382-4 Nicomachus 293 Nifo, Agostine 184 Noailles, Francois de 272 North, John 471 Novara, Domenico Maria 115 objectivity, scientific 13-30 Olschki, Leonardo 473 omnipotent Craftsman 247 Opus tertiwn (Bacon, R.) 52 Optica (Alhazen) 316, 319 optics 54, 55, 56, 58, 63, 99 —, and art 105 —, and colour 45 —, and Galileo 217, 343 —, history of —, —, Alhazen 38, 301-28, 471, 473 —, —, Bacon, R. 52, 292, 316, 317-19, 326 —, —, Crombie 471 —, —, Descartes 345, 348-52, 354 —, —, Euclid 55, 302-3, 305, 308, 471 —, —, Fabrici 320, 325, 334 —, —, Galen 303, 307, 308, 309, 315-16, 325 —, —, Grosseteste 316-17 —, —, Kepler 38, 304-5, 329-45, 347-8, 350, 354-5 —, —, Leibniz 301-2, 354 —, —, Lindberg 471 —, —, Mersenne 348, 352 —, and ocular physiology 301, 473 —, see also eyes Oresme, Nicole 80, 82-3, 277, 454 —, and earth's rotation 470 —, and the world clock 473 —, and scientific vernaculars 469 oriental languages 118 The Origin of the Species (Darwin) 6, 429, 431, 435, 436 Oryx beisa (antelope) 288

511

Osiander, Andreas 257 Oxford 39, 52, 151,264 Pacioli, Luca 115, 131, 376 Pacius, Jules 286 Padua 140, 172, 175, 177, 198, 484 —, and Galileo 134, 178, 225, 227, 492 —, and mathematics 117, 118, 134 —, Peiresc explores 286 —, and philosophy 125, 133 —, and Possevino 126 —, see also under colleges and universities painting 34, 96-7, 173, 320, 343 Paley, William 416, 433 Palladio 132 Pappus 102, 206, 225, 269 Paris 39, 52, 80, 82, 153, 264, 490 —, Leibniz studies in 384 Paris, Matthew 39 Pascal, Blaise 113, 379, 381-2, 384, 3989,447 Pasteur, Louis 446 Pastoreaux rebels 52, 54 Patrizi, Francesco 127, 139-40, 166 Paul of Middleburgh 61 Paul, St 135 Pavia 140 Pecham, John (also Pisanus) 316, 319, 326, 332, 344 Peiresc, Nicolas Claude Fabri de 271, 278, 286-9, 494 —, background 286 —, collections of 288 —, correspondence 287 —, Lettres a Claude Saumaise et a son entourage 287-9 —, and origin of language 288-9 Peiresc (village) 286 Pena, Jean 131, 295 pendulum 179, 208, 270-3, 485 Pequet, Jean 111, 347 perception 26 Pereira, Benito 119, 122-4, 127, 132-3 —, on astromomical hypotheses 184 —, and mathematics 194 —, as source for Galileo's writings 153, 158, 168, 205, 269-70, 485 —, and undated writings of Galileo 221, 226, 227, 486, 487 —, and Vallius 485 —, alluded to 123 periodisation (ancient, medieval, modern) 34, 36, 452, 453

512

Science, Art and Nature in Medieval and Modern Thought

Perrault, Claude 299, 347 Persian language 278 Persio, Antonio 134 perspective 46, 98, 105, 106, 320, 473 —, and Greek mathematicians 441 —, Vieri on 137-8 persuasion see rhetoric Petrarch, Francesco Petrarca 34, 452-3 Petty, William 379, 385 Peurbach, Georg 99 Phaedrus (Plato) 133-6 Philander 132 Philo of Byzantium (2nd C B.C.) 132 Philo Judaeus of Alexandria (1st C A.D.) 70-2, 469-70 Philoponus, John 153, 221 philosophers, mechanistic 27 philosophy 35, 37, 52-3, 54, 126 —, Christian 72 —, empiricism 262 —, English 452 —, ethics 16 —, of Galileo 179, 257-62, 488 —, Greek see Greek philosophy —, of Grosseteste 40, 42-3 —, history of 458, 459 —, humanism 455 —, Italian 166 —, Jesuit 132 —, metaphysics 52, 54, 79, 118 —, natural 149-61, 166 —, Neoplatonism 166 —, Platonic 127, 134 —, positivism 259, 260, 261 —, psychology 26 —, rationalism 89-114 —, scepticism 20, 72, 128, 167 —, Stoics/Stoicism 21, 68, 71, 72, 128 —, see also God; logic; truth physical research and measurement 86-7 physick, history of 462 physics —, experimental 206-7 —, Greek 16 —, in Jesuit education 118 Piccolomini, Alessandro 122, 124, 132, 194, 195 —, and mathematics 123 —, and mechanics 175 —, and rhetoric 236-42, 243, 245, 250 Pico della Mirandola, Giovanni 126, 139, 166 Pico, Gianfrancesco 131 Pico, Giovanni 127

Piero della Francesca 99 Pieroni, Giovanni 271 pigeons 418 pin hole image see camera obscura Pinelli, Giovanni Vincenzo 117, 126, 134, 175, 286 —, and library 288 —, manuscripts 187 —, and undated writings of Galileo 225 Pinelli library 288 Pisa 156, 173, 181, 198 —, and Galileo's writings 227, 479, 486 —, Peiresc's background 286 —, see also under colleges and universities Pisa, Leaning Tower of 259 Pisanus see Pecham, John planets 54, 61, 99, 178, 181, 185 —, Jupiter 179, 217, 287 —, planetary intervals 21 —, Venus 186 —, see also astronomy; cosmology; telescope plants and longevity 57 Plater, Felix 320, 324-5, 329, 334, 335 Plato 32, 134, 139,261,275 —, and acoustics 292 —, and architecture 91-2 —, and creation 71 —, critics of 127 —, and expectation and choice 362 —, and mathematics 123, 196, 197, 198, 200 —, and nature —, —, as a deductive system 21 —, —, laws of 68, 69 —, and origin of language 275 —, philosophy 127, 134 —, and properties/qualities 219 —, and rhetoric 92-3, 237, 362 —, and scientific style 467 —, and undated writings of Galileo 222, 226 —, alluded to 31, 95, 149, 358, 486 Platonism 115-40, 150 Platter see Plater, Felix Plempius, Vopiscus Fortunatus 345 Pliny the Elder 60, 469 Plotinus 72, 138 Plutarch 127, 129, 130 poetry 34 Poland 125, 126 political —, bulverism 28

Index —, history 453 —, role of science 21 politics 21, 28, 29, 95, 453 Ponce de Leon, Pedro 110, 284 population 385 Porphyry 293 Port-Royal 382 Porta, Giambattista della, 223, 301, 328, 329, 335 Posidonius 129 positivism 259, 260, 261 Possevino, Antonio 124-32 —, on astrology 132 —, and calendar reform 125-6 —, diplomatic missions 125 —, friendships 175 —, and influence of Clavius 128, 131 —, and Jesuit society 125, 126 —, as Papal Nuncio 125 —, written work —, —, Bibliotheca selecta 126-32, 133, 175 —, —, on Jesuit universities 125 —, —, on peace mission to Russia 125 Postel, Guillaume 288 postulation, theoretical, of Galileo 268-9 power 27, 67-88, 79-81 power, propogation of 55 Prado, Jeronimo 132n Prague 334 Priestley, John 463 primary properties/secondary qualities 157, 218-19 Princeton 264 Priscian (Priscianus Caesariensis) 31, 223 probabilities 359, 468 —, history of 360-7, 369-74 —, —, arguments from 357-400 —, —, and natural selection 388-400 —, see also expectation and choice probability theories 360-7,387, 389-92 Proclus 123, 131, 217, 269 —, analysis and synthesis 209 —, on Euclid 101, 175 —, and mathematics 195, 196, 198, 216 proof, concept of 68, 466 Protestant reformation 36 Protestantism 455 Psalms, translation of 40 Psellus, Michael 131 psychiatry, Western 446 psychology 26 Ptolemy 59, 60, 62, 131, 175 —, and astronomy 209

513

—, and R. Bacon 55, 58 —, and calendar 47 —, and Clavius 182 —, and experimental argument 467 —, and Grosseteste 45, 46 —, and music 293, 295 —, and optics 96, 303, 308, 313, 317, 471 —, —, eye, history of the 305, 306 —, and planetary tables 469 —, primary properties/secondary qualities 219 —, and refraction 86, 472 —, and rhetoric 238 —, and scientific revolution 456 —, and scientific style 467 —, and tables of refraction 332 —, and undated writings of Galileo 225 public health 448 Pythagoras 127, 131, 139, 149, 296 Querengo, Antonio 254 Quintilian, Marcus Fabius 367 Quintilianus, Aristides 293 Raimondi, Giambattista 116, 139 rainbows 38, 40, 45, 57 —, studies of 471-2 Ralegh (Raleigh), Sir Walter 36 Ramelli, Agostino 320 Ramus, Peter 36 Rashdall, H. 54 ratio 58-59, 268, 270-3, 332 rational artist 89-114 Ray, John 413, 415, 425 Reael, Laurens 270 Redi, Francesco 414 Redondi, Pietro 485, 489, 490 reefs, coral 433 reflection 56, 177 Reformation of Religion 36, 456 refraction 55, 56 Regiomontanus 61 religion and scientific revolution 455 religious reform 36, 456 renaissance 96, 452, 455 reproduction, theories of 422-3 resolution and composition (Galileo) 209 rhetoric 92-3, 231-55, 436 —, and Aristotle 232, 236-40, 243, 2478, 250-2, 362-3 —, and Cardano 249 —, and Colombe 245-6 —, and Copernicus 244

514

Science, Art and Nature in Medieval and Modern Thought

—, and Darwin 6 —, and Descartes 6 —, and Ficino 249 —, and Galileo 6, 180-1, 216, 231-55, 485, 494 —, and Gherardini 149, 239 —, and Gorgias 234 —, and Hippocrates 235 —, and J.D. Moss 231-2 —, and Plato 92-3, 237, 362 —, and Ptolemy 238 Riccardi, Padre, Maestno del Sacro Palazzo 490 Richard of Wallingford 82, 470, 473 Ristoro, Juliano 117 Robertson, William 463 Rocco, Antonio 161, 186 Romanticism 37 Rome 271, 272, 346, 453, 489, 490, 494 —, see also under colleges and universities Ronchi, Vasco 471 Rose, Cipriano de 294 Roshdi Rashed 470 Rossi-Monti, Paolo 267n Rousseau, Jean Jacques 461 Royal Society Catalogue of Scientific Papers 436 The Royal Society 258, 460, 461 Rudolph II, Emperor 331, 494 Rushworth, William 381 Russell, Gul 470 Sabra, A.I. 471 Sacrament of the Eucharist 489 Sacrobosco, Johannes de 60, 486 'Sagredo' (and Galileo) 226, 244, 251 salamander 411 'Salviati' as Galileo 226, 243-5, 247-8, 250-3, 261 Santillana, Giorgio de 257 Santorio Santorio 485 Sarpi, Pietro 176 Saturn 185 Saumaise, Claude 287, 289 Savoy 125 Scaliger, Joseph-Juste 278, 288 Scaliger, Julius Caesar 153 scepticism 20, 72, 128, 167 —, see also Stoics/Stoicism Scheiner, Christopher 180 and history of optics 345-7 science: —, and Clavius 181-3, 184, 185, 187

—, experimental 89-114 —, history of 31-8, 263-70, 440, 443-4, 451-64 —, and Islam 54 —, language of 3, 439-42 —, of music 107-10 —, and nature 1, 19, 54, 165-229 —, new science 35, 36, 279, 459 —, quantitative 20 —, of vision 302 —, —, see also optics —, Western visions of 1-12 scientific language 439-42 scientific method of Darwin 429-37 scientific method of inquiry 10, 11, 12, 467-8 scientific objectivity, Western experience of 13-30 scientific revolution 451-64 scientific style 159, 229, 270, 467-8, 472 scientific thought of R. Bacon 53-63 scorpion 412 Scriptures, Holy 41, 53, 182, 470 sculpture, Galileo's interest in 173 Sedgwick, Adam 433 Semitic groups and origins of language 278 Seneca, Lucius ('the Younger') 34, 51, 60 Sextus Empiricus 218, 365, 366, 379 Shakespeare, William 105, 416 Shea, William 157, 158 shell, tropical, at Shrewsbury 433 Shirley, John 473 Siculus, Diodorus 275 Silvestris, Bernard 33 Simon de Montfort 41, 59 'Simplicio' —, as Aristotle 243, 247, 250, 252, 253 —, and undated writings of Galileo 226 Simplicius 183, 221 Siraisi, Nancy 471 Smith, Adam 392, 394, 396 Snel, Willebrord 349 social responsibility 99 —, see also virtu Socrates 32, 200, 233-6, 466 solar eclipses 329-30, 332 solar radiation 43 Soto, Domingo de 126 sound 42, 108-9, 219, 292, 296, 297-8 —, see also hearing; music South America 431, 434 Spain 110, 284

Index species, classification of 413 Speculum astronomic, authorship question of 61 Speroni, Sperone 126 Sprat, Thomas 461 stars 43, 57, 177, 178, 179 —, see also astronomy; cosmology; planets statistics 11, 385-8, 399, 447, 448 —, and economy 392 —, and evolution 398 —, and Maupertuis 390 Stoffler, Johannes 62 Stoics/Stoicism 21, 68, 71, 72, 128 —, see also scepticism Straker, Stephen 471, 473 Sturm, Johann Christoph 347 Suarez, Francisco 83, 84 submarines 33, 57 sulpher drugs 448 sun 179, 186, 211, 213 sunspots 207, 269 —, Galileo on 211 —, —, First Letter 87, 150, 180, 186, 215, 216 —, —, Second Letter 213 —, —, Third Letter 215 Swammerdam, Jan 414 Sweden 125 Sydenham, Thomas 446 Taccola (Mariano di Jacopo) 106, 320 Tartaglia, Niccolo 132 Tartars 54 Tasso, Torquato 223 taxonomy and scientific style 11, 467-8 technology, modern 448-9 Tedeschi, Leonardo 177 telescope 87, 91, 186, 207, 217, 494 —, discoveries 177, 185, 214 —, of Kepler 343 —, observations 106, 179, 217, 286-7 Telesio 249 Tempier, Bishop Stephen 53, 61, 80 Thabit ibn Qurra 62 Thales 130 Themistius 239, 292 Theodoric of Freiberg 38, 471-2 Theodosius 59 theological letters of Galileo 229 theology 23, 34, 54, 151 —, and Archimedes 470 —, and Aristotle 22, 151, 470 —, Christian 5, 72, 79, 99, 469

515

—, and Galileo 229 —, Hebrew 27, 70, 469 —, Islamic 5 —, and Jesuit education 118 —, and modern science 16, 461 —, Muslim 79 —, see also belief and doubt; Catholicism; Creator; God Theon of Smyrna 219, 293 Theophratus 467 thermometers 111, 203, 485 Thierry of Chartres 31, 32 Thomas Aquinas see Aquinas, St Thomas Thomas de Vio see Cajetan Thorndike, Lynn 59-60 Thucydides 13, 14, 27 tides 43, 47, 160, 179, 185-6, 211 Times Literary Supplement 479, 484, 489-91 Toledan tables 60 Toledo, Francisco de (Toletus) 119, 126, 153, 158 —, written work 168, 172, 269-70, 484 Toletus see Toledo, Francisco de Torres, Balthassar 119 Torricelli, Evangelista 118 Toscanelli, Paolo dal Pozzo 59, 99 Tournefort, Joseph Pitton de 413 Tractationes de mundo et de caelo (Galileo) 151-60, 167, 194 transmutation of species 434 —, see also Darwin, Charles; evolution; natural selection Tribunal of the Holy Office 490 true/false premise 182 truth 23, 24, 53, 381 —, and bulverisation 28 —, and communism 29 —, in modern science 25 Turks' invasion of Greek churches 456 Tuscany 139 Tuscany, Grand Dukes of 134, 159, 247, 492-3 Tycho see Brahe, Tycho Tyndall, John 3 Tyson, Edward 413, 415, 418 United States 59, 264, 476 universal language 277, 278, 282 universities see colleges and universities Urban VIII, Pope 489, 490-1 Valerio, Luca 116, 207 Valla, Giorgio 100, 102, 131

516

Science, Art and Nature in Medieval and Modern Thought

Valle see Vallius Vallesius (Francisco Valles) 126, 177, 284 Vallius, Paulus (Paolo della Valle) 169, 479 —, and Galileo's writings 484 —, and Pererius 485 —, and Zabarella's tracts compared 480-4 Valori, Baccio 134, 139 Vasari, Giorgio 453 Vatican Library 294 Venice 48, 133, 153, 155, 271, 293 —, see also under colleges and universities —, Vincenzo Galilei studies in 294 Venus 185,186 Vere, William de 39 Vesalius, Andreas 320, 324, 325, 328 Vick, Henri de 82 Vickers, Brian 232-3 Vico, Giovanni Battista (Giambattista) 461 Vieri, Francesco 134-9 —, background 134, 138 —, and astrology 136 —, on perspective 137-8 —, Platonic philosophy —, written work 135, 138, 139 Viete, Francois 225, 442, 485, 487 Villalpando, Juan Batiste 132n Villani, Filippo 34, 453 Villard de Honnecourt 97, 473 Vinta, Belisario 179, 224, 227 Vio, Tommaso de see Cajetan Virgil 75 virtu 89-91, 98-9, 104, 112, 113 —, and the Renaissance 89, 453, 477 Vitelleschis, Mutius 485 Vitelo see Witelo Vitruvius 101, 132, 212, 223

Vitry, Philippe de 293 Viviani, Vincenzo 103, 156, 203, 224, 225, 259 Voltaire 258, 408, 409 —, on Maupertuis 409, 410, 411, 417, 427 —, and scientific revolution 451-2, 456, 457, 461, 462-3 Waard, Cornelis de 270, 287 Wallace, Alfred Russel 431, 432, 435 Wallace, William 156, 158, 172-4n, 479, 484, 485 Walter of Odington 293 watermarks on Galileo's paper 156, 157, 162-3 weather 43, 387 weather glass 111 weather, prediction of 52, 136 Welser, Mark 126 Whewell, William 3, 258, 260, 441, 463 William of Auvergne 52 William of Conches 31 William of Ockham 77-8, 80-1 Willis, Thomas 299, 353 Wisan, Winifred 208, 215, 270 witchcraft 372 Witelo 63, 132, 316, 330-1, 342, 344, 471 —, critics 331, 333, 334 —, Ptolemy's tables 332 —, and rainbows 472 Witt, Jan de 379, 384, 387 world, conceptions of 21, 22 Wotton, Henry 343 Young, Thomas 463 Zabarella, Giacomo 140n —, and Vallius tracts compared 480-4 Zarlino, Gioseffe 131, 293, 294, 295, 296 Zonca, Vittorio 320 Zorzi, Benedetto 134