Cambridge and Vienna: Frank P Ramsey and the Vienna Circle

CAMBRIDGE AND VIENNA FRANK P. RAMSEY AND THE VIENNA CIRCLE

VIENNA CIRCLE INSTITUTE YEARBOOK [2004]

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VIENNA CIRCLE INSTITUTE YEARBOOK [2004] 12 Institut ‘Wiener Kreis’ Society for the Advancement of the Scientific World Conception Series-Editor: Friedrich Stadler Director, Institut ‘Wiener Kreis’ and University of Vienna, Austria Advisory Editorial Board: Rudolf Haller, University of Graz, Austria, Coordinator Nancy Cartwright, London School of Economics, UK Robert S. Cohen, Boston University, USA Wilhelm K. Essler, University of Frankfurt/M., Germany Kurt Rudolf Fischer, University of Vienna, Austria Michael Friedman, University of Indiana, Bloomington, USA Peter Galison, Harvard University, USA Adolf Grünbaum, University of Pittsburgh, USA Rainer Hegselmann, University of Bayreuth, Germany Michael Heidelberger, University of Tübingen, Germany Jaakko Hintikka, Boston University, USA Gerald Holton, Harvard University, USA Don Howard, University of Notre Dame, USA Allan S. Janik, University of Innsbruck, Austria Richard Jeffrey, Princeton University, USA Andreas Kamlah, University of Osnabrück, Germany Eckehart Köhler, University of Vienna, Austria Anne J. Kox, University of Amsterdam, The Netherlands Saul A. Kripke, Princeton University, USA Elisabeth Leinfellner, University of Vienna, Austria Werner Leinfellner, Technical University of Vienna, Austria James G. Lennox, University of Pittsburgh, USA Brian McGuinness, University of Siena, Italy Kevin Mulligan, Université de Genève, Switzerland Elisabeth Nemeth, University of Vienna, Austria Julian Nida-Rümelin, University of Göttingen, Germany Helga Nowotny, ETH Zürich, Switzerland Erhard Oeser, University of Vienna, Austria Joëlle Proust, École Polytechnique CREA Paris, France Alan Richardson, University of British Columbia, CDN Peter Schuster, University of Vienna, Austria Jan Šebestik, CNRS Paris, France Karl Sigmund, University of Vienna, Austria Hans Sluga, University of California at Berkeley, USA Elliott Sober, University of Wisconsin, USA Antonia Soulez, Université de Paris 8, France Wolfgang Spohn, University of Konstanz, Germany Christian Thiel, University of Erlangen, Germany Walter Thirring, University of Vienna, Austria Thomas E. Uebel, University of Manchester, UK Georg Winckler, University of Vienna, Austria Ruth Wodak, University of Vienna, Austria Jan, WoleĔski, Jagiellonian University, Cracow, Poland Anton Zeilinger, University of Vienna, Austria

Honorary Consulting Editors: Kurt E. Baier Francesco Barone C.G. Hempel † Stephan Körner † Henk Mulder † Arne Naess Paul Neurath † Willard Van Orman Quine † Marx W. Wartofsky † Review Editor: Michael Stöltzner Editorial Work/Layout/Production: Hartwig Jobst Camilla R. Nielsen Erich Papp Editorial Address: Institut ‘Wiener Kreis’ Universitätscampus, Hof 1 Spitalgasse 2-4, A-1090 Wien, Austria Tel.: +431/4277 41231 (international) or 01/4277 41231 (national) Fax.: +431/4277 41297 (international) or 01/4277 41297 (national) email: [email protected] homepage: http://univie.ac.at/ivc/

The titles published in this series are listed at the end of this volume.

CAMBRIDGE AND VIENNA FRANK P. RAMSEY AND THE VIENNA CIRCLE

Edited by

MARIA CARLA GALAVOTTI Università di Bologna, Italy

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EDITORIAL Frank Plumpton Ramsey, who was born on February 22, 1903 in Cambridge, England, and died in London on the 19th of January 1930, was certainly one of the most important and promising philosophers of the 20th century. Only his early and unexpected death at the age of 26 probably prevented him from becoming one of the leading figures in the philosophy of science and analytic philosophy – perhaps at a par with Ludwig Wittgenstein, his lifelong close friend but also intellectual adversary. It is well known that in his short life Ramsey immensely enriched philosophy and science with his profound and highly topical contributions on the foundation of mathematics, logic, and economics. As a gifted student at Trinity College, Fellow at King’s College and Lecturer at Cambridge University he influenced Wittgenstein, Russell and Keynes as well as the Vienna Circle with his contributions on the foundations of mathematics, logic, and economics. Especially his significance for philosophy with his focus on notions of truth, decision making, belief and probability is worth mentioning. The intellectual context of Ramsey’s thinking can also be illustrated with the famous Bloomsbury Group.1 My perspective of Frank Ramsey’s life and work was shaped by my personal acquaintance with Ramsey’s sister Margaret Paul (whom I met in 1992 when she shared biographical information and research literature on her brother.) Especially the period he spent in Vienna in 1924 and his contacts with the mathematician Hans Hahn, the physicist Felix Ehrenhaft, among others, spurred me to focus on Ramsey’s connection with the early Vienna Circle. I also repeatedly noticed Ramsey’s significance while writing my book on the Vienna Circle:2 Already in 1929, Ramsey was listed in the manifesto of the Vienna Circle and given credit for attempting to further develop Russell’s logicism and cited as an author related to the Vienna Circle. There are references to his articles on “Universals” (1925), “Foundations of Mathematics” (1926), and “Facts and Propositions” (1927). The proceedings of the “First Meeting on the Epistemology of the Exact Sciences in Prague” (September 15-17, 1929) mention Ramsey as one of the “authors closely associated with the speakers and discussions”, together with Albert Einstein, Kurt Gödel, Eino Kaila, Viktor Kraft, Karl Menger, Kurt Reidemeister, Bertrand Russell, Moritz Schlick and Ludwig Wittgenstein.3 1

2

3

Cf. The British Tradition in 20th Century Philosophy. Ed. by Jaakko Hintikka and Klaus Puhl. Vienna: Hölder-Pichler-Temspky 1995. Friedrich Stadler, The Vienna Circle. Studies in the Origins, Development, and Influence of Logical Empiricism. Vienna-New York: Springer 2001. Erkenntnis I, 1930/31, pp. 311 and 329.

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But looking at the earlier communication of Ramsey with Wittgenstein and the Vienna Circle these references are not really surprising: whereas it is rather well known that Ramsey visited Wittgenstein in 1923 and 1924, his communication with Schlick and his probable participation in the Schlick Circle have not been fully appreciated. Carnap’s notes on the discussion in the Schlick Circle include Ramsey’s definition of identity, the foundations of mathematics and probability: July 7, 1927: “Discussion by Carnap and Hahn about Carnap’s arithmetic and Wittgenstein’s objection to Ramsey’s definition of identity”.4 Accordingly, Carnap reported on an earlier discussion (June 20, 1927) in the Wittgenstein group with Schlick and Waismann, in which the great “genius” also objected to Ramsey’s notion of identity. Precisely this issue was on the agenda again 4 years later when Wittgenstein met Schlick and Waismann alone (December 9, 1931).5 His lifelong dealings with Ramsey is documented later on in Carnap’s Philosophical Foundation of Physics (1966) with its special focus on the Ramsey sentence. Another reference is worth mentioning here. Commenting retrospectively on his article “The Role of Uncertainty in Economics” (1934), the mathematician Karl Menger, a member of the Vienna Circle and the founder of the famous “Mathematical Kolloquium”, recognised the relevance of Ramsey’s paper “Truth and Probability” (1931) – unknown to him at the time – for his own research, while distancing his own contribution from this study: 6 But the von Neumann-Morgenstern axioms as well as Ramsey’s were based on the traditional concept of mathematical expectation and on the assumption that a chance which offers a higher mathematical expectation is always preferred to one for which the mathematical expectation is smaller. My study was not.

In connection with his stay in Vienna, there is another fact of Ramsey’s life that merits attention: he underwent a (supposedly successful) psychoanalytic therapy with the lay psychoanalyst and historian of literature Theodor Reik (1888-1969), who, by the way, also gave him a book by the theoretical physicist Hans Thirring. After studying the influence of Logical Empiricism in the Anglo-Saxon world, I turned to the investigation of the mutual relations and influences between Austrian and British philosophy of Science since 1900 by writing a completion of Herbert Feigl’s famous account “The Wiener Kreis in America”. It complements “The Wiener Kreis in Great Britain”7 and can be seen as a reconstruction of the 4 5 6 7

Stadler, The Vienna Circle, p. 238f. Ibid., p. 441. Karl Menger, Selected Papers 1979, p. 260. Friedrich Stadler, “The Wiener Kreis in Great Britain: Emigration and Interaction in the Philosophy of Science”, in: Edward Timms/Jon Hughes (eds.), Intellectual Migration and Cultural Transformation. Refugees from National Socialism in the English-speaking World. Vienna-New York: Springer 2003, pp. 155-180.

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“Austro-British Connection”, with Ramsey as one of the intermediaries and innovators. Here, we can write yet another history with regard to the transfer and transition “from Wiener Kreis to Vienna Circle in Great Britain”: it was, above all, the founder and head of the Vienna Circle, Moritz Schlick, who fostered early intellectual contacts with Britain. Schlick visited England at least twice in the late 1920s as his still unpublished correspondence with Ramsey (1927/28) reveals.8 Ramsey, who invited Schlick to the “Moral Sciences Club” in Cambridge, discussed his personal controversy with Wittgenstein which was triggered by his article “The Foundations of Mathematics” (1925): I had a letter the other day from Mr Wittgenstein criticising my paper ‘The Foundations of Mathematics’ and suggesting that I should answer not to him but to you. I should perhaps explain what you have gathered from him, that last time we didn’t part on very friendly terms, at least I thought he was very annoyed with me (for reasons not connected to logic), so that I did not even venture to send him a copy of my paper. I now hope very much that I have exaggerated this, and that he may perhaps be willing to discuss various questions about which I should like to consult him. But from the tone of his letter and the fact that he gave no address I am inclined to doubt it. 9

This description is also confirmed by Wittgenstein’s critical and ambivalent comments on Ramsey in his Diaries (April 26, 1930).10 These contacts continued, and in one of his last letters before his death, Ramsey reported to Schlick on Wittgensteins’s impact on his own philosophy (namely in the sense that it “quite destroyed my notions on the Foundations of Mathematics”) as well as on Cambridge philosophy in general.11 After Ramsey’s premature death Schlick, whose book on Einstein’s relativity theory was immediately translated into English already in 1920, delivered a programmatic paper on “The Future of Philosophy” at the “Seventh International Congress of Philosophy” in Oxford 1930, announcing the linguistic turn in philosophy.12 Here he advocated the dissolution of the classical philosophical canon by drawing a functional distinction between scientific philosophy on the one hand, and related scientific theorizing on the other. Carnap, too, played an important role in this interaction: on the invitation of Susan Stebbing he delivered three lectures at the University of London in October 1934, where he came into contact with Russell, Woodger and Richard 8

9 10

11 12

Cf. Schlick papers at the Vienna Circle Archives located in Haarlem, The Netherlands. The correspondence will be published as part of the Schlick edition project: http://www.univie.ac.at/ivc/Schlick-Projekt/ Ramsey to Schlick, July 22, 1927. Ibid. Ludwig Wittgenstein, Denkbewegungen. Tagebücher 1930-1932, 1936-1937. Hrsg. von Ilse Somavilla.Frankfurt/M.: Fischer 1999, p. 20f. Ramsey to Schlick, Dec.10, year not dated, op.cit. Cf. Moritz Schlick, “The Future in Philosophy”, in: Schlick, Philosophical Papers, Vol II, ed. by Henk L. Mulder and Barbara van de Velde-Schlick. Dordrecht: Reidel, pp. 210-224.

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Braithwaite, the friend of Ramsey and editor of his collected papers in 1931. Here he also met the young Max Black, who wrote his Ph.D. thesis on “The Theories of Logical Positivism” and published on The Nature of Mathematics (1933) under the influence of Moore and Ramsey. He also translated Carnap’s books The Unity of Science (1934) as well as Philosophy and Logical Syntax (1935). Later on he described the “Relations between Logical Positivism and the Cambridge School of Analysis” (1938/39) concluding that “there should be room for further fruitful exchange of opinions between the two movements”.13 Therefore, it is no coincidence that Black many years later described Ramsey in the Encyclopedia of Philosophy (ed. by Paul Edwards) as one of the most brilliant men of his generation; his highly original papers on the foundation of mathematics, the nature of scientific theory, probability, and epistemology are still widely studied. He also wrote two studies in economics, the second of which was described by J.M. Keynes as ‘one of the most remarkable contributions to mathematical economics ever made’. Ramsey’s earlier work led to radical criticisms of A.N. Whitehead and Betrand Russell’s Principia Mathematica, some of which were incorporated in the second edition of the Principia. Ramsey was one of the first to expound the early teachings of Wittgenstein, by whom he was greatly influenced. In his last papers he was moving toward a modified and sophisticated pragmatism.14

This was only one aspect of the flourishing bilateral exchange of ideas also on the level of institutions and periodicals, e.g., the journal Analysis and the “Analysis Society” (from 1936), of course, with A.J. Ayer as the most important intermediary with his extremely influential book Language, Truth and Logic (1936). In summary, we can say that in Britain there was a lively scholarly dialogue between Central European and English philosophers – with the focus being mainly analysis, as compared to the turn from Carnap’s “Wissenschaftslogik” (logic of science) to “Philosophy of Science” in the U.S.A. But there had also been mutual contacts since around 1900 which cannot be separated from what has been referred to as the Anglo-Saxon ‘Sea Change’ (H.St. Hughes).15 What we have here is a dynamic network at work on different levels with distinct convergences and divergences of ideas and theories. Moreover, it is a network that reflected an intellectual preoccupation with several philosophical and methodological debates conducted between thinkers from different countries: from the Austro-German Methodenstreit and the Positivism disputes (Lenin vs. Mach, Horkheimer vs. Neurath) to the foundational debates in mathematics and logic since the 1920s. But the style and form of theorizing changed under different social conditions in the countries of immigration triggering off selforganizing processes of innovation and scholarly exchange. This can be 13 14 15

In: Erkenntnis/Journal of Unified Science, Vol. VIII, p. 34. Black, “Frank P. Ramsey”, in: P. Edwards (ed.), The Encyclopedia of Philosophy. Vlm. 7/8, p. 65. H.St. Hughes, The Sea Change. The Migration of Social Thought, 1930-1965. New York: McGraw-Hill Book Company 1975.

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exemplified by the Bloomsbury Group, Wittgenstein’s Cambridge, Neurath’s Oxford and last but not least Hayek’s and Popper’s London.16 In 2003 we already witnessed two centenary conferences dedicated to Frank P. Ramsey in Cambridge, UK (June 30 to July 2, 2003) and Paris (October 24-25, 2003). The last one in Vienna (November 28-29, 2003), organized by the Institut Wiener Kreis / Institute Vienna Circle together with the University of Vienna, was deliberately entitled “Cambridge and Vienna” to indicate the focus on the exchange and influence of ideas, as exemplified by Ramsey and the Vienna Circle. This appeared necessary to us because we still lack a profound understanding of Ramsey’s life and work in the German-speaking scientific community. This cannot be compensated by the fact that there is a German translation of Ramsey’s Foundations: Essays in Philosophy, Logic, Mathematics and Economics (ed. by D.H. Mellor in 1978) by the publisher Frommann-Holzboog (Stuttgart-Bad Cannstatt 1980). We are still waiting for the intellectual biography on Ramsey which was already planned by his sister Margaret, who in the meantime has also passed away. Maybe our proceedings will offer another incentive for such a valuable and necessary book in English and German. The organizers and speakers mourned the passing of two friends and extraordinary scholars: Dick Jeffrey had already agreed to come before he died.17 Unfortunately, we also had to commemorate the unexpected death of Donald Davidson (19172003), who had readily accepted our invitation to participate in our Ramsey conference with a paper on “Ramsey and Russell on Subject and Predicate”. This paper was also planned as our distinguished 11th Vienna Circle Lecture 2003. I personally had the privilege and pleasure to meet Donald Davidson once several years ago on the occasion of a dinner with his wife Marcia Cavell and Kurt Fischer here in Vienna and I was very much impressed by his sober and intellectual personality. We then invited him to our conference which he was looking forward to as he expressed in one of his e-mails to me. When we contacted his widow Marcia Cavell to ask her for Donald’s finished manuscript of this conference, we agreed to organise a memorial session for Donald Davidson which friends and colleagues were to attend. And it was a great honor that Patrick Suppes and Michael Dummett agreed to contribute to the memory of their common friend. Although Michael Dummett was not able to

16

17

Cf. D.J. Edmonds and J.A. Eidinow, Wittgenstein’s Poker. The Story of a Ten Minute Argument between two Great Philosophers. London: Faber and Faber 2001. Hans Veigl, Wittgenstein in Cambridge. Eine Spurensuche in Sachen Lebensform Wien: Holzhausen 2004. Cf. Maria Carla Galavotti, “Remembering Dick Jeffrey (1926-2002)”, in: Induction and Deduction in the Sciences. Ed. by Friedrich Stadler. Dordrecht-Boston-London: Kluwer, p. 353f.

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attend our conference for health reasons, we were happy that he sent us his paper together with his memories and an obituary of Donald Davidson, so that all these commemorative pieces by Dummett and Suppes are now included in this volume. Let me express my sincere thanks to all of our speakers for having participated in the conference and contributed to the proceedings. Special thanks go to my colleagues on the program committee: especially to Maria Carla Galavotti, who initiated and chaired the conference and served as editor of its proceedings, and to Eckehart (Kay) Köhler for his help.

Vienna, October 2004

Friedrich Stadler (University of Vienna, and Vienna Circle Institute)

TABLE OF CONTENTS

A. CAMBRIDGE AND VIENNA. FRANK P. RAMSEY AND THE VIENNA CIRCLE

GABRIELE TAYLOR: Frank Ramsey – A Biographical Sketch .............................. 1 BRIAN MCGUINNESS: Wittgenstein and Ramsey ................................................ 19 MICHAEL DUMMETT: The Vicious Circle Principle ............................................ 29 PATRICK SUPPES: Ramsey’s Psychological Theory of Belief ............................. 35 BRIAN SKYRMS: Discovering “Weight, or the Value of Knowledge” ................ 55 STATHIS PSILLOS: Ramsey’s Ramsey-sentences ................................................ 67 ECKEHART KÖHLER: Ramsey and the Vienna Circle on Logicism ..................... 91 J. W. DEGEN: Logical Problems Suggested by Logicism ................................. 123 WERNER LEINFELLNER: The Foundation of Human Evaluation in Democracies from Ramsey to Damasio ...................................................... 139 MARIA CARLA GALAVOTTI: Ramsey’s “Note On Time” .................................. 155

B. GENERAL PART

R EPORT – D OCUMENTATION HELEN E. LONGINO: Philosophy of Science after the Social Turn .................... 167 ALLAN JANIK: Notes on the Origins of Fleck’s Concept of “Denkstil” ........... 179 YAMAN ÖRS: Hans Reichenbach and Logical Empiricism in Turkey .............. 189

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R EVIEWS Steve Awodey & Carsten Klein (eds.), Carnap Brought Home:The View from Jena. Full Circle: Publications of the Archive of Scientific Philosophy. Volume 2. Chicago: Open Court, 2004. (Christopher Pincock) ................................................................................. 213 Bergmann, Gustav, Collected Works Vol. I:Selected Papers I, edited by E. Tegtmeier, Frankfurt/Lancaster: Ontos-Verlag, 2003. (Daniel von Wachter) ................................................................................. 219 Ferrari, Massimo, Ernst Cassirer – Stationen einer philosophischen Biographie. Von der Marburger Schule zur Kulturphilosophie, Meiner: Hamburg, 2003 (German translation of Cassirer. Dalla Scuola di Marburgo alla filosofia della cultura, Florence: Olschki, 1996) (Gabriele Mras) ........................................................................................... 223 Richard C. Jeffrey, Subjective Probability:The Real Thing, Cambridge University Press, 2004. Richard C. Jeffrey, After Logical Empiricism/Depois do Empirismo Lógico, English edition with Portuguese translation by António Zilão, Lisbon: Colibri, 2002. (Matthias Hild) ........................................................................................... 228 Patrick Suppes, Representation and Invariance of Scientific Structures, CSLI publications, Stanford, California (distributed by Chicago University Press). (Claudia Arrighi / Viola Schiaffonati) ........................................................ 231

A CTIVITIES OF THE I NSTITUTE V IENNA C IRCLE

Activities 2004 ................................................................................................. 237 Preview 2005 .................................................................................................... 241

C ONTENTS

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O BITUARIES

Donald Davidson: A Brief Memoir (Michael Dummett) ..................................................................................... 243 Obituary of Professor Donald Davidson (1917–2003) (Michael Dummett)...................................................................................... 245 Memories of Donald Davidson (Patrick Suppes) .......................................................................................... 251

Index of Names ................................................................................................ 253

G ABRIELE T AYLOR

FRANK RAMSEY – A BIOGRAPHICAL SKETCH

I. Over ten years ago, in September 1992, Margaret Paul and I spent a fortnight in Vienna, in the footsteps of Frank Ramsey. Margaret was Frank’s much younger sister. She was a Fellow of Lady Margaret Hall, Oxford, and a tutor in Economics. She was married to George Paul, Philosophy tutor and Fellow of University College, Oxford. They had four daughters. After her retirement in 1983 she began writing a memoir of her brother Frank, a task she found totally absorbing until her illness prevented her from continuing this kind of work. She died last year. The manuscript she left behind is practically complete, and I want to try and give a picture of Frank and his short life as it emerges from those pages. Being so much younger, and Frank dying so young, she cannot be said to have shared his life to any great extent, but of course they shared the same background: both were born into a distinguished academic family in Cambridge. Their father, Arthur Stanley Ramsey, a mathematician, was successively Fellow and Tutor, Bursar and finally President (ViceMaster) of Magdalene College, Cambridge, from 1897 until 1934. Her mother, Agnes, a graduate of Oxford, had a passionate interest in social work and feminism. She was killed in a car accident when Margaret was only 10. There were four children: Frank, the eldest; Michael, the only one of the children not to reject the religion of their parents and grandparents. He was archbishop of Canterbury from 1961-74; Bridget, who became a doctor, and finally Margaret. Obviously, quite apart from having easy access to letters and diaries, she was in a unique position to tell Frank’s story from an insider’s point of view. Frank was 14 when Margaret was born, a scholar at Winchester College. He took a keen interest in the new arrival. His letters home show him giving thought to what sort of book would be suitable to give his baby sister for her christening. He had some suggestions to make: What book? I think the Just-So-Stories nicely bound for 5/- Perhaps Esmond or Ivanhoe or Pickwick or Martin Chuzzlewit or David Copperfield would be better. What do you think? I can easily afford 5/- by eating less at school shop.

Eventually he decided on Thackeray’s Esmond.

1 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 1–18. © 2006 Springer. Printed in the Netherlands.

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The same question occupied him at the time of Margaret’s first birthday: should he give her Shakespeare’s Tragedies, the shorter poems of Browning or perhaps some Carlyle. But again he settled for Thackeray, this time Vanity Fair. Margaret kept these two leather-bound copies, inscribed ‘Elizabeth Margaret Ramsey from her brother Frank’ throughout her life. These early letters from Winchester, quite apart from the charm of their particular subject-matter, indicate characteristics and concerns that were typical of Frank throughout his life. They show, firstly, the amount and range of his reading. He clearly did not neglect English literature while also working at mathematics ahead of his form, and having to cope with a great deal of classics, for which he was said not to have had a natural aptitude. He was very keen to ‘get on’: ‘I ought to get some prizes this term’, he wrote, ‘You see, I could get my classical-form prize, my maths prize, a problem paper prize and a prize for all round…’.1 But particularly, the letters show his interest in his small sister to be clearly focused on her mental development rather than on her present state or desires. This concern for the intellectual well-being of his siblings is expressed in a number of letters sent to his mother over the years. So, for example, he seemed to worry about Bridget’s involvement with and success in various sporting activities, which he thought might interfere with her academic advancement. Again, while in Vienna he was told that Margaret, aged 7, would be sent to the Perse school, where her sister Bridget had already been for some years. Frank sounds quite upset: Gug (Bridget) says you are sending Margie to the Perse; if so, for god’s sake don’t leave her long in that outrageous institution but send her somewhere where she’ll learn something like the amount she is capable of. If she goes on like Gug it will be criminal of you.

The Perse school, incidentally, was the best regarded girls’ school in Cambridge. His brother Michael also gave cause for concern: he got only a II.1 in the first part of the classical tripos, largely because, his father thought, he found the debates at the Union an irresistible attraction; and a General Election in which Liberals hoped for the re-establishment of the Liberal Party as a dominating force in politics soon engrossed much of his time and thoughts.

Frank wrote sympathetically: It is a pity about Mick’s Mays. It looks as if he were in the wrong tack in doing classics; odd seeing how interested he is in them.

The number and the content of Frank’s letters sent home when away from Cambridge show him to have been on very close and affectionate terms with all the members of his family, but particularly so with his mother. He seems to have reported to her everything he thought of importance in his life, all the pleasures and the worries of the moment. His letters written from Vienna are characteristic

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in this respect, and so convey a vivid impression of what he did, felt and thought during that period. Frank went to Vienna on two occasions: first in September 1923 to visit Wittgenstein and discuss the Tractatus with him. On this occasion he only passed through Vienna, on his way to and from Puchberg, where Wittgenstein was teaching in the village school. He went the second time a few months later, in March 1924, to see Wittgenstein again if possible, but mainly for personal reasons. When Margaret and I visited Vienna nearly 70 years later she was deeply involved with her research into Frank’s life. And to this research she devoted her stay in Vienna. That was the point of our visit. So we went to the house where Frank had had lodgings when in Vienna for the second time: in the Mahler str. 7, practically next door to the Opera house, which he visited frequently and where he discovered his love of opera. We went to the house where Wittgenstein’s sister Gretl lived: the Palais Schönborn in the Renngasse. Gretl was married to the American Stonborough, and she and her family occupied the first floor. We got a glimpse of the splendid wide marble staircase but could not explore any further as the house had been taken over by offices. Frank saw Gretl frequently and got very attached to her: he went to call on her shortly after his arrival in Vienna and wrote home: She lives in a baroque palace of the time of Maria Theresa, with a vast staircase and innumerable reception rooms very beautiful. She must be colossally wealthy. She was out, but I gave her secretary my address and I got a message asking me to dinner that day. I went and had an evening tête-à-tête with her. – She is 42, handsome and intelligent, and I enjoyed talking to her very much. And I had a very good dinner. She asked me if I should like to come and visit her regularly, and I said I should love to. So she asked me to a dinner party with music on Saturday and said she would then fix a day of the week for me to dine with her every week.

When, a few months previously, Frank had visited Wittgenstein in Puchberg he saw him living in poverty: He has one TINY room, containing a bed, washstand, small table and one hard chair and that is all there is room for. His evening meal which I shared last night is rather unpleasant coarse bread and butter and cocoa.

After this experience of Wittgenstein’s way of life the discovery of the wealth of the family came as a shock to Frank. His two visits were a contrast in every respect. The first one, in September 1923, just after Frank had taken his final examinations, was undertaken and dedicated entirely to a discussion of the Tractatus. He spent a fortnight with Wittgenstein in Puchberg, the longest time they had together until Wittgenstein returned to Cambridge in 1929. Frank, in his second undergraduate year at Trinity College, aged 18, had translated the Tractatus. There is an account (initially given by I.A. Richards)

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according to which Frank learned to read German to a sufficiently high standard in just over a week. This is not so: he had German lessons at Winchester at least during his last year there. But the teaching of modern languages was not taken very seriously, and as usual Frank thought he was not getting on fast enough. So he consulted Ogden – a friend of the family- as to how best to learn the language. Ogden gave him what turned out to be excellent advice, viz. to read German books side by side with their English translation. He also sent a list of suggestions, among them Brentano’s Vom Ursprung Sittlicher Erkenntnis (The Origins of our Knowledge of Right and Wrong) and Mach’s Analyse der Empfindungen (The Analysis of Sensations). Frank studied these, but he also turned the advice on its head and read works by English philosophers together with their translations into German: he read Berkeley and Hume in German. The method was successful: he won the school prize in German, an event of which he wrote to Ogden: It’s disgraceful that there is no one in the school who knows more German than I do, but there isn’t, and I have won the German prize….

Much more important, of course, than winning any prizes, was that his combined study of German and Philosophy enabled him to translate the Tractatus. As a result of this translation Wittgenstein asked Frank to come and visit him. By the time the visit took place Frank, in his last Lent-term as an undergraduate, had also begun work on a review of the Tractatus for the periodical Mind which was published in October 1923, after his talks with Wittgenstein. These talks were clearly very intense. Frank wrote home: He is prepared to give 4 or 5 hours a day to explaining his book. I have had two days and have got through 7 out of 80 pages + incidental forward references… He has already answered my chief difficulty which I have puzzled over for a year and given up in despair myself and decided he had not seen…. He is great. I used to think Moore a great man, but beside W!

And in another letter: It is terrible when he says “is that clear?” and I say “no” and he says “Damn. It is HORRID to go through all that again”….

Altogether Frank found the fortnight both healthy and intellectually extremely profitable; a pleasant and inexpensive life: in the morning I walk for 3 hours in the mountains…. In the afternoon I listen to W from lunch to dinner. Then I read Gibbon…

After the Puchberg visit Frank and Wittgenstein wrote to each other, on Frank’s side (only his letters survive) full of affection and friendship, referring to personal problems as well as worries about e.g. the axiom of infinity. Both he and

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Russell tried to persuade Wittgenstein to come to Cambridge, but they were not successful. Frank’s second visit to Vienna, a few months later, was certainly also pleasant and no doubt also intellectually stimulating in some way, but it was hardly as healthy and certainly not as inexpensive as the previous one. Nor was it focussed on Wittgenstein or indeed primarily on philosophy. Frank had certainly intended to see Wittgenstein again in Puchberg, but in the end, apart from a brief farewell visit in September, he only saw him on two weekends during the six months of his stay. The reason was at least partly that he had gone to Vienna to be psychoanalysed, and his psychoanalytic sessions occupied much of his time. They also made it harder for him to think about philosophy or about work in general. ‘I am going down to Puchberg’, he wrote in March, ‘though I don’t want to talk about work as I have forgotten almost all about it.’ When he did go, the visit seems to have been a disappointment: I stayed a night at Puchberg last weekend. Wittgenstein seemed to me to be tired, though not ill; but it isn’t really any good talking to him about work, he won’t listen. If you suggest a question he won’t listen to your answer but starts thinking of one for himself. And it is such hard work for him like pushing something too heavy uphill.

The second visit, a couple of months later, was no more successful. He found Wittgenstein more cheerful, but, he adds, ‘he is no good for my work.’ He thought Wittgenstein quite exhausted by his teaching job and frugal way of living, and thought it absurd of him to refuse all financial help from his family, who were so anxious to help him in any way they could. But ‘he rejects all their advances, even Christmas presents or invalid’s food, when he is ill, he sends back.’ This is from a letter to Maynard Keynes. He and Keynes were again discussing the possibility of getting Wittgenstein to Cambridge, and Frank points out that any offer of financial assistance would certainly be refused. He adds that the only thing that would persuade Wittgenstein to come to England would be an invitation from Keynes himself to stay with him in the country, ‘in which case he would come.’ He adds: I’m afraid I think you would find it difficult and exhausting. Though I like him very much I doubt if I could enjoy him for more than a day to two, unless I had my great interest in his work, which provides the mainstay of our conversation.

Keynes evidently shared the view that it would be difficult and exhausting to have this guest: there was no invitation for Wittgenstein that year. Rather than battling with philosophical problems with Wittgenstein, he enjoyed the society of Wittgenstein’s sister Gretl and other members of Wittgenstein’s family; he listened to music, went to the opera and saw the Cambridge friends who were in Vienna at the time. There was briefly Richard Braithwaite, and throughout the time Lionel Penrose, (later the distinguished geneticist), both very close friends for the rest of his life. He also had some contact with some members of the Vienna Circle, at least shortly before leaving Vienna he met

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Moritz Schlick at a dinner at Gretl’s, whom he thought ‘a very nice man’. He was invited to tea by Hans Hahn, where he was rather overawed but also flattered by being included in a discussion entirely in German about atomic theory. But the framework of his daily life was provided by analysis with Theodor Reik, whom he saw every weekday from 12 to 1. II. After the ’14-’18 war psychoanalysis had boomed in England, but there were as yet few British psychoanalysts, and for those wishing to be analysed Vienna was the obvious place to go to. Among the people who influenced Frank in this enterprise were James and Alix Strachey, who did much to spread an interest in this new science in England, and whom Frank knew personally. Both James and Alix had been psychoanalysed by Freud, and Freud had asked them to translate his works – a translation which became their lives’ work and resulted in the 1950ies publication of the English Standard edition. There were other followers of Freud in Cambridge whom Frank knew, e.g. John Rickman, who later became one of the leading figures in the London Institute of Psychoanalysis. Rickman had been at school with Lionel Penrose, and they all met at Cambridge. Another of Frank’s close friends, Sebastian Sprott, had visited Freud in 1922, so Frank would have been well informed about psychoanalytic practice in Vienna. It is then unsurprising that Frank was interested in psychoanalysis, and that, wanting to be psychoanalysed, his thoughts should turn to Vienna, especially since Lionel Primrose, encouraged by Rickman, had gone to Vienna and had a flat there, which Frank could share. But why this desire for psychoanalysis? Partly it seems to have been in the air, the thing to do, in Frank’s particular circle. The idea appealed to Frank particularly because at the time when the thought first came to him, his third year at Trinity, he was in a state of depression. In a rare diary entry during that year he speaks of his feeling of loneliness: I feel lonely…. I need some satisfactory human relationship and have none; I feel this more than ever before. Before I have felt keenly the unsatisfactoriness of some particular relation; but this is more; it is a general feeling of isolation….

The rest of the entry, quite a long one, goes through the list of his friends, all male, and the respects in which they are unsatisfactory. The ones free of such drawbacks are not around, and in any case he doubts that his affection for them is matched by theirs for him. He was in this state of mind when he met, and fell in love with, a young married woman, Margaret Pyke, and his relation with Margaret became his preoccupation throughout that year and beyond. Both she and her husband accepted him as a friend, he visited them often and they seemed very glad to see him. But her feelings for him were nothing like his feelings for her, and for much of the time Frank was tortured by her apparent coldness and

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neglect of him. This of course added to his depression and feeling of isolation. His father became worried about him and wrote, looking back to that time: As his Tripos drew near he suffered a good deal of mental unrest and slept very badly and I began to be afraid whether he would get it over without a breakdown. He was very well prepared in Mathematics and it was not, I think, anxiety about the Examination that worried him but deeper problems about the meaning of life and his relation to other people. (In 80 Years and More.)

Preoccupation with Margaret and work on the Tractatus did not of course prevent Frank from doing brilliantly in Part II of the mathematical Tripos. Although Frank was on very affectionate terms with his mother and reported to her everything of interest in his Viennese life, they did not, naturally, always see eye to eye. There was, firstly, the question of the use of being psychoanalysed. At some stage of his analysis Frank wrote to his mother asking her about events in his early childhood and about children’s books he had liked, which she was to send so that Reik could read them. Agnes was not impressed: if, she suggested, analysis just consisted of putting together facts about his early childhood, Frank could have asked her in the first place without bothering to go to Vienna. Frank replied that information about a person’s childhood was not analysis.2 Agnes was worried also about the analysis being so time-consuming as to prevent Frank from doing much work, and about the expense of the whole enterprise. Both worries were up to a point shared by Frank. Even in Winchester Frank had kept account of his income and expenses, and these figure in his letters from Vienna as well. Shortly after arriving in Vienna he heard that he had won the Allen scholarship, (£250 p.a.) but, Frank thought, even with this addition his financial problems were not solved: the Allen scholarship was meant to help support him while working on his thesis, and while holding it he was not allowed to teach to fill the gap between receipts and expenses. So his immediate financial future did not look rosy. Agnes suggested that he could make a little money, and get himself known, by reviewing for the New Statesman. He replied: ‘it is rot to think you get known (except to the ignorant public) as an authority by reviewing in the NS.’ Shortly after this correspondence Frank had the unexpected and happy news that he had been elected to a Fellowship at King’s College, Cambridge, and his money problems were solved. The question of whether Frank was doing enough work worried Agnes even more persistently than that of the expense. Was not psychoanalysis taking up too much of his time and energy, and could it be right to use some of his scholarship money to support him in Vienna when he was doing so little work? Frank found this attitude rather irritating. He replied, perhaps somewhat defensively: I had a letter from the Registrar saying my residence here is approved. It seems to me perfectly proper to spend a scholarship being analysed, as it is likely to make me cleverer in the future, and discoveries are made by remarkable people not by remarkable diligence. …

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Later in his course of analysis he puts his case more strongly: Psychoanalysis is very important even I think to one’s work. You see obscure unconscious things may decide your attitude about certain things, especially personal factors in a controversial subject. Lots of work on the Foundations of Mathematics is emotionally determined by such things as: 1) Love of mathematics and a desire to save it from those (villainous and silly) philosophers. 2) Whether our interest in mathematics is like that in a game a science or an art. 3) General Bolshevism against authority. The opposite; timidity. Laziness or the desire to get rid of difficulties by not mentioning them. If you can see these in other people you must be careful and take stock of yourself.

These observations don’t perhaps altogether settle the question as to whether psychoanalysis is so important for one’s work, but Frank seemed to be convinced. However, he himself every now and then expressed feelings of guilt about his doing so little work. But he shared his parents’ work ethic and his expectations of himself were extremely high. He was hardly idle: while in Vienna he wrote the greater part of ‘The Foundations of Mathematics.’ Frank’s psychoanalytic sessions seemed to be going well. Reik was a clever and distinguished man, and Frank respected his intellect. Not that he altogether enjoyed the experience: ‘It is surprisingly exhausting and unpleasant’, he wrote to Sebastian Sprott : For about 2 times I said what came into my head, but then it appeared that I was avoiding talking about Margaret, so that was stopped and I was made to give an orderly account of my relations with her… I rather like him, but he annoyed me by asking me to lend him Wittgenstein’s book and saying, when he returned it, that it was an intelligent book but the author must have some compulsive neurosis.

In all his letters from Vienna to his parents and friends Frank says nothing about how, if at all, he thought psychoanalysis had changed him in his attitudes to personal relationships. When he returned to Cambridge in October ’24 he was cured of his infatuation for Margaret Pyke, but of course that might have passed anyway. There is a comment on Frank’s sessions from Alix Strachey, written in November 1924 from Berlin, where she was being psychoanalysed, to her husband James in London. She had met Reik at a conference in Würzburg: (Reik) was enthusiastic about Frank Ramsey’s beautiful character, and seemed to think, analytically, that all was for the best.

And again: He (Reik) said to me that he had done all he could to Frank in the short time at his disposal-that the analysis had gone very well owing to Frank’s crystal clear mind and soulwas enthusiastic about him; and wound up by saying that there’d never been much wrong with him. All of which seems fairly reasonable.

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It is in a later letter, written back in Cambridge at the end of the year to his wifeto-be that Frank indicates how helpful he had found psychoanalysis as far as his personal relationships were concerned: I wrote a long letter to my psychoanalyst saying how happy I was & how grateful I felt to him. Because he did make it possible though you may not see how….

Frank’s six months in Vienna was his first long period away from Cambridge and his home since leaving Winchester nearly four years previously. In some ways his letters to his mother did not change much between Winchester and Vienna: rather like a child he took it for granted that his parents would do all manner of menial tasks for him. They arranged for his belongings to be moved from Trinity to King’s, forwarded his letters, posted books, acted as his banker, bought furniture, ordered taxis, bought clothes for him. They treated him as a mixture between a very special person for whom too much could not be done, and as a rather helpless child. This reliance on his mother prompted some of his more malicious friends to think that Frank needed psychoanalysis not to be cured of his passion for Margaret Pyke, but rather to be cured of his dependence on his mother. Perhaps more surprising than his attachment to his mother is that he also got on so well with his father. Arthur Ramsey was not an easy man to live with. He was absorbed in College affairs and this did not, perhaps, contribute to ease and happiness at home. Margaret Paul describes him sitting ‘at the end of the table at Howfield3 meals, often silent, occasionally telling stories about the latest iniquities at Magdalene, and sometimes roaring abuse at Agnes, or a servant, about some feature of the meal that displeased him.’ Frank appears to be the only one of his children who actively sought his society, asked his advice on books and lectures, went for walks with him and went on holidays with him. But of course Arthur was extremely proud of a son who showed his brilliance very early in life, and whose chosen subject was his own. In many ways Arthur was wholly admirable, a man of integrity, enormously hard working, a good and devoted teacher. Colleagues at College remarked on how intolerant he was of any opinion which differed from his own, but as far as his children were concerned he showed surprising tolerance: ‘Though his children becoming atheists must have been a great sorrow to him,’ his daughter writes, ‘he never protested or even tried to argue with any of them about it. And again, when it came to their marrying, though he was not always pleased by the timing or choice of partner, he accepted their wishes in a good humoured way.’ III. Frank got married to Lettice Baker a year after leaving Vienna. Beyond the statement of this fact there is hardly any comment on either Lettice herself or on the marriage in his father’s (unpublished) Memoirs, written when Arthur was in

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his eighties. He only adds that, having taken the Moral Science Tripos, Lettice was able to some extent to share Frank’s interests. But Michael, at the time of their marriage a third year undergraduate in Cambridge, thought that his parents exercised a ‘kindly tolerance’ towards Lettice: I don’t think, they felt much in common with her probably, but they were entirely friendly as far as I know…. Lettice and they had very different temperaments. You see Frank was different from them and Lettice was still more Frankish than Frank was.

Lettice had enjoyed great freedom as a child and remembered her childhood as an entirely happy one. In 1911, aged 13, she went to Bedales, which was then recently founded, a progressive, co-educational school, and much freer and more friendly than most boarding-schools at the time. There she met and became a close friend of Frances Partridge, the writer and longest surviving member of the Bloomsbury group, and after Lettice’s marriage to Frank a close friend of his as well. Lettice was a graduate of Newnham College, Cambridge, and at the time of meeting Frank in 1924 she was doing some research in the Psychological Laboratory at Cambridge for the Industrial Training Board. She was 5 years older than Frank, considerably more experienced and held unconventional views. It seemed natural to her that she and Frank should live together. Agnes may have shown ‘kindly tolerance’ towards Lettice, (and Lettice herself agrees that she was friendly and generous) but she was so horrified at the discovery of the nature of their relationship, that Frank felt compelled to cancel a weekend away which he had planned with Lettice. He wrote to her at the end of the letter cancelling the weekend: I don’t really feel as if I had enough moral courage to go on living with you; but I can’t say for certain. What about marrying? It is risky, but what do you think? I don’t feel sure of myself… It seems so absurd not to go away as we had planned; but I can’t. I should be worrying about mother and possibly being caught. It is a shame for you. …

Frank’s own view of the situation is not clear. Lettice assumed that of course he had no sympathy at all with his mother’s attitude; and indeed he wrote to her: I had a long argument with mother yesterday about free love, and she maintained that it threatened the order of society and the security of women, and said she was sure my bark was worse than my bite or she would be in a perpetual state of anxiety about me.

But at about the same time he read a paper to the Apostles, the select debating society which Frank attended regularly and with enthusiasm. In it he said that with the decline of religion the old ideas of marriage were collapsing, and we ought to consider whether this movement is a good one, and if so, what, if anything, we should attempt to substitute for the old morality… I think the institution of marriage is a great benefit to the female sex especially if we suppose, as seems reasonable, that apart from it the care and maintenance of children would fall on their mothers.

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This rather seems to echo his mother’s views. It is true, of course, that papers read to the Apostles did not always express the speaker’s own opinions but were put forward merely to elicit views and discussions. Be that as it may, Frank seems to have thought his mother’s case against free love at least worth considering. The year preceding his marriage was a very busy one for Frank. His teaching-obligations were considerable. Each week he lectured three times and gave a dozen or more supervisions. After a year or so of carrying this teaching load he wrote to Maynard Keynes, asking his advice as to whether anything could be done to lessen it. ‘It is not that I dislike teaching’, he said, ‘but that doing so much seems to interfere much too seriously with what I mainly want to do.’ Since, he said, his main interest was in philosophical questions nearly the whole of his teaching was quite disconnected from his own work, and did not involve reading or thinking anything useful for it. And he expressed some envy of tutors at his undergraduate College, Trinity, where the teachingload was much lighter. It seems that nothing could be done about it, but it seems also that a year or so later when, as Frank put it, he was ‘in the swing of it’, teaching was not felt by him as being quite so burdensome. His lectures on the Foundations of Mathematics were a great success, judging by comments of some of those who attended them. So for instance one member of his audience, Sir Douglas Elphinstone wrote to Margaret Paul many years later (1990): … my recollection of him is of a big and rather clumsy man. He generally had his hair in tufts all over the place. I remember him in a brown tweed suit, much more countrified than the conventional grey suits normally worn by other lecturers. And I think he wore his clothes untidily… Shining through all this was a round cheerful face, and his style of lecturing was also cheerful; he imparted an enjoyment of his subject, and spiced a clear exposition with little touches of humour.

He speaks of Frank introducing his audience to rigorous logical methods in analysis, which, he wrote, almost set his (Sir Douglas’s) mind on fire. And he concludes: There were other good lecturers who prepared their work properly and had the gift of clear exposition (for Ramsey’s thoughts and expressions were always clear); there were others who lectured not like a version of a printed text book, but who threw something of themselves into their work. But Ramsey exuded some sort of personal charm into his lectures. It was like going into a friend ’s house to go into his lecture room.

Reactions to Frank’s supervisions were not quite as favourable. His sister writes: ‘He impressed his pupils by his friendliness, but not all profited from his explanations.’ One former pupil wrote: I must honestly admit, that his intelligence, knowledge and teaching was miles above my head and I understood nothing of what he tried to teach me.

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Another one, Alister Watson, who became a friend, described him as an idiosyncratic teacher. So for instance Frank frequently tackled questions in applied mathematics by working out the answer from Newton’s laws, and then roaring with laughter at his success. As usual, Frank worried about not doing enough work, by which of course he meant his own work. But during the first vacation as a Fellow of King’s he completed his paper on the Foundations of Mathematics, on which he had worked during his stay in Vienna. He submitted it for the University Smith Prize, but was not awarded it. His father thought that the reason for this lack of success was that it had baffled the awarders: ‘it is very unlikely that any of them understood it’ he said. Frank himself seems to have been rather downcast by his failure to be given the prize: ‘After it was refused a Smith’s prize I didn’t think I could publish it’ he wrote to Keynes. But he was cheered by praise from Russell, and of course the paper was published. He was still working on what he felt were problems in it he had not solved, and he had a contract with Ogden for a book on the Foundations of Mathematics. But that was never written. Frank also worked on the problem of Universals, a paper which he read to the Moral Science Club and which was published in Mind in October ’25. After reading the paper he was too stimulated to sleep. Instead he wrote a note to Lettice: … The discussion was a very pleasant surprise. It was almost only with Moore who was very reasonable and intelligent…. I wasn’t at all discomfited as I feared, and to one of my arguments against a theory of his he admitted he could see no answer….

So it can hardly be said that during his first year at King’s he neglected his own work altogether. During that year Frank also kept up his interest in psychoanalytic theory. Among his unpublished papers are detailed notes on Freud’s ‘Papers on Metapsychology’, which he greatly admired and thought ‘illuminating’. He helped found a small society which was to meet monthly to discuss psychoanalytic topics. James Strachey, who came from London to attend these meetings, commented after the first one. ‘I was crushed by the unaccustomed intellectual level – especially of Ramsey.’ He also said that Frank thought psychoanalytic theory very muddled: He is thinking of devoting himself to laying down the foundations of Psychology. All I can say is that if he does we shan’t understand them. He seems quite to contemplate, in his curious way, playing the Newton to Freud’s Copernicus.

And finally, during that year, he also greatly enjoyed the social life King’s had to offer. He found good friends of his at the College: Richard Braithwaite, who had also recently been elected to a Fellowship, Alex Penrose and John Maynard Keynes among others. He enjoyed the occasional Feast, but also ordinary, everyday dinners in the company of his colleagues. Richard Braithwaite said of him:

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He had an excellent effect on every company. He was very appreciative of people – modest, added to the pleasure of life- he wasn’t a spoil sport. The least malicious person I have known. … On the other hand, he had a gift for avoiding people he thought of as morons, but if you do it discreetly you can’t be savagely condemned.

IV. Frank’s first year of marriage was a relatively tranquil one, free of disasters and upsets. His brother Michael, then a third year undergraduate at Magdalene College, speaks of him as being very happy, marvellously settling down with a most lovely happy marriage and being a Fellow of King’s, and finding his feet intellectually in these different ways, and having an awfully good circle of friends, and all very happy, friendly with the rest of the family, too….

But the following year, 1926-7, brought many changes. From the point of view of Frank’s work it was fertile: he wrote two philosophical articles: ‘Truth and Probability’ and ‘Facts and Propositions’, and also one of his two economics articles: ‘A Contribution to the Theory of Taxation’. In the domestic sphere it was the year in which his daughter Jane was born. But it was also the year in which Agnes was killed in a car accident, and the year in which he fell in love with a friend of Lettice’s, Elizabeth Denby. Frank’s interest in Economics was long-standing, in at any rate his last year at Winchester he had read enormously widely in Economics – as well as in Philosophy and Politics. By that time he was at least as interested in these subjects as he was in Mathematics. Keynes, in a short biography of Frank, refers to the early age, about 16, at which his precocious mind was intensely interested in economic problems. Economists living in Cambridge have been accustomed from his undergraduate days to try their theories on the keen edge of his critical and logical faculties….

Keynes was editor of The Economic Journal and so received from his Cambridge colleagues many drafts for discussion and publication, and frequently the writer mentioned having shown the article to Ramsey. In June ’28 Frank himself sent to Keynes the draft of the article ‘A Mathematical Theory of Saving’. Keynes described it as ‘one of the most remarkable contributions to mathematical economics ever made,’ but Frank enclosed a letter with the draft in which he said: Of course the whole thing is a waste of time as I’m mainly occupied on a book about logic, from which this distracts me so that I am glad to have done it. But it’s much easier to concentrate on than philosophy and the difficulties that arise rather obsess me.

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It seems that this important economics paper was written in a few weeks as a more or less light relief from his work on logic. His work on logic, however, brought him again in touch with Wittgenstein, who wrote to him in July ’27, commenting on ‘The Foundations of Mathematics’, which Schlick had sent him. The letter broke a two-year silence. In the summer of 1925 Wittgenstein had approached Keynes to suggest a visit, and this time Keynes responded positively. Wittgenstein arrived at the place in Sussex where Keynes was then living in the middle of August. The visit could not have been timed more badly: Keynes himself had just got married, to the ballerina Lydia Lopokova; he had business in London and was preparing for a visit to Russia to meet his wife’s relatives. So he asked Frank to come and help entertain Wittgenstein. It was only days before Frank’s own wedding. Lettice had gone to Dublin to stay with her mother, and had left Frank, perhaps not the most practical of men, to see to the flat they were to live in and to deal with preparations for the wedding, send out invitations and so on. So Frank had his hands full. Still, he went to Sussex for a couple of days. It was during that stay that there was a quarrel – quite untypically as far as Frank was concerned. But he can hardly have been in a state of mind which allowed him to concentrate on Wittgenstein, and Wittgenstein was no doubt disappointed and hurt that the visit did not at all live up to expectations, owing to Keynes’ many other preoccupations. It is not clear what the quarrel was about, except that Frank stated it was not about logic. At any rate, they did not correspond for two years, though in his letters to others Frank, while still annoyed with Wittgenstein, always emphasised his affection for and admiration of him. The renewed correspondence may well have encouraged Wittgenstein to return to Cambridge at the beginning of 1929. Agnes’ death in August ’27 was of course devastating for every member of the family. One of the consequences was that Frank and Lettice decided to leave their flat and move to Howfield, the Ramseys’ house in Huntington Road, so that his father and young sister should not be left alone with just servants. So they, with baby Jane and a nurse, moved in and made it their home-base for about a year, after which they found their own house in Cambridge, where Frank lived for the last 15 months of his life, and Lettice for the remaining 57 years of hers. Perhaps the decision to move to Howfield had been taken too hastily: it was an unhappy time and an unhappy arrangement, since Arthur’s way of life and his expectations of members of his household was not theirs, especially not Lettice’s, who was used to an easy-going social life with friends dropping in unannounced at all hours. So after some months it seemed best for Arthur’s sister Lucy to come and run the household, and for Frank and Lettice to have their own establishment. They had a so-called open marriage. They had also agreed to have no secrets from each other. Both of them seemed to interpret this to mean that they had to tell each other not only of other lovers appearing in their lives, but also to describe in minute detail their affairs, their feelings for the relevant person, and that person’s overwhelming attractions. Not surprisingly, Lettice managed to cope

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better with this state of affairs than Frank did, but even she could not have been pleased with a birthday- letter he sent her to Dublin where she and Jane were staying, which after brief congratulations dealt entirely with the time he was spending with Elizabeth. Christmas ’27 he also spent with Elizabeth on a holiday in France. While there he had a letter from Lettice in Dublin informing him that she had fallen in love with an Irish writer called Liam Flaherty. Frank was outraged by this piece of information and accused her of destroying their happy peace together to which he was looking forward to returning: Frankly your letter gave me an awful shock, I can’t see how you could imagine it wouldn’t. I felt quite furious and still after a lot of reflection it seems to me very sickening…. I feel this is such an unfortunate time. I had decided to give up Elizabeth, and you know how important she is to me….

Lettice, in her turn, was amazed and hurt by his reaction: I do think you rather a pot to be calling me a black kettle…. I can’t help feeling hurt at your seeming unfairness….

There is a fairly hectic exchange of letters over the next few weeks, some angry and accusatory, others apologising for having been angry and accusatory. Frank to Lettice: … I am sorry I am so unreasonable. The truth is since I got your letter… I have been in a frenzy of anger unlike anything I’ve ever in my life experienced before… I have never been one to feel malice for more than a moment, but now I’m simply consumed by anger, hatred and all uncharitableness….

The letter ends: … Really, of course, I must blame myself for not knowing my own mind. I began it with Elizabeth, but I find that in fact I can’t stand the strain of this sort of polygamy and I want to go back to monogamy, but it’s now too late.

Lettice’s affair with Liam fizzled out after a few weeks, and she faithfully reported her consequent misery and depression. Frank, of course, was much relieved by this turn of events, and, with equal honesty, explained his improved state of mind to her. She replied: Well, it’s something that my being unhappy has helped you! What people we are! Let me cheer you by saying I’m still very gloomy and depressed.

Elizabeth, however, remained in Frank’s life. They do not seem to have met very often, but they corresponded regularly. Frank’s letters to her, on her instructions, were burnt after her death in 1965. She never married. Like Frank’ s mother, she was a social reformer, primarily interested in improving the lot of working-class people, and she devoted her life trying to improve working-class housing.

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V. The pen-ultimate chapter in Margaret’s manuscript, with the title ‘Lettice, Elizabeth and Economics’, deals with the correspondence from which I have just quoted, as well as with his work in Economics and Keynes’ reaction to it. In her last chapter, ‘Death’, there are naturally few quotations from Frank himself; they are restricted to a cheerful account of a walking tour in Ireland in August ’29, a couple of notes to G.E. Moore, with whom he had planned weekly discussions which had to be cancelled because of Frank’s illness, and his last letter to Lettice. Of course, there were other important events in his life: he and Lettice had a second daughter, Sarah, and Wittgenstein returned to Cambridge and stayed with them in their house in Mortimer Road for a fortnight, and after that visited them frequently. He seems to have got on well with Lettice, and Frank’s worry, expressed to Keynes, that Wittgenstein might not want to see him again, turned out to be quite unfounded. Wittgenstein went to see Frank after his operation in Guy’s Hospital, London. Since Frank had not come round after the operation he spent some time with Lettice and her close friend Frances Partridge, who writes of the event: When I came back in the evening and went into the cubby-hole again I was surprised to see the remarkable head of Wittgenstein hoist itself over the back of a chair. Everyone reacts differently when the white face of death looks in at the window. Wittgenstein and I were brought closer together than ever before by our intense sympathy for Lettice … Wittgenstein’s kindness, and also his personal grief, were somehow apparent beneath a light, almost jocose tone….

There are other comments from Frances Partridges which, I think, catch particularly well some of Frank’s chief characteristics. She finds him difficult to describe, partly, she says because of his great simplicity. He had a rather quiet voice, he would consider things, I mean he wasn’t one of these volatile talkers at all, he was somebody who listened to other people and responded… In any ordinary sort of thing in life, like going for a walk and looking at the view, sitting on a lawn, eating and drinking, and so on, he was just a very normal person, and totally unselfconscious… I would recognise the quality of his voice more than anything, which had this rather measured and gentle nature to it…. He was not an ambitious man… he was following his thought, he had no desire to make a splash in the world. He was a simple character in many ways… he had a tremendous sense of humour; his whole face cracked when he laughed with a rather hee-hawing noise…it was delightfully easy to get him laughing….

She adds:

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I don’t think Frank ever made conversation. He would talk of what was interesting him but he would probably rather remain silent than talk for the sake of making things go – he was always himself, not always very good socially. (Interview 1982)

Frank’s simplicity and lack of self-consciousness are often remarked upon by his friends, as are his modesty, lack of aggression, and friendliness. Margaret Paul remarks that while his early death may have led to some idealisation, the view of him as exceptionally fortunate in his nature was held by many people before his death. As Frank himself said in the letter to Lettice I quoted: he rarely experienced malice, and when he did then only for a moment or two. He seems to have been free of all the destructive emotions Nor, as far as one can tell, did he arouse them in others. Many of his after all very clever friends (e.g. Richard Braithwaite and Lionel Penrose) thought Frank much more brilliant than they were themselves, but none seems to have felt the least resentment on that account. Perhaps the last word should be left to his brother Michael: when they were both in Cambridge Frank and Michael had a great many conversations together on a wide range of topics, sometimes about religion, about which, of course, they differed entirely, Frank but not Michael thinking Reason the highest court of appeal. Michael thought his brother the cleverest person he knew, and felt himself to be intellectually on a much lower level. ‘But’, he said, ‘there was a total lack of uppishness about him – he never made me feel inferior…. That was the wonderful joy of it.’

N OTES 1.

2.

3.

He found life at Winchester pretty austere and strenuous, and at any rate initially was not happy there. His sister suggests that he tried to cope with his unhappiness by reading and working very hard and becoming competitive, aiming not only at being top but also, at least in mathematics, being top by a considerable margin. Peter Pan, apparently, was a book Frank had been fond of as a child and which was sent to Vienna. A book he had not liked so much was Alice in Wonderland. Agnes, while at St. Hugh’s College, Oxford, had been friendly with Lewis Carroll, who gave her a presentation copy of Alice. As a child Frank was so frightened by some of the strange pictures in it that Agnes cut them all out. The name of their house in Huntingdon Road.

R EFERENCES Margaret Paul: Frank Ramsey Unpublished. Arthur Stanley Ramsey: 80 Years and More. Unpublished. ‘Better than the Stars’. A Radio Portrait of Frank Ramsey, BBC 1978. Ed. Perry Meisel and Walter Kendrick: The Letters of James and Alix Strachey, Basic Books, Inc. Publishers New York 1985.

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GABRIELE TAYLOR

John Maynard Keynes: Essays in Biography, The Royal Economic Society 1972. Frances Partridge: Memories, Phoenix Paperback 1981.

Department of Philosophy University of Oxford 33 Templar Rd. Oxford U.K. [email protected]

B RIAN M C G UINNESS

WITTGENSTEIN AND RAMSEY This is inevitably a tale of two cities – and it is fitting that (as I understand) a parallel celebration has been held in Cambridge. They were the two cities of Wittgenstein obviously enough, but in a measure of Ramsey too. Later than Wittgenstein (by the interval of their difference in age) he came to Vienna as a pilgrim, just as Wittgenstein had gone to Cambridge. He to learn from Wittgenstein as Wittgenstein to learn from Russell. But they were to find other things also in those cities – Wittgenstein the whole ambience of Bloomsbury, Ramsey the home of psychoanalysis, the family of Wittgenstein (like many visitors – and even later biographers – he seem to have fallen in love with Wittgenstein’s powerful sister) and the seeds of the Vienna Circle. My purpose is to see how the two men interacted intellectually and what that tells us about the two cities as intellectual centres. I would not propose a comparative evaluation of the two, for one obvious reason and for one less so – Ramsey died before developing all his powers, while Wittgenstein could die content that he had made his contribution. So much is obvious, but an overlap in the themes they treated has often obscured the fact that they were trying to do quite different things. Needless to detail here how before the First War Russell helped Wittgenstein to make the existential choice between being an aviator (in those days also a constructor of planes) and a logician, largely by bringing him into a group where he could make free use of his intellect. To be surrounded by Moore, Keynes, the Stracheys and even the younger Apostles (then practically the Cambridge branch of Bloomsbury) was a new experience for him. His family background was one of wealth and high culture but not intellectual to the degree cultivated in this new environment. Naturally he wanted to change them – for one, he maintained that mathematics would improve people’s taste because taste comes of thinking honestly. They were all against him. He even attempted to resign from their Society (the Apostles), thinking that the younger members “had not yet made their toilets”. The brittle arguments of the Society, where the paradoxical or the scandalous would be defended for sheer love of argument seemed to him intolerable. And there was another thing: all, even the older members, lacked what he called reverence: even Russell (whom, at that period, he still respected) was so Philistine as to appreciate the advantages of their age as opposed to previous ones. Still between them the members of this group set him on the way to writing his first and in some ways his greatest work. He was to repair Russell’s logic, he was to deal with Keynes’s probability in two or three paragraphs, and he was to

19 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 19–28. © 2006 Springer. Printed in the Netherlands.

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show that ethics, Moore’s field, did not consist of propositions at all. And perhaps this is what they wanted from him: they “looked to him for the next big step in philosophy”, as Russell told Wittgenstein’s sister. The original Abhandlung, whose completion he announced to Russell in 1915, was the product of this Cambridge period, but the additions he made to it in 1916-18 (the passages on God, freedom and the mystical) issued rather from the next two phases in his life. Tolstoy’s religion had taken hold of him in the war and the circle of young disciples of Kraus and Loos whom he met in Olmütz acted as midwives to the utterance of what he had previously and, as he thought, necessarily left unsaid. Russell was shocked by the mysticism that thus entered in, while as for religion the least hint of it was enough to exile one from the drawing rooms of Bloomsbury. “We have lost Tom”, was Virginia Woolf’s comment on T.S. Eliot’s conversion. Still, when the manuscript turned up in Cambridge it made an immediate impression at least on one Trinity undergraduate. C.K. Ogden, as Hugh Mellor recounts, had helped Ramsey to learn German (from Ernst Mach’s Analyse der Empfindungen) while still at Winchester, for he won the German prize there. Later Ramsey undertook to translate Wittgenstein’s newly arrived manuscript when many, even Moore, doubted that this was possible. The translation he dictated in Miss Pate’s office – the typescript still exists and was then worked on by Ogden in correspondence with Wittgenstein – it gives the atmosphere of the work very well, though for a textbook (as it became) less Pathos was needed, as Geach pointed out. Perhaps this atmosphere led to Broad’s quip about his “younger colleagues’ (notice not his own) dancing to the highly syncopated pipings of Herr (if you please) Wittgenstein’s flute” but Ramsey’s review written in the year he graduated as a Wrangler is a model of clarity. Syncopation or complexity where necessary was no barrier to him and it remains one of the best introductions to the Tractatus. The young Apostle then went to see his elder brother, recommended by a host of common acquaintances and by the merit of his own translation. He brought an extraordinary quickness of mind and perhaps equally important a most open manner: I quote Frances Partridge’s diary from a few years later: As with many great men (and I am sure he is one) Frank is outwardly simple and unselfconscious. His tall ungainly frame becomes somewhat thicker at the hips; his broad Slavonic face always seems ready to break into a wide smile and his fine rapidly vanishing hair floats in wayward strands around his impressive cranium. He’s intensely musical etc.1

The last point we shall return to: it is of some importance. The qualification “outwardly simple” is well chosen. Mrs Partridge will have been aware of the inner tensions that worried an admiring father when Ramsey was an undergraduate and the emotional crisis that led him to want analysis in 1924 (it cured him, he said, at any rate of the wish to talk about himself).

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In discussion Ramsey and Wittgenstein went through the Tractatus together. This issued incidentally in a few extra propositions that were to be added in a second printing if any (there have been scores of them) but haven’t been except in our “philologische Ausgabe” (mine and Schulte’s, the publisher is Suhrkamp). I hope they will be more widely published. However, the discussions were principally devoted to a project that Ramsey describes in a letter to Moore (6.2.1924 – he is explaining his application for a scholarship): I am working on the basis of Wittgenstein’s work, which seems to me to show that Principia is wrong not merely in detail but fundamentally. I have got Russell’s manuscript of the stuff he is inserting into the new edition and it seems to me to take no account of Wittgenstein’s work at all. There is a new Theory of Types without the axiom of reducibility, on which however Russell hasn’t succeeded improving a lot of ordinary mathematics, whose truth, he concludes, remains doubtful. But I have got on Wittgenstein’s principles a new theory of types without any doubtful axioms, which gives all the results of Russell’s one and solves all the contradictions. But Wittgenstein and I think it wrong to suppose with Russell that mathematics is more complicated formal logic (tautologies) and I am trying to make definite the vague idea Wittgenstein has of what it does consist of. If I am successful I think it will illuminate not only mathematics but physics also because a successful theory of mathematics will help one to separate and give a true account of the a priori element in physics. (This certainly exists for “this is not both red and blue” is a priori.)2

(It is interesting that exactly this example occurs in Wittgenstein’s discussions with Schlick and Waismann in 1929 (22 December): it was from the Ramsey discussions, not the Vienna Circle ones that these thoughts took their origin.) Later in the year 1924 Ramsey was to try to induce Wittgenstein to return to England and work there: Keynes would have provided the means, but Wittgenstein declined saying the well of his scientific inspiration had dried up. None the less he seems to have done some work with Ramsey, who kept him in touch with mathematical developments during these years, and let his name be known – Becker mentions it as that of a semi-intuitionist. In the biography of Wittgenstein this is quite an important point, since we otherwise know little of what he was doing intellectually during those years as a schoolmaster. Perhaps it needed Ramsey to provoke this re-direction of attention towards the foundations of mathematics, though the original function of the Tractatus had been to replace the first eleven chapters of Principia. Otherwise, for the early and mid-20’s we only have an indication that he involved himself in biography (perhaps autobiography is meant – a fragment remains) and psychology (we know of his exchange of dreams with the sister already mentioned). When Ramsey came to write the entry on Mathematical Logic (s.v. Mathematics) for the Encyclopaedia Britannica 13th edition his faith in Wittgenstein’s system was still entire, except that he now thought it more plausible to maintain that mathematics was reducible to logic. He constructs his article round the Tractatus and concludes:

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By using the work of Wittgenstein a solution has been constructed…, on which the theory of types is so modified that all need for an axiom of reducibility disappears and mathematics consists entirely of tautologies in Wittgenstein’s sense.3

This entry was published in 1926, but there can be little doubt that it was written before the paper on “The Foundations of Mathematics” read to the London Mathematical Society on 12 November 1925 and published in all collections of his work. To the content of that paper I shall return shortly, only saying that I assume Wittgenstein cannot have known it when he met Ramsey in August 1925. That meeting came about with the all the interlacing of intellectual and personal life characteristic of Bloomsbury. Keynes was newly married to the lovable but eccentric Lydia: indeed these days were to have been their honeymoon. Ramsey was on the eve of his marriage but had to leave his bride and come down to Sussex so that Wittgenstein would have someone to talk to. Geoffrey Keynes and his wife were invited to make up the party and Virginia and Leonard Woolf came over from their house nearby. We know the sort of things that went on from other occasions – Lydia’s boutades taken literally by the Bloomsburyites, Wittgenstein discontented when, instead of his being allowed to prevail in an argument, the subject was blithely changed, Keynes and Wittgenstein talking so fast that no one else could get a word in, then for Ramsey long walks with Wittgenstein, which gave them an opportunity to quarrel about psychoanalysis. This last particular Ramsey recounts in a touching letter to his bartered bride, whom he misses so much. Wittgenstein who must have had half an eye on the possibility of returning to England (he communicated with his friend Eccles in Manchester also) decided to stay in Vienna and take over the building of a house for his sister. He seemed to have broken with Ramsey. Contact was resumed only and in a very chilly manner when Wittgenstein had finished the house and was meeting occasionally with a number of members of the Vienna Circle – Carnap, Waismann, and Feigl in particular. A passage in Ramsey’s paper just mentioned now caught his eye and he dictated a letter, typed by Carnap, which denounced the device by which Ramsey had defined identity, in breach of the Tractatus’s exclusion of that concept. Ramsey, in the end, had not followed Wittgenstein’s principles. A handwritten opening of the letter, “Dear Mr Ramsey”, suggested that he might like to reply to Professor Schlick (for whose thinking in fact Ramsey had not great respect). In a draft reply to Schlick Ramsey explains that he has quarrelled with Wittgenstein though not over this issue. (All the same this did become a contested issue to which Wittgenstein returned in his notes and no doubt his conversations several times.) Such conversations there were to be, because Wittgenstein returned to Cambridge at the beginning of 1929. I have called this a tale of two cities but Vienna was not a place for his work: there he would only be a wealthy amateur. When he did come it was enough for Keynes to tell him that he thought he would find Ramsey worth talking to about logic and other things. And in fact their discussions were a joy:

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They’re like some energetic sport and are conducted, I think, in a good spirit. There is something erotic and chivalrous about them. They educate me into a degree of courage in thinking. In science I only like to [quaere only reluctantly] go for a walk on my own.4

The appended sentence is puzzling as written – unless Wittgenstein is thinking of how he otherwise was. Amended (as by Wolfgang Kienzler or myself) it makes more sense but perhaps the most significant point is that Wittgenstein here uses the term “science” (German Wissenschaft) for his own activity and with a positive tone. He had done so in the past, in an enthusiastic letter to Russell of 15.12.1913, and in a significant passage on solipsism: Only from the consciousness of the uniqueness of my life does religion – science – and art arise.5

And his sister echoes this in her reflections on the impossibility of religion, science and ethics being one for them (the family) since religion was missing. Schlick and Frege of course used the word for his and their work, but after his discussions with Ramsey, Wittgenstein no longer did and limited the word to natural science and, with a difference, mathematics. One example from many: My aim is thus other than that of the scientists and my train of thought different from theirs.6

We shall see that Ramsey was partly responsible for this. The topics of the discussions (cut short by Ramsey’s illness and death within a year) are in some cases known to us from papers among the remains of Ramsey edited by Maria Carla Galavotti, others from comments on Ramsey in Wittgenstein’s preliminary or semi-edited notebooks and typescripts. The first twenty or so sections in her book show a number of areas in which Ramsey mulls over, not without criticism of Wittgenstein, problems which appear in the development of a semi-systematic re-writing of the Tractatus such as Waismann was about to begin back in Vienna. Visual space, the nature of meaning, the idea that logic must take care of itself and so on. Later in the selection we find Ramsey talking about the foundations, if any, of physics and mathematics, and above all about the infinite. It seems from later notes of Wittgenstein’s that Ramsey defended an extensional interpretation: I said on one occasion that no extensional infinite existed. Ramsey replied, Can’t one imagine a man living for ever, i.e. simply never dying, and isn’t that extensional infinity? And, to be sure, I can imagine a wheel turning and never stopping. There is a strange difficulty here: it seems to me nonsense to say that there are in a room an infinite number of bodies, as it were by accident. On the other hand I can think in an intentional manner of an infinite law (or an infinite rule) that always produces something new – ad infinitum – but naturally only what a rule can produce, i.e. constructions.7

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The topic recurs in other manuscripts of Wittgenstein’s. Note that “The Infinite” was precisely the topic Wittgenstein chose for the talk actually delivered to the Aristotelian Society in Nottingham in July 1929. Now in fact among Ramsey’s papers there is one in German (with some examples and sentences in English), to which my attention was drawn by Maria-Carla Galavotti and which she entitled “Ist die primäre Zeit unendlich?”, such being its first words. The initial paragraph does indeed appear in the published Philosophische Bemerkungen, as Professor Galavotti remarks, but the remaining paragraphs are drawn from Wittgenstein’s large notebook no. 2 (MS 106), with a few comments or summaries in English and a small number of spelling mistakes not of the usual Wittgensteinian kind. (This point and a good discussion of the content of the paper occur in Wolfgang Kienzler’s Wittgensteins Wende zu seiner Spätphiliosophie 19301932.) This particular selection of Wittgenstein’s remarks does not occur elsewhere, so it is probably not drawn from a prepared document. It seems to me not unlikely that it was dictated to Ramsey as a draft for the Aristotelian Society talk, perhaps for translation. The paper discusses various problems of interest to Wittgenstein and Ramsey at the time (I shall mention one shortly) but ends up (to show its general nature), as follows: Infinite possibility is represented by a variable whose place can be filled in infinitely many ways: and the infinite should not occur in a proposition in any other way.8

At Nottingham Wittgenstein left undiscussed his paper on “Logical Form”, which had been presented in advance and is in fact printed in the Proceedings. Now this paper is also one in which the hand of Ramsey appears. Indeed it is only natural if the paper or papers presented at the Joint Session represented Wittgenstein’s chief preoccupations during the year and hence also his conversations with Ramsey, which were so important to him. This is pre-eminently true of the “Logical Form” paper, which presents, as is well known, a revision of the system of the Tractatus. As Wittgenstein explained to his friends in Vienna, he no longer thought that an elementary proposition was itself confronted with reality. It was now a propositional system that was laid against reality – and this had the consequence not that there were an infinite number of elementary propositions but that there were none, as is indeed said in the paper on the infinite we have just been discussing. Given that this topic is one raised at the very beginning of Ramsey’s contact with Wittgenstein I think there is little doubt that he helped Wittgenstein to solve (sit venia verbi) the problem of colour incompatibility (and more generally that of the synthetic a priori), which had been a trouble since Tractatus 6.3751 and which was a subject of preoccupation in Vienna. The direction of influence between the two thinkers has been a subject of some discussion, Kienzler and Eva Picardi and Rosaria Egidi representing Wittgenstein as making the larger contribution, whereas Ulrich Maier and Mathieu Marion for example think Ramsey taught Wittgenstein to view mathematics in an intuitionist and even finitist way. I cannot enter into all these topics today but it seems to me that influence is not the right word: we might better remember

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Gilbert Ryle’s reply when asked whether he had been influenced by Wittgenstein: “I learnt a lot from him.” Now Wittgenstein clearly learnt a lot from Ramsey and came back to philosophy with a knowledge of the thought of Weyl, Brouwer and Hilbert that he would not have had otherwise. But he certainly did not adopt a position near to intuitionism under Ramsey’s influence – Ramsey’s conversion (if such it was) occurred after their meeting in 1925 and Wittgenstein’s enthusiasm for Brouwer did not result from but was the reason for going to the 1928 lecture. It was not a Cambridge product. Ramsey reports in a letter to Fraenkel in 1928 that [in 1924] Wittgenstein did not accept his (Ramsey’s) solution which avoided the need for an axiom of reducibility but rejected all those parts of mathematics that depended on it: “his conclusions were nearly those of the moderate intuitionists. What he now thinks I do not know.” This position of Wittgenstein’s became known (probably through Ramsey) and, as we have seen, Wittgenstein is quoted as a semi-intuitionist alongside Chwistek in Becker’s book on mathematical existence. Least of all did Wittgenstein owe his finitism to Ramsey: in his passages on the matter (taking the line we have seen) Ramsey is always presented as the believer in an actual infinite whom it is important to refute. The general thesis that Ramsey was the chief inspirer of Wittgenstein’s second philosophy seems to me mistaken, unless by the second philosophy is meant that intermediate phase in which a revised dogmatism still seemed possible. The real change came, and this is indicated even by the tribute to Ramsey in the preface to Philosophical Investigations, with the abandonment of the search for the essence of language, which was inspired by Sraffa and by the reading of that least Viennese of figures, Spengler, or, in other words, with the move away from dogmatism, as Wittgenstein called it in his conversation with Waismann in December 1930. Looking back, in the rough notebook (Ms 157b) used when he was making a determined effort to write the definitive account of his changed view (his 1936-37 Ms 142, most of which survives in the opening sections of Philosophical Investigations), Wittgenstein says that the idea of the family [i.e. family resemblance, by inference and by other references that of Spengler] and [the realization that] understanding was not a pneumatic process were two axe strokes against [his previous doctrine – of the crystal clarity of logic in itself]. Sraffa had shown him that he had to accept as a sign something for which he could not give the rules and grammar. From this point of view it is not surprising that in the original version of his well known list of influences on himself Wittgenstein includes just four – Frege and Russell, Spengler and Sraffa – the muses respectively of his first and of his later philosophy. Ramsey is not even added later (as Hertz, Kraus and others are). Ramsey indeed was (almost) the enemy, though no doubt the enemy within – note that one of Ramsey’s last papers shows that he thinks philosophy consists of definitions, precisely what Wittgenstein wanted to get away from. Ramsey’s

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contribution perhaps consisted in showing the difficulties that arose from Wittgenstein’s earlier position. Of course we do not know how Ramsey would have developed had he lived, nor how this would have affected Wittgenstein. I suspect that Ramsey did not have the willpower to control Wittgenstein nor Wittgenstein the wit to convince Ramsey. Their paths would probably have diverged in any case. I will give a few instances of the passages where Wittgenstein, characteristically unsparing, anticipates this in describing this difference between Ramsey and himself on philosophical matters. They should be set against an awareness of the love and concern that Frances Partridge saw when he accompanied her to Ramsey’s deathbed. Ramsey’s death roughly coincided with Wittgenstein’s gradually distancing himself from Bloomsbury and the circle of the Apostles, to which he had formally returned in 1929 (a dinner was held on the occasion). For a while he interested himself in the literary, dramatic and musical activities of the young, above all the privileged young – “all those Wykehamists”, as Leavis scornfully described them (Wittgenstein’s own phrase was “all those Julian Bells”). He took Dadie Rylands round the College garden explaining how Shakespeare should be produced. He analysed the symbols in the poems of William Empson’s circle. He criticized John Hare’s (the later Lord Listowel’s) singing and commented on the paintings of Julian Trevelyan. Something – more than one thing probably – changed him. His views were perhaps not given the attention they deserved. Rylands smiled at the advice that was given, Julian Bell wrote a poetic epistle, addressed to Braithwaite, protesting against the cultural hegemony claimed by Wittgenstein. John Cornford’s scorn for his teachers may have been directed against, for it was certainly resented by, Wittgenstein. Wittgenstein began to find friends and disciples in less privileged and more earnest circles, who were primarily intent on personal improvement: King, Lee and Townsend, who have published their notes on his lectures; the circle round Skinner; and particularly Drury, Smythies and Rhees, who remained close to him till the end of his life. Each group is worthy of description, but none is remotely to be thought of in connexion with Bloomsbury. They were prepared, however, for the difficult task of discipleship: it meant that they had to get the essential things right and yet be prepared to disagree with Wittgenstein: above all they could not play with ideas, or indeed with much else. He found also friends of his own age and on his own level and, by a social law that I have observed operate at Oxford, these tended to be foreigners who (more than was necessary but not more than was natural) felt themselves outside the cosy world of the colleges. Piccoli, the professor of Italian, was one example. But the chief figure of this kind was undoubtedly Sraffa and here Wittgenstein was confronted with willpower almost equal to his own. If Sraffa made him feel like a tree stripped of its branches, Sraffa in the end found their conversations too much – “I won’t be bullied by you, Wittgenstein”, Smythies (who, you might

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say, had been bullied by both) heard him say. Sraffa resembled Wittgenstein even in some of the methods and aims of his scientific work. He too could use their common friends Ramsey and Alister Watson to help him with the mathematics he needed, but he took strictly what he needed from them. And I am struck by a summary judgement of Amartya Sen9: [Sraffa’s] later work did not take the form of finding different answers to the standard questions in mainstream economics, but that of altering – and in some ways broadening – the nature of the inquiries in which mainstream economics was engaged.

Sen adds that it would be surprising if Sraffa had not been influenced by his own philosophical position but had stayed within “the rather limited boundaries of positivist or representational reasoning commonly invoked in contemporary mainstream economics.” Instead he addressed (according to Sen) foundational economic issues of general social and political interest (some of which have been discussed for over two hundred years). Sen has some valuable suggestions for the influence of Sraffa’s philosophical position on Wittgenstein, but I will not go into those here. I want instead to quote one Cambridge contemporary who felt that Wittgenstein also went, or wanted to go, outside the recognized borders of his subject. No great figure but a thoughtful friend of the Bloomsbury group, Sydney Waterlow, wrote to Moore as follows: [On reading Ramsey] contrast between his quite extraordinary powers and his immense vitality on the one hand and on the other the poverty of his Weltanschauung. Wrong that there should be such a contrast; something has gone terribly wrong. His drift towards stating everything in “pragmatic” terms could not, however arguable, put the wrong right. [Ought we to accept only a limited circle of beliefs that are not nonsense] My own belief is that this simply cannot be the case and nothing that a Ramsey can say to the contrary can affect me in the least. For one thing there is a cocksureness in his attitude which I feel to be cosmically inappropriate. A Russell or a Keynes can never grow out of that pertness – there is no principle of growth in them – but Ramsey is so good that he might have if he had lived. [The unsatisfactoriness of Principia Ethica] But what is satisfactory I haven’t the faintest idea. I rather think Wittgenstein knows and I believe one has got to find out.10

How Moore replied we do not know. He will not have mocked Waterlow as Virginia Woolf does in her diaries, where, however, she tells us something about him that brings him into connexion with Wittgenstein: Waterlow at this time had discovered the other inspirer of Wittgenstein’s Wende, Spengler (the word Weltanschauung betrays it), and this had changed the world for him. It is true the Wende took Wittgenstein in directions not envisaged by Spengler, Waterlow, or followers of Wittgenstein such as Paul Engelmann, but that his tendency was to break the boundaries, to change the donne is undeniable. It is far from clear that Ramsey would have wanted any such thing.

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N OTES 1. 2. 3. 4.

Frances Partridge, Memories, Gollancz 1981 p.129. CUL: Papers of G.E. Moore (letter from F.P. Ramsey 6.2.1924). Encyclopaedia Britannica 13th edition (New Volume 2, p.831). Wittgenstein Papers 105 4 15 Feb.1929. Ich habe sehr genußreiche Diskussionen mit Ramsey über Logik etc. Sie haben etwas von einem kräftigen Sport und sind glaube ich in einem guten Geist geführt. Es ist etwas Erotisches und Ritterliches darin. Ich werde dabei auch zu einem gewissen Mut im Denken erzogen. Es kann mir beinahe nichts Angenehmeres geschehen als wenn mir jemand meine Gedanken gleichsam aus dem Mund nimmt und sie gleichsam im Freien aufrollt. Natürlich ist alles das mit viel Eitelkeit gemischt, aber es ist nicht pure Eitelkeit. Ich gehe in der Wissenschaft nur gern [quaere nur ungern or nicht gern] allein spazieren. 5. Noteboooks 1914-1916 p.79 1.8.1916. Nur aus dem Bewußtsein der Einzigkeit meines Lebens entspringt Religion – Wissenschaft – und Kunst. 6. Wittgenstein papers 109 207 6 Nov.1930. Mein Ziel ist also ein anderes als das der Wissenschaftler und meine Denkbewegung von der ihrigen verschieden. 7. Wittgenstein Papers 105 23 (February 1929). Ich sagte einmal es gäbe keine extensionale Unendlichkeit. Ramsey sagt darauf kann man sich nicht vorstellen daß ein Mensch ewig lebt d.h. einfach nie stirbt, und ist das nicht extensionale Unendlichkeit? Ich kann mir doch gewiß denken daß ein Rad sich dreht und nie stehenbleibt. Hier liegt eine merkwürdige Schwierigkeit: Es scheint mir unsinnig zu sagen daß in einem Raum unendlich viele Körper sind gleichsam als etwas Zufälliges. Dagegen kann ich mir ja intentional ein unendliches Gesetz denken (oder eine unendliche Regel) durch die immer neues produziert wird – ad infinitum – aber natürlich nur was eine Regel produzieren kann, nämlich Konstruktionen. 8. Ramsey Papers 004-23-01. Die unendliche Möglichkeit ist durch eine Variable vertreten die eine unbegrenzte Möglichkeit der Besetzung hat: und auf andere Art darf das Unendliche nicht im Satz vorkommen. 9. Amartya Sen “Piero Sraffa: a student’s perspective”, Atti dei convegni Lincei, vol. 200, Rome 2004, pp.23-60. 10. CUL: Papers of G.E. Moore (letters from Sydney Waterlow 6 & 23 Jul. 1931).

Dipartimento di filosofia e scienze sociali Università degli studi di Siena Via Roma 47 53100 Siena Italy [email protected]

M ICHAEL D UMMETT

THE VICIOUS CIRCLE PRINCIPLE According to Frank Ramsey, and likewise to Gödel, the validity of Russell’s Vicious Circle Principle depends on whether mathematical objects exist independently of us in an abstract realm, or whether they are human creations, brought into being by intellectual constructions we have effected and sustained in being by our ability to repeat those constructions. (A work of fiction or a poem is a human creation, but, once written down or printed, is not sustained in being by human intellectual activity.) The example always given to illustrate the former alternative is that of picking out a particular man in a room as the tallest man in the room. This specification involves quantifying over the set of men in the room, a set of which the individual thus picked out is a member. This apparently violates the Vicious Circle Principle, but is quite evidently legitimate. On the diagnosis of Ramsey and of Gödel, its legitimacy derives from the fact that the men in the room exist independently of any observer or commentator. It is at first sight paradoxical to hold that, in order to determine the validity of a logical principle such as the Vicious Circle Principle, we should first have to settle a grand metaphysical question such as the ontological status of mathematical objects. Surely the validity of the Vicious Circle Principle for any given domain of quantification depends, not on the solution of so large a metaphysical problem, but on how that domain is to be specified. If we try to specify it by appeal to quantification over that very domain, we shall have violated the Vicious Circle Principle: we shall have committed a genuinely vicious circle. Quantification over a domain assumes a prior conception of what belongs to that domain: by trying to specify what belongs to the domain by using quantification over that same domain, we assume as already known what we are attempting to specify. But if we can specify the extent of the domain in some manner which determines the scope of quantification over it without assuming that as already given and available for use in our specification, we shall be free to pick out a particular element of the domain by quantifying over it. Suppose, for example, that we start with some first-order theory, our individual variables ranging over some domain, such as the real numbers, which we take to be well defined. We want to extend our theory by expanding the language to admit a new sort of variables for classes of elements of the original domain. If we explain the notion of such a class predicatively, that is, as associated with a formula of the original unextended theory with one free variable, membership of the associated class being determined by satisfaction of the corresponding formula, there will be no circularity in our manner of specifying the domain of the

29 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 29–33. © 2006 Springer. Printed in the Netherlands.

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new class-variables. But if we were to make the classes correspond in the same sense to formulas of the expanded language, we should by this impredicative specification have violated the Vicious Circle Principle, since formulas of the expanded language will include ones involving quantification over classes; our explanation will indeed be viciously circular. If, on the other hand, we specify that the class-variables are to range over every possible function from elements of the base domain – real numbers, in the example – to the truth-values true and false, we escape this difficulty: we may specify a particular class by quantification over classes. There is much room for doubt whether the intended sense of “possible” is a legitimate or truly comprehensible one, namely, when we speak of all possible functions from real numbers to truth-values, that is, of all possible determinations, for every real number, of whether it belongs to the associated class or not. But there can be no doubt that, if it is legitimate, we shall in this way have evaded the Vicious Circle Principle. Why, then, do Ramsey and Gödel insist that the validity of the Vicious Circle Principle depends upon whether mathematical objects exist independently of us or are created by us in thought? Their idea is surely this. When we wish to specify a domain of quantification consisting of physical objects, all we need to do is to select a suitable concept, in Frege’s sense of “concept”. A Fregean concept is determined by a precise condition for an arbitrary object to fall under the concept. If we wish to quantify over the mammals in the London Zoo, we shall select the concept mammal in the London Zoo; if we wish our domain of quantification to comprise just the elephants in the London Zoo, we shall select the concept elephant in the London Zoo. Making a choice of the relevant concept is all that we need to do in order completely to determine the domain of quantification. We do not need, in addition to selecting the concept that fixes the condition for membership of the domain, to lay down what objects there are which fall under the concept, or how many of them exist: external reality does that for us. Sometimes, indeed, it is like this in the mathematical realm. If, for some reason, we wanted to quantify over prime numbers of the form 2n - 1, we should need simply to specify that our domain was to consist of numbers falling under the concept prime number equal to 2n - 1 for some n. Reality would, as it were, run through the numbers 2n -1 for n = 0, 1, 2, 3, ..., checking each one to see whether it was prime or not, and consigning each such prime number to our domain. We can leave reality to separate out the elements of our domain because we are forming that domain from within a larger, already determinate, domain, that of the natural numbers. The natural numbers form the zoo from among whose denizens we pick out the elements of our new, smaller, domain. If, however, we want our domain to consist of the real numbers, or of the ordinal numbers, the matter appears quite differently to most of us. Associated with the expressions “real number” and “ordinal number” are concepts, just as there are with the words “mammal” and “elephant”. The concept real number is determined by the condition that a mathematical object that is given to us by

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means of some definition or construction rollst satisfy if we are to recognise it as being a real number; we might take this condition to be that of having a determinate position with respect to the rationals, categorising each rational number as being less than or equal to it or greater than it, and some as one and some as the other. (The final phrase is to exclude infinitary end-points of the rational line.) Similarly, the concept ordinal number is determined by the condition for a given mathematical object to be recognised by us as being an ordinal number; we might take this condition to be that of being the order-type of some well-ordered sequence. Such concepts do not, however, appear to most of us to be adequate to determine a domain of quantification. We do not seem to be in a position to require reality to run through all the mathematical objects that there are in order to decide of each one whether it falls under the concept real number or not, or under the concept ordinal number or not. If we are not in that position, then we must do more to fix a definite domain of quantification than to specify a concept under which the elements of our domain must fall. We must also stipulate a criterion for the existence of objects that are to be elements of our domain, or at least for their belonging to the domain over which we intend to quantify. Why this difference? Why do we think that we need to do more than simply to specify the concept under which the elements of our domain are to fall? The reason is that only very few of us are full-fledged realists about the mathematical realm. If we were, we should assume that there is an absolutely determinate totality of mathematical objects, as determinate as the totality of molecules in a particular glass of water or of monkeys in a certain jungle at a given time. In such a case, it would be enough, in order to specify a domain of quantification, to select a concept under which some mathematical objects fall and others do not; for then reality could decide whether any given object fell under the concept as well as we can, once the object is given to us. If we were total or full-fledged realists about the mathematical realm, that is to say, if we interpreted it in just the same way as realists about the physical world interpret that world, we should think that we could specify a domain of quantification simply as consisting of those mathematical objects that fall under the concept real number. It would consist of just those objects that effect a Dedekind cut in the rational line and do nothing else. Whether or not it would contain an element effecting every possible such cut, in the sense intended by platonists who speak of “every possible Dedekind cut”, would depend upon just which mathematical objects reality comprises – which mathematical objects the Creator has chosen to bring into existence. It would be unnecessary, from this uncompromisingly realist standpoint, to specify the domain by speaking of every possible Dedekind cut: rather, it would consist of every mathematical object that there actually was which effected such a cut. Similarly, we could specify a domain as consisting of all the ordinal numbers there are. There need be no fear that this would lead to contradiction via the Burali-Forti paradox. We could modify the concept ordinal number so as to apply only to those order-types of

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well-ordered sequences that had a successor. There would then be just one wellordered sequence that had no ordinal number as its order-type – the sequence of all ordinal numbers; or we might hold that this sequence has no order-type. But this would involve no contradiction. We – or at any rate, all but a small minority of us – are not normally disposed to think of the existence of mathematical objects in this resolutely full-fledged realist manner. Think, for example, of the odd impression made on us by the question whether there exist large cardinals of some particular type. The question may be intended as asking whether it is consistent to assume the existence of such large cardinals. But, if more is being asked than this, what can the question mean? If it is allowed that there may be no contradiction in postulating the existence of large cardinals of that type, but held that there still remains a question whether there really are such cardinals, what could determine the answer to such a question? It is not, surely, a matter of whether God chose to create such cardinals. Kronecker told us that the existence of any mathematical objects other than the natural numbers is the work of man. The existence of monkeys of one or another kind is a contingent matter, a matter of what God has chosen to create. But the existence of mathematical objects should surely be a matter of necessity, of what we could not have found to be otherwise. How should we determine what mathematical objects exist of necessity save by fastening upon same criterion of our own for their existence? Hilbert held that those mathematical objects exist whose existence may be consistently assumed. The mathematical realm, on this view, is maximally full: there are all the mathematical objects that there can be. One who believes that all mathematical theories can be captured in a first-order formalisation may appeal to the completeness theorem in support of this. But this consistency criterion of existence is itself inconsistent. The existence of objects of each of two types may be consistently postulated, and yet a contradiction may result from postulating the existence of both together. It is presumably consistent to assume the existence of the sets which constitute a model of Quine’s NF, but that cannot be combined with the existence of the sets required by ZF, that is, if both are to be sets in the same sense. If we do not think that a first-order axiomatisation can embody every one of our mathematical conceptions, we must allow that there are consistent theories which hold good only if there are only finitely many objects altogether, and others which have only infinite models. Theories which are individually consistent may not be collectively so. I think that full-fledged realism about mathematical objects is a view that is barred to us. We cannot explain what, on such a view, determines which mathematical objects exist; we cannot treat their existence as a matter of what reality holds. I cannot claim that no one is a full-fledged mathematical realist. Professor Timothy Williamson has explained to me in personal correspondence that he hesitates between structuralism and full-fledged realism. In his view, quantification over the elements of a domain has always to he understood as quantification over every object there is, restricted in the standard way by some suitable

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predicate (“is an elephant” or “is a real number”, etc.). Thus if mathematical realism is correct, it must be full-fledged realism. This is certainly a minority view, and I think it untenable. If I am right, we are in no position to declare the Vicious Circle Principle generally irrelevant, as it is when we are quantifying over physical objects The first diagnosis was the right one The Vicious Circle Principle may prohibit us from specifying a domain of quantification in certain ways; it may not apply when we specify the domain in other ways. It is not a matter of whether the elements of the domain exist independently of us or are created by us in thought. It is a matter of the means we adopt to specify that domain and lay down what its elements are to be.

Sir Michael Dummett 54 Park Town Oxford OX2 6XJ UK

P ATRICK S UPPES

RAMSEY’S PSYCHOLOGICAL THEORY OF BELIEF

1. R EJECTION OF F REQUENCY T HEORY AND K EYNES ’ T HEORY OF P ROBABILITY In my analysis of Ramsey’s theory of belief, I shall, in the first part, closely follow the development of his own ideas in his well-known essay, “Truth and Probability”, written in 1926 and published posthumously in 19311. The pagination of my quotations shall be from the 1931 version, edited by Braithwaite. Ramsey begins by admitting some reasons for favoring the frequency theory. More importantly, he endorses it as a proper theory for use in physics, but he immediately goes on to give his reasons for why it is not the proper theory for the logic of partial belief. He doesn’t say a great deal more, but turns immediately to his main object of criticism, Keynes’ Theory of Probability 2. I will not spend much time on these criticisms, but I think it is important to give some sense of what Ramsey has to say about what is wrong with Keynes’ views. His reaction to them shaped many of his own ideas about partial belief. Here is his first point: But let us now return to a more fundamental criticism of Mr. Keynes’ views, which is the obvious one that there really do not seem to be any such things as the probability relations he describes. He supposes that, at any rate in certain cases, they can be perceived; but speaking for myself I feel confident that this is not true. I do not perceive them, and if I am to be persuaded that they exist it must be by argument; moreover I shrewdly suspect that others do not perceive them either, because they are able to come to so very little agreement as to which of them relates any two given propositions. (p. 161)

Notice the line of argument. It is psychological in character. Ramsey simply does not perceive that probability relations are a species of logical relations and, therefore, have full objective validity. The kind of view that Keynes argued for is scarcely defended by anyone today, so I move on to another point. Ramsey states a second view of probability that is also logical in character, but, as he puts it, is ‘more plausible’ than Mr. Keynes’. Here is his summary: This second view of probability as depending on logical relations but not itself a new logical relation seems to me more plausible than Mr. Keynes’ usual theory; but this does not mean that I feel at all inclined to agree with it. It requires the somewhat obscure idea of a logical relation justifying a degree of belief, which I should not like to accept as

35 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 35–53. © 2006 Springer. Printed in the Netherlands.

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indefinable because it does not seem to be at all a clear or simple notion. Also it is hard to say what logical relations justify what degrees of belief, and why; any decision as to this would be arbitrary, and would lead to a logic of probability consisting of a host of socalled ‘necessary’ facts. (p. 165)

The essence of this proposal is to take a more conservative approach and to make probability depend on logical relations, but not be itself a primitive logical concept. This, too, he finds unsatisfactory. Again, this second view is not one that really has, in such bald form, any serious advocacy today. Ramsey returns in several places to other criticisms of Keynes. He seems unable to resist and, I suppose, for good reason. It is hard to think of another book in the history of probability, as badly thought out as Keynes’, which has had so much attention. 2. T HE M EASUREMENT OF P ARTIAL B ELIEF AS S UBJECTIVE P ROBABILITY Ramsey next moves directly to his own theory of the logic of partial belief, and he concentrates on problems of measurement. His section is entitled ‘Degrees of Belief’. At the very beginning, Ramsey starts with the following passage on the importance of measuring partial belief. The subject of our inquiry is the logic of partial belief, and I do not think we can carry it far unless we have at least an approximate notion of what partial belief is, and how, if at all, it can be measured. It will not be very enlightening to be told that in such circumstances it would be rational to believe a proposition to the extent of Ҁ, unless we know what sort of a belief in it that means. We must therefore try to develop a purely psychological method of measuring belief. It is not enough to measure probability; in order to apportion correctly our belief to the probability we must also be able to measure our belief. (p. 166)

We may begin analysis of Ramsey’s theory of measurement of beliefs by his initial paragraph. The important point is his emphasis on the necessity of having a psychological method of measuring belief, in order to have a usable measurement of subjective probability. He does not here use the term ‘subjective probability’, but, for ready reference, it is the term now more current than ‘degree of belief ’. In the next passage, Ramsey summarizes what should be the main ingredients of a procedure for measuring partial belief. Let us then consider what is implied in the measurement of beliefs. A satisfactory system must in the first place assign to any belief a magnitude or degree having a definite position in an order of magnitudes; beliefs which are of the same degree as the same belief must be of the same degree as one another, and so on. Of course this cannot be accomplished without introducing a certain amount of hypothesis or fiction. Even in physics we cannot maintain that things that are equal to the same thing are equal to one another unless we take ‘equal’ not as meaning ‘sensibly equal’ but a fictitious or hypothetical relation. I

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do not want to discuss the metaphysics or epistemology of this process, but merely to remark that if it is allowable in physics it is allowable in psychology also. (p. 168)

In the subsequent paragraph, which I shall not quote, Ramsey emphasizes a point that he makes in several other places, namely, that the measurement of beliefs will be approximate and will sometimes be more accurate than others, but this is not surprising, for exactly the same thing happens in physics. This is perhaps a good point to mention a reference that is surprisingly missing from Ramsey’s discussion of the measurement of belief, which he properly judges as a difficult problem. He does not mention the remarkable efforts at measuring psychological quantities, with a theory of approximation or threshold incorporated, by Norbert Wiener3, published just four years before Ramsey’s manuscript was written. Norbert Wiener was earlier a student in Cambridge studying with G. H. Hardy and Bertrand Russell. Less likely is that Ramsey would have known of the treatment of measurement by the German mathematician Otto Hölder4, which was much more sophisticated in its approach, especially from a mathematical standpoint, than the rather naive approach by Norman Campbell5 that he does occasionally cite. My point is that it is surprising that someone with Ramsey’s combination of interests and knowledge did not know more about the already rather extensive and detailed literature on the theory of measurement. He is, as in some other things, much too caught up in the writings of those at or close to Cambridge. In any case, after a sentence or two I have left out, he continues on the same page in the following way: But to construct such an ordered series of degrees is not the whole of our task; we have also to assign numbers to these degrees in some intelligible manner. We can, of course, easily explain that we denote full belief by 1, full belief in the contradictory by 0, and equal beliefs in the proposition and its contradictory by ½. But it is not so easy to say what is meant by belief Ҁ of certainty, or a belief in the proposition being twice as strong as that in its contradictory. This is the harder part of the task; but it is absolutely necessary; for we do calculate numerical probabilities, and if they are to correspond to degrees of belief we must discover some definite way of attaching numbers to degrees of belief. (p. 168)

What Ramsey recognizes in this passage and what follows is the necessity of finding arithmetical operations corresponding to the physical process of addition, so familiar in physics, so this is what he has to say on the following page: Such is our problem; how are we to solve it? There are, I think, two ways in which we can begin. We can, in the first place, suppose that the degree of a belief is something perceptible by its owner; for instance that beliefs differ in the intensity of a feeling by which they are accompanied, which might be called a belief-feeling or feeling of conviction, and that by the degree of belief we mean the intensity of this feeling. This view would be very inconvenient, for it is not easy to ascribe numbers to the intensities of feelings; but apart from this it seems to me observably false, for the beliefs which we hold most strongly are

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often accompanied by practically no feeling at all; no one feels strongly about things he takes for granted. (p. 169)

Again, it is appropriate to refer to Wiener, for it is exactly the measurement of intensity of feeling, for example, of the loudness of a sound or comparable sensory phenomena that Wiener’s theory of 1921 was concerned with. In this connection, as I could have mentioned earlier, it is also surprising that Ramsey does not mention the elaborate theory of measurement which Wiener built on, and which occupies a large part of the third volume of Principia Mathematica 6. The earlier volumes of which, and the first part of this volume, were of importance in Ramsey’s own work in the foundations of mathematics. But on this last point, I do not really blame Ramsey. Hardly anyone beyond Wiener, as far as I know, has made extensive use of the theory of measurement developed in Part VI of the third volume. It is difficult to read, from a notational standpoint, and does not seem to have really new ideas concerning measurement itself. The treatment of thresholds by Wiener, in contrast, is a genuine new mathematical development, really essentially the first, from a mathematical standpoint, even though the concept of thresholds was introduced much earlier in psychology by Fechner7. (For a detailed survey of the literature, see Suppes, Krantz, Luce and Tversky8.) In any case, Ramsey rejects the use of degree of feeling generated by a belief as a way of measuring the degree of belief. He goes on in the next passage, immediately following, to opt for the degree of belief as a causal property. We are driven therefore to the second supposition that the degree of a belief is a causal property of it, which we can express vaguely as the extent to which we are prepared to act on it. This is a generalization of the well-known view, that the differentia of belief lies in its causal efficacy. (p. 169)

Immediately after this quotation, Ramsey acknowledges that this idea is discussed by Russell in his Analysis of Mind 9. Russell dismisses the causal theory of belief, but Ramsey defends it in a subsequent paragraph. But what Ramsey has to say in its defense is unsatisfactory in terms of a theory of identifying our beliefs. He does make the point, much agreed to by philosophers of many different persuasions, that beliefs play a role of a substantive kind in determining our actions. He states very clearly, on page 173, his firm support of what has come to be called the standard belief-desire model of action, much defended and popularized in more recent years by a number of philosophers. Here is how he summarizes his thought on page 173: I mean the theory that we act in the way we think most likely to realize the objects of our desires, so that a person’s actions are completely determined by his desires and opinions.

A simple part of Ramsey’s defense of this ‘Let us look to the effects’ theory of belief is that he defends that, just as in physics, we can study beliefs without knowing what they are. He uses the excellent example of the attitude toward

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electricity in the nineteenth century. One could, it was recognized, study the effects of electricity and, yet, not really be able to say what electrical current is. James Clerk Maxwell, the most important and original Cambridge scientist of the nineteenth century, strongly supports this view about electricity in the following passage from Volume II of his Treatise on Electricity and Magnetism 10: It appears to me, however, that while we derive great advantage from the recognition of the many analogies between the electric current and a current of material fluid, we must carefully avoid making any assumption not warranted by experimental evidence, and that there is, as yet, no experimental evidence to shew whether the electric current is really a current of a material substance, or a double current, or whether its velocity is great or small as measured in feet per second. A knowledge of these things would amount to at least the beginnings of a complete dynamical theory of electricity, in which we should regard electrical action, not, as in this treatise, as a phenomenon due to an unknown cause, subject only to the general laws of dynamics, but as the result of known motions of known portions of matter, in which not only the total effects and final results, but the whole intermediate mechanism and details of the motion, are taken as the objects of study. (p. 218)

It seems to me that Maxwell gives the right analysis, the one that Ramsey should have used quite directly, in the case of belief, namely, that if all we know are the effects of belief, then, like electricity, beliefs remain an unknown cause. I am belaboring this point, because I think it is often a failure of modern philosophers not to recognize the difficulty of characterizing, in a psychologically and, at the same time, scientifically satisfactory way, the nature of belief, or, to put it bluntly, how do we identify beliefs? It seems to me there are positive arguments of several kinds. And yet we do not want to accept that we can just be satisfied, as Maxwell was not, in the case of electricity, with what we can infer about beliefs as unknown causes. So, Ramsey, we might say, was right in one important aspect of belief, that there is a causal importance of beliefs, but restricting this causal account to their effects is scientifically unsatisfactory. Ramsey returns in several different passages to questioning the theory that beliefs are known by “introspectible” feelings, as he puts it, of varying degrees of belief. In doing so, he implicitly recognizes the attractiveness of this theory. Somewhat surprisingly, given Ramsey’s admiration of Hume, he does not refer to Hume’s strong claim that the intensity of feeling is the mark of a belief. I quote here just the single most famous passage from Hume’s Treatise: Thus it appears, that the belief or assent, which always attends the memory and senses, is nothing but the vivacity of those perceptions they present; and that this alone distinguishes them from the imagination. To believe is in this case to feel an immediate impression of the senses, or a repetition of that impression in the memory. ’Tis merely the force and liveliness of the perception, which constitutes the first act of the judgment, and lays the foundation of that reasoning, which we build upon it, when we trace the relation of cause and effect. (p. 86) 11

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As in many things, Hume puts his finger on the central problem, how indeed do we distinguish a belief from a fancy or an idle thought? In fact, the fallibility of memory makes this one of the great conundrums of forensic epistemology, and raises the problem of the various cases we have to distinguish, now much discussed at some length in both the literature of psychology and of the law. Well, it is not possible to go into the nuances of all this later literature, but it does seem to me it is a criticism of Ramsey that he is much too casual about the problem of identifying or recognizing beliefs and how to separate them from the products of imagination. I come back to this point from a different angle and in somewhat more detail later. 3. R AMSEY ’ S P ROPOSED M ETHOD FOR M EASURING B ELIEFS I now turn to the part of the theory of belief for which Ramsey is justly most famous, namely, his analysis of the problem of measuring beliefs and his proposed solution. He begins this discussion on page 172 and it continues for the next 12 pages. He stresses, as I have already emphasized, his concern to find a method of measuring beliefs as a basis of possible actions, not to develop a general system of beliefs unfocused on any practical or pragmatic applications. Before turning to detailed consideration of Ramsey’s positive theory of measurement, I do want to comment, as an application of an earlier remark I made, on his rejection, in too simple a fashion (p. 171), of the measurement of intensity of feeling based on just perceptual differences. As I mentioned earlier, he makes no reference to the work of Wiener, written earlier and published in 1921, which is more sophisticated, both from a psychological and a mathematical standpoint, than Ramsey’s own development. I quote here just the single passage, which is not sufficiently thought out. This does not mean that what Ramsey has to say about betting, which I will turn to in more detail, is incorrect. It is just that his outright rejection of measuring intensity by thresholds is mistaken and not well thought out. Here is what he says: Suppose, however, I am wrong about this and that we can decide by introspection the nature of belief, and measure its degree; still, I shall argue, the kind of measurement of belief with which probability is concerned is not this kind but is a measurement of belief qua basis of action. This can I think be shown in two ways. First, by considering the scale of probabilities between 0 and 1, and the sort of way we use it, we shall find that it is very appropriate to the measurement of belief as a basis of action, but in no way related to the measurement of an introspected feeling. For the units in terms of which such feelings or sensations are measured are always, I think, differences which are just perceptible: there is no other way of obtaining units. But I see no ground for supposing that the interval between a belief of degree ѿ and one of degree ½ consists of as many just perceptible changes as does that between one of Ҁ and one of 5/6, or that a scale based on just perceptible differences would have any simple relation to the theory of probability. On the other hand the probability of ѿ is clearly related to the kind of belief which would lead to

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a bet of 2 to 1, and it will be shown below how to generalize this relation so as to apply to action in general. (p. 171)

A much later detailed theory of measuring subjective probability with thresholds is to be found in Domotor and Stelzer12. I examine the developments from page 172 to 187 in numbered remarks, in which I try to lay out clearly the elements of Ramsey’s detailed proposal, because it is of great historical importance, even though it is possible to criticize it from a later perspective that is crowded with many subsequent formal and empirical developments. 1. Betting. Ramsey begins with this clear endorsement: The old-established way of measuring a person’s belief is to propose a bet, and see what are the lowest odds which he will accept. This method I regard as fundamentally sound; but it suffers from being insufficiently general, and from being necessarily inexact. (p. 172)

Ramsey mentions in the next few sentences a classical problem with betting, namely, the diminishing marginal utility of money, as confounding the interpretation of the odds ratio. 2. Beliefs and desires. He then goes on to say that the way to success is to ‘take as a basis a general psychological theory, which is now universally discarded, but nevertheless comes, I think, fairly close to the truth in the sort of cases with which we are most concerned. I mean the theory that we act in the way we think most likely to realize the objects of our desires, so that a person’s actions are completely determined by his desires and opinions.’ Then Ramsey remarks that he regards this theory as a useful approximation, even if not exact, and it being a somewhat artificial system of psychology, but one that can, as he puts it, ‘like Newtonian mechanics ... still be profitably used, even though it is proved to be false.’ (p. 173) 3. Goods not pleasures. The theory of belief and desires should not be confused with utilitarianism. He distinguishes pleasures from “goods”, but he also says that, to start with, before developing a theory, he will assume that goods are numerically measurable and additive. He returns to the detailed theory later. 4. Good and bad, not ethical. “It should be emphasized that in this essay good and bad are never to be understood in any ethical sense but simply as denoting that to which a given person feels desire and aversion.” (p. 174) 5. Taking account of uncertainty. How are we ‘to modify this simple system to take account of varying degrees of certainty in his beliefs’. (p. 174)

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This concern for uncertainty, as I would put it, is, of course, central to Ramsey’s theory of partial belief. In these passages Ramsey is just outlining in a summary way the ingredients he will bring together in his axioms. 6. Mathematical expectation. He now asserts the following important proposal: I suggest that we introduce a law of psychology that his [a person’s] behaviour is governed by what is called the mathematical expectation. (p. 174)

He makes use of the ordinary notion, but I’ll use his terminology because it has this unusual plural usage of goods and bads. So, mathematical expectation is this: ... if p is a proposition about which he is doubtful, any goods or bads for whose realization p is in his view a necessary and sufficient condition enter into his calculations multiplied by the same fraction, which is called the ‘degree of his belief in p’. We thus define degree of belief in a way which presupposes the use of the mathematical expectation. (p. 174)

Of course, later, he converts this explicitly into the standard formula for maximizing the expected utility with respect to the utility function and the subjective probability function. I comment on this again. 7. A simple example of computations. Ramsey now gives on pages 175-176 a simple example of how computations of goods and bads with degrees of belief should be made. It’s a rather nice example about the costs of seeking directions when going on an unknown road. I will not go through the details, but it is useful, pedagogically, to make clear how he is going to tackle the question of measurement from the standpoint of how things are working in this intuitive example. 8. Minimal assumptions about measurement. He now says that we do not want to assume that goods are additive. So, the details of how we can measure goods and bads need to be worked out. This leads up to his treatment of utility. What is critical, as he already makes clear (p. 176), is that we need to get a way of judging that the distance between any two goods or bads can be equal to or greater than, or less than, the difference between any two other goods or bads. Or, as I would put it in more current terminology, we will use the formulation of qualitative utility differences governed by an ordering principle. 9. A difficulty solved. Ramsey points out there is a difficulty with his formulation of how to go about measuring these utility differences. We need an ethically neutral proposition. He says this means we want to find a proposition p, which we may call ‘ethically neutral if two possible worlds differing only in regard to the truth of p are always of equal value’. (p. 177) He notes in a footnote that he is assuming Wittgenstein’s theory of propositions – not that he is using very much of that theory in what is going on here.

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10. Defining degree of belief ½. Ramsey now makes the important step, which he describes as follows: We begin by defining belief of degree ½ in an ethically neutral proposition. The subject is said to have belief of degree ½ in such a proposition p if he has no preference between the options (1) Į if p is true, ȕ if p is false, and (2) Į if p is false, ȕ if p is true, but has a preference between Į and ȕ simply. (p. 177)

He does not give a sustained argument for there existing such an ethically neutral proposition p, but makes the existence of such a proposition his first axiom on the next page. 11. Operational definition of utility differences. He now gives the belief of degree ½, – but I will not go through the details –, an operational definition of what is meant by the measured difference in value between two goods or bads being to the difference in two others (for details see the equivalence (1) in the next remark). What Ramsey is doing here is very much what is still done, even though the language has changed and, certainly, the sort of casual talk about goods and bads is no longer current. Davidson and I used Ramsey’s idea extensively in our 1950s theoretical and experimental studies 13,14. 12. Axioms. On pages 178-179, Ramsey states his axioms. What is important to note is that he is not giving axioms for the measurement of the belief directly, but for measuring utility. The following point is relevant, particularly for readers familiar with de Finetti15 and Savage16, especially de Finetti, who does not directly and formally use utility or value at all in his approach to quantifying subjective probability. Ramsey’s measurement of subjective probability, as we shall see after we finish with the axioms, is based on first measuring utility, having available in doing so only events of probability ½. By the way, it is useful to make clear how this difference works. If we have the event ½ and we think of having the utility of four goods or bads Į, ȕ, Ȗ, į, we can write the following simple equivalent equations, with ½ being the only probability that enters the expectation calculation: ½ u(Į) + ½ u(ȕ) = ½(Ȗ) + ½(į) if and only if u(Į) - u(į) = u(Ȗ) - u(ȕ) . Ramsey does not work out the detailed consequences of his axioms, but it is apparent that they are essentially correct and there are many modern discussions of such axioms for the measurement of utility or value, as the modern terminology tends to put the matter. For an extensive review of the literature up to the beginning of the 1970s, see Krantz, Luce, Suppes and Tversky17.

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13. Measurement of belief. Having laid down axioms for the measurement of utility, as discussed, Ramsey is now in a position to define the measurement of belief without additional axioms, simply by using the quantitative measure of utility to do so. Here is the way he describes the matter in words. If the option of Į for certain is indifferent with that of ȕ if p is true and Ȗ if p is false, we can define the subject’s degree of belief in p as the ratio of the difference between Į and Ȗ to that between ȕ and Ȗ; which we must suppose the same for all Į’s, ȕ’s and Ȗ’s that satisfy the conditions. (p. 179)

This is standard and quite familiar in the literature. 14. Conditional probability. Ramsey now takes the additional important step of introducing conditional beliefs, which lead to conditional subjective probabilities. He spends some time with this topic, including stating various laws that hold for conditional probability, which I shall not review in detail, but refer the reader to what he terms the ‘fundamental laws of probable belief’ on page 181. These laws are all elementary as laws of probability, but essential for a coherent theory of belief, as is emphasized in the next point. 15. Belief and consistency. This is what Ramsey says about the elementary laws of probability he lists: Any definite set of degrees of belief which broke them would be inconsistent in the sense that it violated the laws of preference between options, such as that preferability is a transitive asymmetrical relation, and that if Į is preferable to ȕ, ȕ for certain cannot be preferable to Į if p, ȕ if not-p. (p. 182)

16. Probability laws as laws of consistency. We can see from this last remark their importance. We extend the logical notion of consistency to include the satisfaction of these elementary laws of probability. So, from Ramsey’s standpoint the laws of subjective probability are ‘laws of consistency, an extension to partial beliefs of formal logic, the logic of consistency’. (p. 182) 17. Three final remarks. Ramsey concludes these developments by three remarks. The first is that the developments are based fundamentally on the idea of betting, an idea which de Finetti also took as fundamental. Second, the developments are based throughout on the idea of mathematical expectation. This is the way of computing what is to be maximized in choice. To move in some other direction is to make a radical change in the standard theory of maximizing expected utility. His third remark is that he has said nothing about how to deal with matters when the number of alternatives is infinite. It is possible to make a pun here and say that, by now, the number of papers dealing with having the set of alternatives be infinite is nearly infinite. This part of the theory has been

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developed thoroughly in subsequent mathematical publications by others. Again, an extensive review is to be found in the reference cited above18. I just want to make one concluding conceptual remark of my own about Ramsey’s important stress upon mathematical expectation. It was the original hope – and attempt – of de Finetti to simply give axioms on subjective belief alone, so de Finetti’s strategy was to introduce an ordering of the form event A is at least as probable as event B. This ordering was assumed to be transitive and connected. Other axioms were introduced to express additivity of subjective probability of disjoint events, and so forth. The problem was that what started out to be a very simple set of axioms did not have a simple result. The axioms de Finetti stressed in earlier work19 were shown by Kraft, Pratt and Seidenberg20 to be inadequate. Namely, a counterexample could be given which showed that the standard representation theorem, to be proved about the quantitative nature of subjective probability, could not be given without further, stronger axioms. There is a tale of many attempts in this direction that I will not review here. My point is just to mention that probably the simplest set of axioms that are necessary and sufficient, expressed just in terms of probabilistic concepts without any introduction of utility, were those given by Mario Zanotti and myself 21. The important point, and the reason for this remark, is that those axioms found it necessary to use as primitive the concept of qualitative expectation, rather than the concept of subjective probability. Perhaps the most important technical reason for requiring this shift is that mathematical expectation is additive in an unrestricted way, whereas the addition of event probabilities requires that the events be mutually exclusive. This restriction causes many formal difficulties. 4. T HE L OGIC OF C ONSISTENCY After completing the section on the measurement of partial belief, that is, the measurement of subjective probability, the next section of Ramsey’s essay is devoted to the logic of consistency. Here, he makes a number of significant and useful remarks about the relation between logic and probability and between our view of the consistency of each of them. Again, he focuses an immediate criticism on Keynes’ theory, saying that Keynes tries to reduce probability to formal logic, but that this is mistaken in several different ways, which I will not examine in detail. What he does do, in terms of his own view, going back to some of the ideas of Peirce, is make a clear distinction between inductive and deductive logic. He insists on the point, on the vast difference between the consistency of logic and the consistency of a person’s set of partial beliefs. The vast difference between these two is exemplified by the elementary fundamental laws of probability, including conditional probability, that he derived from axioms in the previous section.

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He next discusses, in perhaps the most useful topic in this section, the relation between the calculus of consistent partial belief and the interpretation of the laws of probability in terms of frequencies. He mentions the usual connection between the two via Bernoulli’s Theorem. He does mention one idea that is not often found in more recent discussions. This is: ... the very idea of partial belief involves reference to a hypothetical or ideal frequency; supposing goods to be additive, belief of degree m/n is the sort of belief which leads to the action which would be best if repeated n times in m of which the proposition is true; or we can say more briefly that it is the kind of belief most appropriate to a number of hypothetical occasions otherwise identical in a proportion m/n of which the proposition in question is true. (p. 188)

It is worth mentioning that this device of idealizing a large number of possible observations is also supported by de Finetti22 as a method of evaluating subjective probabilities, especially ones that are very small. The second important remark in this section is Ramsey’s dismissal of the Principle of Indifference as a fundamental part of probability theory. Again, he mentions that ‘... it is fairly clearly impossible to lay down purely logical conditions for its validity, as is attempted by Mr. Keynes.’ (p. 189). Interestingly enough, he does not mention Laplace, who is the one who made this principle so famous in the history of probability. The third and final problem discussed in this section, once again, is centered on a Keynesian problem, but it is interesting from a general standpoint, so I quote Ramsey’s remark. A third difficulty which is removed by our theory is the one which is presented to Mr. Keynes’ theory by the following case. I think I perceive or remember something but am not sure; this would seem to give me some ground for believing it, contrary to Mr. Keynes’ theory, by which the degree of belief in it which it would be rational for me to have is that given by the probability relation between the proposition in question and the things I know for certain. He cannot justify a probably belief founded not on argument but on direct inspection. (p. 190)

What he is doing here, of course, is showing how devastatingly incorrect any attempt to settle questions of the probability of uncertain propositions, by knowledge of certain ones, is, as any kind of general strategy. The argument really is pointing out that Keynes seems to have no way in his system to accept what would amount to conditionalization, based upon possibly fallible memory or perception. 5. T HE L OGIC OF T RUTH The fifth and final section of the 1926 essay, whose title I have also used, is, we might think, in terms of the current patois of philosophy and logic, about

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Tarski’s and later definitions of truth. But Ramsey does not have this in mind at all. What he has in mind is, as he calls it, the human logic of truth. Let us therefore go back to the general conception of logic as the science of rational thought. We found that the most generally accepted parts of logic, namely, formal logic, mathematics and the calculus of probabilities, are all concerned simply to ensure that our beliefs are not self-contradictory. We put before ourselves the standard of consistency and construct these elaborate rules to ensure its observance. But this is obviously not enough; we want our beliefs to be consistent not merely with one another but also with the facts. (p. 191)

His central concern is to give a clearer meaning to the question of ‘What is reasonable for a person to have as a given degree of belief in a given proposition?’ Put another way, ‘When is it reasonable to hold a particular subjective probability concerning the occurrence, for example, of some future event?’ Ramsey’s answer to this question is, to my mind, one of the most interesting parts of the essay from a psychological standpoint. In giving the answer that I want to consider, he acknowledges his indebtedness to the writings of Peirce. I will not try to document the relevant parts of Peirce, but will look at the arguments that Ramsey himself gives. Ramsey’s central idea is that The human mind works essentially according to general rules or habits; a process of thought not proceeding according to some rule would simply be a random sequence of ideas; whenever we infer A from B we do so in virtue of some relation between them. We can therefore state the problem of the ideal as “What habits in a general sense would it be best for the human mind to have?” This is a large and vague question which could hardly be answered unless the possibilities were first limited by a fairly definite conception of human nature. (p. 194)

The first point that Ramsey then makes about habits is that he is not restricting habits to just ordinary ones that we learn as children, or sometimes as adults, but is including any rule or law of behavior, as well as instinct. In my own view, this is an excellent generalization of what is often too narrow a use of the concept of habit. He does not expand upon this idea in a way that deals with many of our current controversies about nature versus nurture, but his stand is, for me, very much on the side of the angels. Habits can be found on both sides of that controversy. I also like the fact that he not only emphasizes rules, but also laws. The emphasis on laws and instinct means that we are not caught in some explicit and mistaken rule-type formulation. Consequently, as I discuss later, laws of association or of conditioning can be included in the discussion of habits, as can the kind of instinctive behavior of many lower species, for example, of insects having habits which are patterns of behavior that are not learned, but strongly embedded in the DNA of a given species.

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He focuses this discussion on degrees of belief. He talks about observing a number of occurrences of common phenomena, such as inedible toadstools or the habit of expecting thunder after lightning. He summarizes nicely his view. Thus given a single opinion, we can only praise or blame it on the ground of truth or falsity: given a habit of a certain form, we can praise or blame it accordingly as the degree of belief it produces is near or far from the actual proportion in which the habit leads to truth. We can then praise or blame opinions derivatively from our praise or blame of the habits that produce them. (p. 196)

He then goes on to apply this not only to habits of observation and inference, but also to habits of memory, and raises the question of what is the best degree of confidence to place, for example, in specific memories. Or, to use his language more exactly, ‘a specific memory feeling’. Our confidence in such a memory feeling should depend on ‘how often when that feeling occurs the event whose image it attaches to has actually taken place’. (p. 196) Following a brief discussion of Hume, Ramsey next asks the question ‘What do we have to say about the person who would make no inductions?’ And he replies that we would think that he ‘had not got a very useful habit, without which he would be very much worse off, in the sense of being much less likely to have true opinions.’ (p. 197). He remarks of this that his view here is a kind of pragmatism. We judge mental habits by whether they work and, so, to adopt induction is a useful habit. Notice he has not spelled out, in really technical detail, what he means by induction, but he intends it to be in terms of what he has laid down as the fundamental laws of partial belief in the earlier formal treatment. Finally, in the last paragraph of this section, he extends the search for inductive or human logic to general methods of thought, or what we might now call methods of scientific inference, but his remarks here do not go very far beyond his casual mention of Mill’s methods and of Hume’s general rules in the chapter ‘Of unphilosophical probability’ in The Treatise 23. My problem with this section, which closes the 1926 essay on truth and probability, is not what he says about habits and the human logic of induction, but what he does not say. He almost takes a turn toward a deeper psychological approach, but does not explore it with any care, and turns back to familiar remarks and rather general remarks customary in the subject and already present in the writings of Hume, Mill and Peirce. In other words, in this section, as opposed to his treatment of the measurement of partial beliefs, and also of utility, where he makes a new and quite original contribution, matters are otherwise. 6. W HAT IS M ISSING IN R AMSEY : P SYCHOLOGICAL M ECHANISMS OF B ELIEF F ORMATION Ramsey writes about many different topics beyond what are included in the essay on truth and probability. These topics range from the foundations of

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mathematics to statistical mechanics. His own contributions, of course, greatly vary in depth. He had important and original ideas about the foundations of mathematics, which were early known to be significant contributions. In contrast, although he seemed to know a great deal about physics and many of his remarks about physical ideas and laws are interesting, he, in fact, has no sustained treatment, as far as I know, of any part of the foundations of physics. Matters are more complicated in the case of psychology. In one sense, what he did in his careful analysis and surrounding discussion about the theory of partial belief, and the measurement of such beliefs, is a genuine contribution, not only to philosophy, but also to the systematic science of measurement within psychology, a subject that has a large and controversial history. Indeed, what Ramsey has to say is important and interesting, just in terms of the history of psychology alone, quite apart from its philosophical import. But in this section, I want to examine the extent to which Ramsey probed deeper into looking for a psychological theory of mechanisms to account for partial beliefs. There is not much systematic evidence, as I have, in various ways, already indicated, but there is a useful early piece24, unpublished until the appearance of the book of notes by Ramsey, edited by Galavotti (1991). What is a particularly striking piece in this volume is Ramsey’s imaginary conversation with John Stuart Mill, dated 26 January 1924. I quote two passages: [Mill] ‘I knew that all mental and moral feelings were the results of association, that we love one thing and hate another, take pleasure in one sort of action or contemplation, and pain in another sort, through the clinging of pleasurable or painful ideas to those things from the effect of education or experience. As a corollary to this it is one of the objects of education to form the strongest possible associations of the salutary class; associations of pleasure with all things beneficial to the great whole, and pain with all things hurtful to it. But it seems to me that teachers occupy themselves but superficially with the means of forming and keeping up these salutary associations. They seem to trust altogether to the old familiar instruments, praise and blame, punishment and reward. Now there is no doubt that by these means intense associations of pain and pleasure may be created and produce desires and aversions capable of lasting undiminished to the end of life. But there must always be something artificial and casual in associations thus produced.’ ... Here he [Mill] paused and I broke in at once ‘But you know psychology has advanced since your day, yours is very out of date.’ ‘Has it?’ he answered ‘I don’t think so. You have advanced in philosophy in a way that excites my profound admiration but in psychology hardly at all. Perhaps you are thinking of the followers of Freud, who seem to regard the analysis of the mind as a panacea.’ ‘Yes’ said I, ‘I am thinking of them; you are probably put off by their absurd metaphysics, and forget that they are also scientists describing observed facts and inventing theories to fit them.’ (pp. 305-306)

The next two pages contain Ramsey’s response. [Ramsey] ‘But of course he would dispute your psychology; he [Freud] would say, that the most important associations in determining your desires were those formed very early in life and no longer accessible to consciousness. So that your explanation of your depression must be entirely illusory, in his terminology a ‘rationalization’. The relevant associa-

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tions could not possibly be dissolved by your own unaided introspection. If you suffer from claustrophobia you may perceive that there is no real danger in closed spaces but nevertheless you cannot bear to be in one.’ (Ramsey, 1991, pp. 306-307)

There is more. First is the imaginary response by Mill, followed by Ramsey’s response to that. ‘I don’t believe it’ he [Mill] answered ‘about the ordinary man; his ‘unconscious’ if he has one is of trivial importance. Freud’s theory was developed from observations not of the normal but of the abnormal, who came to him for treatment. It is not in the least clear that it applies to the ordinary man.’ [Ramsey] ‘But surely the laws of psychology should apply to all cases, normal and abnormal alike, and must be obtained from observations of all kinds of men. The psychoanalysts analyse not only patients but also their pupils who are fairly normal. And their work throws doubt on your psychology as being on much too simple lines; desires and aversions are not generally developed by the simple process of associations of pleasure and pain but by far more complicated laws and mechanisms.’ (Ramsey, 1991, p. 307)

This is fascinating, – and especially fascinating, written by such a very young man –, but it is also evident that there is no move in the direction of psychology as a systematic science. Moreover, this is well reinforced by the kind of statement about these matters one would expect from Ramsey. In the last papers at the end of the 1931 volume, there is one entitled “Probability and Partial Belief ” 25. The first two sentences of this fragment are certainly worth quoting. The defect of my paper on probability was that it took partial belief as a psychological phenomenon to be defined and measured by a psychologist. But this sort of psychology goes a very little way and would be quite unacceptable in a developed science. (p. 256)

In other words, Ramsey recognized, in an unblinkered way, that what he had to say about psychology did not amount to anything like a serious detailed foray into an analysis of the psychological mechanisms producing partial beliefs. The very last quotation, Ramsey’s statement about the work of psychoanalysts that throws doubt on Mill’s psychology of association, begins a line of theory that actually did not have much scientific development in Ramsey’s time, that is, the search for ‘far more complicated laws and mechanisms’ than the ‘simple’ processes of associations. The laws of association had been the dominant approach to cognitive and other psychological mechanisms in philosophy and psychology at least since Hume’s time. His Treatise is not the first, but it is certainly the most significant philosophical treatise to claim priority of place for association above all other mechanisms of the mind. I just recall for you that Hume thought of the mechanism of association doing for the laws of human nature what gravitation did for the laws of nature. In his essay “Truth and Probability”, and elsewhere, Ramsey mentions approvingly, Hume, Mill and Peirce, but he does not discuss, except in the passage quoted above, as far as I know, the theories of association adopted by these three

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philosophers as fundamental foundational theories for psychology. At least, I do not know of other passages where he systematically examines their ideas in this respect. From several angles, this is surprising. Book II of Hume’s Treatise, which deals with the passions, or, as we might say now, the emotions, is, in many respects, the scientifically deepest and most clever part of the Treatise. As far as I know, Ramsey does not deal anywhere with the main themes of this book, especially such matters as the subtle use of the concept of association to explain the nature of pride in the first part of Book II. Nor does he examine Mill’s systematic account of the laws of association as a part of his conception of a system of logic. For readers who have forgotten, I remind them that Book VI of Mill’s System of Logic 26 is on the logic of the moral sciences. Chapter IV of this book is on the laws of the mind. Here, Mill certainly gives pride of place to the laws of association. He commends the more extensive work of Alexander Bain and, at the same time, laments the extent to which in philosophy the application of the laws of association in psychology have been neglected. (Mill, 1843/1936, p. 561.) Mill’s chapter IV of this book on the laws of the mind is clearly and systematically written. Without agreeing with everything that he has to say there, I think he presents a very substantial challenge to anyone who wants to deny the central place of the laws of association. Given how well Ramsey knew the writings, in many ways, of Hume and Mill, as well as those of Peirce, it is surprising that there seems to be no extensive confrontation in which he develops systematically and carefully his opposition to the concept of association and the laws associated with this concept as a fundamental basis of psychological theory. Casually, he was skeptical about the laws of association, as expressed in the last 1924 passage above, but that is about as far as it goes. He simply did not enter into any systematic attempt to go deeper into an explanation of the psychological mechanisms that generate partial beliefs. What I said about Ramsey is also true of those two other important and significant forefathers of the twentieth century, Bruno de Finetti and Jimmie Savage. In fact, if anything, they have less to say about psychological mechanisms for generating partial beliefs than Ramsey does. Casually, one might contrast the apparent depth of the work in the foundations of mathematics by Frege, Hilbert, Brower and others to the less developed foundational literature about beliefs and desires. But, in some ways, this would be a mistake in the wrong direction. If we ask for a psychological account of mathematical thinking, for example, an analysis of the mechanisms used in verifying the correctness of a mathematical proof, we will find the literature just as thin as in the case on which I have been dwelling. This is not an idle request. Essentially no deep mathematical theorems of the sort considered fundamental in current research are verified formally. So, what are the psychological mechanisms of cognition and perception that are actually used in checking for correctness? So, let me end on a note which is controversial. It is certainly not agreed to by most of those who have written the modern canon of logic. The recognition

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that there is something directly psychological about subjective probability is rather widespread and is certainly given a place in Ramsey’s ideas. Indeed, he regards his method of measuring subjective probability and partial beliefs as being, in one sense, a contribution to psychology. Frege, in contrast, to take the beginnings of the modern canon, desires to rid himself of any taint of psychology in logic. I am far from accepting Frege’s view, but there are many aspects that separate the degree of need for psychological mechanisms to account for partial beliefs and psychological mechanisms to account for our claims about the objective correctness of mathematical proofs. This is not the place to enter into a detailed analysis of this difference, – this I have begun in a closely related article27 –, but there is one obvious reason for thinking that the demand for explanation of the psychological mechanisms of partial belief has a more immediate and natural place than a similar demand in the mathematical case. This is that in the mathematical case, all the emphasis is on moving outside individuals to a completely agreed upon objective result – objective in the sense of being the same for all persons. It is exactly the opposite, in some sense, in the case of partial belief. We accept, in the beginning, individual differences in partial beliefs and in the particular assignments of subjective probabilities. It is then natural, in a way it is not, in mathematics, to ask for the psychological mechanisms that account for the differences in partial beliefs. I do not think what I have said is fully satisfactory, but it is, at least, perhaps, a kind of justification of my emphasis on the need for a theory of the psychological mechanisms generating partial beliefs, without, at the same time, asking for a psychological theory justifying the wide agreement about the truth of many mathematical statements and the correctness of many mathematical proofs. But where there is not agreement, as, for example, between formalists and intuitionists, psychological theories of cognitive and perceptual mechanisms become relevant to mathematics, or, at least, so I would claim. Ramsey, in his important article on the foundations of mathematics (1931), did not venture into this territory. N OTES 1. 2. 3. 4. 5. 6. 7.

Frank Plumpton Ramsey, “Truth and Probability”, in: Richard Braithwaite, (Ed.), The Foundations of Mathematics. London: Kegan Paul, Trench, Trubner & Co., 1926/1931. John Maynard Keynes, A Treatise on Probability. London: Macmillan 1921. Norbert Wiener, “A New Theory of Measurement: A Study in the Logic of Mathematics”, in: Proceedings of the London Mathematical Society, 19, 1921, pp. 181-205. Otto Hölder, “Die Axiome der Quantität und die Lehre vom Mass”, in: Ber. Verh. Kgl. Sächsis. Ges. Wiss. Leipzig, Math.-Phys. Classe, 53, 1901, pp. 1-64. Norman Campbell, Physics The Elements. Cambridge: Cambridge University Press 1920. Alfred N. Whitehead/Bertrand Russell, Principia Mathematica. Cambridge: Cambridge University Press 1913. Gustav Theodor Fechner, Elemente der Psychophysik. Leipzig: Druck und Verlag von Breitkopfs Härtel [Elements of Psychophysics (Vol. 1). New York: Holt, Rinehart & Winston 1966] (1860/1966).

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8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

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Patrick Suppes/David H. Krantz/R. Duncan Luce/Amos Tversky, Foundations of Measurement, Vol. II. San Diego, CA: Academic Press 1989, p. 303. Bertrand Russell, Analysis of Mind. London: G. Allen & Unwin 1921. James Clerk Maxwell, A Treatise on Electricity and Magnetism, Vol. II. Third edition. London: Geoffrey Cumberlege. Oxford University Press 1872/1892. David Hume, A Treatise of Human Nature. London: John Noon 1739. Quotations from L.A. Selby-Bigge's edition, London: Oxford University Press 1888. Zoltan Domotor/John Herbert Stelzer, “Representation of Finitely Additive Semiordered Quantitative Probability Structures”, in: Journal of Mathematical Psychology, 8, 1971, pp. 145158. Donald Davidson/Patrick Suppes, “A Finitistic Axiomatization of Subjective Probability and Utility”, in: Econometrica, 24, 1956, pp. 264-275. Donald Davidson/Patrick Suppes/Sidney Siegel, Decision Making: An Experimental Approach. Stanford, CA: Stanford University Press 1957. Bruno de Finetti, “La Prevision: Ses Lois Logiques, Ses Sources Subjectives”, in: Ann. Inst. H. Poincare, 7, 1937, pp. 1-68. Translated into English in H. E. Kyburg, Jr./H. E. Smokler, (Eds.), Studies in Subjective Probability. New York: Wiley 1964. L. Jimmie Savage, The Foundations of Statistics. New York: Wiley 1954. David H. Krantz/R. Duncan Luce/Patrick Suppes/Amos Tversky, Foundations of Measurement, Vol. I. New York: Academic Press 1971. Ibid. de Finetti, “La Prevision: Ses Lois Logiques, Ses Sources Subjectives”, op. cit. Charles Hall Kraft/J .W. Pratt/A. Seidenberg, “Intuitive Probability on Finite Sets”, in: The Annals of Mathematical Statistics, 30, 1959, pp. 408-419. Patrick Suppes/Mario Zanotti, “Necessary and Sufficient Conditions for Existence of a Unique Measure Strictly Agreeing with a Qualitative Probability Ordering”, in: Journal of Philosophical Logic, 5, 1976, pp. 431-438. Bruno de Finetti, Theory of Probability, Vol. I. New York: Wiley. 1974, p. 310. Translated by A. Machi and A. Smith. Hume, A Treatise of Human Nature, op.cit. Frank Plumpton Ramsey, “An Imaginary Conversation with John Stuart Mill”, in: Maria Carla Galavotti, (Ed.), Frank Plumpton Ramsey: Notes on Philosophy, Probability and Mathematics. Naples, Italy: Bibliopolis 1924/1991. Ramsey, “Probability and Partial Belief”, in: The Foundations of Mathematics, op..cit., pp. 256257. John Stuart Mill, System of Logic, London: Longmans, Green and Co. 1843/1936. Patrick Suppes, “Where Do Bayesian Priors Come From?” (In Press)

Center for the Study of Language and Information Stanford University 220 Panama Street Stanford, CA 94305 - 4115 U.S.A. [email protected]

B RIAN S KYRMS

DISCOVERING “WEIGHT, OR THE VALUE OF KNOWLEDGE”

I. I NTRODUCTION In the summer of 1986, I went to Cambridge to look through Ramsey’s unpublished papers. It turned out that the Ramsey archives existed only on microfilm at Cambridge – the originals having been purchased at auction by Nicholas Rescher for the Archives of Logical Positivism at the University of Pittsburgh. Hugh Mellor kindly arranged for me to be allowed to study the microfilm. I still have my temporary library card as a memento. Later, I was able to see the originals at the University of Pittsburgh. I was looking for something, but found something different. What I found of most importance consisted of two manuscript pages, the first of which was entitled “Weight, or the Value of Knowledge.” They were not consecutive in the numbering that had been given to these unpublished manuscripts, but they clearly went together. A few years later, Nils Eric Sahlin published a transcription of these in the British Journal for Philosophy of Science [Ramsey (1990)]. There is also a transcription contained in Maria Carla Galavotti’s collection of Ramsey’s papers [Ramsey (1991)]. I included a facsimile of the second manuscript page in my book, The Dynamics of Rational Deliberation. Today I will tell you something about what I was looking for, what I found, and the relationship between the two. This is an old story, but I will add a few new twists. II. W HAT I WAS L OOKING F OR I was looking to see whether Ramsey had any discussion of coherence of beliefs across time – diachronic coherence –, or of the related question of coherent rules for updating belief. These questions were the focus of intense philosophical discussion at the time (and to some extent still are.) Ramsey says just enough in “Truth and Probability” to whet the imagination, and to hold out the promise of something more. Ramsey introduced the question of coherence to the discussion of degrees of belief, noting that violation of the laws of probability allows a Dutch book:

55 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 55–65. © 2006 Springer. Printed in the Netherlands.

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If anyone’s mental condition violated these laws, his choice would depend on the precise form in which the options were offered to him, which would be absurd. He could have a book made against him by a cunning bettor and would then stand to lose in any event.

The converse, that coherent degrees of belief preclude a Dutch book, is stated two paragraphs later: Having any definite degree of belief implies a certain measure of consistency, namely willingness to bet on a given proposition at the same odds for any stake, the stakes being measured in terms of ultimate values. Having degrees of belief obeying the laws of probability implies a further measure of consistency, namely such a consistency between the odds acceptable on different propositions as shall prevent a book being made against you.

Ramsey was writing a paper for a philosophy club, and did not provide the mathematical details, but they were soon independently supplied by de Finetti. Regarding coherent change in degrees of belief, Ramsey has only this to say: Obviously, if p is the fact observed, my degree of belief in q after the observation should be equal to my degree of belief in p given q before, or by the multiplication law to the quotient of my degree of belief in p&q by my degree of belief in p. When my degrees of belief change in this way we can say that they have been changed consistently by my observation.

He is saying that belief change by conditioning on “the fact observed” is coherent belief change. Again, proofs were only later supplied by others. [See Freedman and Purves (1969), Putnam (1975), Teller (1973), and the review in Lane and Sudderth (1984).] But what about the case of uncertain evidence, where there is no clear-cut “fact observed” within the domain of an individual’s probability function? [Jeffrey (1968), Armendt (1980), Diaconis and Zabell (1982)] Did Ramsey even consider the possibility? And what exactly is the coherence claim in terms of which conditioning on the fact observed constitutes coherent belief change in the cases where it does apply? III. W HAT I F OUND In those two manuscript pages I found an account of the Value of Knowledge – that is to say, the expected utility of pure, cost-free information. The word “Weight” in the heading of the first page is a clear reference to Keynes’ Treatise on Probability. Keynes thought that degrees-of-belief needed two dimensions: probability, which showed how likely an event was judged to be, and weight, which measured quantity of evidential support behind the probability judgement. The following passages indicate both the general nature of Keynes’ concerns and the degree to which he has misconceived the problem:

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The second difficulty... is the neglect of the ‘weights’ in the conception of ‘mathematical expectation.’ ... if two probabilities are equal in degree, ought we, in choosing our course of action, to prefer that one that is based on the greater body of knowledge? The question appears to me to be highly perplexing, and it is difficult to say much that is useful about it. ... Bernoulli’s maxim that in reckoning a probability we must take into account all the information which we have, even when reinforced by Locke’s maxim that we must get all the information that we can, does not seem completely to meet the case. [Keynes (1921) p. 313]

Ramsey clearly saw the answer. Thirty years after Keynes, Bernoulli’s maxim was restated as Carnap’s “total evidence condition” [Carnap (1950)], and the correct analysis was presented to the philosophical community by I. J. Good. (1967). Good cites the treatment of the expected value of new information in Raiffa and Schlaifer (1961). The basic case of pure, cost-free information is already treated by Savage (1954) in Ch. 7 and appendix 2, but Ramsey’s unpublished note anticipates Savage by three decades. The basic principles at work are easy to illustrate in the case of two acts. Suppose that you are going to either buy, or not buy an item on E-bay. You are inclined to buy it. But you have the option of postponing your decision for a minute and reading others’ reports of past transactions with this individual. This information costs nothing more than a mouse click. This could bring negative information about the reliability of the seller that would cause you to forego the purchase, or it might bring information that would confirm your predisposition to buy. To simplify the exposition, we suppose that there are only two possible pieces of information that may come up if you look, one positive and one negative. Then the expected value of buying and of not buying, can be plotted as a function of the probability that the information is positive – as shown in figure 1.

Figure 1

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If you look and get positive information you move to the right side; if you look and get negative information you move to the left side; before looking you are somewhere in the middle. The lines plotting the expected values of the acts are straight lines because they are averages. Which act is optimal depends on the probabilities of good and bad information. If we take the optimal act at every value and plot it we get the expected value of the Bayes (optimal) act as a function of the probability of good information, as shown in bold in figure 2. You can see that it’s shape is that of a convex function ( It dishes down in the middle). At any point, your expected value of choosing the act that looks best to you in that informational state is just the value of this function.

Figure 2

What is the expected value now, of clicking the mouse, getting the additional information and then deciding? It is a point falling on the dashed line connecting the value of buying with good information on the right, and not buying with bad information on the left in figure 3. It is obviously greater than the value of acting now without the additional information, because the dashed line falls above the bold line except at the endpoints. That is because the dashed line, being an average, is straight, while the bold line – as noted previously – is convex. One can even measure the expected value of information at any point, as the difference between the two curves. The principles illustrated in this simple example hold in more complex cases. There might, for instance, be an infinite number of possible acts, resulting from the setting of some continuously variable control parameter. That would make no real difference in the argument. The expected utility of the Bayes act would still be convex, and the argument would still work. This is the case addressed by

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Ramsey in his two pages of notes. The second page contains a diagram that you could immediately recognize by its resemblance to figure 3.

Figure 3

Ramsey goes a bit further. He supposes that what is to be learned does not take us all the way to the left or right side of the diagram but only part way in each direction. This might be thought of as a model of less than ideal evidence, but the evidence learned is still modeled as evidence that is learned with certainty. The effect of learning the imperfect evidence is assumed to be a shift to a new probability by conditioning on what was learned. [See my (1990) book for a fuller discussion.] IV. D IACHRONIC C OHERENCE We can, by now, say quite a bit about the topic I was looking for but didn’t find – the question of diachronic coherence of degrees of belief. I will take an indirect, but scenic route to the central result. There is a close connection between Bayesian coherence arguments and the theory of arbitrage. [See Shin (1992)] Suppose we have a market in which a finite number of assets are bought and sold. Assets can be anything – stocks and bonds, pigs and chickens, apples and oranges. The market determines a unit price for each asset, and this information is encoded in a price vector x =<x1, ...xn>. You may trade these assets today in any (finite) quantity. You are allowed to take a short position in an asset, that is to say that you sell it today for delivery tomorrow. Tomorrow, the assets may have different prices, y1, ...,ym. To keep things simple, we initially suppose that there are a finite number of possibilities for tomorrow’s price vector. A portfolio,

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p, is a vector of real numbers that specifies the amount of each asset you hold. Negative numbers correspond to short positions. You would like to arbitrage the market, that is to construct a portfolio today whose cost is negative (you can take out money) and such that tomorrow its value is non-negative (you are left with no net loss), no matter which of the possible price vectors is realized. The fundamental theorem of asset pricing states that you can arbitrage the market if and only if the price vector today falls outside the convex cone spanned by the possible price vectors tomorrow. [If we were to allow an infinite number of states tomorrow we would have to substitute the closed convex cone generated by the possible future price vectors.] The value of a portfolio, p, according to a price vector, y, is the sum over the assets of quantity times price, that is the dot product of the two vectors. If the vectors are orthogonal the value is zero. If they make an acute angle, the value is positive; if they make an obtuse angle, the value is negative. An arbitrage portfolio, p , is one such that p•x is negative and p•yi is non-negative for each possible yi ; p makes an obtuse angle with today’s price vector and is orthogonal or makes an acute angle with each of the possible price vectors tomorrow. If p is outside the convex cone spanned by the yis, then there is a hyperplane which separates p from that cone. An arbitrage portfolio can be found as a vector normal to the hyperplane. It has zero value according to a price vector on the hyperplane, negative value according to today’s prices and non-negative value according to each possible price tomorrow. On the other hand, if today’s price vector in the convex cone is spanned by tomorrow’s possible price vectors, then (by Farkas’ lemma) no arbitrage portfolio is possible. The matter is easy to understand visually in simple cases. Suppose the market deals in only two goods, apples and oranges. One possible price vector tomorrow is $1 for an apple, $1 for an orange. Another is an apple will cost $2, while an orange is $1. These two possibilities generate a convex cone, as shown in figure 4. (We could add lots of intermediate possibilities, but that wouldn’t make any difference to what follows.)

Figure 4

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Let’s suppose that today’s price vector lies outside the convex cone, say apples at $1, oranges at $3. Then it can be separated from the cone by a hyperplane (in 2 dimensions, a line), for example the line oranges = 2 apples, as shown in figure 5.

Figure 5

Normal to that hyperplane we find the vector <2 apples, -1 orange>, as in figure 6.

Figure 6

This should be an arbitrage portfolio, so we sell one orange short and use the proceeds to buy 2 apples. But at today’s prices, an orange is worth $3, so we can pocket a dollar, or – if you prefer – buy 3 apples and eat one. Tomorrow we have to deliver an orange. If tomorrow’s prices were to fall exactly on the hyperplane, we would be covered. We could sell our two apples and use the proceeds to buy the orange. But in our example, things are even better. The worst that can happen tomorrow is that apples and oranges trade 1-to-1, so we might as well eat another apple and use the remaining one to cover our obligation for an orange.

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In the foregoing, assets could be anything. As a special case they could be tickets paying $1 if p, nothing otherwise, for various contingent propositions, p. The price of such a ticket can be thought of as the market’s collective degree-orbelief or subjective probability for p. We have not said anything about the market except that it will trade arbitrary quantities at the market price. The market could be implemented by a single individual – the bookie of the familiar Bayesian metaphor. Without yet any commitment to the mathematical structure of degrees of belief, or to the nature of belief revision, we can say that arbitrage-free degrees of belief today must fall within the convex cone of degrees of belief tomorrow. This is the fundamental diachronic coherence requirement. We might go further and suppose that tomorrow we learn the truth. In that case a ticket worth $1 if p; nothing otherwise, would be worth either $1 or $0 depending on whether we learn whether p is true or not. By itself this does not tell us a great deal, only that arbitrage-free prior degrees of belief must be nonnegative. Now suppose that we have three assets being traded which have a Boolean logical structure. There are tickets worth $1 if p; nothing otherwise, $1 if q; nothing otherwise, and $1 if p or q; nothing otherwise. Furthermore, p and q are incompatible. This additional structure constrains the possible price vectors tomorrow, so that the convex cone becomes the two dimensional object: z = x + y, x, y, non-negative, as shown in figure 7. Arbitrage-free degrees of belief must be additive. Additivity of subjective probability comes from the additivity of truth value and the fact that additivity is preserved under convex combination. One can then complete the coherence argument for probability by noting that coherence requires a ticket that pays $1 if a tautology is true to have the value $1.

Figure 7

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Notice that from this point of view the synchronic Dutch books are really special cases of diachronic arguments. After all, you really do need the time when you find out the truth for the synchronic argument to be complete. (This point has been raised by some as an objection to the application of subjective probability to the confirmation of scientific laws.) If anything, the assumption that there is a time when the truth is revealed is a much stronger assumption than anything that preceded it in this development. (One who rejects this assumption might reject additivity, but still require degrees-of-belief today to fall within the convex cone spanned by degrees of belief tomorrow.) Today the market trades tickets that pay $1 if pi; nothing otherwise, where the pis are some assertions about the world. All sorts of news comes in and tomorrow the price vector may realize a number of different possibilities. (We have not, at this point, imposed any model of belief change.) The price vector for these tickets tomorrow is itself a fact about the world, and there is no reason why we could not have trade in tickets that pay off $1 if tomorrow’s price vector is p, or if tomorrow’s price vector is in some set of possible price vectors, for the original set of propositions. The prices of these tickets represent subjective probabilities about its subjective probabilities tomorrow. Some philosophers have been suspicious about such entities, but they arise quite naturally. And in fact, they may be less problematic than the first-order probabilities over which they are defined. The first-order propositions, pi, could be such that their truth value might or might not ever be settled. But the question of tomorrow’s price vector for unit wagers over them is settled tomorrow. Coherent probabilities of tomorrow’s probabilities should be additive no matter what. Let us restrict ourselves to the case where we eventually do find out the truth about everything [perhaps on Judgment Day], so degrees of belief today and tomorrow are genuine probabilities. We can now consider tickets that are worth $1 if the probability tomorrow of p = a and p; nothing otherwise, as well as tickets that are worth $1 if probability tomorrow of p =1. These tickets are logically related. Projecting to the 2 dimensions that represent these tickets, we find that there are only two possible price vectors tomorrow. Either the probability tomorrow of p is not equal to a, in which case both tickets are worth nothing tomorrow, or probability tomorrow of p is equal to a, in which case the former ticket is has a price of $a and the latter has a price of $1. The cone spanned by these two vectors is just a ray as shown in figure 8. So today, the ratio of these two probabilities (provided they are well-defined) is a. In other words, today the conditional probability of p, given probability tomorrow of p = a, is a. It then follows that to avoid a Dutch book, probability today must be the expectation of probability tomorrow. [See Goldstein (1983) and van Fraassen (1984)]

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Figure 8

V. D IACHRONIC C OHERENCE AND THE V ALUE OF K NOWLEDGE The traditional setting for the Value of Knowledge theorem is one in which it is assumed that experience delivers up an evidence statement, one of a set of possible evidence statements which partition the space of possibilities. The decision maker then adopts new degree of belief equal to the old degrees of belief conditional on the evidence. If a decision maker believes that the impending learning situation answers to this description, then his probability today will be his expectation of his probability tomorrow. But probability today can well be the expectation of probability tomorrow in a far less structured learning situation. Following Dick Jeffrey [1968], we should pay attention to the fact that evidence may not arrive with certainty. The decision maker may not have in her grasp the observation sentences required to implement that classical model – or even if she has them, she may lack the probabilities conditional on them to implement probability change by conditioning on the evidence. In these cases too, diachronic coherence still has a bite. Probability today must still be the current expectation of probability tomorrow. This happens to be all that is required to prove the theorem that pure, costfree information has non-negative expected value. This was first shown by Paul Graves (1989) in the context of a discussion of Jeffrey’s probability kinematics. The following proof highlights the essential features of our example, and generalizes smoothly to more complicated cases. Let B(p) be the expected utility of the Bayes act according to probability p We write E for current expectation. Because of the convexity of B, (by Jensen’s inequality): E[B(probability after learning)] >= B[E(probability after learning)] By diachronic coherence we can replace E(probability after learning) with (probability before learning). So, E[B(probability after learning)] >= B[probability before learning]

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In other words, ex ante an informed decision is surely at least as good, and perhaps better than, an uninformed one. Diachronic coherence implies the value of knowledge. R EFERENCES Armendt, B. (1980) “Is There a Dutch Book Theorem for Probability Kinematics?” Philosophy of Science 47: 583-588. Carnap, R. (1950) Logical Foundations of Probability Chicago: University of Chicago Press. de Finetti, B. (1970) Teoria Della Probabilità v. I. Giulio Einaudi editori: Torino, tr. as Theory of Probability by Antonio Machi and Adrian Smith (1974) Wiley: New York. Diaconis, P. and Zabell, S. (1982) “Updating Subjective Probability” Journal of the American Statistical Association 77:822-830. Freedman, D.A. and R.A. Purves (1969) “Bayes’ Method for Bookies” Annals of Mathematical Statistics 40: 1177-1186. Graves, P. (1989) “The Total Evidence Principle for Probability Kinematics” Philosophy of Science 56, 317-324. Goldstein, M. (1983) “The Prevision of a Prevision” Journal of the American Statistical Association 78: 817-819. Good, I.J. (1967) “On the Principle of Total Evidence” British Journal for the Philosophy of Scence 17, 319-321. Jeffrey, R. (1968) “Probable Knowledge” In The Problem of Inductive Logic ed. I. Lakatos. Amsterdam: North Holland. Keynes, J.M. (1921) A Treatise on Probability. Harper Torchbook edition (1962). New York: Harper and Row. Lane, D.A. and Sudderth, W. (1984) “Coherent Predictive Inference” Sankhya, ser. A, 46: 166-185. Levi, I. (2002) “Money Pumps and Diachronic Dutch Books” Philosophy of Science 69 [PSA 2000 ed. J.A. Barrett and J.M. Alexander] S235-S264. Putnam, H. (1975) “Probability Theory and Confirmation” in Mathematics, Matter and Method. Cambridge: Cambridge University Press. Raiffa, H. and R. Schlaifer (1961) Applied Statistical Decision Theory. Boston: Harvard School of Business Administration. Ramsey, F.P. (1990) “Weight or the Value of Knowledge” Transcribed by N.-E. Sahlin. The British Journal for the Philosophy of Science, 41, (1990), 1-3. Ramsey, F.P. (1991) Notes on Philosophy, Probability and Mathematics. Edited by Maria Carla Galavotti. Bibliopolis: Napoli. Shin, H.S. (1992) “Review of The Dynamics of Rational Deliberation” Economics and Philosophy 8: 176-183. Skyrms, B. (1990) The Dynamics of Rational Deliberation Cambridge, Mass.: Harvard University Press. Teller, P. (1973) “Conditionalization and Observation” Synthese 26, 218-258. van Fraassen, B. (1984) “Belief and the Will” Journal of Philosophy 81: 235-256.

Logic and Philosophy of Science University of California, Irvine 3151 Social Science Plaza Irvine, California U.S.A. [email protected]

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RAMSEY’S RAMSEY-SENTENCES ∗

1. C ONTEXT AND A IMS Frank Ramsey’s posthumously published Theories has become one of the classics of the 20th century philosophy of science. The paper was written in 1929 and was first published in 1931, in a collection of Ramsey’s papers edited by Richard Braithwaite. Theories was mostly ignored until the 1950s, though Ramsey’s reputation was growing fast, especially in relation to his work on the foundations of mathematics. Braithwaite made some use of it in his Scientific Explanation, which appeared in 1953. It was Carl Hempel’s The Theoretician’s Dilemma, published in 1958, which paid Ramsey’s paper its philosophical dues. Hempel coined the now famous expression ‘Ramsey-sentence’. When Rudolf Carnap read a draft of Hempel’s piece in 1956, he realised that he had recently re-invented Ramsey-sentences. Indeed, Carnap had developed an “existentialised” form of scientific theory. In the protocol of a conference in Los Angeles, organised by Herbert Feigl in 1955, Carnap is reported to have extended the results obtained by William Craig to “type theory, (involving introducing theoretical terms as auxiliary constants standing for existentially generalised functional variables in ‘long’ sentences containing only observational terms as true constants)” (Feigl Archive, 04-172-02, 14). I have told this philosophical story in some detail elsewhere (1999, chapter 3). I have also discussed Carnap’s use of Ramsey-sentences and its problems (see my 1999 chapter 3; 2000a; 2000b). In the present paper I want to do two things. First, I want to discuss Ramsey’s own views of Ramsey-sentences. This, it seems to me, is an important issue not just because of its historical interest. It has a deep philosophical significance. Addressing it will enable us to see what Ramsey’s lasting contribution to the philosophy of science was as well as its relevance to today’s problems. Since the 1950s, when the interest in Ramsey’s views mushroomed, there have been a number of different ways to read Ramsey’s views and to reconstruct Ramsey’s project. The second aim of the present paper is to discuss the most significant and controversial of these reconstructions, i.e., structuralism. After some discussion of the problems of structuralism in the philosophy of science, as this was exemplified in Bertrand Russell’s and Grover Maxwell’s views and has reappeared in Elie Zahar’s and John Worrall’s thought, I will argue that, for good 67 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 67–90. © 2006 Springer. Printed in the Netherlands.

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reasons, Ramsey did not see his Ramsey-sentences as part of some sort of structuralist programme. I will close with an image of scientific theories that Ramsey might have found congenial. I will call it Ramseyan humility.1 2. R AMSEY ’ S T HEORIES Theories is a deep and dense paper. There is very little in it by way of stagesetting. Ramsey’s views are presented in a compact way and are not contrasted with, or compared to, other views. In this section, I will offer a brief presentation of the main argumentative strategy of Theories.2 Ramsey’s starting point is that theories are meant to explain facts, those that can be captured within a “primary system” (1931, p. 212). As an approximation, we can think of it as the set of all singular observational facts and laws. The “secondary system” is the theoretical construction; that part of the theory which is meant to explain the primary system. It is a set of axioms and a “dictionary”, that is “a series of definitions of the functions of the primary system (…) in terms of those of the secondary system” (1931, p. 215). So conceived, theories entail general propositions of the primary system (“laws”), as well as singular statements, (“consequences”), given suitable initial conditions. The “totality” of these laws and consequences is what “our theory asserts to be true” (ibid.). This is a pretty standard hypothetico-deductive account of theories. Ramsey then goes on to raise three philosophical questions. Here are the first two: (1) Can we say anything in the language of this theory that we could not say without it? (1931, p. 219) (2) Can we reproduce the structure of our theory by means of explicit definitions within the primary system? (1931, p. 220)

The answer to the first question is negative (cf. 1931, p. 219). The secondary system can be eliminated in the sense that one could simply choose to stick to the primary system without devising a secondary system in the first place. The answer to the second question is positive (cf. 1931, p. 229). But Ramsey is careful to note that this business of explicit definitions is not very straightforward. They are indeed possible, but only if one does not care about the complexity or arbitrariness of these definitions. The joint message of Ramsey’s answers is that theories need not be seen as having excess content over their primary systems. These answers point to two different ways in which this broadly anti-realist line can be developed. The first points to an eliminative instrumentalist way, pretty much like the one associated with the implementation of theories of Craig’s theorem. Theoretical expressions are eliminated en masse syntactically and hence the problem of their significance does not arise. The second points to a reductive empiricist way, pretty much like the one associated with the early work of the Logical Empiricists – before their semantic liberalisation. Theoretical

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expressions are not eliminated; nor do they become meaningless. Yet, they are admitted at no extra ontological cost. So far, Ramsey has shown that the standard hypothetico-deductive view of theories is consistent with certain anti-realist attitudes towards their theoretical part. He then raises a third question: (3) [Are explicit definitions] necessary for the legitimate use of the theory? (1931, p. 229)

This is a crucial question. If the answer is positive, then some form of anti-realism will be mandatory: the necessary bedfellow of the hypothetico-deductive view. But Ramsey’s answer is negative: “To this the answer seems clear that it cannot be necessary, or a theory would be no use at all” (1931, p. 230). Ramsey offers an important methodological argument against explicit definitions. A theory of meaning based on explicit definitions does not do justice to the fact that theoretical concepts in science are open-ended: they are capable of applying to new situations. In order to accommodate this feature, one should adopt a more flexible theory of meaning, in particular, a theory which is consistent with the fact that a term can be meaningfully applied to new situations without a change of meaning (cf. 1931, p. 230). The important corollary of the third answer is that hypothetico-deductivism is also consistent with the view that theories have excess content over their primary systems. So the possibility of some form of realism is open. It is significant that Ramsey arrived at this conclusion by a methodological argument: the legitimate use of theories makes explicit definitions unnecessary. The next issue then is what this excess content consists of. That is, what is it that one can be a realist about? 3 This, I suggest, is the problem that motivates Ramsey when he writes: The best way to write our theory seems to be this (∃ α, β, γ) : dictionary . axioms (1931, p. 231).

Ramsey introduces this idea with a fourth question: (4) Taking it then that explicit definitions are not necessary, how are we to explain the functioning of the theory without them?

Here is his reply: Clearly in such a theory judgement is involved, and the judgement in question could be given by the laws and consequences, the theory being simply a language in which they are clothed, and which we can use without working out the laws and consequences (1931, p. 231).

Judgements have content: they can be assessed in terms of truth and falsity. Theories express judgements and hence they can be assessed in terms of truth and falsity. Now, note the could in the above quotation. It is not there by accident, I suggest. Ramsey admits that the content of theory could be equated

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with the content of its primary system. Since the latter is truth-evaluable, it can express a judgement. But this is not the only way. There is also the way (“the best way”) he suggests: write the theory with existential quantifiers in the front. 3. E XISTENTIAL J UDGEMENTS Ramsey’s observation is simple but critical: the excess content of the theory is seen when the theory is formulated as expressing an existential judgement. In his Causal Qualities, Ramsey wrote: “I think perhaps it is true that the theory of general and existential judgements is the clue to everything” (1931, p. 261). In his Mathematical Logic, he (1931, p. 67ff.) spent quite some time criticising Weyl’s and Hilbert’s views of existential claims. Both of them, though for different reasons, took it that existential claims do not express judgements. Being an intuitionist, Weyl took it that existential claims are meaningless unless we possess a method of constructing one of their instances. Hilbert, on the other hand, took them to be ideal constructions which, involving as they do the notion of an infinite logical sum, are meaningless. Ramsey subjected both views to severe criticism. Its thrust is that existential propositions can, and occasionally do, express all that one does, or might ever be able to, know about a situation. This, Ramsey said, is typical in mathematics, as well as in science and in ordinary life. As he says: “(…) it might be sufficient to know that there is a bull somewhere in a certain field, and there may be no further advantage in knowing that it is this bull and here in the field, instead of merely a bull somewhere” (1931, p. 73). Ramsey criticised Hilbert’s programme in mathematics sharply because he did not agree with the idea that mathematics was symbol-manipulation. He did not deny that Hilbert’s programme was partly true, but stressed that this could not be the “whole truth” about mathematics (1931, p. 68). He was even more critical of an extension of Hilbert’s programme concerning “knowledge in general” (that is, to scientific theories as well) (cf. 1931, p. 71). As we have seen, Ramsey took theories to be meaningful existential constructions (judgements), which could be evaluated in terms of truth and falsity. The extension of Hilbert’s programme to apply to science had been attempted by Moritz Schlick (1918/1925, pp. 33-4). He saw theories as formal deductive systems, where the axioms implicitly define the basic concepts. He thought implicit definitions divorce the theory from reality altogether: theories “float freely”; “none of the concepts that occur in the theory designate anything real (…)” (1918/1925, p. 37). Consequently, he accepted the view that the “construction of a strict deductive science has only the significance of a game with symbols” (ibid.). Schlick was partly wrong, of course. An implicit definition is a kind of indefinite description: it defines a whole class of objects which can realise the formal structure, as defined by a set of axioms. Schlick did not see this very clearly. But he did encounter a problem. Theories express judgements; judgements designate facts (1918/1925, p. 42); a true judgement designates a set of

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facts uniquely (1918/1925, p. 60); but the implicit definitions fail to designate anything uniquely; so a theory, if seen as a network of implicit definitions of concepts, fails to have any factual content. This is an intolerable consequence. Schlick thought that it is avoided at the point of application of the theory to reality. This application was taken to be partly a matter of observations and partly a matter of convention (cf. 1918/1925, p. 71). In his (1932), he came back to this view and called it the geometrisation of physics: by disregarding the meaning of the symbols we can change the concepts into variables, and the result is a system of propositional functions which represent the pure structure of science, leaving out its content, separating it altogether from reality (1932, p. 330).

Seen in this structuralist light, the predicate letters and other constants that feature in the axioms should really be taken to be genuine variables. What matters is not the meaning of these non-logical constants, but rather the deductive – hence structural – relations among them. Scientific theories are then presented as logical structures, logical implication being the generating relation. The hypothetical part comes in when we ask how, if at all, this system relates to the world. Schlick’s answer is that when one presents a theory, one makes a hypothetical claim: if there are entities in the world which satisfy the axioms of the theory, then the theory describes these entities (cf. 1932, p. 330-1). Against the backdrop of Schlick’s approach, we can now see Ramsey’s insight clearly. We need not divorce the theory from its content, nor restrict it to whatever can be said within the primary system, provided that we treat a theory as an existential judgement. Like Schlick, Ramsey does treat the propositional functions of the secondary system as variables. But, in opposition to Schlick, he thinks that advocating an empirical theory carries with it a claim of realisation (and not just an if-then claim): there are entities which satisfy the theory. This is captured by the existential quantifiers with which the theory is prefixed. They turn the axiom-system from a set of open formulas into a set of sentences. Being a set of sentences, the resulting construction is truth-valuable. It carries the commitment that not all statements such as ‘α, β, γ stand to the elements of the primary system in the relations specified by the dictionary and the axioms’ are false. But of course, this ineliminable general commitment does not imply any specific commitment to the values of α, β, γ. (This last point is not entirely accurate, I think. But because it’s crucial to see in what sense it is inaccurate, I shall discuss it in some detail in section 7). 4. R AMSEY - SENTENCES As the issue is currently seen, in order to get the Ramsey-sentence RTC of a (finitely axiomatisable) theory TC, we conjoin the axioms of TC in a single sentence, replace all theoretical predicates with distinct variables ui, and then

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bind these variables by placing an equal number of existential quantifiers ∃ui in front of the resulting formula. Suppose that the theory TC is represented as TC (t1,...,tn; o1,...,om), where TC is a purely logical m+n-predicate. The Ramseysentence RTC of TC is: ∃u1∃u2...∃unTC (u1,...,un; o1,...,om). For simplicity let us say that the T-terms of TC form an n-tuple t=, and the O-terms of TC form an m-tuple o=. Then, RTC takes the more convenient form: ∃uTC(u,o). I will follow customary usage and call Ramsey’s existential-judgements Ramsey-sentences. This is, I think, partly misleading. I don’t think Ramsey thought of these existential judgements as replacements of existing theories or as capturing their proper content (as if there were an improper content, which was dispensable). Be that as it may, Ramsey-sentences have a number of important properties. Here they are: RTC is a logical consequence of TC. RTC mirrors the deductive structure of TC. RTC has exactly the same first-order observational consequences as TC. So RTC is empirically adequate iff TC is empirically adequate. TC1 and TC2 have incompatible observational consequences iff RTC1 and RTC2 are incompatible (Rozeboom 1960, p. 371). TC1 and TC2 may make incompatible theoretical assertions and yet RTC1 and RTC2 be compatible (cf. English 1973, p. 458). If RTC1 and RTC2 are compatible with the same observational truths, then they are compatible with each other (cf. English 1973, p. 460; Demopoulos 2003a, p. 380). Let me sum up Ramsey’s insights. First, a theory need not be seen as a summary of what can be said in the primary system. Second, theories, qua hypothetico-deductive structures, have excess content over their primary systems, and this excess content is seen when the theory is formulated as expressing an existential judgement. Third, a theory need not use names in order to refer to anything (in the secondary system). Existentially bound variables can do this job perfectly well.4, 5 Fourth, a theory need not be a definite description to be a) truth-valuable, b) ontically committing, and c) useful. So uniqueness of realisation (or satisfaction) is not necessary for the above. Fifth, if we take a theory as a dynamic entity (something that can be improved upon, refined, modified, changed, enlarged), we are better off if we see it as a growing existential sentence. This last point is particularly important for two reasons. The first is this. A typical case of scientific reasoning occurs when two theories TC1 and TC2 are conjoined (TC1 & TC2=TC) in order to account for some phenomena. But if we take their Ramsey-sentences, then ∃uTC1(u, o) and ∃uTC2(u, o), they do not entail ∃uTC(u, o). Ramsey was aware of this problem. He solved it by taking scientific theories to be growing existential sentences. That is to say, the theory is already in the form ∃uTC(u, o) and all further addi-

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tions to it are done within the scope of the original quantifiers. To illustrate the point, Ramsey uses the metaphor of a fairy tale. Theories tell stories about the form: “Once upon a time there were entities such that ...”. When these stories are modified, or when new assertions are added, they concern the original entities, and hence they take place within the scope of the original “once upon a time”. The second reason is this: Ramsey never said that the distinction between primary and secondary system was static and fixed. So there is nothing to prevent us from replacing an existentially bound variable by a name or by a constant (thereby moving it into the primary system), if we come to believe that we know what its value is. His Causal Qualities is, in a sense, a sequel to his Theories. There, Ramsey characterises the secondary system as “fictitious” and gives the impression that its interest lies in its being a mere systematiser of the content of the primary system. But he ends the paper by saying this: Of course, causal, fictitious, or ‘occult’ qualities may cease to be so as science progresses. E.g., heat, the fictitious cause of certain phenomena (…) is discovered to consist of the motion of small particles. So perhaps with bacteria and Mendelian characters or genes. This means, of course, that in later theory these parametric functions are replaced by functions of the given system (1931, p. 262).

In effect, Ramsey says that there is no principled distinction between fictitious and non-fictitious qualities. If we view the theory as a growing existential sentence, then this point can be accommodated in the following way. As our knowledge of the world grows, the propositional functions that expressed ‘fictitious’ qualities (and were replaced by existentially bound variables) might well be taken to characterise known quantities and hence be re-introduced in the growing theory as names (or constants).6 Viewing theories as existential judgements solves another problem that Ramsey faced. He did not see causal laws (what he called “variable hypotheticals”) as proper propositions. As he famously stated: “Variable hypotheticals are not judgements but rules for judging ‘If I meet a φ, I shall regard it as a ψ’” (1931, p. 241). Yet, he also took the secondary system to comprise variable hypotheticals (cf. 1931, p. 260). Taking the theory as an existential judgement allows Ramsey to show how the theory as a whole can express a judgement, though the variable hypotheticals it consists of, if taken in isolation from the theory, do not express judgements. The corollary of this is a certain wholism of meaning. The existential quantifiers render the hypothetico-deductive structure truth-valuable, but the consequence is that no ‘proposition’ of this structure has meaning apart from the structure.7

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5. R USSELL ’ S S TRUCTURALISM In this section, I want to examine the link, if any, between Russell’s structuralism and Ramsey’s existential view of theories. This issue has been discussed quite extensively and has given rise to the view called ‘structural realism’. In The Analysis of Matter, Russell aimed to reconcile the abstract character of modern physics, and of the knowledge of the world that this offers, with the fact that all evidence there is for its truth comes from experience. To this end, he advanced a structuralist account of our knowledge of the world. According to this, only the structure, i.e., the totality of formal, logico-mathematical properties, of the external world can be known, while all of its intrinsic properties are inherently unknown. This logico-mathematical structure, he argued, can be legitimately inferred from the structure of the perceived phenomena (the world of percepts) (cf. 1927, pp. 226-7). Indeed, what is striking about Russell’s view is this claim to inferential knowledge of the structure of the world (of the stimuli), since the latter can be shown to be isomorphic to the structure of the percepts. He was quite clear on this: (...) whenever we infer from perceptions, it is only structure that we can validly infer; and structure is what can be expressed by mathematical logic, which includes mathematics (1927, p. 254).

Russell capitalised on the notion of structural similarity he himself had earlier introduced. Two structures M and M' are isomorphic iff there is an 1-1 mapping f (a bijection) of the domain of M onto the domain of M' such that for any relation R in M there is a relation R' in M' such that R(x1…xn) iff R'(fx1…fxn). A structure (“relation-number”) is then characterised by means of its isomorphism class. Two isomorphic structures have identical logical properties (cf. 1927, p. 251). How is Russell’s inference possible? Russell relied on the causal theory of perception: physical objects are the causes of perceptions.8 This gives him the first assumption that he needs, i.e., that there are physical objects which cause perceptions. Russell used two more assumptions. The second is what I (2001) have called the ‘Helmholtz-Weyl’ principle, i.e., that different percepts are caused by different physical stimuli (cf. 1927, p. 226, p. 252, p. 400). Hence, to each type of percept there corresponds a type of stimuli. The third assumption is a principle of “spatio-temporal continuity” (that the cause is spatio-temporally continuous with the effect). From these Russell concluded that we can have “a great deal of knowledge as to the structure of stimuli”. This knowledge is that there is a roughly one-one relation between stimulus and percepts, [which] enables us to infer certain mathematical properties of the stimulus when we know the percept, and conversely enables us to infer the percept when we know these mathematical properties of the stimulus (1927, p. 227).

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The “intrinsic character” of the stimuli (i.e., the nature of the causes) will remain unknown. The structural isomorphism between the world of percepts and the world of stimuli isn’t enough to reveal it. But, for Russell, this is just as well. For as he claims: “(...) nothing in physical science ever depends upon the actual qualities” (1927, p. 227). Still, he insists, we can know something about the structure of the world (cf. 1927, p. 254). Here is an example he uses: Suppose that we hear a series of notes of different pitches. The structure of stimuli that causes us to hear these notes must be such that it also forms a series “in respect to some character which corresponds causally with pitch” (1927, p. 227). The three assumptions that Russell uses are already quite strong but, actually, something more is needed for the inference to go through. The establishment of isomorphism requires also the converse of the Helmholtz-Weyl principle – viz., different stimuli cause different percepts. Hence, to each type of stimuli there corresponds a type of percept. If the converse of the Helmholtz-Weyl principle is not assumed, then the isomorphism between the two structures cannot be inferred, for the required 1-1 correspondence between the domains of the two structures is not shown.9 The notion of structural similarity is purely logical and hence we need not assume any kind of (Kantian) intuitive knowledge of it. So an empiricist can legitimately appeal to it. It is equally obvious that the assumptions necessary to establish the structural similarity between the two structures are not logical but substantive. I am not going to question these assumptions here (see my 2001).10 Let us grant them. An empiricist need not quarrel with them. Hence, since Russell’s inference is legitimate from an empiricist perspective, its intended conclusion, viz., that the unperceived (or unobservable) world has a certain knowable structure, will be acceptable too. With it comes the idea that of the physical objects (the causes, the stimuli) we can only know their formal, logico-mathematical properties. This inference, as Russell says, “determines only certain logical properties of the stimuli” (1927, p. 253). Russell’s structuralism has met with a fatal objection, due to M.H.A. Newman (1928): the structuralist claim is trivial in the sense that it follows logically from the claim that a set can have any structure whatever, consistent with its cardinality. So the actual content of Russell’s thesis, viz., that the structure of the physical world can be known, is exhausted by his first assumption, viz., by positing a set of physical objects with the right cardinality. The supposed extra substantive point, viz. that of this set it is also known that it has structure W, is wholly insubstantial. The set of objects that comprise the physical world cannot possibly fail to possess structure W because, if seen just as a set, it possesses all structures which are consistent with its cardinality. Intuitively, the elements of this set can be arranged in ordered n-tuples so that set exhibits structure W.11 Newman sums this up by saying:

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Hence the doctrine that only structure is known involves the doctrine that nothing can be known that is not logically deducible from the mere fact of existence, except (‘theoretically’) the number of constituting objects (1928, p. 144).

Newman’s argument has an obvious corollary: the redundancy of the substantive and powerful assumptions that Russell used in his argument that the structure of the world can be known inferentially. These assumptions give the impression that there is a substantive proof available. But this is not so. 6. M AXWELL ’ S S TRUCTURALISM Russell’s thesis was revamped by Maxwell – with a twist. Maxwell took the Ramsey-sentence to exemplify the proper structuralist commitments. He advanced “structural realism” as a form of representative realism, which suggests that i) scientific theories issue in existential commitments to unobservable entities and ii) all non-observational knowledge of unobservables is structural knowledge, i.e., knowledge not of their first-order (or intrinsic) properties, but rather of their higher-order (or structural) properties (cf. 1970a; 1970b). The key idea here is that a Ramsey-sentence satisfies both conditions (i) and (ii) above. If we know the Ramsey-sentence we know that there are properties that satisfy it (because of the existentially bound quantifiers), but of these properties we know only their “structural properties”. Maxwell’s association of Russell’s structuralism with Ramsey’s views (cf. 1970b, p. 182) is, at least partly, wrong. To see this, recall that Russell’s structuralism attempted to provide some inferential knowledge of the structure of the world: the structure of the world is isomorphic to the structure of the appearances. I think it obvious that Ramsey-sentences cannot offer this. The structure of the world, as depicted in a Ramsey-sentence, is not isomorphic to, nor can it be inferred from, the structure of the phenomena which the Ramsey-sentence accommodates. Now, the distinctive feature of the Ramsey-sentence RTC of a theory TC is that it preserves the logical structure of the original theory. We may say then that when one accepts RTC, one is committed to a) the observable consequences of the original theory TC; b) a certain logico-mathematical structure in which (descriptions of) the observable phenomena are deduced; and c) certain abstract existential claims to the effect that there are (non-empty classes of) entities which satisfy the (non-observational part of the) deductive structure of the theory. In this sense, we might say that the Ramsey-sentence, if true, gives us knowledge of the structure of the world: there is a certain structure which satisfies the Ramsey-sentence and the structure of the world (or of the relevant worldly domain) is isomorphic to this structure.12 I suppose this is what Maxwell really wanted to stress when he brought together Russell and Ramsey. The problem with Maxwell’s move is that it falls prey to a Newman-type objection. The existential claim italicised above follows logically from the fact that the Ramsey-sentence is empirically adequate, subject to certain cardinality

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constraints. In other words, subject to cardinality constraints, if the Ramsey-sentence is empirically adequate, it is true. The proof of this has been given in different versions by several people.13 Its thrust is this: Take RTC to be the Ramsey-sentence of theory TC. Suppose RTC is empirically adequate. Since RTC is consistent, it has a model. Call it M. Take W to be the ‘intended’ model of TC and assume that the cardinality of M is equal to the cardinality of W. Since RTC is empirically adequate, the observational sub-model of M will be identical to the observational sub-model of W. That is, both the theory TC and its Ramseysentence RTC will ‘save the (same) phenomena’. Now, since M and W have the same cardinality, we can construct an 1-1 correspondence f between the domains of M and W and define relations R' in W such that for any theoretical relation R in M, R(x1…xn) iff R'(fx1…fxn). We have induced a structure-preserving mapping of M on to W; hence, M and W are isomorphic and W becomes a model of RTC. Another way to see the problem is to look at Carnap’s assimilation of Ramsey’s sentences (see my 2000a). Carnap noted that a theory TC is logically equivalent to the following conjunction: RTC & (RTCÆTC), where the conditional RTCÆTC says that if there is some class of entities that satisfy the Ramsey-sentence, then the theoretical terms of the theory denote the members of this class. For Carnap, the Ramsey-sentence of the theory captured its factual content, and the conditional RTCÆTC captured its analytic content (it is a meaning postulate). This is so because the conditional RTCÆTC has no factual content: its own Ramsey-sentence, which would express its factual content if it had any, is logically true. As Winnie (1970, p. 294) observed, under the assumption that RTCÆTC – which is known as the Carnap sentence – is a meaning postulate, it follows that RTCÅÆTC, i.e., that the theory is equivalent to its Ramseysentence.14 In practice, this means that the Carnap sentence poses a certain restriction on the class of models that satisfy the theory: it excludes from it all models in which the Carnap-sentence fails. In particular, the models that are excluded are exactly those in which the Ramsey-sentence is true but the theory false. So if the Ramsey-sentence is true, the theory must be true: it cannot fail to be true. Is there a sense in which RTC can be false? Of course, a Ramseysentence may be empirically inadequate. Then it is false. But if it is empirically adequate (if, that is, the structure of observable phenomena is embedded in one of its models), then it is bound to be true. For, as we have seen, given some cardinality constraints, it is guaranteed that there is an interpretation of the variables of RTC in the theory’s intended domain. We can see why this result might not have bothered Carnap. If being empirically adequate is enough for a theory to be true, then there is no extra issue of the truth of the theory to be reckoned with – apart of course of positing an extra domain of entities. Empiricism can thus accommodate the claim that theories are true, without going a lot beyond empirical adequacy.15 Indeed, as I have argued elsewhere (1999 chapter 3, 2000a), Carnap took this a step further. In his own account of Ramsey-sentences, he deflated the issue of the possible existential commitment to physical unobservable entities by taking the existentially bound

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Ramsey-variables to extend beyond mathematical entities. Of the Ramseysentences he said: the observable events in the world are such that there are numbers, classes of such etc., which are correlated with the events in a prescribed way and which have among themselves certain relations; and this assertion is clearly a factual statement about the world (1963, p. 963).

Carnap’s thought, surely, was not that the values of the variable are literally numbers, classes of them etc. How possibly can a number be correlated with an observable event? Rather, his thought was that a) the use of Ramsey-sentences does not commit someone to the existence of physical unobservable entities (let alone, to for instance, electrons in particular); and b) the things that matter are the observable consequences of the Ramsey-sentence, its logical form, and its abstract claim of realisation. Let me grant that this equation of truth with empirical adequacy is quite acceptable for an empiricist, though I should say in passing that it reduces much of science to nonsense and trivialises the search for truth.16 But reducing truth to empirical adequacy is a problem for those who want to be realists, even if just about structure. For, it is no longer clear what has been left for someone to be a realist about. Perhaps, the structural realist will insist that the range of the Ramsey-variables comprises unobservable entities and properties. It’s not clear what the reason for this assertion is. What is it, in other words, that excludes all other interpretations of the range of Ramsey-variables? But let’s assume that, somehow, the range of Ramsey-variables is physical unobservable entities. It might be thought that, consistently with structuralism, the excess content of theories is given in the form of non-formal structural properties of the unobservables. Maxwell, for instance, didn’t take all of the so-called structural properties to be purely formal (cf. 1970b, p. 188). In his (1970a, p. 17), he took “temporal succession, simultaneity, and causal connection” to be among the structural properties. But his argument for this is hardly conclusive: “for it is by virtue of them that the unobservables interact with one another and with observables and, thus, that Ramsey sentences have observable consequences”. Hearing this, Ramsey would have raised his eyebrow. In Theories, he had noted: “This causation is, of course, in the second system and must be laid out in the theory” (1931, p. 235).17 The point, of course, is that we are in need of an independent argument for classifying some relations, e.g., causation, as ‘structural’ and hence as knowable. When it comes to causation, in particular, a number of issues need to be dealt with. First, what are its structural properties? Is causation irreflexive? Not if causation is persistence. Is causation asymmetric? Not if there is backward causation. Is causation transitive? Perhaps yes – but even this can be denied (in the case of probabilistic causation, for instance). Second, suppose that the structural properties of causation are irreflexivity, asymmetry and transitivity. If these properties constitute all that can be known of the relevant relation, what is there

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to distinguish causation from another relation with the same formal properties, e.g., a relation of temporal ordering? Third, even if causation were a non-formal structural relation, why should it be the case that only its structural properties could be known? Note a certain irony here. Suppose that since causation is a relation among events in the primary system, one assumes that it is the same relation that holds between unobservable events and between unobservable and observable events. This seems to be Maxwell’s view above. Now, causal knowledge in the primary system (that is causal knowledge concerning observables) is not purely structural. The (intrinsic) properties of events (or objects) by virtue of which they are causally related to one another are knowable. If causation is the very same relation irrespective of whether the relata are observable or unobservable, why should one assume that the (intrinsic) properties of unobservable events (or objects) by virtue of which they are causally related to one another are not knowable? There seems to be no ground for this asymmetry. In both cases, it may be argued, it is by virtue of their (intrinsic) properties that entities are causally related to each other. In both cases, it might be added, causal relations supervene on (or are determined by) the intrinsic properties of observable or unobservable entities.18 Indeed, these last points are fully consistent with Russell’s (and Maxwell’s) views. Recall that according to the causal theory of perception, which Maxwell also endorses, our percepts are causally affected by the external objects (the stimuli, the causes), which must be in virtue of these objects’ intrinsic properties. (Surely, it is not by their formal properties.) The Helmholtz-Weyl principle (that different percepts are caused by different stimuli) implies that the different stimuli must differ in their intrinsic properties. So the latter are causally active and their causal activity is manifested in the different percepts they cause. In what sense then are they unknowable?19 The general point is that Maxwell’s Ramsey-sentence approach to structuralism faces a sticky dilemma. Either there is nothing left to be known except formal properties of the unobservable and observable properties or there are some knowable non-formal properties of the unobservable. In the former case, the Ramsey-sentence leaves it (almost) entirely open what we are talking about. In the latter case, we know a lot more about what the Ramsey-sentence refers to, but we thereby abandon pure structuralism. 7. W ORRALL AND Z AHAR ’ S S TRUCTURALISM The points raised in the last section are particularly relevant to the Zahar-Worrall (2001) view that adopting the Ramsey-sentence of the theory is enough to be a realist about this theory. Indeed, they are aware of the problems raised so far. They do deal with Putnam’s model-theoretic argument against realism and admit that if this argument is cogent, then the Ramsey-sentence of a(n) (epistemically ideal) theory is true. Note that a theory’s being epistemically ideal includes its

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being empirically adequate. But it’s not hard to see that Putnam’s argument is a version of the Newman challenge.20 Zahar and Worrall (2001, p. 248) ask: “should the structural realist be worried about these results?” And they answer: “(…) the answer is decidedly negative”. So Zahar and Worrall do accept the equation of the truth of the theory with the truth of its Ramsey-sentence. In fact, they want to capitalise on this in order to claim that truth is achievable. They claim that two seemingly incompatible empirically adequate theories will have compatible Ramsey-sentences and hence they can both be true of the world (cf. 2001, pp. 248-9). We have already seen the price that needs to be paid for truth being achievable this way: truth is a priori ascertainable, given empirical adequacy and cardinality. But it is interesting to note that Zahar and Worrall are not entirely happy with this equation. They carry on to stress that “the more demanding structural realist” can say a bit more. He (they?) can distinguish between different empirically adequate Ramsey-sentences using the usual theoretical virtues (simplicity, unification etc.), opt for the one that better exemplifies these virtues (e.g., it is more unified than the other) and claim that it is this one that should be taken “to reflect – if only approximately – the real structure of W [the world]” (2001, p. 249). But I doubt that this, otherwise sensible, strategy will work in this case. For one, given that the theoretical virtues are meant to capture the explanatory power of a theory, it is not clear in what sense the truth of the Ramsey-sentence explains anything. If its truth is the same as its empirical adequacy, then the former cannot explain the latter. Further, there is something even more puzzling in the Zahar-Worrall claim. If two theories have compatible Ramsey-sentences, and if truth reduces to empirical adequacy, in what sense can the theoretical virtues help us deem one theory true and the other false? Clearly, there could be a straightforward sense, if truth and empirical adequacy were distinct. But this is exactly what the Zahar-Worrall line denies. Could they simply say that there is a sense in which one Ramsey-sentence is truer than the other? They could, but only if the truth of the theory answered to something different from its empirical adequacy. If, for instance, it was claimed that a theory is true if, on top of its being empirically adequate, it captures the natural structure of the world, then it is clear that a) one theory can be empirically adequate and yet false; and b) one of two empirically adequate theories can be truer than the other. 21 Now, there could be another sense in which an appeal to the theoretical virtues could distinguish between the claim that a theory is true and the claim that its Ramsey-sentence is empirically adequate. This is by conceptually equating truth with empirical adequacy plus the theoretical virtues. If this equation went ahead, then someone could claim that a theory could be empirically adequate and false, if the theory lacked in theoretical virtues. Or, someone could claim that among two empirically adequate theories, one was truer than the other if the first had more theoretical virtues than the second; or if the first fared better vis-à-vis the theoretical virtues than the second. But these claims would amount to an endorsement of an epistemic account of truth. In particular, they would amount

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to forging an a priori (conceptual) link between the truth of the theory and its possession of theoretical virtues. I will not criticise this move now. Suffice it to say that such a move has disputed realist credentials. So it is not open to those who want to be realists.22 In his reply to Russell’s structuralism, Newman pointed to a way in which Russell’s claim would not be trivial, viz., if the relation that generated the required structure W was “definite”, that is if we knew (or claimed that we knew) more about what it is than that it exists and has certain formal properties. Couldn’t we distinguish between “important” and “unimportant” relations and stay within structuralism? Not really. The whole point is precisely that the notion of an ‘important relation’ cannot be part of a purely structuralist understanding. Newman saw this point very clearly (see 1928, p. 147). In order to pick as important one among the many relations which generate the same structure on a domain, we have to go beyond structure and talk about what these relations are, and why some of them are more important than others. It’s not hard to see that the very same objection can be raised against a Maxwell- or a Zahar-Worrall structural realism. And it is equally obvious what the remedy could be. Structural realists should have a richer understanding of the relations that structure the world. Suppose there is indeed some definite relation (or a network, thereof) that generates the structure of the world. If this is the case, then the claim that the structure W of the physical world is isomorphic to the structure W' that satisfies an empirically adequate Ramsey-sentence would be far from trivial. It would require, and follow from, a comparison of the structures of two independently given relations, say R and R'. But structural realists as well as Russell deny any independent characterisation of the relation R that generates the structure of the physical world. On the contrary, structural realists and Russell insist that we can get at this relation R only by knowing the structure of another relation R', which is deemed isomorphic to R. We saw that the existence of R (and hence of W) follows logically from some fact about cardinality. It goes without saying that treating these relations as “definite” would amount to an abandonment (or a strong modification) of structuralism.23 The natural suggestion here is that among all those relations-in-extension which generate the same structure, only those which express real relations should be considered. But specifying which relations are real requires knowing something beyond structure, viz., which extensions are ‘natural’, i.e., which subsets of the power set of the domain of discourse correspond to natural properties and relations. Having specified these natural relations, one may abstract away their content and study their structure. But if one begins with the structure, then one is in no position to tell which relations one studies and whether they are natural or not.

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8. R AMSEY AND N EWMAN ’ S P ROBLEM As noted above, Ramsey’s crucial observation was that the excess content of the theory is seen when the theory is formulated as expressing an existential judgement. If, on top of that, Ramsey meant to assert something akin to the structural realist position, i.e., that this excess content, so far as it is knowable, is purely structural, then he would have landed squarely on the Newman problem. So should this view be attributed to Ramsey? Before I canvass a negative answer, let me go back to Russell once more. Russell (1927) took theories to be hypothetico-deductive systems and raised the issue of their interpretation. Among the many “different sets of objects [that] are abstractly available as fulfilling the hypotheses”, he distinguished those that offer an “important” interpretation (1927, pp. 4-5), that is an interpretation which connects the theory (as an abstract logico-mathematical system) to the empirical world. This was important, he thought, because all the evidence there is for physics comes from perceptions. He then went on to raise the central question that was meant to occupy the body of his book: when are physical theories true? As he (1927, pp. 8-9) put it, there is a wider sense in which physics is true: Given physics as a deductive system, derived from certain hypotheses as to undefined terms, do there exist particulars, or logical structures composed of particulars, which satisfy these hypotheses?

“If ”, he added, “the answer is in the affirmative, then physics is completely ‘true’”. Actually, he took it that his subsequent structuralist account, based on the causal theory of perception, was meant to answer the above question affirmatively. Now, Russell’s view has an obvious similarity to Ramsey’s: theories as hypothetico-deductive structures should be committed to an existential claim that there is an interpretation of them. But there is an interesting dissimilarity between Russell and Ramsey. Russell thought that some interpretation was important (or more important than others), whereas Ramsey was not committed to this view. Russell might well identify the theory with a definite description: there is a unique (important) interpretation such that the axioms of the theory are true of it. But, as we have seen, one of Ramsey’s insights is that there is no reason to think of theories as definite descriptions – i.e., as requiring uniqueness. It seems likely that it was this Russellian question that inspired Ramsey to formulate his own view of theories as existential judgements. In fact, there is some evidence for it. In a note on Russell’s The Analysis of Matter, Ramsey (1991, p. 251) said: Physics says = is true if (∃ α, β, … R, S): F(α, β, … R, S…) (1).

He immediately added a reference – “Russell p. 8” – to The Analysis of Matter.24

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(1) looks very much like a Ramsey-sentence. But unlike Russell, Ramsey did not adopt a structuralist view of the content of theories. This may be seen by what he goes on to say: the propositional functions α and R should be “nonformal”. And he adds: “Further, F must not be tautological as it is on Eddington’s view”. As it is clear from another note (1991, pp. 246-50), Ramsey refers to Eddington’s The Nature of the Physical World. In his review of this book, Braithwaite criticised Eddington severely for trying to turn physics “from an inductive science to a branch of mathematics” (1929, p. 427). According to Braithwaite, Eddington tried to show how the laws of physics reduce to mathematical identities, which are derivable from very general mathematical assumptions. This must be wrong, Braithwaite thought, for in mathematics “we never know what we are talking about”, whereas in physics “we do know (or assume we know) something of what we are talking about – that the relata have certain properties and relations – without which knowledge we should have no reason for asserting the field laws (even without reference to observed quantities)” (1929, p. 428). The point might not be as clear as it ought to have been, but, in effect, Braithwaite argued against Eddington that natural science would be trivialised if it was taken to aim at achieving only knowledge of structure.25 I don’t know whether Ramsey discussed Eddington’s book with Braithwaite or whether he had read Braithwaite’s review of it (though he had read Eddington’s book – see 1991, pp. 246-50). It is nonetheless plausible to say that he shared Braithwaite’s view when he said of the relation F that generates the structure of a theory that it should not be tautological “as it is on Eddington’s view”. In fact, in the very same note, Ramsey claims that in order to fix some interpretation of the theory we need “some restrictions on the interpretation of the other variables. i.e., all we know about β, S is not that they satisfy (1)”. So I don’t think Ramsey thought that viewing theories as existential judgements entailed that only structure (plus propositions of the primary system) could be known. It’s plausible to argue that Ramsey took Ramsey-sentences (in his sense) to require the existence of definite relations, whose nature might not be fully determined, but which is nonetheless constrained by some theoretical and observational properties. To judge the plausibility of this interpretation, let’s look into some of his other papers. In The Foundations of Mathematics, Ramsey insisted on the distinction between classes and relations-in-extension, on the one hand, and real or actual properties and relations, on the other. The former are identified extensionally, either as classes of objects or as ordered n-tuples of objects. The latter are identified by means of predicates. Ramsey agreed that an extensional understanding of classes and relations is necessary for mathematics. Take, for instance, Cantor’s concept of class-similarity. Two classes are similar (that is, they have the same cardinality) iff there is an one-one correspondence (relation) between their domains. This relation, Ramsey (1931, p. 15) says, is a relation-in-extension: there needn’t be any actual (or real) relation correlating the two classes. The class of male angels may have the same cardinality with the class of female

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angels, so that the two classes can be paired off completely, without there being some real relation (“such as marriage”) correlating them (1931, p. 23). But this is not all there is to relations. For it may well be the case that two classes have the same cardinality because there is a “real relation or function f (x, y) correlating them term by term” (ibid.). He took it that the real propositional functions are determined “by a description of their senses or imports” (1931, p. 37). In fact, he thought that appealing to the meaning of propositional functions is particularly important when we want to talk of functions of functions (Ramsey’s f(φx)), that is (higher-level) propositional functions f whose values are other propositional functions (φx). He wrote: “The problem is ultimately to fix as values of f(φx) some definite set of propositions so that we can assert their logical sum or product” (1931, p. 37). And he took it that the best way to determine the range of the values of f(φx) is to appeal to the meanings of the lower-level propositional functions (φx) (1931, pp. 36-7). Recall Ramsey’s Ramsey-sentence (∃ α, β, γ) : dictionary . axioms. The open formula dictionary . axioms (α, β, γ ) is a higher-level propositional function, whereas the values of α, β, γ are lower-level propositional functions. The Ramsey-sentence itself expresses the logical sum of the propositions that result when specific values are given to α, β, γ. This situation is exactly analogous to the one discussed by Ramsey above. So, it’s plausible to think that the values of α, β, γ are some definite properties and relations. That is, they are not any class or relation-in-extension that can be defined on the domain of discourse of the Ramsey-sentence. This point can be reinforced if we look at Ramsey’s Universals. Among other things, Ramsey argues that the extensional character of mathematics “is responsible for that great muddle the theory of universals”, because it has tended to obscure the important distinction between those propositional functions that are names and those that are incomplete symbols (cf. 1931, pp. 130-1 & p. 134). The mathematical logician is interested only in classes and relations-in-extension. The difference between names and incomplete symbols won’t be reflected in any difference in the classes they define. So the mathematician disregards this difference, though, as Ramsey says, it is “all important to philosophy” (1931, p. 131). The fact that some functions cannot stand alone (that is, they are incomplete symbols) does not mean that “all cannot” (ibid.). Ramsey takes it that propositional functions that are names might well name “qualities” of individuals (cf. 1931, p. 132). Now, Ramsey puts this idea to use in his famous argument that there is no difference between particulars and universals.26 But the point relevant to our discussion is that propositional functions can be names. Given a) Ramsey’s view that the propositional functions of physics should be non-formal, b) his insistence on real or actual properties and relations, and c) his view that at least some relations can be named by propositional functions, it seems plausible to think that he took the variables of his Ramsey-sentence to extend beyond real properties and relations – some of which could be named. I am not aware of a passage in his writings which says explicitly that the variables

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of the Ramsey-sentence extend beyond real or actual properties and relations. But his contrasting of mathematics (in which the variables are purely extensional) to science suggests that he might well have taken the view described above. Now, the other claim, i.e., that some of the Ramsey-variables can be names, also follows from his view, seen in section 4, that some propositional functions can give way to names of properties, as science grows. If I am right, the Newman challenge cannot be raised against Ramsey’s views. Ramsey takes theories to imply the existence of definite (or real) relations and properties. Hence, it’s no longer trivial (in the sense explained above) that if the theory is empirically adequate, it is true. His Ramsey-sentences can be seen as saying that there are real properties and relations such that …. Note that, in line with Ramsey’s denial of a distinction between universals and particulars, the existentially bound variables should be taken to quantify over properties and relations in a metaphysically non-committal way: they quantify over properties and relations which are not universals in the traditional sense, which renders them fundamentally different from particulars.27 The corollary is that Ramsey’s views cannot be described as pure structuralism. The claim that there are real properties and relations is not structural because, to say the least, it specifies the types of structure that one is interested in. Besides, Ramsey does not claim that only the structure (or the structural properties) of these relations can be known. Well, it might. Or it might not. This is certainly a contingent matter. If my interpretation is right, I have a hurdle to jump. It comes from Ramsey’s comment on “the best way to write our theory”. He says: “Here it is evident that α, β, γ are to be taken purely extensionally. Their extensions may be filled with intensions or not, but this is irrelevant to what can be deduced in the primary system” (1931, p. 231). But this comment is consistent with my reading of his views. The propositional variables may range over real properties and relations, but when it comes to what can be deduced in the primary system, what matters is that they are of a certain logical type, which the Ramsey-sentence preserves anyway. Indeed, deduction cuts through content and that’s why it is important. In any case, the comment above would block my interpretation only if what really mattered for theories was what could be deduced in the primary system. I have already said enough, I hope, to suggest that this view was not Ramsey’s. 9. R AMSEYAN H UMILITY Let me end by sketching an image of scientific theories to which the above interpretation of Ramsey’s Ramsey-sentences might conform. As already noted, I call it Ramseyan humility. We treat our theory of the world as a growing existential statement. We do that because we want our theory to express a judgement: to be truth-valuable. In writing the theory, we commit ourselves to the existence of things that make our

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theory true and, in particular, to the existence of unobservable things that cause or explain the observable phenomena. We don’t have to do this. But we think we are better off doing it, for theoretical, methodological and practical reasons. So we are bold. Our boldness extends a bit more. We take the world to have a certain structure (to have natural joints). We have independent reasons to think of it, but in any case, we want to make our theory’s claim to truth or falsity substantive. The theoretical superstructure of our theory is not just an idle wheel. We don’t want our theory to be true just in case it is empirically adequate. We want the structure of the world to act as an external constraint on the truth or falsity of our theory. So we posit the existence of a natural structure of the world (with its natural properties and relations). We come to realise that this move is not optional once we have made the first bold step of positing a domain of unobservable entities. These entities are powerless without properties and relations, and the substantive truth of our theories requires that these are real (or natural) properties and relations.28 That’s, more or less, where our boldness ends. We don’t want to push our (epistemic) luck too hard. We want to be humble too. We don’t foreclose the possibility that our theory might not be uniquely realised. So we don’t require uniqueness: we don’t turn our growing existential statement into a definite description. In a sense, if we did, we would no longer consider it as growing. We allow a certain amount of indeterminacy and hope that it will narrow down as we progress. Equally, we don’t foreclose the possibility that what the things (properties) we posited are might not be found out. Some things (properties) must exist if our theory is to be true and these things (properties) must have a natural structure if this truth is substantive. Humility teaches us that there are many ways in which these commitments can be spelled out. It also teaches us that, in the end, we might not be lucky. We don’t, however, draw a sharp and principled distinction between what can and what cannot be known. We are not lured into thinking that only the structure of the unobservable world can be known, or that only the structural properties of the entities we posited are knowable or that we are cognitively shut off from their intrinsic properties. These, we claim, are imposed epistemic dichotomies on perfect epistemic continua. We are reflective beings after all, and realise that dichotomous claims such as the above need independent argument to be plausible. We read Kant, we read Russell, Schlick, Maxwell, Redhead and Lewis, but we have not yet been persuaded that there is a sound independent argument for pushing humility too far (though we admit that we have been shaken). So we choose to be open-minded about this issue. The sole arbiter we admit is our give-and-take with the world. A further sign of our humility, however, is that we treat what appear to be names of theoretical entities as variables. We refer to their values indefinitely, but we are committed to their being some values that make the theory true. As science grows, and as we acquire some knowledge of the furniture of the world, we modify our growing existential statement. We are free to replace a variable with a name. We are free to add some new findings within our growing

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existential statement. We thereby change our theory of the world, but we had anticipated this need. That’s why we wrote the theory as a growing existential statement. We can bring continuity and change under the same roof. The continuity is secured by the bound Ramsey-variables and the change is accommodated by adding or deleting things within their scope. In the meantime, we can accommodate substantial disagreement of two sorts. Scientific disagreement: what exactly are the entities posited? In fostering this kind of disagreement, we are still able to use the theory to draw testable predictions about the observable world. But we do not thereby treat the theoretical part of the theory simply as an aid to prediction. For, we have not conceded that all that can possibly be known of the entities posited is that they exist. We can also accommodate metaphysical disagreement: what is the metaphysical status of the entities posited? Are they classes? Universals? Tropes? Some kind of entity which is neutral? Still, in fostering this kind of disagreement, we have taken a metaphysical stance: whatever else these entities are, they should be natural. To be conciliatory, I could describe Ramseyan humility as modified structuralism. Structuralism emerges as a humble philosophical thesis, which rests, however, on a bold assumption – without which it verges on vacuity – viz., that the world has a natural structure that acts as an external constraint on the truth or falsity of theories. I don’t claim that the image sketched is Ramsey’s. But he might have liked it. In any case, I take it that something like it is true. It’s not attractive to someone who is not a realist of some sort. But it is flexible enough to accommodate realisms of all sorts.

N OTES ∗

An earlier version of this paper was presented in Vienna in November 2003 at the Vienna Circle Institute Ramsey Conference. I would like to thank the organisers (Maria Carla Galavotti, Eckehart Koehler and Friedrich Stadler) for their kind invitation to talk about Ramsey’s philosophy of science. They, Patrick Suppes and Brian Skyrms should also be thanked for their excellent comments. I should also thank William Demopoulos and D H Mellor for their encouragement, and Nils-Eric Sahlin and Robert Nola for many important written comments on an earlier draft.

1.

The name was inspired by the title of Rae Langton’s splendid book Kantian Humility. Langton’s Kant was epistemically humble because he thought that the intrinsic properties of thingsin-themselves were unknowable. I am not claiming that Ramsey was humble in the same way. After I presented this paper in Vienna, D H Mellor told me that there was an unpublished paper by the late David Lewis with the title “Ramseyan Humility”. Stephanie Lewis has kindly provided me with a copy of it. Langton’s book is obviously the common source for Lewis’s and my Ramseyan Humility. But Lewis’s Ramseyan Humility is different, stronger and more interesting, than mine. Still the best overall account of Ramsey’s philosophy of science is Sahlin’s (1990, chapter 5). Here, I disagree with Sahlin’s view that Ramsey was an instrumentalist. As he says, in a slightly different context, “though I cannot name particular things of such kinds I can think of there being such things” (1991, p.193).

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6. 7. 8. 9. 10. 11. 12.

13. 14.

15. 16. 17. 18. 19.

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This is a point made famous by Quine. As he put it: “Variables can be thought of as ambiguous names of their values. This notion of ambiguous names is not as mysterious as it first appears, for it is essentially the notion of a pronoun; the variable ‘x’ is a relative pronoun used in connection with a quantifier ‘(x)’ or ‘(∃x)’. Here, then, are five ways of saying the same thing: ‘There is such a thing as appendicitis’ (…) ‘The word ‘appendicitis’ is a name’ (…) ‘The disease appendicitis is a value of a variable’ (…)” (quoted by Alex Orenstein (2002, pp.25-6). Compare what Ramsey says of the blind man who is about to see: “part of his future thinking lies in his present secondary system” (1931, p.261). One of Carnap’s lasting, if neglected, contributions in this area is his use of Hilbert’s ε-operator as a means to restore some form of semantic atomism compatible with Ramsey-sentences. See my (2000b) for details. This is an inductively established assumption, as Russell took pains to explain (cf. 1927, chapter 20). Russell agonises a lot about this. He knows that the relation between percepts and stimuli is one-many and not one-one. See (1927, pp.255-6). See also Mark Sainsbury’s excellent (1979, pp.200-11). More formally, we need a theorem from second-order logic: that every set A determines a full structure, i.e., one which contains all subsets of A, and hence every relation-in-extension on A. For an elegant and informative presentation of all the relevant proofs, see Ketland (2004). This is not, however, generally true. For every theory has a Ramsey-sentence and there are cases of theories whose Ramsey-sentence does not give the isomorphism-class of the models that satisfy the theory. This has been recently highlighted by Demopoulos (2003b, pp.395-6). For some relevant technical results, see van Benthem (1978, p.324 & p.329). Winnie (1967, pp.226-227); Demopoulos & Friedman (1985); Demopoulos (2003a, p.387); Ketland (2004). In a joint paper (see appendix IV of Zahar 2001, p.243), Zahar and Worrall call the Carnap-sentence “metaphysical” because it is untestable. What they mean is actually equivalent to what Carnap thought, viz., that the Carnap-sentence has no factual content. They may well disagree with Carnap that it is a meaning postulate. Be that as it may, the Carnap-sentence is part of the content of the original theory TC. So Zahar and Worrall are not entitled to simply excise it from the theory on the grounds that it is metaphysical. The claim that the variables of the Ramseysentence range over physical unobservable entities is no less metaphysical and yet it is admitted as part of the content of the Ramsey-sentence. This point is defended by Rozeboom (1960). I am not saying that striving for empirical adequacy is a trivial aim. By no means. It is a very demanding – and perhaps utopian – aim. What becomes trivial is searching for truth over and above empirical adequacy, since the former comes for free, if the latter holds. For some similar thoughts, see Russell (1927, pp.216-7). This, however, is what Langton’s Kant denies. See her (1998). This whole issue has been haunted by a claim made by Russell, Schlick, Maxwell and others that intrinsic properties should be directly perceived, intuited, picturable etc. I see no motivation for this, at least any more. Note that this is not Lewis’s motivation for the thesis that the intrinsic properties of substances are unknowable. For Lewis’s reasons see his “Ramseyan Humility”. For a more detailed defence of the claim that pure structuralism cannot accommodate causation, see my ‘The Structure, the Whole Structure and Nothing but the Structure?’, presented at the Austin PSA meeting in November 2004. http://philsci-archive.pitt.edu/archive/00002068 For more on this, see Demopoulos 2003a. Maxwell (1970a; 1970b) as well as Zahar and Worrall (2001) take Ramsey to have argued that the knowledge of the unobservable is knowledge by description as opposed to knowledge by acquaintance. This, as we have seen, is true. But note that though they go on to argue that this knowledge is purely structural, and that the intrinsic properties of the unobservable are unknowable, this further thesis is independent of the descriptivist claim. So, it requires an independent argument. It is perfectly consistent for someone to think that the unobservable is knowable only by means of descriptions and that this knowledge describes its intrinsic properties as well. For an excellent descriptivist account of Ramsey-sentences, see David Papineau (1996). For more on this see my “Scientific Realism and Metaphysics” (2005).

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23. A similar point has been made by Demopoulos (2003b, p.398). It is also made by James van Cleve (1999, p.157), who has an excellent discussion of how the problem we have discussed appears in Kant, and in particular in an interpretation of Kant’s thought as imposing an isomorphism between the structure of the phenomena and the structure of the noumena. 24. In some notes on theories that Ramsey made in August 1929, he seems not to have yet the idea of the theory as an existential judgement. He writes: “We simply say our primary system can be consistently constructed as part of a wider scheme of the following kind. Here follows dictionary, laws, axioms etc.” (1991, p.229). 25. Braithwaite came back to this issue in a critical notice of Eddington’s The Philosophy of Physical Science. He (1940) argued against Eddington’s structuralism based on Newman’s point against Russell. He noted characteristically: “If Newman’s conclusive criticism had received proper attention from philosophers, less nonsense would have been written during the last twelve years on the epistemological virtue of pure structure” (1940, p.463). Eddington replied in his (1941). For a critical discussion of this exchange, see Solomon (1989). 26. Propositional functions can name objects no less than ordinary names, which are normally the subjects of propositions. Hence, ultimately, Ramsey denies any substantive distinction between individuals and qualities: “all we are talking about is two different types of objects, such that two objects, one of each type, could be sole constituents of an atomic fact” (1931, p.132). These two types of objects are “symmetrical” and there is no point in calling one of them qualities and the other individuals. 27. This might address worries that the Ramsey-sentence involves second-order quantification. For more on this, see Sahlin (1990, p.157). 28. I think this is the central message of Lewis (1984) devastating critique of Putnam’s model-theoretic argument against realism

R EFERENCES R. B. Braithwaite, “Professor Eddington’s Gifford Lectures”, in: Mind, 38, 1929, pp.409-35. R. B. Braithwaite, “Critical Notice: The Philosophy of Physical Science”, in: Mind, 49, 1940, pp.45566. Rudolf Carnap, “Replies and Systematic Expositions”, in: P. Schilpp (Ed.), The Philosophy of Rudolf Carnap, La Salle IL: Open Court, 1963, pp.859-1013. William Demopoulos & Michael Friedman, “Critical Notice: Bertrand Russell’s The Analysis of Matter : its Historical Context and Contemporary Interest”, in: Philosophy of Science, 52, 1985 pp.621-639. William Demopoulos, “On the Rational Reconstruction of Our Theoretical Knowledge”, in: The British Journal for the Philosophy of Science, 54, 2003a, pp.371-403. William Demopoulos, “Russell’s Structuralism and the Absolute Description of the World”, in: N. Grifin (Ed.), The Cambridge Companion to Bertrand Russell, Cambridge: Cambridge University Press, 2003b. Arthur S. Eddington, “Group Structure in Physical Science”, in: Mind, 50, 1941, pp.268-79. Jane English, “Underdetermination: Craig and Ramsey”, in: Journal of Philosophy, 70, 1973, pp.45362. Jeff Ketland, “Empirical Adequacy and Ramsification”, in: The British Journal for the Philosophy of Science, 55, 2004, pp.287-300. Rae Langton, Kantian Humility. Oxford: Clarendon Press 1998. David Lewis, “Putnam’s Paradox”, in: Australasian Journal of Philosophy, 62, 1984, pp.221-236. Grover Maxwell, “Theories, Perception and Structural Realism”, in: R. Colodny (Ed.), The Nature and Function of Scientific Theories, Pittsburgh: University of Pittsburgh Press, 1970a, pp.3-34. Grover, Maxwell, “Structural Realism and the Meaning of Theoretical Terms”, in: Minnesota Studies in the Philosophy of Science, IV, Minneapolis: University of Minnesota Press, 1970b, pp.181192. M. H. A. Newman, “Mr. Russell’s ‘Causal Theory of Perception’”, in: Mind, 37, 1928, pp.137-148. Alex Orenstein, W V Quine. Chesham: Acumen 2002.

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David Papineau, “Theory-Dependent Terms”, in: Philosophy of Science, 63, 1996, pp.1-20. Stathis Psillos, Scientific Realism: How Science Tracks Truth. London & New York: Routledge 1999. Stathis Psillos, “Carnap, the Ramsey-Sentence and Realistic Empiricism”’, in: Erkenntnis, 52, 2000a, pp.253-79. Stathis Psillos, “An Introduction to Carnap’s ‘Theoretical Concepts in Science’” (together with Carnap’s: “Theoretical Concepts in Science”), in Studies in History and Philosophy of Science, 31, 2000b, pp.151-72. Stathis Psillos, “Is Structural Realism Possible?”, in: Philosophy of Science (Supplement), 68, 2001, pp.S13-24. Stathis Psillos, “Scientific Realism & Metaphysics”, in Ratio, 18, 2005. Frank Ramsey, The Foundations of Mathematics and Other Essays. (Edited by R. B. Braithwaite). London: Routledge and Kegan Paul 1931. Frank Ramsey, Notes on Philosophy, Probability and Mathematics. (Edited by M. C. Galavotti). Bibliopolis 1991. William W. Rozeboom, “Studies in the Empiricist Theory of Scientific Meaning”, in: Philosophy of Science, 27, 1960, pp.359-373. Bertrand Russell, The Analysis of Matter. London: Routledge and Kegan Paul 1927. Mark Sainsbury, Russell. London: Routledge and Kegan Paul 1979. Nils-Eric Sahlin, The Philosophy of F P Ramsey. Cambridge: Cambridge University Press 1990. Moritz Schlick, General Theory of Knowledge. (2nd German Edition, A. E. Blumberg trans.). Wien & New York: Springer-Verlag 1918/1925. Moritz Schlick, “Form and Content: An Introduction to Philosophical Thinking”, 1932, in: Moritz Schlick’s Philosophical Papers, Vol. II, Dordrecht: D. Reidel P. C., 1979, pp.285-369. Graham Solomon, “An Addendum to Demopoulos and Friedman (1985)”, in: Philosophy of Science, 56, 1989, pp.497-501. J. F. A. K. van Benthem, “Ramsey Eliminability”, in: Studia Logica, 37, 1978, pp.321-36. James van Cleve, Themes From Kant. Oxford: Oxford University Press, 1999. John Winnie, “The Implicit Definition of Theoretical Terms”, in: The British Journal for the Philosophy of Science, 18, 1967, pp.223 –9. John Winnie, “Theoretical Analyticity”, in: R. Cohen and M. Wartofsky (Eds.), Boston Studies in the Philosophy of Science, Vol.8, Dordrecht: Reidel, 1970, pp.289-305. Elie Zahar, Poincaré’s Philosophy: From Conventionalism to Phenomenology. La Salle IL: Open Court 2001.

Department of Philosophy and History of Science University of Athens Panepistimioupolis (University Campus) Athens 15771 Greece [email protected]

E CKEHART K ÖHLER

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1. S CANDAL OF P HILOSOPHY AND M ATHEMATICS I think it is a scandal of philosophy that Logicism – the reducibility of mathematics to logic – receives so little attention anymore, as if it were dead. It is not dead. Instead it has been shamelessly abandoned. Issues for which some of the greatest thinkers such as Frege, Russell and Ramsey fought passionately now barely elicit yawns from “sophisticated” philosophical logicians, who seem to assume that the issue was long ago “settled” in the twenties. Oddly enough, the issue of what relation logic has to mathematics has in the meantime been settled by default in another way: mathematics departments have simply requisitioned logic from philosophy as one of the specialties of mathematics, on the one hand – philosophy having given up the mathematized beast they never had much patience with anyway. But as such a specialty, on the other hand, the mathematicians have, by way of compensation, at least given set theory back to logic, where it has always belonged.1 I first got acquainted with Logicism in Stegmüller’s philosophical institute at the University of Munich in 1960, when Frege was still virtually unknown. Once I read his analysis of the natural number concept, especially the concept of the ancestrals using his new theory of relations, and his sophisticated treatment of measurement,2 I became completely convinced that mathematics was reducible to logic and that the main thesis of Logicism was proven. When I later read more literature on foundations of mathematics, I was quite distressed to discover that, in the meantime, Logicism was widely regarded as a failure.3 What had happened? Well, the antinomies had happened, stopping Frege, and Russell had taken over the torch. Logicism had become a complete hostage of special, newly discovered thorny problems in the logic of Russell which I never thought were so immediately relevant to the reduction of mathematics. Russell created Type Theory, with all its special complexities and artificialities, getting caught in thickets of controversies and blind alleys. What Russell did or did not achieve is still a central question concerning Logicism even now – all the more so because Carnap’s logic (in particular the Logical Syntax of Language) uses a variant of Russell’s Type Theory. Gödel (1944) wrote the severest and most exacting critique of Russell’s contributions, including comments on and praise for Ramsey’s 91 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 91–121. © 2006 Springer. Printed in the Netherlands.

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refinements. Nevertheless, the complexities of Type Theory unfairly draw attention away from the central claim of Logicism, which should be judged in partial isolation – a standpoint shared by Boolos (1998) shortly before his death, and by Clark (2004). Part of the problem lies simply in Frege’s having raised expectations of rigor to a very high degree in his effort to demonstrate that no intuitions extraneous to logic, no Anschauungen were surreptitiously slipping in to spoil the reduction of mathematics to pure logic. If he had merely kept to the lower level of rigor which Cantor, Dedekind and Zermelo applied, he would perhaps have escaped much of the onus he suffered, as Cantor did with his comparatively informal approach. Instead, Frege (1879) developed his famous Begriffschrift, the world’s first “logistic system” (Church), comparable in rigor to a programming language and only surpassed by Gödel when proving the Incompleteness Theorems.4 Russell in his Type Theory backslid considerably from Frege’s level of rigor back to that of Peano, who had been the “discovery of his life” (not Frege!). But even that level of rigor was sufficient to quickly entangle him in many distracting thorny issues. As everybody knows, Ramsey played a major role in rescuing Type Theory from some of these thorns, but unfortunately his yeoman work was insufficient to persuade either the philosophical community or mathematicians of the virtues of Logicism. One of the worst aspects of Russell’s original Type Theory involved “Ramified Types” or orders, used to solve semantic or intensional antinomies such as Richard’s paradox. Ramsey simply pointed out that the reduction of mathematics to logic doesn’t require any intensional principles, so ramification could be eliminated. In retrospect, we may say that Russell was simply trying to do too many things at once: in his zeal to make logic do all things for all seasons, attempting to realize Leibniz’s dream of a characteristica universalis by creating a universal language, Russell crammed machinery into his formalism to deal with a few semantic issues which we nowadays treat much better in semantic metatheories.5 Instead, he should have ignored some of his ambitions and concentrated on the most important issue in the grand British tradition of dividing and conquering: that of reducing mathematics to a more streamlined logic. And in the same years that Russell was developing his baroque Ramified Type Theory, more practical-minded mathematicians such as Zermelo were “streamlining” Cantor’s jungle of set theory, coming up with a axiom systems (Z, ZF, NB) paradigmatic for the majority of mathematicians today. Bingo! Classical mathematics is easily reducible to set theory! It is peculiar that practically every mathematician is roughly familiar with the fact that, in both major variants of set theory, Zermelo–Fraenkel (ZF) and von Neumann–Bernays–Gödel (NBG),6 as well as in the systems of Quine (NF and ML), natural number theory and analysis are straightforwardly derivable, once suitable models for progressions and continuous point sets are set up. And yet, although set theory has meanwhile been conventionally classified as a branch of logic, one would think the issue of Logicism ought to be regarded as settled positively – open-and-shut case! Even if one still regarded set theory as contro-

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versial (which “good” logic is not supposed to be!), it is so primarily with respect to exotic questions of large cardinality axioms of uncertain relevance for classical mathematics, and with respect to the fact that no axioms have been found which imply the Continuum Hypothesis (CH), whose solution will always remain the ultimate goal of set theory and all of mathematics since Cantor and Hilbert. But we are farther away from this goal than we ever seemed to be before. There is a patent injustice in the inconsistent ways in which mathematicians judge the success of the Bolzano–Weierstrass reduction program for analysis and the closely related Frege–Russell reduction program for arithmetic. Since the old Bolzano–Weierstrass program of “arithmetizing” analysis has met with very widespread approval (except perhaps among the lovers of the recently revived infinitesimal theory, and among the minority of constructivists – and even Brouwer was a radical arithmetizer), and since this program uses the same set theory sometimes regarded as too dubious for the reduction of arithmetic, it would seem patently unjust to withhold approval of the “remaining” reduction of cardinal-number arithmetic to set theory alone. It seems two significantly different criteria are being applied here, for if Frege–Russell Logicism is rejected because of doubts about Type Theory (a variety of set theory), then the Bolzano– Weierstrass arithmetization of analysis should also be rejected for the same doubts. Conversely, if set theory is sound enough for Bolzano–Weierstrass, it is sound enough for Frege–Russell. So there is a strange reluctance to concede victory to Logicists – as if mathematics were to lose its freedom and integrity if hordes of impertinent logicians and proof theoreticians were suddenly to invade analysis and topology seminars and begin inquisitions on proofs and axioms! (Come to think of it, maybe that would be good at times!) At the same time that mathematicians were being unfair to logic, logicians were being eccentric, too. Even the great disciple of Russell and Carnap, Van Orman Quine, ultimately put set theory outside of logic!7 It is not supposed to be logic’s business to make such contentual, ontologically committing claims; it should rather remain just “structural”; but set theory is famous particularly for claiming existence of infinite sets – most notoriously for power sets. Kneale & Kneale (1962) take the same position as Quine in restricting logic to first-order predicate theory (only second-order and higher-order theories explicitly assume concepts or sets). This seems absurd to me. Logic always dealt with concepts and concept formation, with their intensions and extensions, in addition to propositions and inference; and sets are extensions of concepts (Frege).8 Indeed, as the early Russell saw, doing set theory doesn’t even require sets, all it needs is concepts (his intensional “propositional functions”). But of course, the pioneer of set theory, Cantor, was officially a mathematician, not a philosopher, and his formulations obscured the connection with the logic of concepts. His ally, the mathematician Dedekind, was fairer: he proclaimed that set theory definitely belongs to logic and fell under the “laws of reasoning”. The way Frege separated his symbols into those designating apparently intensional concepts9 and

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extensional objects (Gegenstände), including sets (Wertverläufe), made it seem as if they were fundamentally different, and Russell inherited this view. But Ramsey saw the light: there is no fundamental difference between concepts and objects, both depend equally on their role in propositions. This is close to the position Carnap (1947) came to, in which all signs in the language have both extensions and intensions assigned to them, where individual objects have “individual concepts” assigned to them. The membership relationship of set theory ∈ is really identical to the satisfaction or fulfilment relationship between properties and the objects falling under them, and in this sense, it belongs to logic if ever anything does. Since all existence claims of set theory may be regarded as statements about ∈ , (hence about satisfaction), they are statements about logic. Furthermore, existence claims for sets can all be formulated syncategorematically, i.e. without using empirical concepts. This makes them all candidates – acceptable or not – for logical postulates. We see the main problem was unclarity on the nature of logic in general, and in particular whether certain axioms, principles or rules were logically valid, such as the Axiom of Infinity; and a secondary problem was finding an acceptable boundary line between logic and mathematics. I shall say more about these issues in the course of this paper. It should of course never be forgotten how blindingly new modern logic really is, considering the considerable age of logic; how long it took philosophy to recover from the cultural devastation of the Dark Ages; how late the great publications of Frege came; and how long the great predecessors of Frege and Russell, Leibniz and Bolzano, remained largely unpublished or unread in old journals, virtually unknown among academic philosophers. People’s judgments concerning mathematics and logic are dominated by intuitions which stubbornly resist change and remain anchored in the half-knowledge and prejudices of their age. 2. T HE U NCERTAIN B OUNDARY BETWEEN L OGIC AND M ATHEMATICS At the beginning of the twentieth century, when the Logicist claims of Dedekind, Peano, and especially Frege and Russell first attracted attention, Henri Poincaré, always somewhat conservative, doubted the new doctrine. To be sure, there is a certain justice to one of Poincaré’s objections to Logicism: that it illicitly hijacks mathematical motifs into its new logic, and only by doing this can it get the Principle of Complete Induction, for example. Frege’s theory of relations was “brand new”, not accepted in the classical cannon of logic, because this was monomaniacally fixated on the (monadic) subject-predicate forms of Syllogistics, due to Aristotle’s domination of Scholasticism. Hence Poincaré, with seeming plausibility, could argue that Frege’s treatment of concepts as functions (enthusiastically taken over by Russell as “propositional functions”) simply incorporates mathematical functions right into the basis of the new logic. Thus, Frege’s

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(1879) reduction of complete mathematical induction to ancestrals of relations could be seen as a reduction of mathematics to mathematics, so far as relation theory is regarded as a theory of (mathematical) functions in disguise. Despite Poincaré, most people nevertheless agreed that relation theory naturally did belong to logic, simply because relations treated as two-placed (dyadic) predicates so obviously seem to be extended from the notion of one-placed predicates, used in Syllogistics, as the grammar of ordinary language persuades us. In addition, despite the “second-rank” status of the logic of relations, various principles belonging to it are repeatedly mentioned or used in traditional logical literature, where it seemed to take a natural place, prominently even in Aristotle. In retrospect it seems amazing to us now how hard a struggle Leibniz, perhaps the most brilliant philosopher in history, had with relations and orderings.10 Much more deeply perplexing was the status of Cantor’s set theory, to which Whitehead & Russell devoted major attention in the Principia Mathematica. Set theory was in a long tradition of generalizations in algebra, especially applications of function theory using the notion of series. Sets obviously fit into the mathematical zoo together with groups, fields and series. Russell saw no problem reinterpreting set theory as logic, since sets were easily identifiable with classes interpreted as extensions of one-place attributes or predicates.11 Here Russell was influenced by Frege’s notion of “range of values” (Wertverläufe); Russell already had clearly enough spelled out his view independently of Frege in his Principles of Mathematics (1903), following traditional lines established by Venn, Boole and Dodgson (Lewis Carroll) on the way in which extensional classes are related to intensional properties: Just as Frege had characterized his “Sinn” as “die Art des Gegebenseins eines Gegenstands” (sense is the manner in which objects are presented), Russell originally thought of classes as being generated by intensional procedures.12 That is, every (intensional) property has a procedure which discriminates objects satisfying the property into a class obtained by running through the procedure. Russell naturally supposed that intensions were mental, in the tradition of Idealism, whereas classes (or sets) were thought to be extra-mental, quasi-physical (Gödel).13 Russell’s approach seemed to crash into a dead end when Zermelo (1903, 1908) published his famous proof of the Well-Ordering Theorem using his newly discovered Axiom of Choice (AC). The Axiom of Choice immediately became a great bone of contention between Constructivists and Platonists (or Realists).14 Russell had by this time, after his pioneering study on Leibniz (1900), become a Platonist and was perfectly willing to grant the validity of the AC (which Whitehead had discovered independently of Zermelo and had called the Multiplicative Axiom), especially since the AC was crucial for several famous mathematical theorems, as Zermelo had made clear. But what did worry Russell quite a bit was that the AC seemed to guarantee the existence of sets independently of generation by any intensional classification procedure. If the AC somehow was a characteristic set theoretical axiom, this fact seemed to imply that sets were sui generis and existed independently of being generated by any (mental or logical)

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classifying procedure; or similarly, that they were “quasi-physical” in Gödel’s term. Consequently set theory now seemed to Russell to be independent of logic! Frege also came to just this conclusion after Russell sent him news of his famous Antinomy in 1902, and Frege abandoned the disgraced Grundgesetz V which converted equivalences of intensional properties into identities of extensional sets. Apparently as a result of breaking the previously assumed bond with the mental, most mathematicians began regarding sets as quasi-physical entities sui generis, typically beginning with the famous “purely mathematical” notion of the null set and iterating all other sets from that narrow starting point. I don’t see what the fuss is about. Russell should have interpreted the AC not as divorcing choice sets from intensional classifications (i.e., concepts), but rather as simply making the admittedly rather powerful claim that, even in the infinite, some selection procedure can always be devised by a sufficiently strong mind to generate any choice class. (The “strong mind” simply runs through all subsets, randomly selects a member of each and assigns it to the choice set.) This is perfectly compatible with Idealism; the problem is merely that it accentuates the theological, perhaps Hegelian, side of Idealism; in particular, the strong mind generating the choice class would be outside the realm of the elements. Mathematics routinely makes many extreme and transfinite rationality assumptions like this, e.g. that ʌ can be uniquely determined by the completion of an infinite calculation. Mathematicians accept transcendental numbers which can’t even be calculated like ʌ . So then what’s so special about the AC? I say: not much! Ramsey (1926a, §V) himself was sure that under his interpretation the AC was “the most evident tautology” (albeit, under Russell’s original interpretation, the AC was “really doubtful”). Moreover, all sets, just like the classes in von Neumann–Bernays set theory, can be regarded as extensions of properties; and indeed all sets, whether Zermelo-Fraenkel’s or von Neumann–Bernays’s, can be reduced to intensions, as Carnap, Church and others later showed from the forties onward: Set theory can always be embedded within concept theory. I will return to this later when I discuss Quine’s Set Theory and Its Logic. 3. T ROUBLES WITH T YPE T HEORY , R AMSEY ’ S R ESCUE , AND V IENNA By the twenties, opinions on the success or failure of Logicism focused on Russell’s Type Theory, since Russell was the most prominent Logicist.15 It was a serious mistake to restrict such opinions to Type Theory without also considering Zermelo’s axiomatized set theory of 1908, later extended by Fraenkel, since set theory competes with Type Theory as a logic. Frege could or even should have taken the path of using Zermelo’s comprehension axioms instead of his Grundgesetz V. Frege’s Logicist program thus became unfortunately and unnecessarily tied to the misfortunes of Russell’s procrustean Type Theory. A balanced assessment of Logicism’s fate taking set theory into consideration would have resulted in a much more favorable reception by the ’30s. To be sure, Type

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Theory is to an extent completely natural the way it forms hierarchies; but the restrictions it poses on theory formation makes it at the same time distressingly unnatural, forcing us into contortions when approaching even elementary mathematical problems. For example, in analysis, it leads to rather artificial difficulties with the concepts of limits and accumulation points. Such problems provided Quine (1940) with his principal motivation for using set theory rather than Type Theory. Thus attention was fixated on the special problems which Type Theory faced, which the main alternative, Zermelo’s set theory, did not. Briefly, those problems included 1) the Byzantine labyrinths of ramified types and its horridly ad hoc Reducibility Axiom, and 2) the Axiom of Infinity, needed in order to obtain number theory on the third type level. In addition, 3) the Axiom of Choice (AC) was regarded as somehow more dubious in Type Theory than in set theory, because it seemed less plausible to consider it to be logically valid than as mathematically useful. At this point, the young and promising Ramsey entered the picture, amazingly gifted and solid both in his technical mathematical ability as well as in his philosophical judgment. And he was a glowing adherent of the idea of Logicism, so he was very set on revising Type Theory sufficiently to persuade philosophers and mathematicians of the virtues of Logicism. This effort early on caught everyone’s attention in the Vienna Circle, from Hahn’s to Carnap’s and the younger students like Gödel’s. Most attractive was Ramsey’s elimination of ramified types and the concomitant Reducibility Axiom,16 immediately making Type Theory much more presentable. This was Ramsey’s main influence on Carnap’s Logical Syntax of Language (1934), duly honored by Carnap in §60a and elsewhere in that work. Ramsey’s approach was guided by his famous classification of antinomies into two classes, which we may call intensional and extensional, or perhaps better semantical and object-theoretical; Ramsey found that Ramified Type Theory was needed to deal with semantical antinomies like Richard’s Paradox, but not needed to deal with object-theoretical antinomies like Russell’s Paradox. Ramsey proposed ridding Type Theory of intensions (whose semantic nature was only implicit before Tarski) and moving to a purely extensional theory. This move ironically contravened a prior move of Russell’s for which Russell had become famous, viz. the so-called “no-class” approach, whereby an entire ontological category was subjected to Occam’s razor, leaving only intensional propositions and propositional functions. (Tarski furthermore pointed out that only one category is needed here, since propositions could be construed as zero-argument propositional functions.) Ramsey preferred wielding the razor in the other direction, and the extensionalists generally approved. That included Carnap at the time. In fact, Carnap’s extensionalist formulation of Type Theory in his Abriss der Logistik (1929, §30), the first textbook of mathematical logic for philosophers, has long been regarded as the standard in the field. Carnap was personally directly indebted to Russell, who had written out in longhand for him the main definitions and theorems of

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Principia Mathematica in the early twenties when it was impossible for Carnap to purchase any books. Church (1940) finally provided the definitive formalization, later (1951) extending this to a sophisticated formalization of intensions and extensions, close to Russell’s original motive, although directly aimed at explicating Frege. But as we all know, Carnap (1947) himself became a famous intensional logician, placing meaning at the center of logic again – this time using Tarski’s quasi-Hilbertian metatheoretical approach. It is appropriate at this place to insert an anachronistic remark concerning Quine’s much later, didactically brilliant treatment of Type Theory and set theory within one homologous setting in his Set Theory and Its Logic (1963). Usually this book of Quine’s is taken to imply that Type Theory is just a variety of set theory, in a way pushing Ramsey’s approach to its natural conclusion. This then suggests, however, that Type Theory is really as “mathematical” as set theory is usually held to be, whereas the older, intensionally-oriented view was that Type Theory was “logical” because it explicitly dealt with concepts (“propositional functions”), whose intensionality implied semantics – and semantics had been naïvely but perceptively (and correctly!) called “psychological” by both Ramsey and Carnap in the ’20s. But au contraire , Quine could have drawn quite the opposite conclusion from his homologization, namely that set theory is at least as logical as Type Theory – and as a follower of Russell he really ought to have done so. However Quine was perhaps constrained by his famous prejudice against intensional theories, which he didn’t like and preferred to avoid, no matter how inherently logical and traditional they were. Therefore, although Quine’s main program originally was to improve on Type Theory in deriving arithmetic, he was curiously poorly motivated to rescue Logicism. 4. R AMSEY AND C ARNAP ON THE A XIOM OF I NFINITY Once the main problem of Russell’s original Type Theory was removed by Ramsey, the Axiom of Infinity (AI) took center stage as the remaining serious bone of contention. Ordinary Type Theory cannot be revised to avoid this axiom, however, without sacrificing much of mathematics, which requires the existence of infinite sets. The problem is that, looking at type level 0, we aren’t sure if the universe has infinitely many particles in it.17 But we need that many to obtain infinite sets at any level above 0. Thus is AI usually interpreted to be an empirical claim. Ramsey (1925), at the end of his “Foundations of Mathematics”, gave a nice argument showing that, however many individuals n there may exist at type level 0, the proposition that it has exactly n individuals will be tautological, and that it has > n individuals is contradictory; from which he concludes … the Axiom of Infinity in the logic of the whole world, if it is a tautology, cannot be proved, but must be taken as a primitive proposition. And this is the course which we must adopt, unless we prefer the view that all analysis is self-contradictory and

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meaningless. We do not have to assume that any particular set of things, e.g. atoms, is infinite, but merely that there is some infinite type which we can take to be the type of individuals.

By “some infinite type” Ramsey means “some type level with infinitely many classes”. But we might ask immediately: must all types be < Ȧ ? What about a type levels beyond the infinite? We will always have all the mathematics we want at levels • Ȧ ! And, without AI, we don’t care that number theory and analysis are invalid at levels < Ȧ . Hilbert (1926, p. 184) already proposed transfinite types, and Gödel (1931) suggested them concerning attempts at completeness. Wolfgang Degen (1993, 1999, 2000) has worked with great success on exactly this idea, “vindicating” Logicism. Of course, conservative theoreticians may protest that transfinite types are egregious monsters. But set theory also is exceedingly generous – no one blinks at ℘(Ȧ) or at 2ℵ3 . It just has betterstreamlined axioms. Those prejudiced against any reduction of arithmetic to logic such as Poincaré would no doubt find something to complain about, come what may.18 Ramsey considered the Axiom of Infinity an extra-logical proposition which could be tautological, depending on whether the universe contained infinitely many bodies. Russell before him was more straightforward: he conceded that it was even an empirical proposition; most others followed him in this. As much as others, Carnap of course disliked this mixing of logic with empirical considerations when the derivation of arithmetic depended on it, and he figured out in his Logical Syntax of Language (1934, §§3, 15) a way of verifying the Axiom of Infinity in ordinary Type Theory without assuming any knowledge of the number of individuals: let the level-0 objects simply be positions in dimensions (whose metric properties are left unspecified, e.g. the units used).19 This avoids making specific empirical existence claims, yet makes the Axiom of Infinity logically plausible – because our scales of measurement can have infinitely extended dimensions without the existence of infinitely many or infinitely large bodies. Be that as it may, Carnap had little influence with his idea, although it really deserved consideration. Thus, primarily because the Axiom of Infinity was regarded as not logically valid, Logicism was held to have failed. Gödel flatly regarded it as a failure, AI being partly responsible, in addition to Gödel’s strict interpretation of Logicism as requiring completeness. Wittgenstein also had become very negative towards Logicism, but for quite different, possibly ideological or aesthetic reasons which moved him towards ultrafinitism in logic and opposition to higher types and quantifiers, a position I find hard to accept as a serious one for scientific research because it utterly weakens logic. Other mathematicians, in particular those in the Hilbert school, shared Gödel’s view.

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5. C ARNAP THE L OGICIST? By the mid-thirties, after Carnap’s famous Logical Syntax of Language appeared in Vienna in 1934, a reassessment of Logicism seemed to be called for even by its most enthusiastic partisans. I can’t go into much detail here, but fortunately Herbert Bohnert (1975) has written a profound and fascinating review of the development of Carnap’s thinking about Logicism, so this is not necessary. Suffice it to say that Carnap (1934, §84) unfortunately withheld the core claim of classical Logicism: that of reducing numbers to concepts – despite his effort in making the Axiom of Infinity a logically plausible proposition.20 Carnap followed Hilbert’s idea – which was also Gödel’s practice in his Incompleteness Theorem (1931) – of putting natural numbers at type level 0, and so all number theory automatically became available at level 1 of Carnap’s version of Type Theory already, and Peano’s axioms followed straight out of the syntactic metatheory. This made a Frege–Russell definition of numbers superfluous, which is only mentioned in passing (in the context of a discussion of Russell’s elimination of classes as entities separate from concepts in § 38). As Bohnert has it, Logicism then shriveled to the mere statement that logic and mathematics simply belong together. In a sense, this confirms Poincaré’s suspicion that Logicism hijacked mathematics; but Poincaré was an old-fashioned Kantian and insisted that mathematics differed essentially from logic by having content and being based on intuition, whereas logic was empty, as Kant thought. Carnap’s rejection of intuition in his Syntax made it easy for him to put logic and mathematics together. It should be stressed, as Hao Wang has done, that Frege (like Bolzano and Leibniz before him) already emphasized that the basic reason why mathematics is logical is the simple fact that its laws, like the laws of logic, apply to everything: they are in a precise sense super-universal. Mathematics shares with logic the semantic function of theoretically representing reality; both equally involve truth. They are super-universal: they are more universal than physical laws because they are valid no matter what the empirical universe is like. (In Leibniz’s classically baroque image, they hold in all possible worlds!) Wittgenstein totally deflated this hyperbole and persuaded Schlick, Hahn and Carnap that both mathematics and logic are universal because they have no empirical content, i.e. are tautologies. I would like to point out that this claim, which in the first instance seems rather trivial, in fact amounts to a crucial correction of a bad error of traditional Platonism: this often was made to say that mathematics (e.g. geometry21) only applied (strictly) to “ideal objects”, whereas “real objects” never satisfy mathematics exactly. Despite Frege, and despite protests from Occam to Berkeley against the illegitimate dualism of both ideal and real objects, very many naïve people22 say that mathematics deals with a special domain of abstract (“ideal”)

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objects like sets and numbers, often called “structures”, in distinction from empirical science, which deals with concrete (“real”) objects. This is all nonsense, and Berkeley’s (and Neurath’s) scathing criticism of Platonist Verdopplung is quite correct. Plato himself knew this criticism perfectly well, as the second part of Parmenides makes clear; but he had no suitable answer. Frege did. To see the point, just consider that all the allegedly non-empirical (“abstract”) sets and numbers magically gain empirical content the minute mathematics is applied: in a mathematically formulated physics, all functions and all sets used are physical concepts. For example, the n-tuple assigning magnetic field strength to points in space is the magnetic field itself. Classic authorities have claimed logical validity, or analyticity, to be characterized by what I have labeled “super-universality”. Leibniz of course did so; Bolzano as well. More recently Schröder (1890) did so, and Skolem followed him. Carnap also tried very hard to define Allgemeingültigkeit as the culmination of his Syntax-program, being helped by Gödel in his effort. Unhappily the definition failed, in my opinion, because he failed to realize how unlimitedly powerful the theoretical apparatus he needed for his syntax language. Two remarks are apropos. First, there is an even more fundamental reason why Carnap’s characterization misses the essence of logical validity, and why his approach opened him to the criticism of Quine against the analytic /synthetic dichotomy. Universality plainly and simply cannot be used to distinguish between logic and mathematics, because mere universality does not give us any modal distinction between logical and physical necessity. Second, it is an interesting and deep historical fact that the Leibniz–Schröder–Skolem concept of universal validity in all subject domains is identical with Aristotle’s main characterization of metaphysics! Therefore, to find out what logic is, it will pay to look at Platonic Dualism in more detail, this time avoiding the errors of Verdopplung which even Plato made fun of in his dialogues (e.g. the second part of the Parmenides). 6. T HE R EAL N ATURE OF L OGICAL V ALIDITY The distinction underlying Platonist Dualism which really makes sense is the modal distinction for which Hume became famous in his analysis of “Is” and “Ought”. (Concrete) Reality is Hume’s “Is”, (Abstract) Ideality is Hume’s “Ought”. No “Is” implies an “Ought” and vice versa : the Naturalistic Fallacy is to be avoided. The Abstract and Concrete by themselves are not the basis for Platonic Dualism, since both always appear together anyway; as Aristotle observed for matter and form, they’re inseparable. Example: we have electromagnetic fields all over Nature, they are part of empirical reality. Yet if we look carefully at the definition of such fields, we cannot escape that they involve highly theory-laden structures associating vector forces with positions in space in a complex, multi-dimensional manifold.

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This distinction between Ought and Is (or between the Ideal and the Real) quickly sets the stage for clarifying the famous analytic /synthetic distinction. As we all know, discussions of the true nature of logic typically devolved to a search for some acceptable characterization of analyticity. The Vienna Circle thought it lay in Wittgenstein’s Tautology. Carnap struggled to extend the domain of tautologies to all mathematics in his Logical Syntax program, an effort which famously earned the negative judgment of Quine (1951), who complained that Carnap had only promulgated a Dogma of Empiricism without providing a plausible common feature of analyticity in all the various systems allowed by the Principle of Tolerance. There is no general, non-arbitrary non-modal characterization of logical truth for all of the infinitely many language systems. Quine’s critique was justified up until 1965, when Carnap finally revealed to an astounded group of top philosophers of science that (rational) intuition was what justified belief in logical principles and rules. Alas, Bohnert, whose papers on Carnap’s views on both Logicism in particular as well as on the analytic/synthetic distinction in general are wonderfully perceptive, almost completely missed this epoch-making event in the history of Logical Empiricism. Bohnert refers to intuition mainly to affirm the well-known fact that it was “officially” rejected among orthodox Logical Empiricists ever since the twenties, when Hahn and Schlick determined that Kant’s Anschauung was too broken to fix, a view almost everyone followed, from Richard von Mises to Hans Reichenbach (except the phenomenologist Kaufmann and the Platonist Gödel). Nevertheless Bohnert has several quite interesting things to say regarding intuition. He expresses an interesting opinion, although rather non-commitally, that Carnap had a “significantly ambivalent attitude toward the power of man’s intuition, both in general and as applied to matters of logic and mathematics”.23 Bohnert is exonerated from not paying attention to a paper Carnap (1968) held under the heading of inductive logic, because Carnap apparently didn’t mention intuition to Bohnert during the several-day-long discussions they had on logicism in 1968, two years before Carnap’s death. In connection with learning logic, Bohnert does stress the pragmatic aspects of learning meanings – the foundation for judgments of logical validity: first that they begin in childhood, and they “seep” gradually wider and wider, interlocking more and more. Bohnert discovers that this very pragmatic view was already hinted at in the Logical Syntax of Language §38a, p. 142. This insight is important, since it captures exactly how intuition develops from vague gropings to gradually increasing certainty and precision. The history of mathematics, logic and statistics – to say nothing of that of law, accounting, measurement standards and many other areas of norms – confirms that at every stage in their development, intuitions are refined, corrected, polished, extended more and more. What’s more, pragmatic criteria for acceptance of principles and rules were always admitted by Carnap throughout his career, even in the medium-rigorous, apparently anti-semantical period of the Syntax program. The best discussion of this key aspect is by Bryan Norton (1977), who argues (correctly in my opinion),

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that it is precisely with reference to pragmatic motives and interests which lend objectivity to formal abstractions, grounding discriminations of validity of logic. 7. A FFINITIES BETWEEN R AMSEY AND C ARNAP In the 1950s, Carnap came much closer to Ramsey’s philosophy after reading Shimony (1953, 1955), who first discovered extremely important connections between Carnap’s confirmation theory and the subjective probability theories of de Finetti (1937) and Ramsey (1926), particularly between Carnap’s concept of regularity and the Ramsey–de Finetti concept of coherence. The culmination of that work was Carnap (1962). Another area where Carnap was deeply influenced by Ramsey was empirical theory construction, for which Carnap (1958, 1966) made famous use of so-called “Ramsey-sentences”, first introduced in Ramsey (1929). But Carnap had something much more deeply in common with Ramsey, and that was his general approach to philosophy and its relation to human concerns. Ramsey (1929, pp. 263, 269) wrote In philosophy we take the propositions we make in science and everyday life, and try to exhibit them in a logical system with primitive terms and definitions, etc. Essentially a philosophy is a system of definitions … The chief danger to our philosophy, apart from laziness and woolliness, is scholasticism, the essence of which is treating what is vague as if it were precise and trying to fit it into an exact logical category. A typical piece of scholasticism is Wittgenstein’s view that all our everyday propositions are completely in order and that it is impossible to think illogically.

Carnap (1950, Ch. 1) wrote a famous chapter on the methodology of explication, which is central to all good philosophy, and nothing could be closer to the spirit of Ramsey (1929) than that! In particular, although both were strongly influenced by Wittgenstein, both opposed him on the exactly the same issue: both participated in the ideals of the Enlightenment of using reason constructively to improve knowledge and thereby to improve man; whereas Wittgenstein was a pessimist in the tradition of Schopenhauer and Spengler, cynical about improvements through reason (something Wittgenstein and Heidegger have in common). Ramsey was no doubt much more gifted than Carnap in mathematics and in original theorizing, but their principles were in remarkable harmony. One may say the underlying principle behind this harmony was applying a strong faith in the Testability Criterion of meaning to solve philosophical problems, strongly emphasizing the scientific nature of philosophy: Neurath’s Unity of Science !? The central question always was: What is the “cash value” of a concept? What kind of data can we find to decide an issue? This implied a strong motivation to look for technical tools and willingness to legislate new norms (Carnap’s explications and “language engineering”) and assuming responsibility for solid craftsmanship. It was the Testability Criterion that was behind their

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common interest in betting quotients to measure strength of belief; simultaneously both gladly imposed norms of rationality on how beliefs should evolve. Similarly, both worked hard to find the occult power of theoretical concepts, both fully appreciating the key role they play in science and its evolution. It’s unfortunate they didn’t meet in Vienna, but Ramsey was too much involved with the always troubled Wittgenstein, as well as with his own intensive psychoanalysis. (Apropos psychoanalysis: Ramsey, Carnap and Gödel all got deeply involved in extended psychoanalyses of dubious value.) A major difference between them was their divergent attitudes towards Realism, which Carnap (1928; 1934, § 17), the ultra-Conventionalist, was famous for opposing, whereas Ramsey was quite at home with Russell’s post-Idealistic Platonist Realism.24 For example, Ramsey (1925; 1931, p. 21) insisted that Richard’s paradox is not merely linguistic, as Peano claimed, but constitutes a violation of logical rationality. Calling it a mere linguistic faux pas amounts to an invitation to both logicians and linguists to dismiss it; it absolutely requires solution, and The only solution which has ever been given, that in Principia Mathematica, definitely attributed the contradictions to bad logic, and it is up to opponents of this view to show clearly the fault in what Peano calls linguistics, but what I should prefer to call epistemology, to which these contradictions are due. (1931, p. 21)

Thus Ramsey, the champion of Realism. (No wonder he became disenchanted with Wittgenstein.) Carnap’s Conventionalism of the Syntax period would seem to put him opposite Ramsey here, but in fact he was much closer than it appears. First of all, Ramsey’s Realism is strongly qualified by what may be called Cognitivist Behaviorism – to be seen in Ramsey’s explication of knowledge in terms of reliable causal chains, where observation and inference “behave” correctly; also to be seen in Ramsey’s (1929a) “explication away” of theoretical concepts as otherwise unspecified existentially quantified variables.25 Conversely, Carnap was passionately interested in logical legislation just like Ramsey. Carnap was a language engineer, but for him language was the tool of epistemology subject to pragmatic criteria which were not nearly as arbitrary as Carnap pretended at the time. Like Ramsey, Carnap was willing to put ordinary language and “conventional” philosophical traditions far behind. In a specific sense, Carnap was a closet Platonist all along. Prime evidence for this is his insistence on separating all logical sentences in the Syntax (and throughout his later research) into analytic and synthetic ones, tertium non datur, leading to his debate with Quine in defense of just this distinction. Carnap’s Kantian Apriorism was holding tough (and Kant was a Platonist in this sense). Surely Ramsey would have been on Carnap’s side here. Carnap himself ultimately solved his confusion by acknowledging fallibilistic intuition, a position whose consequences he had no time left to explore.

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Both Ramsey and Carnap side with Realism on the issue of permitting nonconstructive concepts, the logical core of the issue concerning Mach’s banishment of theoretical concepts. Ramsey (1925; 1931, p. 37) wrote My method, on the other hand, is to disregard how we would construct them, and to determine them by a description of their senses or imports; and in so doing we may be able to include in the set propositions which we have no way of constructing, just as we include in the range of values of ij x propositions which we cannot express from lack of names for the individuals concerned.

This is exactly the approach Carnap takes to his “indefinite” Language II in his Syntax (1934, Ch. III), where e.g. “indefinite” (impredicative) concepts are admitted, and the non-constructive notion of logical consequence (Folgerung) is admitted, in contrast to the constructive notion of proof (Beweis) of his Language I. Similarly, Carnap (1956) freely allowed all logical methods in his work on empirical concept formation. Incidentally, Carnap was encouraged by Gödel to use just such concepts in his Syntax; and once, after a talk Carnap gave at Neurath’s apartment on psychological (psychoanalytic) concept formation, Gödel reminded Carnap that he (Gödel) had recommended dropping the usually imposed restriction on empirical concepts that they be directly (constructively) definable. As Russell had pointed out during the heyday of Platonistic Logicism, a “robust sense of Realism” forms an essential component of the motivation for successful research. Judging by the logical conventions he actually made, Carnap was behaving for all the world like a robust Realist. 8. G ÖDEL ’ S I NCOMPLETENESS , AND H IS E QUATION OF S ET T HEORY WITH P ROOF Finally, I’d like to close with a comment on Gödel’s position. I mentioned that Gödel thought Logicism was a failure because of problems with Type Theory. But there has arisen the widely held view that Gödel’s Incompleteness Theorems refute Logicism as much as they refuted Hilbert’s Program; the reason being that no specifiable theory can ever provably contain all mathematical truths. Indeed, Gödel showed earlier than Tarski that truth for any theory is not definable within that theory; this follows easily from the first Incompleteness Theorem. Many decades later, for example, Harris and Parrington (1977) first showed that combinatorial complexity theorems of the sort first discovered by Ramsey (1928), including Ramsey’s Theorem itself, although patently number theoretical, cannot be derived in second-order Peano arithmetic. Even certain much weaker Diophantine equations require assumptions from higher analysis to prove. Wilder’s recent proof of Fermat’s Last Theorem also used, apparently essentially, some very exotic higher analysis. Hence it seems the Frege–Russell program of formalizing a logic and then deriving mathematics from that formalization is doomed to failure.

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I disagree. Logicism is not inalienably anchored to any specific formalization of logic, nor is it necessarily forced to derive all possible mathematics. The Harris–Parrington proof did not show that Peano arithmetic failed tout court, it showed rather that Peano arithmetic needs extension: “generally accepted” proof rules or logical axioms need strengthening – whereby it is a pragmatic matter whether to strengthen rules or axioms, which Frege emphasized. Although Frege strove of course for high rigor, he made no absolute claims that his axioms and proof rules were definitive. He did not even specify any absolute criterion for formalization; in particular, he did not demand finite axiomatizability, an assumption made by those who think Gödel’s Incompleteness destroys Logicism. After experimenting with exactly one proof rule in (1879, §6), namely modus ponens, Frege later settled for a small number of finitary rules in (1893, § 48) of a sort which Hilbert regarded as models for his finitary approach. However, Frege had no clear idea whether his list of rules were “complete”, only that they seemed strong enough to prove the theorems he aimed for. Frege (1879, §6) explicitly declares it a practical matter how many proof rules should be used and what strength they should have: In logic, one counts a whole series of inference rules (Schlussarten), according to Aristotle; I use just this one – at least in all cases where, from more than one theorem (Urtheil), a new one is derived –. … Thus, an inference following any kind of inference rule can be reduced to our case. Since it is accordingly possible to make do with a single inference rule [modus ponens], the need for perspicuity [Übersichtlichkeit] therefore calls for doing so. Moreover it may be added that there would otherwise be no reason to stop with Aristotelian inference rules, but that we could indefinitely continue adding new ones: out of every theorem expressed in a formula in §§ 13 to 22, a special inference rule could be made.

The demand for perspicuity could subsequently be contravened by the contrary demand for brevity, therefore this does not rule out, writes Frege (1879, p. xiii), that, at some later time, transitions from several theorems to a new one which are possible only indirectly with this single rule could be transformed into a direct one by taking a shortcut. This may indeed be recommendable in later applications. New inference rules would thereby come about.

Thus, Frege (1893, §48) lists eight inference rules, four substitution rules and six rules for parentheses. It is clear that, in general, Frege allowed theorems to be transformed into proof rules. But then what can stop a follower of Frege from converting any transfinite axiom or theorem into a corresponding transfinite rule? Now we face the issue of finitary methodology in the sense of Hilbert, which was definitively formulated only in Gödel (1931). (NB: Hilbert never gave an exact characterization of his “finitary standpoint”; that “homework” waited for Gödel to accomplish – thus Bernays.) Frege famously demanded that all assumptions be made explicit and all proofs be without gaps, in order to guarantee

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that nothing extraneous slips in. But Frege was not as much fixated, as Hilbert was, on the Phenomenalist ideal of concretely surveying proofs. In particular, I can nowhere find wording in Frege which explicitly excludes transfinite rules. As far as I can see, Frege would merely require that rules have to be explicitly stated, just like transfinite axioms – the position Carnap (1934, §43; 1935) takes, where Carnap employs transfinite rules to divide all logical statements into analytic and contradictory classes. More specifically, I think Frege would have agreed with Ramsey (1925; 1931, p. 37), quoted in the previous section, that “indefinite” concept formation, and hence transfinite axiomatizations, are permissible. The arch-finitist Hilbert (1931) himself was the first to publish such a transfinite rule, now called the Ȧ-rule, claiming it was finitary; Carnap was the first to put transfinite (“indefinite”) rules to work, although he (1934, §48) denied Hilbert’s claim, backed up by Tarski, who had already broached a similar transfinite rule in 1927. Methodologically, Hilbert’s Program was officially restricted to “concrete intuition” (roughly Kant’s sinnliche Anschauung), but as the perceptive Bernays pointed out, there is nothing much concrete left of even second-order Peano arithmetic, which Hilbert needed to arithmetize his desired completeness proof for mathematics. But Frege was a Platonist who rejected psychologistic / phenomenalistic restrictions to concrete observability and who believed that logical insight enables us to grasp logical structures beyond that which our mere empirical senses give us. So despite the prominence in Frege of what looks like a strictly finitary syntax (Begriffschrift), I think it more likely than not that Frege would have supported Carnap’s tolerant attitude toward transfinite syntax rules – so long as they are clearly specified, so that their applicability is definite. But this utterly changes the picture for those who think Logicism requires finite axiomatizability. It is true that Frege wanted his logic to cover all of classical arithmetic. Frege excluded geometry from this reduction, which he thought to be based on intuition and for this reason not logical – although he did mention geometry as a candidate for formalization using a Begriffschrift, together with physics and chemistry. It is hence not clear after all whether Frege wanted to reduce all analysis to logic, for analysis might contain some geometrical intuition. (Brouwer took a radically different path from Frege’s: whereas Frege “displaced” arithmetic intuition by logical insight (Einsicht, the same term Bolzano used) but preserved a special place for geometrical intuition, Brouwer discounted geometrical intuition as well as logical insight and gave arithmetic intuition the dominant role for all analysis! This is why the Intuitionists’ analysis contradicts most people’s geometric intuition, with its highly unexpected propositions about the continuum). Russell was famously quite cavalier about rigor compared to Frege; but on the other hand, Russell was doubtless much more insistent on reducing everything that mathematics could ever contain to logic – e.g. Cantor’s transfinite numbers. Frege had seen no need for a consistency proof, which would have required completeness. For this reason as well, it is rather unclear “how complete” Logicism is required to be. Of course philosophers of mathematics are well-

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acquainted with the famous debate between Frege and Hilbert on whether mathematics had to specify content: Hilbert’s Formalism “officially” ignored content, so Hilbert shifted the responsibility of mathematics to merely checking for consistency. But as Gödel (1953) emphasized, if one is convinced of the correctness of one’s theory based on one’s intuition of some content, a consistency proof is not crucial. Moreover, a misconception should be cleared up which is frequently overlooked (but not by Gödel): so long as we don’t have a proof of the contrary, a set of axioms in what Gödel called “subjective mathematics” can very well be complete despite the Incompleteness Proof ; we simply can’t prove it’s complete! There are after all, as Gödel (1951, p. 313) emphasized, other ways to “know” mathematics than by deduction, namely by induction or, to avoid equivocation, by probable reasoning, which can after all attain what Gödel calls “empirical certainty” – not to be sneezed at! We can gradually become convinced that a theory is complete if we use it for a time and find it covers everything we can imagine. This is what proponents of a “theory of everything” in physics hope for – spiting Gödel’s first Incompleteness Theorem (which after all holds for any physical theory containing arithmetic as well). There is something very deep in a certain observation of Gödel’s. He pointed out that every particular set theory is equivalent to some proof theory of a particular strength, and vice versa. Ultimately this insight must go back to Hilbert’s (Leibniz’s!) original vision of proof theory as a kind of arithmetic, in order to accomplish his consistency proof – which is what “metamathematics” is for. But Göttingen had to wait for Vienna to embarrass it with Gödel’s negative result before it was clear how the proof concept is to be mathematized: with Gödel-numbering! In the following sense Gödel equates mathematics with logic, although he still distinguishes them: Gödelization actually shows, through coding, how arithmetic is equivalent to a particular proof system – essentially the one Frege had in his more-or-less finitary Begriffschrift. Once Hilbert (1931) began to consider stronger proof rules, we can understand how theories stronger than arithmetic – e.g. various stages of analysis and on to higher set theories – would be equivalent to transfinite proof systems. Such an equivalence by encoding should not be misunderstood: Although proofs can be interpreted as set theoretical calculations, proofs still remain different from sets and are governed by different intuitions. But the equivalence by encoding allows enterprising mathematicians to go from one area to the other to double-check results, or to find results at all, just as Descartes’ discovery of analytic geometry allowed a deeper interchange and mutual enrichment of algebra and geometry. Now Gödel shared with Carnap and many others the idea that logical truth is what follows from the meaning of concepts alone. But meaning is inherently intensional and thus mental – like proofs.26 At the same time, as mentioned before, sets are taken to be non-mental, and indeed quasi-physical, as Gödel repeatedly remarked! 27 But if Gödel’s encoding equivalence is valid, we thereby discover that something mental is equated with something physical. This tantalizing problem I will leave the reader to ponder.

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A PPENDIX : A L ETTER FROM R AMSEY TO F RAENKEL [The following manuscript is contained in Carnap’s papers at the University of Pittsburgh Library (where Ramsey’s papers also are). The formulas are in Carnap’s handwriting. Fraenkel had influenced Carnap to clarify the foundations of mathematics, which ultimately led to Carnap’s Logical Syntax (1934). According to his diary, Carnap met with Fraenkel in Vienna on 14, 15 and 25 March 1928, and Fraenkel presumably allowed him to copy some of the text at that time. We can be rather sure Carnap showed the text to Gödel by the following fall, who studied with him in the winter semester 1928/29 in a seminar on “Philosophische Grundlagen der Arithmetik”, where just the themes of the letter were treated, and regularly met with him in cafés. Others whom Carnap may have shown it would have been Waismann and Kaufmann, but also Schlick, who told Carnap about his correspondence and visits with Ramsey.]

081-38-01 Abschrift Ramsey an Fraenkel. Jan. 26 1928. Howfield, Buckingham Road, Cambridge. ... the fact that the so called "non-predicative processes" were of several essentially different kinds. It has always seemed to me very unfortunate that Russell's use of his Vicious-Circle Principle tended to conceal the fact that the circles he wished to eliminate were of two quite distinct kinds. I think that in a general discussion of non-predicative processes there are three things which should be clearly distinguished. First there is the entirely harmless process of describing an object by reference to a totality of which it is a member; an instance of this is "the tallest man in the room". To this process I do not see that objection can reasonably taken; certainly Russell has no such objection, and it seems to me that perhaps some slight alteration ... [X-d over by Carnap] Secondly there is the process of forming a class which is a member of itself. It seems to me that the objection to this is not that it is circular, since (if the Theory of Types be sound) it is equally wrong to suppose that the class is not a member of itself, but simply that it is nonsense. .. (It has always seemed to me that the arguments by which Russell deduced this part of the theory of types from his vicious circle principle were fallacious, but that the theory was nevertheless right in spite of the reasoning being wrong). Thirdly there is the formation of the non-elementary property of having all properties of a certain sort. It is this that makes the real difficulty, because it does seem as if the property arises subsequently to the collection of properties involved in its definition and so cannot be a member of it; whereas in the first or harmless kind of non-

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predicative process the object described is evidently independent of that way of describing it. Your first example of "the maximum value of a function" is, of course, the harmless kind. In Russell's symbolism it is

( x) (( ∃ y ) ƒ x = f (y) ƒ;;ƒ (z) ƒ x • f (z)) This is a ij1 (x) first-order [formula] and no sort of circle can arise, because only individual and not functional apparent variables are involved. The third or serious non-predicative process only comes in in the proof that the maximum value or upper bound exists, not in the notion of such a value. In Russell's symbolism we can say that if a function ȥ x is defined thus

ȥ x ƒ;;ƒ = ƒ;;ƒ (ij) ƒ f (ij ˆ;;z , x)

Df

we get a danger of a circle. But a definition of the form

a=

{(

x) (ij x)

Df;; the ij

is not circular whatever the form of

ijx. ———————————— ... I thought that by using Wittgenstein's work the need for the axiom of reducibility could be avoided, but he had no such idea and thought that all those parts of analysis which use the axiom of reducibility were unsound. His conclusions were more nearly those of the moderate intuitionists; what he thinks now I do not know. ... I am very glad to find that you still regard Russell as a possible alternative to Hilbert and Brouwer. I had the impression that in Germany he was regarded as entirely superseded. ... Sheffer's Theory of Notational Relativity was a manuscript which he sent to Russell; he said he was going to publish a book but has not yet done so. This manuscript dealt with various problems of combinatory analysis, from which he promised to make most remarkable applications to logic. Neither Russell nor I could in the least understand how the applications were to be made.

———————————— 8th March 1928. P.S. I ought to confess that what I said in my paper about the Axiom of Infinity doesn't now seem to me satisfactory, nor do I know what ought to be said. But the Multiplicative Axiom I don't feel to be so difficult.

C OMMENT ON R AMSEY : I NTUITING I MPREDICATIVE P ROPERTIES It may be possible to understand Impredicativity better using some ideas discussed between Gödel and Wang (1974, Ch. VI; 1996) concerning “idealized intuition”. Boolos (1971) and Parsons (1977) later took up the topic. The main idea is that of “running through” an infinite set somehow in finite time and making a judgment based on the result of applying some operation. I would like to suggest various ways to strengthen the rather simple, quasi-constructive

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approach used by resorting to what may be called “hyper-processes” of perception and inference.28 For example, instead of somehow sequentially running through an infinite set, we might imagine an infinitely large array of receptors (sensory organs) with denumerably many or even continuum receptors wired together in parallel yielding an output in finite time and viewing infinitely much during one observational cycle. Not only that, we could also imagine what may be called “hyper-feedback”, such that the global state of a system is input back into one of the local registers of the system with no wait-cycles (action at a distance). In such a way, we could “amplify” the perceptual and cognitive powers of an ideal mind, obtaining perhaps what Laplace had in mind with his demon. Notice that Maxwell’s demon seems to be like Laplace’s in the first instance, but according to Szilárd’s (1929) explication of Maxwell’s demon, it obeys the laws of thermodynamics actually thought to hold in our universe; whereas Laplace’s clearly cannot; cf. Frank (1932, Ch. II, 1). This is because Maxwell’s demon, although very quick and accurate, is not assumed by Szilárd to execute “supertasks”, whereas Laplace’s demon clearly must to be able to predict the entire future of the universe from a single time-slice: Laplace’s demon must have a continuum of infinitely fast receptors, and he must solve infinitely many differential equations infinitely quickly to make his infinitely complex prediction in finite time. By the way, Parsons (1977) makes an interesting point that the ideal intuition used to iterate sets seems to be incompatible with a widely held view of theology that God cannot be active but is static, because he must be eternal, beyond time and space. This may be solvable by considering cosmologies with non-Archimedean time orderings: a “hyper-universe” could occasionally gain access to a sub-universe through worm-holes, such that, from the point of view of an observer in the hyper-universe, an infinitely long activity in the sub-universe appears to occur instantaneously in the hyper-universe. Of course, succession remains normal. But there are also cosmologies such as Gödel’s where there are closed time loops here and there. These could also be considered in configuring mental processes for ideal intuition. (Our imagination need only be limited by the demand for consistency.) Such hyper-physical processes (super-tasks) would become mental merely by being used in brain functions of an infinite mind in a hyper-world. Intelligence is just process, as Whitehead was wont to say. My guess is that, by proper configuration of suitable processes such as “hyper-feedback” and closed time-loops, an ideal intuition could be established with the capacity to “run through” any impredicative concept, so long as it’s consistent, thereby “verifying” the principle it’s based on. Constructivists won’t be pleased, because their restrictions will be violated; but their restrictions arbitrarily restrict concept formation to what they think is humanly possible – even thought they all go way beyond human capacities anyway. As Ramsey said, human ability to perceive (and reason with) only finitely many objects at once is a merely empirical accident which logic should not be bound by.

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N OTES 1.

2.

3.

Thus the authoritative Barwise (1977, p. vii): “Mathematical logic is traditionally divided into four parts: model theory, set theory, recursion theory and proof theory”. It should also be noted, however, that computer science departments have requisitioned logic as well: most courses taught and textbooks written in the areas of model theory and recursive functions are doubtless taught and written there. And lest anyone surmise that these courses and textbooks are restricted to finitary theories such as Turing Machines, he will be disabused of his error by glancing at IEEE Transactions periodicals in engineering libraries brimming with articles on transfinite machines and continuum game-playing automaton scenarios! All too few know that, in addition to his famous definition of cardinal number, in his Grundgesetze II, Frege (1903) also made considerable progress towards a very beautiful theory of real quantities (Positivklassen). The relation-theoretical notion of the ancestral of a relation (independently discovered by Russell 1901) was already published in Frege (1879). The explication of cardinal number was published in Frege (1884), who first stated all the Peano (1889) axioms, also independently anticipated by Dedekind (1888). Dedekind (1888, p. iii) is clearly a Logicist: “In science, nothing capable of proof ought to be accepted without proof. As reasonable as this demand seems, yet has it by no means been held to in recent expositions [a footnote refers to Schröder, Kronecker and Helmholtz], even in the foundations of the simplest science, namely that part of logic dealing with number theory. In speaking of arithmetic (algebra, analysis) as a part of logic, I frankly mean to say that I hold the number concept to be entirely independent of our notions or intuitions of space and time, but rather that it proceeds immediately from the laws of thought.” [Translation E.K.] So much for Kant! But Dedekind, on p. x of the 2nd edition of his Was sind und was sollen die Zahlen?, also selflessly gives Frege priority to his own discovery of the number axioms. Despite Dedekind’s demand for a reduction of arithmetic to logic, it needs to be emphasized that Dedekind did not actually prove his number axioms from (some version of) set theory, as Frege (1893) did! In the 3rd edition of 1911, well after the appearance of Russell’s Paradox, Dedekind movingly upholds his conviction in Logicism: “When I was requested about eight years ago to replenish the 2nd edition, already out of print, by a 3rd, I had reservations in complying because meanwhile doubt had been thrown on the reliability of important foundations of my viewpoint. Even now I make no mistake about the importance and legitimacy, in part, of this doubt. But my trust in the inner harmony of our logic has not been shaken thereby; I believe that an exact investigation of the creative power of our mind to create out of specific elements a specifically new object, their system [set], which necessarily differs from every one of its elements, will certainly lead to the design of a flawless foundation of my work [Schrift].” This important statement, so different from Frege’s disappointed withdrawal of his Logicist program, was unfortunately not included in the 1963 Dover reprint of Dedekind’s famous brochure. Dedekind seems to indicate some kind of Vicious Circle Principle in his concluding sentence to eliminate membership loops like that of Russell’s Paradox, but Dedekind’s formulation, as it stands, would exclude e.g. even his own Dedekind cuts from analysis. Ramsey (1926, § III) provided a proposal using “predicative functions” to solve this famous problem (see also Ramsey’s letter to Fraenkel in the Appendix of the present article); but ZF going back to Zermelo (1908), unfortunately not referred to by Dedekind, is already thought to have dealt adequately with the problem. Finally, Dedekind’s frank Idealism is notable in his reference to the “mind’s creation of systems”, which clearly distinguishes his Logicism from the strictly anti-psychologist Logicism of Bolzano and Frege. However, in Köhler (2000), I show that neither Bolzano nor Frege can escape psychologism, as the reference to “pure thought” in the subtitle of Frege (1879) veritably concedes. A treatment expressing rather standard negative views was Black (1933), who had studied in Göttingen and who argued that Whitehead & Russell’s Principia Mathematica made essential use of non-logical axioms in its “reduction” of mathematics to logic, violating Logicism’s original intention. In particular, the Axiom of Infinity remains even after Ramsey’s attempt to elimi-

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nate the Axiom of Reducibility. Gödel basically agreed with similar lines of criticism in discussion remarks with Carnap in 1929. 4. Davis (1965) is the standard source book on the original recursion-theoretical (computability) literature, containing classic pioneering papers by Gödel, Church, Turing, Rosser, Kleene and Post, which now form a central part of the computer science curriculum. 5. Ramified Type Theory didn’t even contain the principal semantic relations of naming or satisfaction, to say nothing of logical consequence, so it was very paltry in semantics, and we may really ask: why bother with it at all? In Russell’s Foreword to the English version of Wittgenstein’s Tractatus, he famously called for the creation of a metatheory to solve Wittgenstein’s “puzzles” about allegedly not being able to say what could at best be shown about logical truths. Wittgenstein disavowed Russell’s Foreword; and metatheory had to wait for Hilbert, Carnap and Tarski. 6. The literature on set theory is extremely rich and variegated, ranging e.g. from “topoi” to “fuzzy sets”! For an authoritative treatment of much of set theory, mainly from Zermelo’s point of view, see Fraenkel, Bar-Hillel & Levi (1973); the system of von Neumann–Bernays (NB) is also discussed here, but the main source is Bernays (1958). The standard source for NBG is Gödel (1940). The early history of Z’s reception is dealt with in Moore (1977). For Quine’s NF and ML see Quine (1937) and (1940); but these systems are widely considered non-standard. 7. Originally, Quine (1937, p. 70 f.) put set theory in logic, but later, e.g. Quine (1963a, § II) and Quine (1970, pp. 64–74), he pulled it out again, for methodological reasons: first-order predicate logic is decidable and accepted as a universal standard since Hilbert & Ackermann (1928), whereas set theory is a quasi conventionalist, experimental science; cf. Orenstein (1977, p. 94) and Romanos (1983, § 2.4). This is like punishing logic for bad behavior by cutting off one of its main branches. To be sure, mathematics has misbehaved often, worst of all before Bolzano and Weierstrass cleaned up analysis. If we let the puritan Quine have his way, much of mathematics should, by parity of reasoning, be demoted to the status of accounting rules! 8. The “iterative concept of set” developed by Boolos (1971), Wang (1974, Ch. 6) and Parsons (1977) makes sets seem independent of concepts, but in fact the set-iteration procedures themselves constitute concepts! Remember that concepts are any procedures usable to classify objects, and are identical with Frege’s intensions (Arten des Gegebenseins von Gegenständen). 9. Oddly enough, Frege’s concepts (Begriffe) are in fact not any more intensional than Frege’s objects, as Pavel Materna has shown (they are “functions-in-extension”, in Russell’s terminology), whereas Bolzano’s concepts are truly intensional. 10. Leibniz’s fixation on monadic predicates is of course the main story in the pioneering book by Russell (1900): much of Leibniz’s metaphysics of monadology was dominated by his logic of monadic predicates. Couturat (1901, 1905) followed Russell. Körner (1979) thinks Russell went awry, but authoritative Leibniz-scholars such as Mates (1986), Rescher (1967) and Wilson (1989) largely side with Russell. BocheĔski (1956) and Kneale & Kneale (1962) provide fragments of relation-theoretical logic scattered throughout the history of logical texts; but (of course aside from Frege 1879), the first systematic treatment of relations was Schröder (1890– 1905), based mainly on the incomplete researches of Peirce; and, independently of Frege, Russell (1901). Structural features of relations such as symmetry, transitivity or reflectivity were naturally always felt to belong to logic, despite the tenacious fixation on syllogistics. Of course Poincaré is right in feeling that the same structures are dealt with by mathematical functions (which Frege, Peirce and Russell easily defined in terms of relations) and the algorithms they represent. One may perhaps say logic and mathematics have “equal claim” to relations. 11. The most detailed and authoritative history of logic for this period is Grattan-Guinness (2000); Coffa (1991) also provides very solid philosophical guidance, especially on semantic aspects; Hylton (1990) provides a very illuminating account of Russell’s transition from Idealism to the logic of the Principia and discusses in particular Russell’s approach to comprehension and perception of classes (i.e., sets). NB: Only after von Neumann–Bernays set theory was introduced in the thirties were classes distinguished from sets in the way now widely accepted by mathematicians. Earlier on, Bolzano had a place for them in his ontological panoply of logical objects, identifying sets with manifolds, i.e. Mannigfaltigkeiten. 12. This is close to the classic view of Cantor (1895, p. 481): “By a set ( Menge) we are to understand any collection into a whole (Zusammenfassung zu einem Ganzen) M of definite and sepa-

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14. 15. 16.

17. 18.

19.

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rate objects m (which are called the ‘elements’ of M) of our intuition or our thought.” Dedekind was also a quasi-Idealist. The “collection” follows a “law” according to Cantor (1883, fn. 1): “Theory of Aggregates. With this word I denote a theoretical concept encompassing very much, which I have previously tried to develop only in the special guise of an arithmetic or geometric set theory. By an ‘aggregate’ or ‘set’ I understand in general every multiplicity which can be thought of as a unity, i.e. every quintessence of specific elements which can be combined by a law to a whole; and I believe I am thereby defining something which is related to the Platonic İȚįȠȢ or ȚįȑĮ , as well as with that which Plato calls μȚțIJȩȞ in his dialogue Philebus, or the Highest Good. He contrasts this with the ȐʌİȚȡȠȞ, i.e. the unbounded, indefinite, which I call the improper infinite (Uneigentlich-unendliche), as well as with ʌȑȡĮȢ , i.e. the bounded, and declares it to be an ordered ‘mixture’ of the latter two. That these concepts are of Pythagorean origin is indicated by Plato himself … .” This was not so for Cantor and Dedekind, however, insofar as both let sets be “legislated” by a mind. In Köhler (2001), I argue that the subject–object (or mental–physical) dichotomy is relative, and that both mental and physical interpretations can be found for both intensional and extensional entities in logic. The standard treatment of this famous episode in the history of logic and mathematics is Moore (1982). Immediately concerned is the famous “Vicious-Circle Principle”, first promulgated by Poincaré; see the authoritative treatment by Hallet (1984). This had of course been developed most fully in Whitehead & Russell (1910–13), but Russell originated its main ideas already in 1903 and developed them in detail in 1908 – the same year as Zermelo’s main publication on axiomatic set theory. Linsky (1997) thought the notorious Axiom of Reducibility could indeed be considered logical. The case is not closed. Ramsey’s ideas were discussed inside and outside the Schlick Circle meetings on Thursday evenings, but unfortunately none of the protocols by Rose Rand mention this. Of course, when Ramsey (1931) appeared, it was immediately read and discussed, in particular by Carnap and Gödel, but also by Schlick and Waismann. In correspondence, we have a better idea of what was discussed, and I reproduce a letter by Ramsey to Fraenkel of which Carnap copied a part in an appendix to this paper. Or infinitely wide dimensions. But once we consider “adjusting” dimensions, we will quickly arrive at Carnap’s clever solution of letting the individuals of type level 0 be – not physical bodies but – positions on scales of measurement. See below. At this Point in my original paper, I tendered the idea of proving the Axiom of Infinity – rather than Russell’s assuming it – by adding to the positive types negative ones descending infinitely deep. I thought this plausible on the ground that pure logic should not prejudice the empirical question of how deep the foundation of real objects goes, including whether the foundation is finitely deep. With infinitely many descending types, every type level automatically obtains infinitely many infinitely large propositional functions (or classes, or sets). In the discussion after my paper, Wolfgang Degen objected that no known proof rule could show this. I now conjecture that the situation is far worse: the cardinality of every type probably is immeasurably large, presumably exploding any and all limitations of size which are characteristically employed in the known axiom systems to avoid the paradoxes. So much for my idea of negative types. Carnap obviously came up with this idea through his familiarity with coordinate systems assigning numbers to objects through scales of measurement such as Relativity Theory presupposes; cf. Carnap (1922, 1926). Nowadays we would justify the “logical necessity” that infinitely many indexical positions exist with Carnap’s much later idea of “Meaning Postulates” (1952), which essentially state measurement norms as logic postulates. For example “nothing blue is red” or “nobody is taller than himself ”. Carnap (1963, p. 11 ff. ) was one of the very few students Frege had at the University of Jena; according to Gabriel (1996), only Carnap provided complete sets of lecture notes. Flitner (1986, p. 126f.) describes how Carnap even kept Frege’s lectures alive by motivating other students to attend. Carnap (1929, § 21b), (1950, §6), (1953, §34c) presented Frege’s famous explication of cardinal number as a model for all philosophy and mathematics of how to explicate a concept by characterizing it in terms of more elementary ones. Carnap emphasized that, in contrast to Peano’s

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treatment of number, only Frege’s definition clarified exactly how cardinal numbers are used to count things, thereby proving that the cardinal number concept has to be defined the way he did. One wonders why Carnap didn’t prominently say this in his Syntax (1934) as well. Perhaps he skirted the issue because of the general disaffection with Logicism. Knowing that both Wittgenstein and Gödel rejected it, it was difficult to present a view that did not represent important members of his circle of colleagues, as Carnap strove to present his circle’s position. Geometry is a bad example, since it should properly be reckoned to physics; but it is the example foremost in the minds of Platonists, including Plato himself. Arithmetic, on the other hand, clearly is mathematical; unfortunately it’s not at all a plausible example, as Frege discovered. In Köhler (2002), I provide an explication of Platonism partly based on Gödel’s own definition, although I criticize Gödel for repeating the ancient error of assuming a Verdopplung of object domains and failing to realize that Platonic Dualism is instead based on the fact that mathematical truth has a different modality, namely normative validity. Using this simple insight, I could also solve the famous dispute between Carnap and von Neumann on information theory and entropy in Köhler (2001). My apologies to Gödel; even Frege sometimes says this. Bohnert adds the significant counter that “On the other hand, he had great hope for man’s ability to use formalism to construct an instrument whereby he could double-check intuitions by making them explicit … Indeed, he saw in formalism an instrument capable of leading man over intellectual chasms where his intuition seemed to fail altogether.” These comments are well-motivated but misleading, as “formalism” is also based on intuition, as Gödel insisted and as Carnap should have admitted. After all, the leading formalist, Hilbert, gave concrete intuition the central rôle in his epistemology, a fact consistently avoided in Carnap’s Syntax (1934). Here Ramsey was much closer to the ultra-Platonist Gödel, the “Mozart of mathematics” (Karl Menger), with whom he also shared a great and multifaceted mathematical creativity. A really “robust” Realist would claim that our intuition is powerful enough to see and identify the theoretical entities specifically ; like Russell’s “the king of France”, the variables used for theoretical entities aren’t assumed to denote anything specifically identifiable anymore. Still, by Quine’s famous existence criterion, the mere use of the variables at least implies ontological commitment to something not directly observable. But meaning is also normative, embedded in norms of rationality constitutive of mind, a fact which even Gödel missed, as a consequence of which he and Quine and many others failed to capture the true difference between logic / mathematics and natural science. Davidson’s philosophy makes essential use of just this modal distinction without realizing it. E.g. in Wang (1996), 8.1.9, 8.5.6. In Köhler (2001) and (2006), I treat the relation between the mental and the physical in much detail. On the one hand, I argue that all proofs or any other mental acts can somehow be “physicalized”; but conversely that all sets – as well as all physical objects – can be “mentalized”. The key to understanding this is simply to attend to whether one is on an object-level or a meta-level. The reason why semantics always involves mind is that semantics always uses a metatheory – whose purpose is to describe entire conceptual frameworks in order to reflect reality on some “higher level”, i.e. in some mind. Any attempt to separate theory from mind, as Bolzano, Frege and Husserl tried to do, is impossible, because theories constitute (part of) the knowledge of a mind. What Bolzano, Frege and Husserl really wanted was to distinguish empirical from normative psychology, but they didn’t realize this because they didn’t realize that logic is normative. Only in the title of Frege (1879) may the embarrassing implication be made that “pure thought” is the object of logic; and only later did Kantians widely realize that “pure” means normative. Benacerraf (1963) calls these intellectual processes “super-tasks” in honor of Zeno and the Eleatics. It is clear that the foundations of analysis and the infinitesimal calculus presuppose their existence in some sense or other; and that is a central problem for the epistemology of mathematics. To help understand super-tasks, I propose in Köhler (2002b) that they are to be situated in what I call “hyperworlds”, i.e. quasi-physical universes whose laws permit instantaneous communications which allow infinitely large receptors to observe infinite data, and infinitely fast processors to allow infinite proofs, etc.

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Gottlob Frege (1879): Begriffschrift. Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Louis Nebert, Halle; reprinted Georg Olms, Hildesheim 1964. Gottlob Frege (1884): Die Grundlagen der Arithmetik. Eine logisch-mathematische Untersuchung über den Begriff der Zahl, Breslau; reprinted by Georg Olms, Hildesheim 1961; translated by J.L. Austin, Oxford 1960. Gottlob Frege (1893, 1903): Grundgesetze der Arithmetik, begriffschriftlich abgeleitet I, II, Jena; reprinted Georg Olms, Hildesheim 1962; translated by Montgomery Furth as The Basic Laws of Arithmetic, University of California Press, Berkeley 1967. Gottfried Gabriel (1996): “Gottlob Frege. Vorlesungen über Begriffschrift. Nach der Mitschrift von Rudolf Carnap”, History and Philosophy of Logic 17. Maria Carla Galavotti and Friedrich Stadler (eds.) (2004): Induction and Deduction in the Sciences, Vienna Circle Institute Yearbook 11, Kluwer, Dordrecht. Kurt Gödel (1931): “Über formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme I ”, Monatshefte für Mathematik und Physik 38, 35–72; translated in van Heijenoort (1967); reprinted with commentary by S.C. Kleene in Gödel (1986). Kurt Gödel (1940): The Consistency of the Axiom of Choice and of the Generalized ConinuumHypothesis with the Axioms of Set Theory, Annals of Mathematics Studies 3, Princeton University Press, Princeton; 7th reprinting 1966; reprinted with commentary by R.S. Solovay in Gödel (1990). Kurt Gödel (1944): “Russell’s Mathematical Logic”, in Schilpp (1944); reprinted with commentary by Charles Parsons in Gödel (1990). Kurt Gödel (1951): “Some Basic Theorems on the Foundations of Mathematics and Their Implications”, in Gödel (1995); this is the so-called “Gibbs-Lecture” held at the AMS meeting at Brown University. Kurt Gödel (1953): “Is Mathematics Syntax of Language?”, in Gödel (1995); this was originally intended for the Schilpp volume (1963) on Carnap, but withdrawn. Kurt Gödel (1986, 1990): Collected Works I, Publications 1929–1936; II Publications 1938–1974, edited by Solomon Feferman (editor-in-chief), John W. Dawson, Jr., Stephen C. Kleene, Gregory H. Moore, Robert Solovay and Jean van Heijenoort, Oxford University Press, New York. Kurt Gödel (1995): Collected Works III, Unpublished Essays and Lectures, edited by Solomon Feferman (editor-in-chief), John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert Solovay Oxford University Press, New York. Ivor Grattan-Guinness (2000): The Search for Mathematical Roots, 1870–1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel, Princeton University Press, Princeton. Michael Hallet (1984): Cantorean Set Theory and Limitation of Size, Oxford Univ. Press, Oxford. Jean van Heijenoort (ed.) (1967): From Frege to Gödel. A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge MA. Paul Henle, Horace Kallen and Susanne K. Langer (eds.) (1951): Structure, Method and Meaning: Essays in Honor of Henry M. Sheffer, with a forward by Felix Frankfurter, Liberal Arts Press, New York. David Hilbert (1926): “Über das Unendliche”, Mathematische Annalen 95, 161–190; partially translated in Benacerraf & Putnam (1983). David Hilbert and Wilhelm Ackermann (1928): Grundzüge der theoretischen Logik, Springer-Verlag, Berlin; 4th edition 1959 ; translated as Principles of Mathematical Logic, Chelsea Publishing Co., New York 1950. Jaakko Hintikka (ed.): Rudolf Carnap, Logical Empiricist, Reidel Publ. Co., Dordrecht 1975. Peter Hylton (1990): Russell, Idealism and the Emergence of Analytic Philosophy, Oxford University Press, Oxford. Felix Kaufmann (1930): Das Unendliche in der Mathematik und seine Ausschaltung, Franz Deuticke, Vienna; reprinted by the Wissenschaftliche Buchgesellschaft, Darmstadt 1968; translated by Paul Foulkes as The Infinite in Mathematics, edited by Brian McGuinness with an Introduction by Ernest Nagel, Vienna Circle Collection 9, Reidel, Dordrecht 1978. Hubert C. Kennedy (1980): Peano. Life and Works of Giuseppe Peano, Reidel, Dordrecht.

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William and Martha Kneale (1962): The Development of Logic, Oxford Univ. Press, Oxford. Eckehart Köhler (2000): “Logic Is Objective and Subjective”, in Timothy Childers & Jari Palomäki (eds.): Between Words and Worlds. A Festschrift for Pavel Materna, Filosofia, Prague. Eckehart Köhler (2001): “Why von Neumann Rejected Carnap’s Dualism of Information Concepts”, in Rédei & Stöltzner (2001). Eckehart Köhler (2002): “Gödel und der Wiener Kreis”, in Köhler, Weibel et al. (2002). Eckehart Köhler (2002a): “Gödels Jahre in Princeton”, in Köhler, Weibel et al. (2002). Eckehart Köhler (2002b): “Gödels Platonismus”, in Buldt, Köhler et al. (2002). Eckehart Köhler (2006): “Intuition Regained. Gödel’s Views on Intuition, and How Carnap Abandoned Empiricism by Accepting Intuition as Evidence”, forthcoming, Synthese. Eckehart Köhler, Peter Weibel, Michael Stöltzner, Bernd Buldt, Carsten Klein und Werner DePauliSchimanovich-Göttig (eds.) (2002): Kurt Gödel: Wahrheit und Beweisbarkeit 1. Dokumente und historische Analysen, öbv&hpt, Vienna. Stephan Körner (1979): “On Russell’s Critique of Leibniz’s Philosophy”, in Roberts (1979). Imre Lakatos (ed.) (1968): The Problem of Inductive Logic. Proceedings of the International Colloquium in the Philosophy of Science, London, 1965, Vol. 2, North-Holland Publ. Co., Amsterdam. Leonard Linsky (1997): “Was the Axiom of Reducibility a Principle of Logic?”, in Tait (1997). Benson Mates (1986): The Philosophy of Leibniz, Oxford Univerity Press, Oxford. Gregory H. Moore (1982): Zermelo’s Axiom of Choice, Its Origins, Development, and Influence, Springer-Verlag, Heidelberg. Bryan Norton: Linguistic Frameworks and Ontology. A Re-Examination of Carnap’s Meta-Philosophy, Janua Linguarum, Mouton Publishers, The Hague 1977. Alex Orenstein (1977): Willard Van Orman Quine, Twayne’s World Leaders Series 65, H.K. Hall, Boston. Jeff Paris and Leo Harrington (1977): “A Mathematical Incompleteness in Peano Arithmetic”, in Barwise (1977). Charles Parsons (1977): “What Is the Iterative Conception of Set?”, in Logic, Foundations of Mathematics, and Computability Theory, Proceedings of the 5th International Congress of Logic, Methodology and the Philosophy of Science (London ON 1975), edited by Robert Butts & Jaakko Hintikka, Reidel, Dordrecht 1977; reprinted in Benacerraf & Putnam (1983). Giuseppe Peano (1889): Arithmetices principia, nova methodo exposita, Bocca, Turin; reprinted in Opere scelte 2, Edizione cremonese, Rome; transl. with a biographical sketch by Hubert C. Kennedy: Selected Works of Giuseppe Peano, University of Toronto Press, Toronto 1973. Willard Van Orman Quine (1937): “New Foundations for Mathematical Logic”, American Mathematics Monthly 44, 70–80; reprinted in Quine (1953). Willard Van Orman Quine (1940): Mathematical Logic, Harvard University Press, Cambridge MA; rev. 1951. Willard Van Orman Quine (1951): “Two Dogmas of Empiricism”, in Quine (1953). Willard Van Orman Quine (1953): From a Logical Point of View: Logico-Philosophical Essays, Harvard University Press, Cambridge MA. Willard Van Orman Quine (1963): Set Theory and Its Logic, Harvard University Press, Cambridge MA. Willard Van Orman Quine (1963a): “Carnap and Logical Truth”, in Schilpp (1963); reprinted in Quine (1966). Willard Van Orman Quine (1966): The Ways of Paradox and Other Essays, Random House, New York. Willard Van Orman Quine (1970): Philosophy of Logic, Prentice-Hall, Englewood Cliffs NJ. Frank Plumpton Ramsey (1925): “Foundations of Mathematics”, Proceedings of the London Mathematical Society 25, 338–384; reprinted in Ramsey (1931, 1978). Frank Plumpton Ramsey (1926): “Truth and Probability”; reprinted in Ramsey (1931, 1978). Frank Plumpton Ramsey (1928): “On a Problem of Formal Logic”, Proceedings of the London Mathematical Society 30, 338–384.

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Frank Plumpton Ramsey (1929): “Theories”, in Ramsey (1931, 1978). Frank Plumpton Ramsey (1929a): “Philosophy”, in Ramsey (1931). Frank Plumpton Ramsey (1931): The Foundations of Mathematics and Other Logical Essays, ed. by R.B. Braithwaite with an Introduction by G.E. Moore, Routledge & Kegan Paul, London. Frank Plumpton Ramsey (1978): Foundations. Essays in Philosophy, Logic, Mathematics and Economics, re-edited version of Ramsey (1931) with a different selection of texts, including especially the two papers on taxation and savings, by D.H. Mellor with introductions by D.H. Mellor, L. Mirsky, T.J. Smiley and Richard Stone, Routledge & Kegan Paul, London 1978. Miklós Rédei and Michael Stöltzner (eds.) (2001): John von Neumann and the Foundations of Quantum Mechanics, Vienna Circle Institute Yearbook 8, Kluwer, Dordrecht. Nicholas Rescher (1967): The Philosophy of Leibniz, Prentice-Hall, New York. George W. Roberts (ed.) (1979): Bertrand Russell Memorial Volume, Allen & Unwin, London. George Romanos (1983): Quine and Analytic Philosophy, MIT Press, Cambridge MA. Bertrand Russell (1900): A Critical Exposition of the Philosophy of Leibniz, Cambridge University Press, Cambridge; 2nd ed. Allen & Unwin, London 1937. Bertrand Russell (1901): “Sur la logique des relations avec des applications à la théorie des séries”, Revue de Mathématique (Rivista di Matematica) VII, 115–148; translated in Russell (1956). Bertrand Russell (1903): The Principles of Mathematics, Allen & Unwin, London; 2nd ed. 1937. Bertrand Russell (1908): “Mathematical Logic as Based on the Theory of Types”, American Journal of Mathematics 28, 222–262; reprinted in Russell (1956). Bertrand Russell (1914): “On the Nature of Acquaintance”, The Monist XXIV, 1–16, 161–187, 435– 453; reprinted in Russell (1956). Bertrand Russell (1956): Logic and Knowledge: Essays 1901–1950, edited by Robert Charles Marsh, Allen & Unwin, London. Paul Arthur Schilpp (ed.) (1944): The Philosophy of Bertrand Russell, Library of Living Philosophers V, Northwestern University Press, Evanston IL. Paul Arthur Schilpp (ed.) (1963): The Philosophy of Rudolf Carnap, Library of Living Philosophers XI, Open Court Publishing Co., La Salle IL. Ernst Schröder (1890–1905): Vorlesungen über die Algebra der Logik I–III, Leipzig. Abner Shimony (1953): A Theory of Confirmation, Ph.D. dissertation at Yale University. Abner Shimony (1955): “Coherence and the Axioms of Confirmation”, Journ. o. Sym. Log. 20, 1–28. Friedrich Stadler (ed.) (2000): Elemente moderner Wissenschaftstheorie, Veröffentlichungen des Instituts Wiener Kreis 8, Springer-Verlag, Vienna. Leo Szilárd (1929): “Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen”, Zeitschrift für Physik, 53, 840–856; translated as “On the Decrease of Entropy in a Thermodynamic System by the Intervention of Intelligent Beings” by Anatol Rapoport and Mechthilde Knoller in Behavioral Science, 9, 301–310; the latter reprinted in Szilard (1972). Leo Szilárd (1972): The Collected Works of Leo Szilard: Scientific Papers, ed. by B.T. Field and G. Weiss, MIT Press, Cambridge MA. William W. Tait (ed.) (1997): Early Analytic Philosophy: Frege, Russell, Wittgenstein, Open Court Publishing Co., La Salle IL. Hao Wang (1974): From Mathematics to Philosophy, Humanities Press, New York; Ch. VI “The Concept of Set” is reprinted in Benacerraf & Putnam (1983). Hao Wang (1987): Reflections on Kurt Gödel, MIT Press, Cambridge MA. Hao Wang (1996): A Logical Journey: From Gödel to Philosophy, MIT Press, Cambridge MA. Alfred North Whitehead and Bertrand Russell (1914): Principia Mathematica, Cambridge University Press, Cambridge; the 2nd edition of 1925 included a long new Introduction largely influenced by Ramsey. Catherine Wilson (1989): Leibniz’s Metaphysics: A Historical and Comparative Study, Princeton University Press, Princeton. Ernst Zermelo (1904): “Beweis, dass jede Menge wohlgeordnet werden kann”, Mathematische Annalen 59, 139–141; translated in van Heijenoort (1967).

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Ernst Zermelo (1908): “Neuer Beweis für die Möglichkeit einer Wohlordnung”, Mathematische Annalen 65, 107–128; translated in van Heijenoort (1967). Ernst Zermelo (1908a): “Untersuchungen über die Grundlagen der Mengenlehre I”, Mathematische Annalen 65, 261–281; translated in van Heijenoort (1967).

Dept. of Business Administration University of Vienna – BWZ Brünnerstraße 72 1210 Vienna Austria [email protected]

J.W. Degen

Logical Problems Suggested by Logicism

The mathematics of logic is difficult, the logic of mathematics is even more difficult.

1. Introduction Let us call the Logicist Thesis, or the Thesis of Logicism, or simply Logicism the thesis that [LT] Pure Mathematics is part of Logic. The founding fathers of Logicism are Frege and Russell. Roughly, Frege maintained that (at least) higher-order arithmetic is part of logic, but definitively not geometry, whereas for Russell even all of pure mathematics was to be part of logic. Unfortunately, Frege’s system GGA (Grundgesetze der Arithmetik, 1893, 1903) [6] by means of which he wanted to prove his version of [LT] was shown to be inconsistent by Russell. However, had GGA been consistent it would have proved, provided it is logic, a much stronger version of [LT] than Frege envisaged since GGA contains all of set theory despite the more modest title Grundgesetze der Arithmetik.1 Russell’s manifesto of his Logicism is to be found in his Principles of Mathematics of 1903; it is firmly repeated in the second edition of 1938 [11]2. The formal implementation followed 1908 in Russell’s Mathematical logic as based on the theory of types [12], and then in the Principia Mathematica written with Whitehead, published 1910–13. The second edition of PM of 1927 [14] seems to be still in print. The sentence [LT] as stated above contains three undefined phrases: (1) Pure Mathematics (2) is part of (3) Logic Furthermore, even if these three notions are defined in some way or other, there remains the following ambiguity in [LT]: nonuniform[LT]: For every (sharply delineated) piece M of Pure Mathematics there exists a logic LM such that M is part of LM .

123 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 123–138. © 2006 Springer. Printed in the Netherlands.

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uniform[LT]: There is one universal logic Luniv such that all of Pure Mathematics is part of Luniv . Finally, we have the following weak version of the logicist thesis. weak[LT]: The (or some) main part of Pure Mathematics is part of some Logic. The cautious distinctions just given are necessitated by the mathematical and logical experience between 1903 and 2003. It is possible to refute even the version weak[LT]. For instance, let us say that Logic is just first-order logic, and that each main part of pure mathematics must contain some nontrivial arithmetic. Then weak[LT] is false. Also, even if we admit pure classical type theory CT , i.e. P M \ inf inity as a logic, weak[LT] will become false. On the other hand, if we admit ZF C as Logic, and are not squeamish about the vast incompleteness of ZF C, then we may even argue for uniform[LT]. Considering as the main part of Pure Mathematics ordinary mathematics as known by Russell, namely classical analysis, algebra and certain parts of Cantor’s set theory (below ℵω ) and admitting P M as logic, then at least weak[LT] can be vindicated.

2. Some Preparatory Clarifications In my talk I do not want to refute any of these logicist theses, not even the strongest among them. Rather, I will prove (a version of) weak[LT]. Furthermore, I claim that my proof is non-trivial and will yield new information and logical (or mathematical) problems about the logical (or mathematical) status of CT , P M , extensions and variants thereof. I must admit that a philosophically satisfactory analysis of Logicism should dwell more carefully on big questions such as: What is mathematics? What is Logic? I decide these questions by fiat in order not to impair my message by difficulties extraneous to its (rather precisely statable) mathematicallogical content.3 2.1 Rich Model-theoretic Logics For our purpose, let us define a model-theoretic logic L to be a triple (M, |=, L). Here M is a class of models, L is a language4 conceived of as a class of sentences; and for M ∈ M and ϕ ∈ L we mean by M |= ϕ that M makes ϕ true. By V alid(L) we understand the valid sentences of L, i.e. those sentences which are true in all models M ∈ M. We call a (model-theoretic) logic rich if M is large, i.e. a big set or a proper class of pairwise non-equivalent5 models. If L is rich then V alid(L) captures the intuitive notion of a universally (or logically) true sentence, i.e. a sentence true under all possibilities or true in all possible worlds. Of course, if M consists of just one or two models, then V alid(L) is far from being a set of universally true sentences, in the intuitively required sense.6

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Let now L be a rich logic, and P a part of pure mathematics. We will say that ∗ L (semantically) captures P if there is a syntactic interpretation (−) such that (I) For all results π of P : π ∗ ∈ V alid(L). Thus far, we have not said anything about the way P is presented; nor what it means that π is a result of P . Indeed, we have not said what P really is. It may be a structure or a theory, or an activity or whatnot. However, it must be something definite if we want to prove something about it. Our discussion hitherto is connected with Logicism by the stipulation that the interpretation π ∗ is to be a universally valid sentence of a rich logic. Nothing is stipulated about the genuine or intrinsic logicality of the notions representable by the language L of the model-theoretic logic L. In spite of this generality, several possibilities are already ruled out, e.g., the case that π ∗ is a set-theoretic sentence (of the first-order standard language {∈} of set theory) which is true just in the model (Vω+ω , ∈). But it does not rule out the related case where the model class considered is Mzermelo = {(Vα , ∈) : α a limit ordinal ≥ ω + ω}. Definition (I) gives a semantic version of weak[LT] with respect to the rich model-theoretic logic L, and the chosen part P of pure mathematics. Now, if P is ordinary pure mathematics formulated in set-theoretic terms, and we take the rich model-theoretic logic Lzermelo = (Mzermelo , |=, {∈}), then Lzermelo captures P (semantically). Neither Frege nor Russell had such a purely semantic version of Logicism in mind, although there exists a precise one, as just explained. Nevertheless, something like our semantic version of Logicism was surely implied by their logicisms. Moreover, Frege and Russell had (also) some system of proofs in mind, and – being of the highest importance for their project – several lists of so-called logical definitions of mathematical concepts. However, the semantic version of Logicism has, as a foundational standpoint, no great a priori plausibility, and the possible fruits of a realization of this version are rather dubious. For let us take as an example of pure mathematics the (or a) second-order theory T of the real numbers qua completely ordered field (this is really third-order arithmetic in so far as real numbers can be modelled as sets of natural numbers). Then, why should every theorem ϕ of T translate into a sentence ϕ∗ ∈ V alid(L) for some rich model-theoretic logic L? That is to say: why should all or at least many sentences which are true in some individual structure translate into sentences which are true in all structures of a certain kind? Neither Frege nor Russell had the conceptual tools even to formulate this question. But we can see already from these considerations that there is a big lack of motivation in the very idea of Logicism, at least when formulated semantically; for, why should a sentence which is true in few mathematical structures, or just in the field of real numbers, not belong to pure mathematics? Does truth in all structures endow a sentence with a dignity over and beyond those sentences which are true in just one structure?

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2.2 Logical proofs Besides the rich logic L we are now going to introduce proofs into our picture since, as just mentioned, both Frege and Russell explicitly envisaged proofs as part of their logicist programme. Suppose that Σ is a system of proofs which is correct with respect to L, i.e. if Σ  ϕ, then ϕ ∈ V alid(L). Then we will say that Σ captures (syntactically) the piece P of mathematics if (II) For all results π of P : Σ  π ∗ . Of course, (II) implies (I), but not the other way around unless Σ is (semantically) complete with respect to (the model class of) L. Version (II) commands the most interest when the proofs of the proof system Σ are logical proofs. But what is a logical proof? An unobjectionable definition would run like this. Let a rich logic L be given. A proof is a sort of tree whose nodes are sentences from the language L connected by applications of inference rules. Such a proof is logical (with respect to L) if its leaves are members of V alid(L) and the inferences preserve membership in V alid(L). Note that nothing in our definitions presupposes that the sentences of the rich logic L are finite symbolic configurations, or that the proofs in Σ are finite trees. Moreover, we do not assume that the models in L are finite. Why should we? 3. The Argument Now I will present the promised proof; it will use a certain system Σℵ1 of logical proofs, and two associated rich logics. In order to prove (mathematically, or logically) my claim that Σℵ1 syntactically (and therefore semantically) captures a part P of mathematics, this P must be made precise. Although it may seem, prima facie, both logical and historical nonsense, we set P := P M , that is, unramified Principia Mathematica with a full comprehension schema and an axiom of infinity. The perfectly exact definition of P M will be given presently. I have promised a nontrivial proof of weak[LT]. If P M is a logic (and I do not deny this), then we have a proof of weak[LT] via P M  π =⇒ P M  π ∗ ∗ with (−) the identity function. Certainly, this proof is trivial. Regardless of whether P M is a logic or not, Σℵ1 will be logical in a higher degree than P M , and that in a precise sense of logical; moreover, Σℵ1 will turn out to be a natural and systematic strengthening of P M . That P M , in turn, captures a large part of mathematics is well known; it captures more mathematics than anyone of us will ever learn. Disregarding incompletenesses of G¨odelian 1931-type and purely set-theoretic questions like hypotheses about the continuum, P M is “practically complete" for ordinary mathematics (perhaps when enlarged by forms of the axiom of choice). Thus, if P M as it stands is a logic, Russell and Whitehead have proved Logicism at least in the version weak[LT].

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The announced system Σℵ1 is just one in an infinite hierarchy of type logics all of which have a very simple definition. This hierarchy, along with two related hierarchies concerning forms of AC, are fully presented and investigated in my paper [3]. First, the types. Let κ be ℵ0 , ℵ1 , ℵ2 , . . .7 Then the κ-types are defined as follows (1) 0 is a κ-type. (2) if α < κ, and if (τξ )ξ<α is an α-sequence of κ-types, then [(τξ )ξ<α ] is a κ-type. If κ = ℵ0 , then we have just the structure of all finite types, which underlies PM. Formulae and terms of the various  κ-types are built up as expected. We note that we use negation ¬, conjunctions , quantifications ∀, and relation-abstraction λ, the last three of any length α < κ. Besides the notions just listed, we have for α < κ a relation of α-ary typed predication8 denoted simply by brackets, −(−−−), thus τ

T [(τξ )ξ<α ] (T0τ0 , . . . , Tξ ξ , . . .) . This defines the type-theoretic language Lκ . In the case κ = ℵ1 , an expression of Lκ may be infinite, but its length α is a countable ordinal, i.e. α ∈ ℵ1 . The language Lκ may contain for certain types τ several nonlogical constants of type τ . If not, Lκ may be called the pure language. The proof system Σκ is then a sequent calculus consisting of the following: Axioms of the formϕ =⇒ ϕ. Weak structural rules. Rules for the left and right introduction of ¬, , ∀ and λ (together with −(− − −)). As a special feature, these rules allow the introduction of arbitrarily many signs of the same sort at once (so-called block-inferences). No cut rule is assumed.9 We could assume, but do not, an extensionality rule. As a first example we give a special case of the rule that introduces λ in the succedent: τ

[1]( =⇒ λ)

Φ =⇒ Ψ, F[(Tξ ξ )ξ<α ] τ

τ

τ

Φ =⇒ Ψ, λ(Xξ ξ )ξ<α .F[(Xξ ξ )ξ<α ]((Tξ ξ )ξ<α )

Here [1] in [1]( =⇒ λ) signifies that just one λ is introduced. As we have said, we can introduce arbitrarily many λ’s into the succedent (and also into the antecedent), since we have block inferences. A second example is the following rule with infinitely many premisses. 

 Φ =⇒ Ψ, ϕi i<ω  Φ =⇒ Ψ, (ϕi )i<ω  If we want to introduce more than one at once into the succedent, the premisses will become more complicated. [1]( =⇒

)

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There are two rich model-theoretic logics associated with Σκ : (1) StdLκ = (Mκ , |=, Lκ ). Here, an element M from Mκ consists of a domain M τ for each κ-type τ . M 0 is simply any non-empty set of things (socalled individuals). M [(τξ )ξ<α ] is the set of all α-ary relations whose arguments are from the M τξ ’s. These are the standard (or full) models. (2) GenLκ = (Hκ , |=, Lκ ) is like StdLκ but with a sort of Henkinean general models instead of the standard models Mκ . In an H ∈ Hκ a domain H [(τξ )ξ<α ] ∈ H may be only a definitionally closed subset of the set of all pertinent relations. Then we can prove (see [3]) (a) Σκ + (cut) is correct with respect to GenLκ (and hence also with respect to StdLκ ); and (b) Σκ [without (cut)!] is complete with respect to GenLκ . But even Σκ +(cut) is incomplete with respect to StdLκ .10 From (a) and (b) we have cut elimination for all Σκ . This was known as Takeuti’s Conjecture in the case of Σℵ0 and was proved by Prawitz and Takahashi. The case of Σℵ0 is excellently presented in Sch¨utte’s Proof Theory [13]. Now for our precise version of P M This is Σℵ0 + (cut) enlarged by the following “nonlogical axiom” concerning a binary relation constant R[00] (inf inity) : =⇒ ∀x0 ¬R[00] (x0 , x0 ) ∧ R[00] trans ∧ ∀x0 ∃y 0 R[00] (x0 , y 0 ) Obviously, the sequent (inf inity) has no finite model. Using the sequent (inf inity) we can prove in (our precise) P M that each Frege-Russell natural number11 is non-empty, which is the form of the axiom of infinity adopted in Principia Mathematica. Note that the sequent (inf inity) does belong neither to V alid(StdLℵ0 ) nor to V alid(GenLℵ0 ). In this precise sense, P M is not a “pure" logic. Remark. The version of P M just defined is consistent. If this were not the case, then in Σℵ0 + (cut) we could prove the sequent (††) ∀x0 ¬R[00] (x0 , x0 ), R[00] is transitive, ∀x0 ∃y 0 R[00] (x0 , y 0 ) =⇒ Then Σℵ0 would also prove (††) by a cut-free proof π. Since (††) contains only first-order quantifiers, π would also be a cut-free proof of (††) in first-order logic. But this supposition can be refuted in primitive recursive arithmetic. This consistency proof (observed by Takeuti already before the solution of his Conjecture) shows the metamathematical strength of the cut elimination property for Σℵ0 .12 The consistency problem for P M was one of the many logical problems suggested by Logicism. We think this problem has by now been solved, although not constructively, i.e. not quite in the sense of Hilbert’s programme. ∗

Next we show that there is an interpretation (−) such that for all sequents S

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If P M  S, then Σℵ1  S ∗ . We further assume that Σℵ1 is based upon the pure language, i.e. upon Lℵ1 without any nonlogical constant. What we have to do is to find a translation of the [τ,τ ] term R[00] into a term R∗ of pure Lℵ1 for some ℵ1 -type τ such that the interpreted ∗ sequent (inf inity) becomes provable in Σℵ1 . There are several options. We develop one such possibility, not necessarily the simplest, in detail in order to show the expressive power of Lℵ1 . The type superscripts are omitted if they can easily be restored. And of course, several obvious abbreviations are used. In particular, (Leibniz) equality is defined by T1σ = T2σ := ∀X [σ] (X(T1 ) → X(T2 )) for  the type we write the conjunction (ϕξ )ξ<α σ.  If (ϕξ )ξ<α is an α-sequence of formulae  as ξ<α ϕξ . Similarly for disjunctions . Henceforth, let τ be the ω-long type [[ ][ ][ ] . . .]. Observe that [ ] is a type by our definition; it is the type of 0-ary relations, i.e. of propositions. Define F := ∀x[ ] x[ ] and T := ∃x[ ] x[ ] . These propositions are refutable and provable [] [] in Σℵ1 , respectively. Next define SEQ[(Ai )i<ω ] as saying that (Ai )i<ω is an  [] F, T-sequence (of length ω). So we have SEQ[(Ai )i<ω ] : ⇐⇒ i<ω (Ai = T ∨ Ai = F) Next we order these F, T-sequences lexicographically, where F is taken to be smaller than T. That is, we define LEX[(A  i )i<ω , (Bi )i<ω ] : ⇐⇒ SEQ[(Ai )i<ω ] ∧ SEQ[(Bi )i<ω ] ∧  ( i<ω k≤i Ak = Bk ∧ Ai+1 = F ∧ Bi+1 = T) . Then we define [] SEQun[B τ ] : ⇐⇒ ∃(Xi )i<ω (B((Xi )i<ω ) ∧ SEQ[(Xi )i<ω ]) ∧ ∀(Xi )i<ω ∀(Yi )i<ω (SEQ[(Xi )i<ω ] ∧ SEQ[(Yi )i<ω ] ∧ B((Xi )i<ω ) ∧ B((Yi )i<ω ) → ∀Z τ (Z((Xi )i<ω ) → Z((Yi )i<ω ))) . The universe for the interpretation is U [τ ] := λX τ SEQun[X τ ]. [τ τ ] Finally, R∗ (Aτ , B τ ) says that the F, T-sequence in A is lexicographically smaller than the F, T-sequence in B. So we have the formal definition [τ τ ] := λX, Y (U(X)∧U(Y ) ∧ ∃(xi )i<ω ∃(yi )i<ω (X((xi )i<ω )∧Y ((yi )i<ω )∧ R∗ LEX[(xi )i<ω , (yi )i<ω ])). [τ τ ] Then (inf inity)∗ is (inf inity) with R[00] replaced by R∗ and the quantifiers relativized to U [τ ] . This interpretation (−)∗ can be extended to all of PM by translating the type 0 to the type τ throughout, and inductively any ℵ0 -type σ to the corresponding ℵ1 -type σ ∗ . We can rephrase the result just proven as follows: [τ τ ] The pair (U [τ ] , R∗ ) constitutes an inner model of Σℵ1 + (cut) + (inf inity) within the system Σℵ1 +(cut) and hence within Σℵ1 , by the cut-elimination theorem. Since Σℵ1 is trivially consistent, Σℵ1 + (cut) + (inf inity) and a fortiori P M is consistent; this is another, though unnecessarily complicated, consistency proof for PM.

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Remark. The axiom of choice plays no significant role in our considerations. If necessary we assume tacitly the presence of enough choice in our systems. See [3] for extensions of the Σκ ’s by Hilbertian choice terms together with appropriate rules. Thus, there is a logicist justification also of the axiom of choice. 3.1 Summary of this chapter Let us summarize what we have achieved by our proof of weak[LT] which was, I hope, not quite trivial. We have formulated a hierarchy Σκ , κ = ℵ0 , ℵ1 , . . ., of type logics. These are logics in the following sense: (1) They are complete and correct with respect to rich model-theoretic logic whose model class consists of certain Henkinean models. (2) The axioms and rules of each Σκ are logical in that the former are trivial (i.e. obviously tautological) and the latter consists only of introduction rules for  the logical signs ¬, , ∀, λ and typed predication −(− − −). (3) Then we showed how to interpret P M in Σℵ1 . The hard part is (1); in contradistinction to this, (2) and (3) may be called observations. So we can in Σℵ1 prove in a purely logical way that there are infinitely many primes, the Heine-Borel Theorem, the Cantor-Bendixson Theorem, and so on.13But what is this good for? Kreisel would ask: what do we know more about a true mathematical sentence ϕ when we know that ϕ is provable in Σℵ1 ? I am unable to give a satisfactory answer. I think that even the founding fathers of Logicism, Frege and Russell, had no answer to the natural and obvious question: What do we know more about a mathematical truth if we have a purely logical proof of it? Neither in the Grundgesetze der Arithmetik nor in the Principia Mathematica do we find proofs of deeper theorems from mainstream mathematics.14 Of course, Russell and Whitehead were well in the position to include a P M -proof P, say, of the Prime Number Theorem. But then, what would they have done with this purely logical proof P? Would they have unravelled P in order to gain more information about the Prime Number Theorem? Let me add that if we take P M itself as the logic, then Logicism with respect to P M can be merely a Properly Partial Logicism, since Zermelo’s set theory Z cannot be interpreted in P M , and Z is universally regarded as mathematics.15 This non-interpretability follows from the fact that the consistency of P M can be proven in Z; then simply cite G¨odel’s second incompleteness theorem. But there must be a proof of this non-interpretability that avoids G¨odel’s theorem. Find an interesting one!

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4. Reflections on Ramsey 1925 In this section, I will confine myself to a few remarks about Ramsey’s famous paper The foundations of mathematics of 1925 in [10]. First a quotation. “It might be possible to sacrifice infinite well-ordered series to logical rigour, but the theory of real numbers is an integral part of ordinary mathematics, and can hardly be the object of a reasonable doubt. We are therefore justified in supposing that some logical axiom which is true will justify it. The axiom required may be more restricted than the axiom of reducibility, but, if so, it remains to be discovered.” p. XLV of the first volume of the second edition of Principia Mathematica [14] (1927).16 Did Ramsey in his 1925 paper discover such a substitute for the axiom of reducibility? As the quotation shows, Russell did not acknowledge such a discovery. Although Ramsey is mentioned in a footnote for his “valuable criticisms and suggestions", Ramsey’s 1925 paper is not mentioned in any of the three volumes of [14] as far as I could verify. However, as we shall see, Ramsey claims in his 1925 paper to have discovered a substitute for the Axiom of Reducibility. Ramsey apparently never doubted that the mathematical strength of Principia Mathematica is sufficient for ordinary pure mathematics. His main criticism, as is well known, focussed on a version P M † with a certain ramification regime together with the anticlimactic axiom of reducibility. Recall that Russell introduced orders besides types to be able to keep track of the definitional complexity of what he called propositional functions. Thus if T ≡ T [τ1 ...τk ] is a term (for a propositional function) of the indicated type, T may contain quantifiers both of types lower and higher than any of the types τi . Depending on the occurrences of higher-type quantifiers, the term T will get a certain correspondingly high order in addition to its type [τ1 . . . τk ]. One says that the orders ramify the types. Russell used only natural numbers as orders, but for the purpose of fine-tuning one may also use transfinite ordinals. The ramification of types has to be mirrored in the structure of the axioms and/or inference rules: suppose that T has order 100, then the bound variable in the conclusion of a ( =⇒ ∃) [equivalently of a (∀ =⇒ )] applied to T must have also order 100 (or higher), in addition to its type [τ1 . . . τk ]. As a consequence of this ramification regime, several theorems of classical mathematics cannot be proven. A hackneyed example is the least upper bound principle in analysis. Also, despite Russell’s hope to prove the induction principle for natural numbers within the ramification regime, this cannot be done, as was finally shown by J. Myhill in [9] (1974). Already in 1944 G¨odel expressed some doubts; see [7]. The axiom of reducibility (AR) was introduced precisely in order to regain such standard theorems of classical mathematics as the least upper bound principle. (AR) is really an axiom schema; it postulates that every term is equivalent to a term of order 0. In terms of inference rules, this can simply be done by allowing the bound variable in the conclusion of a ( =⇒ ∃)-inference to be of order 0.

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We have just described P M † , i.e. the system which Ramsey attacks in his paper. As explained, (AR) abolishes the ramification regime together with its orders – so that we may reasonably ask what the orders were good for to begin with. 4.1 Ramsey’s criticism of the axiom of reducibility (AR) In this criticism Ramsey makes two main points: (1) (AR) goes far beyond logic; we read pp. 162–3 the following: [the (AR) is] “a genuine proposition, whose truth or falsity is a matter of brute fact, not of logic. It is, therefore, not a tautology in any sense, and its introduction into mathematics is inexcusable.” And on p. 180: “For as I can neither accept the Axiom of Reducibility nor reject ordinary analysis, I cannot believe in a theory which presents me with no third possibility.” These are hard words. (2) The introduction of the ramification regime was motivated by the avoidance of certain paradoxes as the Liar (or more generally, by the dubious vicious-circle principle).17 Ramsey argues that such (linguistic or epistemological) paradoxes do not concern mathematics proper. The other more mathematical paradoxes, as Russell’s own, are disposed of just by introducing types, without refinement by orders. Ramsey also dispels the fear of vicious circles by an example which has become famous afterwards in this context: “... just as we may refer to a man as the tallest in a group, thus identifying him by means of a totality of which he is himself a member without there being any vicious circle.” (p. 192) 4.2 Ramsey’s predicative propositional functions Ramsey’s decisive transformation of P M † (with ramification regime, (AR) and axiom of infinity) into a mathematically equivalent (!)18 theory is based upon a new notion of predicative (propositional) functions contained in Chapter III (pp. 183– 200). This chapter is rich in detail but sometimes difficult to understand. One of the main ideas of Ramsey’s notion of predicativity consists in the real or merely posited elimination of quantifiers in favour of (possibly) infinite conjunctions. So we read on p. 190: “A predicative function of individuals is one which is any truth-function of arguments which, whether finite or infinite in number, are all either atomic functions of individuals or propositions.” And on p. 191: “Now consider the function of x, (ϕ).f (ϕˆ z , x). Is this a predicative function? It is the logical product ... for different ϕ’s ...” Then Ramsey concludes that the function in question is predicative too since he assumes, I think correctly, that the predicative propositional functions are closed under even infinite truth-functions. Ramsey does not give a formal, not even a semi-quasi-formal, system based on the sketched infinitary notion of predicative functions; the time was not yet ripe for this. A direct implementation would lead to an infinitary system like Σℵ1 or a

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predicative subsystem thereof. But Ramsey primarily wanted to give a justification of a new form of P M whose language is finitary. Thus he seems to have used his detour through infinite expressions, notably infinite truth-functions, only to show that quantifiers do not lead out of the realm of his predicative functions. Ramsey says that he does not need (AR). But what does he assume instead? What was, after all, Ramsey’s substitute for the Axiom of Reducibility? Although he does not say so explicitly, he assumes the full comprehension principles in an unramified language, which is virtually our language Lℵ0 ; the principle thus reads (comp)

∃Y [τ1 ...τk ] ∀X1τ1 . . . Xkτk (Y (X1 . . . Xk ) ↔ F[X1 . . . Xk ]) .

where F is any formula, which may contain arbitrarily high quantifiers. Such a form of comprehension is nowadays called impredicative, despite Ramsey’s different nomenclature. In our systems, full comprehension (comp) is deducible by the following unrestricted rules: ( =⇒ ∃), (λ =⇒ ), ( =⇒ λ), ( =⇒ ∀) and some propositional inferences. It is easy to show that (AR) in a ramified context is equivalent to (comp) in an unramified context. In this sense, Ramsey has not replaced the axiom of reducibility by an essentially different axiom. This he himself concedes on p. 207. See [10] p. 207. Since Ramsey assumes also an axiom of infinity, his improved version of P M † is just our P M discussed above. Moreover, P M † and our P M are mutually interpretable. 4.3 Ramsey on the axioms of infinity and choice In the final chapter of his paper, Ramsey discusses the Multiplicative Axiom, i.e. the Axiom of Choice, and the Axiom of Infinity. He thinks “the introduction of these two axioms is not so grave as that of the Axiom of Reducibilty, because they are not in themselves such objectionable assumptions,...” p. 207. One is tempted to say: Quite the contrary. For, if logicality (or tautologicality) is to be preserved, then the axiom of infinity presents an obstacle. Recall that (inf inity) ∈ V alid(StdLℵ0 ). Ramsey claims that the Multiplicative Axiom is, under his interpretation, a tautology. His arguments for that are hard to follow; but they contain the interesting conjecture that the Multiplicative Axiom cannot be proved in P M . (The difficulty of the independence proof depends on the form of the axiom of infinity.) We have not given a logicist justification of the Axiom of Choice in the present talk; but we may mention in passing that we have constructed cut-free systems εΣκ (resp. τ Σκ ) in which axioms of choice can be proven via logical rules for Hilbertian ε-terms (resp. τ -terms). See [3]. I now quote the final passage of Ramsey’s paper in full: “Similarly the Axiom of Infinity in the logic of the whole world, if it is a tautology, cannot be proved, but must be taken as a primitive proposition. And this is the course which we must adopt, unless we prefer the view that all analysis is self-contradictory

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and meaningless. We do not have to assume that any particular set of things, e.g. atoms, is infinite, but merely there is some infinite type which we can take to be the type of individuals.” p. 212. This is heavy going. However, if Ramsey had implemented his infinitary intuitions in a system like Σℵ1 , he would have recognized the Axiom of Infinity as an infinitary tautology, i.e. as a sentence in V alid(StdLℵ1 ) and would have proved it by a proof similar to ours. 4.4 What we have omitted We have not commented upon Ramsey’s dependence on Wittgensteinian ideas and insights. The main point here is the idea of infinitely long propositional tautologies; this idea indeed occurs in the Tractatus19. But Wittgenstein himself does not make much of the infinitary character of his tautologies, he certainly does not use them to correct Principia Mathematica. It is unknown to me what Wittgenstein did remark on Ramsey’s paper, especially on the use of infinitely long tautologies. However, G¨odel made some pertinent critical remarks in [7]. Ramsey’s criticism of (AR) is anticipated in the Tractatus; see 6.1232 and 6.1233. Let us point out that Wittgenstein makes a very haughty but totally mistaken remark on the axiom of infinity, 5.535 “Damit erledigen sich auch alle Probleme, die an solche Scheinsa¨ tze geknu¨ pft waren ... Das, was das Axiom of infinity sagen soll, wu¨ rde sich in der Sprache dadurch ausdru¨ cken, dass es unendlich viele Namen mit verschiedener Bedeutung ga¨ be.” Now, let us extend the system Σℵ0 by the following set of axioms =⇒ ¬ci = cj f or i = j, the ci s being constants of type 0 . Then no axiom of infinity can be proved in the extended system. For this system is locally finite in the sense that each single theorem of it has a finite model. 5. Conclusion and Open Logical Problems Though Ramsey’s invective against (AR) is full of brillant passages it is not sufficiently cogent to justify the “hard words" I have adduced. I have mentioned above in a footnote that Ramsey himself stated that his improved version of Principia Mathematica differs only in the meaning attached to it. For my part, I remain unconvinced about the alledged viciousness of (AR). For, to begin with, ramifications by themselves are both logically and mathematically as interesting as the types. This was borne out by many subsequent mathematical and logical investigations. For instance, G¨odel’s constructible sets are a generalization of Russell’s ramified type structure. Another example is the proof theory of Ramified Analysis, see, e.g., Sch¨utte’s book [13].

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Finally, I do not find anything wrong in introducing Axioms of Reducibility into a given ramified framework. I intentionally used the plural form Axioms; for, one does not need to reduce every order to the order 0, more modest reductions are possible and sensible. It is not clear why any Axiom of Reducibility should be contradictory to Logicism. We close by stating some logical problems suggested by logicism, as announced in the title of our talk. (I) Define and investigate ramified versions of Σℵ1 . Are there (interesting) ramified versions of Σℵ1 (or of Σℵ2 ) which embed all of P M ? (II) It can be shown that Σℵ1 proves finitary sequents, i.e. sequents belonging to Lℵ0 , which are not provable in P M . Nevertheless, such sequents are valid with respect to standard models. This means, that standard validity for finitary sequents is better approximated by Σℵ1 than by Σℵ0 . Next we can use Σℵ2 for a still better approximation, and so on. This phenomenon calls for thorough investigation. (III) In Σℵ1 we can get complete first-order arithmetic. In which system Σκ can we get complete second-order arithmetic? (IV) The language of Σℵ1 should be made more effective, e.g., by using definability in admissible sets. (V) There are many sensible subsystems of Σℵ1 . For instance, to embed P M we do not need all ℵ1 -types as shown by our embedding described above. A second example is Σ 12 ℵ1 . This is the system with only ℵ0 -types but with countably long  ’s and ∀’s. Prove a semantic completeness theorem for Σ 12 ℵ1 ; and perhaps a cutelimination theorem. Since Σ 12 ℵ1 remains consistent if we stipulate that every type be finite, P M cannot be interpreted in Σ 12 ℵ1 . But we can axiomatically enlarge Σ 12 ℵ1 by adding the sequent (inf inity). Then we can deduce complete first-order arithmetic. For that purpose, we can also drop infinitely long ∀’s. (VI) What will happen if we remove from Σℵ1 all quantifiers? It seems that Ramsey (and perhaps also Wittgenstein) at some time had such a system in mind. (VII) Finally, one should develop a methodology for the construction and presentation of infinitary proofs. These all are logical problems which can be raised about Russellian logicism – although the infinitary context would perhaps have been repugnant to Russell’s nominalistic mind. With respect to Fregean logicism there has been made, in the last decades, much progress concerning weakenings of the wicked Grundgesetz V, for instance to what is called Hume’s Principle. Another line of research is suggested in [1] where a system named pra¨ Kid is defined which retains the full Grundgesetz V, but weakens comprehension. The consistency of pra¨ Kid is still open but plausible.

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Notes 1.

2.

3.

4. 5. 6.

7. 8.

9.

10.

11. 12.

13.

That Frege’s logicism encompasses at least second-order arithmetic, and is bounded from above by, say, fourth-order arithmetic, can only be gleaned from the contents of [6]; there is no explicit demarcational statement made by Frege, neither for “arithmetic" nor for “logic" (of course not). On p. V we read: “The fundamental thesis of the following pages, that mathematics and logic are identical, is one which I have never since seen any reason to modify.” This statement implies a fortiori that logic is part of mathematics; we may call this Reverse Logicism. There is, up to now, no literature about reverse logicism. I have given several proofs of (or arguments for) weak[LT]. The first proof appeared in [1] and was made much clearer in [4]. These two proofs make use of a cumulative type structure, which is rather different from the type structure of the system Σℵ1 to be introduced below. The proof in the present paper was first outlined in [2], and detailed in [3]. Nevertheless, I think the representation in the present paper contains a deeper conceptual analysis which goes beyond that in [2] and [3]. Or rather a class of similar languages. Here equivalence may be isomorphism, or L-elementary equivalence, or something like that. It is an open and vexing problem to give a precise sense to the notion of an analytic statement (“Urteil"), in contradistinction to synthetic statements. I think that to be in V alid(L) for some rich model-theoretic logic L is a good candidate for an explication of analyticity. Recall that Frege in [5] and [6] wanted to show that arithmetical statements are analytic, contrary to Kant for whom they were synthetic. In a sense, Frege’s logicism with respect to arithmetic simply says that arithmetic theorems are analytic. But Frege gave no definition of analytic, except by equating analytic = purely logical. By the way, it is difficult to tell what Kant would have subsumed under the title arithmetic beyond sentences like 7 + 5 = 12. Observe that if this sentence is synthetic, then the sentence 12 = 7 + 5 should be analytic, according to Kant’s definition. It is more than enough to consider κ < ℵω . Beyond that, no essentially new results seem to be provable. However, to avoid oddnesses, κ is always assumed to be a regular cardinal. This typed predication −(− − −) may also be conceived of as a typed membership relation; from the standpoint of a many-sorted first-order logic, −(− − −) appears as a non-logical notion. But within a type-theoretic framework, −(− − −) is usually considered as a logical notion. As I said above, I decide such questions about the intrinsic logicality by fiat. The cut rule itself may be regarded as a non-logical rule in so far as it does not introduce logical signs. Therefore, strictly logical systems should not contain the cut rule; but they should perhaps be closed under the cut rule. Considering the vast variety of rules possible in the framework of sequent calculi (e.g. the topic of substructural rules) there is simply no criterion to tell logical and non-logical rules apart, if we shun semantic criteria. For κ = ℵ0 , this semantic incompleteness follows from G¨odel’s incompleteness theorem and the categoricity of the second-order Peano axioms. The other cases can be shown quickly as follows. Let κ > ℵ0 be a regular cardinal. We forget all κ-types that contain 0, i.e. we start our inductive definition of the κ-types with [ ]. Then there is exactly one standard model Mκ for this restricted type structure. We can formulate the continuum hypothesis CH adequately by using the restricted language (Hint: use the type [[ ][ ][ ] . . .]). Now suppose Σκ + (cut) were complete with respect to StdLκ ; since CH is either true of false in Mκ , then either the sequent CH =⇒ or the sequent =⇒ CH should be provable. However, this alternative can be refuted by adapting known settheoretic results. Note that for κ > ℵ0 G¨odel’s incompleteness theorem cannot be used to show that Σκ + (cut) is incomplete with respect to StdLκ since all these systems contain complete arithmetic, and are, of course, not recursively axiomatizable. For instance, the Frege-Russell natural number 2[[0]] is λX [0] .∃x, y(X(x) ∧ X(y) ∧ ¬x = y ∧ ∀z(X(z) → z = x ∨ z = y)). Clearly, the cut elimination property implies consistency. However the consistency of Σℵ0 + (cut) is provable in a fragment of primitive recursive arithmetic. By G¨odel’s second incompleteness theorem, the cut elimination property for Σℵ0 cannot be proven in even in full P M . This shows that the cut elimination property of a logical system may be vastly stronger than its consistency. It is well known that BD (= Borel Determinacy) is not provable in Zermelo’s set theory together with AC, hence not in P M + AC. From time to time I try to prove BD in Σℵ1 .

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14. It seems to be a desideratum in the history of mathematical logic to describe and assess the real mathematical content contained in the printed pages of the book Principia Mathematica. 15. Thus, e.g., ZF may not be mathematics since it contains too much platonic nonsense. Perhaps, by the same token, not even Z is (real) mathematics, and so on. In [4] one can find logical systems which embed stronger and stronger extensions of Z. 16. There seems to be a problem about the exact date of publication of the second edition of PM; my copy has the date 1927, for each of the three volumes. But elsewhere I found dates like 1923–27, and 1925–27. 17. One formulation of this principle is: “Whatever involves a l l of a collection must not be one of the collection.” [14] p. 37. The main source of ambiguity lies in the muddle-headed term involves. A thorough analysis of the vicious-circle principle has been given by G¨odel in his [7]. 18. See [10] p. 207: “Formally it [i.e. Ramsey’s version of P M ] is almost unaltered; but its meaning [my emphasis] has been considerably changed.” In view of this statement, the hard words in (1) above seem to be grossly exaggerated. 19. See [15] 5.502 and 6, where there is put no finite bound on the number of arguments.

References [1] J. W. Degen : Systeme der kumulativen Logik, Philosophia Verlag, Munich (1983) [2] J. W. Degen : Two formal vindications of logicism, in: Philosophy of Mathematics, Proceed. 15th Intern. Wittgenstein Symp. ed. J. Czermak, Wien (1993), 243–250 [3] J. W. Degen : Complete infinitary type logics, Studia Logica 63 (1999), 85–119 [4] J. W. Degen and J. Johannsen : Cumulative higher-order logic as a foundation for set theory, Math. Log. Quart. 46, 2 (2000), 147–170 [5] G. Frege : Die Grundlagen der Arithmetik, Breslau (1884) [6] G. Frege : Grundgesetze der Arithmetik, Jena (1893, 1903) [7] K. G¨odel : Russell’s Mathematical Logic, in: Philosophy of Mathematics, eds. P. Benacerraf and H. Putnam, Englewood Cliffs (1964) [8] Jean van Heijenoort : From Frege to Go¨ del. A Source Book in Mathematical Logic, 1879–1931, Harvard University Press (1967) [9] G. Nakhnikian (ed.) : Bertrand Russell’s Philosophy, Duckworth (1974) [10] F. P. Ramsey : Foundations, ed. Mellor, Routledge & Kegan Paul (1978) [11] B. Russell : The Principles of Mathematics. 2nd edition, Norton & Company (1938) [12] B. Russell : Mathematical logic as based on the theory of types, American Journal of Mathematica 30 (1908), 222–262, also in: [8] [13] K. Sch¨utte : Proof Theory, Springer (1977) [14] A. N. Whitehead and B. Russell : Principia Mathematica. 2nd edition, Cambridge (1927) [15] L. Wittgenstein : Tractatus logico-philosophicus, Hrsg. von B. McGuinness u. J. Schulte, Suhrkamp (1989)

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Institute for Computer Science University of Erlangen-Nuernberg Martensstrasse 3 D-91058 Erlangen Germany [email protected]

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W ERNER L EINFELLNER

THE FOUNDATION OF HUMAN EVALUATION IN DEMOCRACIES FROM RAMSEY TO DAMASIO

T HE NEW R AMSEYAN THEORY OF VALUES IN THE WORK OF LATER UTILITY AND VALUE THEORISTS Today’s individual and collective decision theory, game theory and evolutionary game theory, collective choice theory, microeconomics, and even welfare economics are based on a preferential “if-then” ordering of human evaluation and decision making. The historically earlier axioms of the RNMNS method, defined later in this paper, are the “if” condition and the “then” part consists of the ordered preferences and values. The “if-then” structure was at first introduced by Ramsey and improved later on by others. Ramsey’s foundation of evaluation and the measurement of values, R (1931e: 178-184), then, rest on the “if” condition formulated as axioms. If we can impose serially ordering axioms on given preferences, we can order and measure them serially and thus introduce scientifically justified values, opinions, and beliefs. If not, the preferences stay unordered and remain as so-called ordinary values, opinions, and beliefs. The same holds for the Neumann-Morgenstern axioms, NM (1961 [1944]: 24-31), for Suppes/Zinnes, S (1963b: 1-74), and for the Nash conditions, N (2002b [1950]: 38-40). Their common purpose is the reason why we speak here of a RNMNS method. We support this method by introducing additional conditions C1-C3 for their empirical application and use in democracies. R AMSEY ’ S FOUNDATION AS A REVISION OF N ASH As a teenager, Nash sent an as yet unpublished paper to Neumann at a time not ascertained. The article has been recently published in a volume edited by Kuhn/Nasar in 2002 (Nash 2002b: 38-41). Nash emphasizes strongly the mathematical (and therefore conscious) processing of evaluations, starting with preferences and ending with scientific, or expert, opinions as internal anticipations of future outcomes. The following Nash method N1-N5 uses prescriptive evaluation rules; they are rule-like assumptions, not axioms, while Ramsey and Neumann/Morgenstern speak of “axioms.” The assumptions show how we convert given preferences into conscious, e.g.,

139 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 139–153. © 2006 Springer. Printed in the Netherlands.

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mathematical, values, opinions, and beliefs. We need value canons for conflict solving, be this a conflict of alternatives, a social conflict in democracies, or some other conflict. N1-N5 show clearly that Nash had contemporary psychology in mind when he formulated his mathematico-logical reconstruction of the mental processing of values: N1. An individual offered two possible anticipations can decide consciously which one is preferable or that they are equally desirable. N2. The ordering thus produced is transitive: if A is better than B, and B is better than C, then A is better than C. N3. Any probability combination of equally desirable states is just as desirable as either. N4. If A, B, and C are as in assumption (2 [= N2]), then there is a probability combination of A and C which is just as desirable as B (continuity assumption). N5. If 0 ” p ” 1 and A and B are equally desirable, then pA + (1-p)C and pB +(1-p)C are equally desirable. Also, if A and B are equally desirable, A may be substituted for B in any desirability ordering relationship satisfied by B. Nash’s method as included in the RNNMS method starts with given and conscious preferences and computes the necessary values for making specific social decisions. These values, then, are representations of ordered given preferences; this order assigns to each preference a real number as value. If u is a value function, then also au + b, provided a > 0. A representative value function represents the order of serial preferences unto conscious neo-cardinal values (Allais 1994a; b). This utility function is not unique, but a neo-cardinal one. It will satisfy the following rule-like properties: (i) u(A) > u(B) is equivalent to: A is more desirable than B, etc. (ii) If 0 ” p ” 1, then u[pA + (1-p)B] = pu(A) + (1-p)u(B) We now adduce the 3 criteria C1-C3 for meaningful preferences: Criterion C1: If an evaluation procedure is to begin, the given preferences should be empirical or at least potentially empirically realizable. Criterion C2: The evaluation procedure starts with imposing a strong order of given preferences (N2 in Nash 2002b [1950]: 39; Arrow 1963: 13). Individual processing should proceed rationally in a wider sense: either deductively or inductively-probabilistically (nonlinear) (Ramsey 1931c [1928]: 204ff; 1931d [1929]: 256; 1931e [1926b]: 192). Criterion C3: The order of values in any canon, i.e., the opinion, should enable solutions of social conflicts which are empirically feasible. The solutions should be compatible with superimposed democratic laws in representative democracies and democratic welfare states.

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S CIENTIFIC / EXPERT OPINIONS AND NONSCIENTIFIC , ORDINARY OPINIONS ( VALUE HIERARCHIES ) Firstly: The RNNMS method and the criteria C1-C3 reconstruct very well how human values are established and formed, given rational and conscious preferences. Secondly, and most importantly: Its greatest advantage is that we now have a scientific tool, the RNMNS method, to decide whether a value hierarchy, a value canon, or opinion (belief), is scientific/expert, or not. Thirdly: The application of the criteria C1-C3, especially C3, define “socially optimal” in democracies. The greatest advantage of the RNMNS tool cum C1-C3 is that they offer a criterion whether a value is scientifically feasible. But it has its disadvantages, too. Firstly: It cannot be used to explain where preferences originally come from. Secondly: It cannot be used to explain how new values and value canons (opinions) are created, and how values are changed, adapted, in short: how they evolve (Damasio 2003: 48f, 110f, 161-164). “New” means “not previously existing,” “not existing within living memory.” The question remains: What are we to do with ordinary values which cannot be “proven” with the RNMNS tool cum C1-C3? The RNMNS method or procedure is a new scientific and mathematical reconstruction of an internal (psychological) human process leading from consciously given preferences to quantitative individual values. According to C1C3, “given preferences” means that the preferences can be empirically observed, realized, etc. The new quantitative utility theory, or approach, founded on RNMNS and C1-C3, replaces the traditional qualitative philosophy of value. This new theory works only because its background are the principles of modern representative democracies and democratic welfare societies, DP (= democratic principles). This background often goes unmentioned and is just assumed. Moreover, values are always embedded in value hierarchies, i.e., value canons, i.e. opinions, or democratic principles. Instead of “value hierarchy” or “value canon” we often use only “opinion.” Ramsey and later theorists, then, have reconstructed human individual evaluation in mathematical terms, not unlike Aristotle who reconstructed human reasoning in logical terms (see also Ramsey 1931b [1926a]: 62f, 68; 1931e [1926b]: 192). But the question from where and how preferences and human values originate remained open. Traditional answers assumed that they were introduced by external superior deities as legislators, by their successful use in societies in the course of human evolution, and so on. Damasio’s three books develop a new somatic and brain-physiological foundation of the creation of given preferences, discussed later. According to Nash, human preferences and individual values are psychic “anticipations” (ex ante values; Nash 2002b: 39-40). Since Pigou’s welfare

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economics, Ramsey and others have defined values as individual and social values as expected values (Pigou 1912: 72f; cf. Neumann/Morgenstern 1961 [1944]: 3.1-3.8, especially 3.3.2 and 3.4.6). A comprehensive final version of this approach was worked out by Suppes/Zinnes 1963b (cf. also Leinfellner 1964a; b; 1974). From then on, the individual evaluation method RNMNS cum C1-C3, as first installed by Ramsey, was an important economic topic (Nash 2002b [1950]; Neumann/Morgenstern 1961 [1944]). Suppes/Zinnes 1963b improved the methods of scientifically turning given preferences into values. Here we call this procedure the “RNMNS method (procedure)” – “RNMNS” after the names of Ramsey, Nash, Neumann/Morgenstern, and Suppes. It became the mathematical hard core and cornerstone of modern quantitative utility (value) theory (we often simply say “RNMNS” method and “criteria C1-C3,” to mean “something akin / comparable to the RNMNS method,” and the like). Utility theory is the foundation of today’s game and decision theory, collective choice theory, and microeconomics. Collective choice theory explains how, in representative democracies and democratic welfare states, individual values become collective values. Collective choice theory peaked in the sixties of the last century with the welfare economists Arrow, Sen, and Harsanyi, Nobelists in economy all three. The consequences of the RNMNS method turned out to be a new probabilistic, nonlinear method. The concept of values as anticipations changed our previous, deterministic view of all social sciences, particularly microeconomics, political science, sociology, and evolution theory: From now on they are seen as nonlinear. This method helps us to understand how, and if, individual and social values can be measured quantitatively, how individual values and also canons of values, or opinions, can be computationally derived from given psychological preferences, why social sciences become nonlinear and are no longer able to predict deterministically, and when not. Once we have come that far, we can solve and even compute social conflicts in “nonlinear” democracies, be the values competitive or cooperative or, simply: expected averages or risks. In this paper, “democracy” is used also as a synonym both for “representative democracy” and its extension, “democratic welfare state.” This is possible because both have the same goal when it comes to the socially optimal solving of future conflicts. The improvement of future individual and, at the same time, future social, collective welfare replaces deterministic predictions. Democratic conflict solving is progressive and dynamic, an evolutionary process for short, based on the RNMNS method and its criteria C1-C3. In this process, the environment, the society, external and internal random events, etc. play an active role. In democracies, therefore, humans adapt continuously their individual and social values to uncertain situations and to democratic laws (Rawls, Neumann / Morgenstern) when they have to solve social conflicts in a socially optimal way. In all the social sciences, the traditional one-one causal predictions have become obsolete and must be replaced by the computation of future expected plusses (increases; risks) or future expected losses (risks), especially in the case of the current crisis of sinking individual and collective welfare standards. For

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more than 75% of the EU citizens nothing seems more important than to maintain the incredibly high individual and collective welfare standard which has been achieved since 1900. In the countries of the EU, democratic laws for the solution of social conflicts have been adopted, governed by the new supreme principle of Human Rights HR. (The quantification achieved by the RNMNS method is a sine qua non condition of the application of the HR.) By the Human Rights principle HR we mean the principle as formulated by the United Nations and introduced, for instance, into the Austrian Constitution (since September 3, 1958). The Human Rights stipulate categorically that progress in democracies means to improve the individual and collective welfare without decreasing, exploiting, or harming one specific part of the population; the rich should not be getting richer, and the poor, poorer (Samuelson 1970: 764). But how can we execute the Human Rights in democracies without measuring progress quantitatively, thus, without a RNMNS method cum C1-C3? In this spirit, already Pigou and Ramsey proposed a democratically acceptable fiscal taxation policy, formulated quantitatively, for democracies. When democratic states are encumbered with debts, there is, in representative democracies and the EU, no other way out of debt than by paying it back in a democratic way that is socially fair or just. This is not possible without quantification (missing, e.g., in Rawls 1971 and 2001). Such crises are either caused by extremely egoistic trends in the societies themselves, or they are the negative consequences of random events or of mistakes, or caused by ordinary values, opinions, beliefs, which are typical for evolutionary processes. When a democratic government has committed itself irrevocably to a progressive course of action in order to terminate a social conflict between egoistic and cooperative, altruistic interests, it cannot turn back, since this would mean its self-destruction (Dahrendorf 1988). In economics, similar considerations are expressed quantitatively by the Hicks-Kaldor and the Scitovsky criterion. Their basis is the RNMNS method cum C1-C3. If democracies cease to defend the Human Rights HR, they violate a series of democratic principles DP (see below), rely on empty promises and ordinary, nonscientific values and opinions or nondemocratic principles and are digging their own grave. T HE NEW METHOD OF R AMSEY , N ASH , N EUMANN /M ORGENSTERN , AND S UPPES AND ITS NONLINEAR CONSEQUENCES In the years between approximately 1926 and 1928, Ramsey had the ingenious idea for the first scientific, mathematical reconstruction of how individuals consciously form and process individual values. Ramsey’s reconstruction of what the individual does by estimating and evaluating looks like this: He, and his followers as well, start with the individual’s given preferences and then use serial conditions (Nash) and conditional probabilities and the concepts of non-linear

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betting to quantitatively measure future values as expectations of a better individual and collective welfare. Betting and hedging are means to cope with the pragmatic, good or bad consequences of random events when we foretell the outcomes of future solutions of societal conflicts, that is, the expected winnings or losses for the individual and for a democratic society. Today, this replaces the traditional deterministic prediction. Generally, in democracies social and collective values always carry with them a specific empirical “meaning” in form of their pragmatic future consequences for us, i.e., their utility for us and/or for the society, be it the value of things, commodities, individuals, their actions, decisions, individual or societal conflict solutions, culturefacts, etc. (Leinfellner 1984). Values without this specific form of “meaning” are empty; they are merely platonistic, merely mathematical. Pragmatically meaningful scientific values in canons of social values, or opinions, specify certain positive or negative consequences for human decisions, and they are restricted to a specific empirical domain D. Such a domain D is, e.g., the domain of competitive and/or cooperative games or the domain of common conflicts in democracies. The computed or expected solutions, which are based on individual and societal values, value canons, or opinions, must be empirically realizable or feasible, at least in democracies (see Criteria C1-C3). This pragmatic usefulness is expressed in modern economics by expected utilities, as represented by the RNMNS method cum C1-C3. The RNMNS method was later worked out in detail by authors of the Theory and Decision journal and book series; other, earlier names to be mentioned are Marschak (1974), De Finetti (1937), Leinfellner (1964a; b; 1974), and many others. These authors reconstruct quantitatively individual human value formation in terms of the mathematical RNMNS method; they separate traditional values from probable ones. Private conflicts, which have no bearing on anyone except the solitary decision maker and conflict solver, have to be excluded. Such values are prescriptive for specific social solutions only, and they can be replaced by better ones, adapted to a certain new task, changed, rejected offhand, etc., provided the procedure is democratic according to C3. They are dynamic and subject to evolutionary processes. They are stored in the individual and collective conscious memories (Leinfellner 1984: 268; Damasio 2003: 270; Tulving 1983: 127). Majority voting creates collective value canons, opinions, or beliefs (Arrow 1963: 76; Sen 1970: 23; Munier 2001). Legislation in democracies, finally, lay down such canons in constitutions and laws. It was an important step that Neumann/Morgenstern founded their own game theory on utility theory. We have already said that utility theory is based on the RNMNS method. This enabled quantitative scientific conflict-solving in democratic societies. The rules established by game theory and utility theory use a more empirical form of the RNMNS method cum C1-C3 than Ramsey did. When we solve social conflicts, they guarantee that a mathematically computed solution of social conflicts can be found, is scientifically o.k., and fits into democratic societies. Finally, when game theory turned into a dynamic, evolutionary

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theory, the RNMNS method was just as indispensable (Weibull 1996; Gintis 2000; Leinfellner 1998; 2000). C OLLECTIVE CHOICE THEORY AND THE RNMNS METHOD In collective choice theory, the individual values obtained by the RNMNS method were taken as the starting point for a mathematical reconstruction of collective democratic values by Arrow 1963, Rawls 1971 and 2001, and Sen 1970. Pigou’s (1912: 71-77) early foundation of welfare economics foreshadows such a reconstruction. This branch of welfare economics is a prescriptive economico-social science and showed formally how collective social values originate from individual values obtained by the RNMNS method and the C1-C3 criteria. It produced most of the Nobel prizes in economics. It permits to reach the goal of welfare societies: to maximize (improve) both the individual and the social welfare in the future (Leinfellner 1998). Seen in retrospect: In collective choice theory, but also in utility and game theory, their prescriptive rules have always been tailored after the pattern (rules) of democratic and economic principles. The imposition of these democratic welfare principles on the RNNMS mathematical apparatus facilitated the computation of social conflict-solving. In the course of 20th-century history, these disciplines “borrowed” more and more democratic values (value canons, opinions) from the democracies themselves (Rawls 1971; 2001). In some way, they all used the basic RNMNS method and its new criteria C1-C3 of application in democracies. This is a partial and quantified renaissance of Parsonian sociology. Arrow’s collective choice theory of 1951 and Sen’s of 1970 are pioneering and epoch-making reconstructions of how individual scientific values obtained by the application of the RNMNS method cum C1-C3 in representative democracies are represented2 technically by social welfare (utility2) functions into common democratic values and opinions. Historically, both use logical methods but come to the conclusion that logic and axiomatization alone cannot explain how democracies work. Here again, the reason is that social choice theory had been based on the RNMNS method which renders linear deductive methods obsolete (Arrow 1951: 11-14, Axiom 1 and 2; Sen 1970: 94-99). Indeed, it led to inconsistencies, such as captured in Arrow’s impossibility theorem. Firstly, the RNMNS method permits a representation1 of given individual preferences unto scientific values. Then social choice theory explains how these individual scientific values are represented2 by a following special representation2 unto common democratic social values and opinions, as for example by majority voting (MV) in representative democracies. Secondly, for that collective representation2 the social choice theory imposes empirically established democratic principles DP, borrowed from democratic usage, on gametheoretical democratic decision rules and models to compute

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quantitative optimal solutions of societal conflicts in welfare democracies. Rawls 1971 tried the same but his theory is only a qualitative one. A RROW ’ S IMPOSSIBILITY THEOREM AND THE RNMNS METHOD The clash known as Arrow’s impossibility theorem, is a theorem, since it derives from supposedly logical axioms and the essential democratic principles DP = (U & P & I & ˜D & MV & HR) ¬ D. The supposed contradiction is: “From D ˜ follows logically D.” The elements of this set, value canon, or scientific/expert opinion DP are: U = unrestricted liberal domain or free choice between democratically possible alternatives, permitting the greatest democratically possible liberal freedom of choice; P = understood here as the extended Pareto Principle; I = independence of irrelevant alternatives, for instance, one cannot chose someone as president solely because of his or her race or telegenic qualities; D = the ˜ conflict solution should not depend on a dictator, i.e., non-dictatorship; dictators are not necessarily political dictators who rule by force; in democracies, there may be cultural dictators (Arrow 1963: 30f, 85; Sen 1970: 21-32, 37f, 42, 45-46, 48-55). MV is the majority vote. The Human Rights principle HR holds in welfare democracies only. One of the consequences of Arrow’s impossibility theorem is: Complex theories of how democracies work cannot be modelled in a purely logical fashion. It is one of the impossibility problems, which haunt philosophies, whether social, logical, or something else. Gödel’s purely logical impossibility theorem is the most famous one. According to this theorem, it is impossible to formalize a consistency proof for a complex logical system within this system itself. In our case, we know that the culprit is the RNMNS method and the empirical social principles which induce nonlinearity, intransitivities, and unpredictability (Barrow 1999: 242-247). The same holds when we introduce random events into traditional deductive systems. The impossibility of using a merely logical reconstruction of democracies is one of the consequences of the RNMNS method which, in the last century, shook the fundament of traditional economics and its deterministic predictions. For example, the C1-C3 conditions exclude in democracies deterministic future predictions for single individual values and opinions and allow only average expectations. Another example is any majority decision in democracies. It holds if many opposing individuals prefer a valuei or opinioni and its number is greater as the number of individuals voting for valuej or opinionj. In democracies, any fifty:fifty vote (distribution) means an undecided vote and has to be annulled or repeated. But logically, undecided votes are not possible and the system becomes nonlinear. In this nonlinear system, solutions which would be considered contradictory in a logical system, are now characterized simply by ȕ = 0.5 and (1-ȕ) = 0.5. To sum it up: In nonlinear theories of democratic societies, Arrow’s impossibility theorem withered away.

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It is no wonder that collective choice theory suffered in the eighties the same fate as the natural sciences in the thirties when their deterministic natural laws had to be changed into highly confirmed statistical laws or default rules. Another example: When in the eighties, traditional game theory became an evolutionary game theory, it lost its deductive character (Weibull 1996; Gintis 2000; Leinfellner 1984; 1988; 1995; 2000; 2001; Leinfellner/Köhler 1998). Thus, under the influence of the RNMNS method cum C1-C3, democratic principles became default rules, and collective choice theory a nonlinear, causally “soft” and complex theory. Social solutions S of conflicts and predictions are now always statistical mixtures of [ȕ S1 , (1-ȕ)S2], where ȕ indicates the frequency distribution or the common social strength of individual values or opinions, e.g., after a vote in democracies. This “soft”, nonlinear collective choice theory freed traditional social choice theory from its deductive straitjacket. Democracies do not function as deduction would prescribe: They are evolutionary, open systems which are regulated by democratic, empirical, prescriptive, and accepted pragmatic welfare rules, not by logical principles or axioms. Here, a generation after Ramsey, we see again the strong impact of the RNMNS method and Criteria C1-C3. Social choice theory, utility or value theory, decision theory, game theory, evolutionary game theory, and related theories function under pragmatic democratic principles or laws and rest on the RNNMS method and the criteria C1-C3. Without the democratic principles DP, collective choice theories could not be formulated (Arrow 1963; Rawls 1971; Sen 1970; Leinfellner 1995; 2001). Arrow (1963: Ch. 3) and, later on, Sen (1970) have defined an effective minimal set DP, or value canon, of democratic principles as descriptive default rules which are imposed on mathematical, e.g., gametheoretical, rules for the computation of socially optimal solutions in democratic societies. T HE PURPOSE OF THIS PAPER The purpose of this section is to show that Damasio’s somatic, brainphysiological theory can be used as the physiological and neurological fundament of a general theory of value creation, which begins with the human creation of values, continues with the RNMNS method cum C1-C3, and ends with the collective choice theory. The intended result is a general value theory for representative and welfare democracies. The steps are the following: 1. Damasio’s fundamental theory explains in detail how the human body blindly, at random creates unpredictable mixtures M, i.e., random sets, of all kind of values, e.g., potentially scientific ones, ordinary nonscientific ones, opinions, beliefs; the values may be completely new. In the course of further processing, some values of the random set M may reach our consciousness as given preferences; we consider these values as prima facie values. Damasio’s theory, then, provides a new fundament for the somatic and brain-based RNMNS

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method and the C1-C3 conditions, since it deals with the origin and creation of preferences and values out of a bodily and brain-based cognitive neuronal value processing. 2. After the values have been created, the RNMNS method and C1-C3 allow us to separate the given preferences into scientific, empirically applicable values, opinions and beliefs, and all the others. Thereby, the traditional social sciences become nonlinear which may be considered a disadvantage by some. An advantage is that we are now able to measure scientific values with the aid of the utility functions of utility theory and offer quantitative, empirically applicable solutions of social conflicts. 3. Finally, with C3, collective choice theory imposes democratic collective welfare principles DP on scientific individual values, opinions, and beliefs. Furthermore, collective choice theory allows us to explain how individual scientific values, opinions, and beliefs can be changed into social collective ones by means of social welfare functions, provided a democratic framework. One of the democratic welfare functions is the majority principle. 4. The unification of 1, 2, and 3 has the advantage that we can now explain how scientific values, opinions, and beliefs work quantitatively in democracies and how to optimally solve social conflicts in democracies, not necessarily in other forms of government. The disadvantage is that scientific values are not the only one that may get the majority in, e.g., democratically elected parliaments. In such a case, only the RNMNS method and the criteria C1-C3 can come to the rescue and help us to avoid catastrophes and the breakdown of democracies caused by nonscientific and empirically unfeasible values, opinions, beliefs. We will now discuss some details of such a general theory of values. According to Damasio, such theory cannot be any longer a dualistic body-mind theory. D AMASIO ’ S SOMATIC MARKER THEORY AND THE CREATION OF HUMAN SCIENTIFIC AND NONSCIENTIFIC VALUES , OPINIONS , AND BELIEFS Damasio investigated brain-physiologically and practically for the first time in history how human evaluations, values, and opinions originate from bodily, chemically and physiologically aroused somatic markers, (primary and secondary) emotions, and feelings. The body-brain is described as a dynamic unit of them. The incoming sensations generate at first in our bodies chemically and physiologically aroused somatic states, i.e., somatic markers, or primary emotions, felt as pain, pleasure or plus of individual, or even primitive collective welfare according to Harsanyi (1976: 46). Patterns of primary emotions emerge. This interactive value processing can be described schematically as a constantly occurring sequence of bodily aroused markers p primitive emotions p secondary emotions pfeelings p conscious preferences. This process, then, is a bod-

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ily induced, brainphysiological, cognitive, memory-bound Bayesian learning which lasts as long as we live, even though each individual value process lasts only for milliseconds. It is the internal creation of primary and secondary emotions (feelings) as predecessors of conscious preferences, values, and opinions which steer our human conscious decision making (Damasio 1999: 20, 83-85, 134, 191; Leinfellner 1988: 349-353). Thus the body provides ground level (primary and secondary) emotions, or feelings, which are signalled to the somatosensory cortex of the brain and back (Damasio 1994: 133, 173, 184). Via feelings, emotions gradually become conscious. In the beginning, feelings are only prestages of conscious, linguistically expressible preferences and values. It is their neural representation unto the brain stem (the amygdala) and the human forebrain which bestows degrees of consciousness by feelings, and, finally, full consciousness on them. The steadily ongoing individual processing, i.e., the representation of bodily emotions and feelings unto our forebrain, creates step by step somatically or neocortically half or fully conscious values expressible in language. Damasio explains that, without the creation of new values, there is no purposeful acting, no decision making possible (Damasio 1994: 177; 1999: 319f). Once values, preferences etc. have become conscious, one can separate scientific from nonscientific values etc. by the RNMNS method cum C1-C3, as already described. The value processing continues with the formation of collective values as already discussed. Social choice theory explains how values become social collective values. T WO MAIN KINDS OF VALUES : S CIENTIFIC VERSUS ORDINARY VALUES Besides other things, Damasio’s theory explains the somatic and brain-based, step-by-step creation not of single values but of unpredictable mixtures M of potentially scientific and nonscientific values, where ȕ indicates the frequency of scientific values SV and (1-ȕ) the frequency of ordinary values SV: M= [ȕ SV, ˜ (1-ȕ) SV] in any society (cf. Damasio 1999: 8-10; 2003: 319). Some of these values˜may pass the RNMNS procedure cum C1-C3 and become checked scientific values. The process thus described can be a creative, self-organizing process which is supported by a primitive memory and learning (Damasio 2003: 3-33; 1999: 68, 272, 318-320). To sum it up: In any democratic system, there exist in M two completely different kinds of values, opinions, and beliefs with changing frequencies: 1. scientific ones which have successfully passed, or will pass, the tests prescribed by the RNMNS method and the C1-C3 criteria; 2. values, opinions, beliefs which did not pass the RNMNS method and the C1-C3 criteria. The latter are going around in our minds just like scientific values, opinions, and beliefs; they are being discussed and published, they spread and replicate also in democracies. In the worst case, they may even become the opinion of the majority and win elections by majority voting. They may also become programs

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and platforms of ruling parties. But ordinary, superfluous values can be corrected and improved, hopefully before they have caused any damage. The improved version may be accepted as scientific values, since improvement is an evolutionary process. One reason for the spread of nonscientific values, opinions, beliefs is: In democracies, the freedom of speech provides a wide leeway also for the discussion of ordinary values and opinions and does not hinder the spread of nonscientific values, opinions, and beliefs unhampered by the RNMNS method and the C1-C3 criteria. These are treacherous if one persuades the citizens to accept them as scientific, despite the fact that they are false, for instance pre-election pledges which cannot be fulfilled. Ordinary values, opinions, and beliefs are used frequently in spite of being empirically inapplicable even though they may be sometimes serially ordered; often they are chaotic. If we, against better knowledge, use ordinary values and opinions in politics and economics, we have to bear sooner or later their bad consequences. Even in democracies, then, these two sets of values exist side by side. “Leftover” ordinary opinions are in most instances not empirically applicable in democracies, since they have not passed or cannot pass the RNMNS procedure cum C1-C3. They are, nevertheless, abundant. The question, Where do both come from? Who or what created them? has been answered by Damasio. As already said: Damasio offers a completely new answer: Both are constantly created prima facie by a somatic-neurological, physiological, and brain-based primitive cognitive process. T HE PRESENT CRISIS OF VALUES , OPINIONS AND BELIEFS IN DEMOCRACIES We will now shortly discuss also the fate of nonscientific, “leftover” values and opinions and their social, political, economic, and cultural role in democracies. Despite the fact that the RNMNS method and the C1-C3 criteria are our most important means to separate scientific, rational values and opinions from not rational, not scientific ones – “rational” understood as in Criterion C2 – the nonscientific values can often become more important than the scientific ones. Unfortunately, in democracies scientific, often irrational, empirically false, popular, chaotic, and postmodern values, opinions, and beliefs have their own way of life. The situation becomes critical and worse when nonscientific values, opinions and beliefs multiply and, by a majority vote, may proceed to dominate our life in democracies. Seen evolutionarily, both kinds of values and opinions grow in democracies by imitation and replication, survive or disappear (Schuster/Sigmund 1983; Sigmund 1993). If nonscientific, but powerful and dominant values, opinions, beliefs cannot be improved so that they fulfill the RNMNS and the C1-C3 tests, they may become detrimental for democracies and even ruin them, when they dominate the parliaments.

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Finally, this throws a new light on the RNMNS method and the C1-C3 criteria, which turn out to be our most important scientific tool for all social sciences and for our representative democracies in order to prevent the takeover of nonscientific values, opinions and beliefs, and to save, at the same time, the presently endangered welfare democracies. Nevertheless, nonscientific values, opinions etc. are created constantly. It would need a deus ex machina to prevent them in advance. H UMAN V ALUE P ROCESSING : R ANDOMIZERS AND CREATIVITY Somatic markers and bodily emotions are constantly produced and literally created by the cognitive body-brain interaction as responses to external sensations and random changes. Random changes now are the fundamental precondition of being innovative and creative, but not all random changes lead to innovations. Since somatic markers are dependent on random events, their creation is blind and the produced mixture M is generated at random and unpredictable (Boden 1991; Leinfellner 2001: 222-232). Somatic, brain-physiological creative processes create new values, values which have not existed within living memory, and begin with the creation of new somatic markers. They cannot be planned or predicted (Damasio 1999: 122; Leinfellner 2001). The processes of the creation of new values provide more than consciousness, logic, and even science can provide. Creation means simply to go where nobody has gone before. Any innovative, creative process begins with the production of huge random sets M of possible values out of which we can select by the RNMNS method and C1-C3 those scientific ones which serve our democracies. To summarize: Since preferences, values must be created by our body and its value processing brain, human creativity is unthinkable without neuronal and bodily randomizers which produce a random set M. As already mentioned, M may contain not yet used and not previously existing, possible, prima facie values, opinions, beliefs. From this random set M of potentially scientifically correct and potentially nonscientific values, of ordinary values and opinions, of empirically inapplicable and even chaotic, abstruse and postmodern “anything goes” values and opinions only our RNMNS and C1-C3 testing can separate the new scientific values and opinions. This is a complex Bayesian trial-and-error approach, based on somatic neuronal randomizers which generate the set M (Leinfellner 2001). Only the RNMNS and the C1-C3 criteria together with the democratic rules DP can help us to prevent our falling into the trap of unfounded ordinary values, opinions, and beliefs. So far, this functions successfully only in representative democracies and democratic welfare states. As Abraham Lincoln has said: “You may fool all the people some of the time; you can even fool some of the people all the time; but you can’t fool all of the people all the time.”

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In a recent prepublication of the Boltzmann Institute for Scientific Research of the University of Graz, Leinfellner has outlined the consequences of the RNNMS method and their Criteria C1-C3 for the contemporary social, political, economic sciences, for neuropsychology and for post-modernism. To explain this in detail would go beyond the scope of this article.

R EFERENCES Allais, Maurice. 1994a. Absolute Satisfaction. In: Allais/Hagen 1994: 1-29. Allais, Maurice. 1994b. Determination of Cardinal Utility According to an Intrinsic Invariant Model. In: Allais/Hagen 1994: 31-64. Allais, Maurice/Hagen, Ole (eds.). 1994. Cardinalism: A Fundamental Approach. Dordrecht/Boston: Kluwer. Arrow, Kenneth J. 1963 (2nd edition). Social Choice and Individual Values. New Haven/London: Yale University Press. Barrow, John D. 1998. Impossibility: The Limits of Science and the Science of Limits. London [etc.]: Vintage/Random House. Basar, Erol (ed.). 1988a. Dynamics of Sensory and Cognitive Processing by the Brain. Berlin [etc.]: Springer. Basar, Erol. 1988b. Dynamics and Evoked Potentials in Sensory and Cognitive Processing by the Brain. In: Basar 1988a: 30-55. Boden, Margaret A. 1991. The Creative Mind: Myths and Mechanisms. n.p.: Basic Books. Dahrendorf, Ralf. 1988. The Modern Social Conflict. New York, NY: Weidenfeld and Nicolson. Damasio, Antonio. 1994. Descartes’ Error: Emotion, Reason, and the Human Brain. New York, NY: Putnam. Damasio, Antonio. 1999. The Feeling of What Happens: Body and Emotion in the Making of Consciousness. New York, NY [etc.]: Harcourt, Brace & Co. Damasio, Antonio. 2003. Looking for Spinoza: Joy, Sorrow, and the Feeling Brain. London, GB [etc.]: Random House. de Finetti, B. 1937. La Prévision, ses lois loguiqes, ses sources subjectives. Republished in English in: Kyburg/Smokler 1964. Gintis, Herbert. 2000. Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction. Princeton, NJ: Princeton University Press. Götschl, Johann (ed.). 1995. Revolutionary Changes in Understanding Man and Society: Scopes and Limits. Dordrecht, NL [etc.]: Kluwer. Götschl, Johann (ed.). 2001. Evolution and Progress in Democracies: Towards a New Foundation of a Knowledge Society. Dordrecht [etc.]: Kluwer. Harsanyi, John C. 197a. Essays on Ethics, Social Behavior, and Scientific Explanation. Dordrecht, NL / Boston, MA: Reidel. Kuttner, Robert. 1991. The End of Laissez-Faire: National Purpose and the Global Economy after the Cold War. New York, NY: Knopf. Kyburg, H. E./Smokler, H. (eds.). 1964. Studies in Subjective Probabilities. New York, NY: Wiley. Leinfellner, Werner. 1964a. Werttheorien und ihre formale Behandlung I. In: Wissenschaft und Weltbild Vol. 17 (1964): 195-214. Leinfellner, Werner. 1964b. Werttheorien und ihre formale Behandlung II. In: Wissenschaft und Weltbild Vol. 17 (1964): 268-278. Leinfellner, Werner. 1974 (third edition). Einführung in die Erkenntnis- und Wissenschaftstheorie. Mannheim: Bibliographisches Institut. Leinfellner, Werner. 1984. Evolutionary Causality, Theory of Games, and Evolution of Intelligence. In: Wuketits 1984: 233-276. Leinfellner, Werner. 1988. The Brain-Wave Model as a Protosemantic Model. In: Basar 1988: 349353. Leinfellner, Werner. 1995. The New Theory of Evolution: A Theory of Democratic Societies. In: Götschl 1995: 149-191. Leinfellner, Werner. 1998. Game Theory, Sociodynamics, and Cultural Evolution. In: Leinfellner / Köhler 1998: 197-210.

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Leinfellner, Werner. 2000. The Role of Creativity and Randomizers in Societal Human Conflict and Problem Solving. In: La Nuova Critica: Nuova Serie, Vol. 36: 5-27. Leinfellner, Werner. 2001. Towards a Bayesian Theory of Self-Organization, Societal Evolution, Creativity, and the Role of Randomizers in the Societal Evolution. In: Götschl 2001: 211-238. Leinfellner, Werner/Köhler, Eckehart (eds.). 1998. Game Theory, Experience, Rationality. Dordrecht, NL [etc.]: Kluwer. Marschak, Jacob. 1974. Economic Information, Decision, and Prediction: Selected Essays, Vol. 1. Dordrecht, NL/Boston, MA: Reidel. Munier, Bertrand R. 2001. Market Uncertainty and the Process of Belief Formation. In: Götschl 2001: 107-122. Nash, John. 2002a. The Essential John Nash, ed. by Harold W. Kuhn/Sylvia Nasar. Princeton / Oxford: Princeton University Press. Nash, John. 2002b [1950]. The Bargaining Problem. In: Nash 2002a: 37-46. Neumann, John von/Morgenstern, Oskar. 1961 [1944]. Spieltheorie und wirtschaftliches Verhalten. Würzburg: Physica. Pigou, Arthur Cecil. 1912 [Facsimile Reprint 1998]. Wealth and Welfare. London: MacMillan [Reprint Düsseldorf: Wirtschaft und Finanzen]. Ramsey, Frank Plumpton. 1931a. The Foundations of Mathematics and Other Logical Essays, ed. by R. B. Braithwaite. London [etc.]: Kegan Paul [etc.]. Ramsey, Frank Plumpton. 1931b [1926a]. Mathematical Logic. In: Ramsey 1931a: 62-81. Ramsey, Frank Plumpton. 1931c [1928]. Further Considerations. In: Ramsey 1931a: 199-211. Ramsey, Frank Plumpton. 1931d [1929]. Probability and Partial Belief. In: Ramsey 1931a: 256-257. Ramsey, Frank Plumpton. 1931e [1926b]. Truth and Probability. In: Ramsey 1931a: 156-198. Rawls, John. 1971. A Theory of Justice. Cambridge, MA: Harvard University Press/Belknap Press. Rawls, John. 2001. Justice as Fairness: A Restatement. Cambridge, MA: Harvard University Press / Belknap Press. Samuelson, Paul A. 1970 (8th edition). Economics. New York, NY [etc.]: McGraw Hill. Schuster, P./Sigmund, K. 1983. Replicator Dynamics. In: Journal of Theoretical Biology 100: 533538. Sen, Amartya K. 1970. Collective Choice and Social Welfare. San Francisco, CA [etc.]: Holden-Day [etc.]. Sigmund, Karl. 1993. Games of Life: Explorations in Ecology. Evolution, and Behaviour. London, GB [etc.]: Penguin. Suppes, Patrick/Zinnes Joseph L. (eds.). 1963a. Handbook of Mathematical Psychology, Vol. 1. New York, NY [etc.]: Wiley. Suppes, Patrick/Zinnes Joseph L. 1963b. Basic Measurement Theory. In: Suppes/Zinnes 1963a: 1-76. Tulving, Endel. 1983. Elements of Episodic Memory. New York, NY [etc.]: Oxford University Press. Weibull, Jörgen W. 1995. Evolutionary Game Theory. Cambridge, MA/London, GB: MIT Press. Wuketits, Franz (ed.). 1984. Concepts and Approaches in Evolutionary Epistemology. Dordrecht / Boston: Reidel.

Boltzmann Institute for Scientific Research University of Graz Mozartgasse 14 A-8010 Graz Austria

M ARIA C ARLA G ALAVOTTI

RAMSEY’S “NOTE ON TIME”

F OREWORD Ramsey’s “Note on Time”, published here for the first time, belongs to the Ramsey Collection, held at the Hillman Library of the University of Pittsburgh as part of the “Archives for Scientific Philosophy in the Twentieth Century”. Before we turn to Ramsey’s text, a few remarks on the Ramsey Collection are appropriate. The collection includes about 120 documents (for the most part manuscripts), contained in seven boxes, for a total of roughly 1500 pages. A number of them are manuscript versions of articles which appeared in print during Ramsey’s lifetime, or in the three collections The Foundations of Mathematics edited by Richard Bevan Braithwaite in 1931, and Foundations (1978) and Philosophical Papers (1990), both edited by Hugh Mellor – all of which cover to a large extent the same material. From 1989 on, a remarkable number of manuscripts belonging to the Ramsey Collection were published, like the articles “Principles of Finitist Mathematics”, edited by Ulrich Majer for the History of Philosophy Quarterly, 1989, and “Weight or the Value of Knowledge”, published with a “Preamble” by Nils-Eric Sahlin in the British Journal for the Philosophy of Science, 1990. In addition, the volume On Truth, edited by Nicholas Rescher and Ulrich Majer, appeared in 1991, containing the material written by Ramsey between 1927 and 1929 as part of a planned book, meant to bear the title On Truth and Probability, of which there are a number of tables of contents in the Collection. The volume On Truth includes two more papers belonging to the Ramsey Collection, namely “The Nature of Propositions”, read at the Cambridge Moral Sciences Club in 1921, and “Induction: Keynes and Wittgenstein”, read to the “Apostles” in 1922, plus the note “The ‘Long’ and the ‘Short’ of it or a Failure of Logic”, which is a slightly different version of the article “Achilles and the Tortoise”, published in The Forum in 1927 – and more recently republished in volume X of Bertrand Russell’s Collected Papers 1. One more collection of Ramsey’s papers, edited by myself under the title Notes on Philosophy, Probability and Mathematics, was published in 1991. The collection contains the transcription of 86 documents of the Ramsey Collection, most of which appeared there in print for the first time. The papers cover a wide range of topics: from meaning to identity, theories, hypothetical propositions and 155 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 155–165. © 2006 Springer. Printed in the Netherlands.

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probability. Various topics on the foundations of mathematics, such as formalism, intuitionism and finitism are also covered. In addition, the volume includes eight papers read to the Apostles between 1921 and 1925, a letter from Wittgenstein to Ramsey on identity dated 1927, and two drafts of Ramsey’s reply. The note on time which is published here does not appear in Notes on Philosophy, Probability and Mathematics. The Ramsey Collection still comprises a group of unpublished papers, including various technical writings focused on the decision problem (the so-called Entscheidungsproblem) and commentaries on such thinkers as Plato, Aristotle, Hume, Kant, Johnson, Moore, Bradley, Bosanquet, Keynes, Russell, Peirce, Hilbert, Bernays, Brower, Skolem, Weyl, and many others, including Freud. Ramsey’s early papers on political and philosophical topics, contained in three notebooks written when he was an undergraduate, are also of interest. On their own, these papers would make for a publication that would not only be a testimonial of Ramsey’s extraordinary precocity and brilliance, but also a historical document reflecting the social and cultural atmosphere of his time. The Ramsey Collection has a few more treasures to be disclosed to researchers of good will. R AMSEY ’ S MANUSCRIPT The text reported hereafter is a transcription of Ramsey’s “Note on Time”. This represents manuscript 002.07.02 of the Ramsey Collection, Archives for Scientific Philosophy in the Twentieth Century, Hillman Library, Pittsburgh, here quoted by permission of the University of Pittsburgh. All rights reserved. The editing has been done in such a way as to preserve as much as possible of the original text: words or passages which appear struck out in the manuscript have been restored and reported in footnotes. The editor’s insertions throughout the text have been put in square brackets. As editor of this note, I warmly thank the late Margaret Paul, Ramsey’s sister, for her help in deciphering a few words of the manuscript during a visit I paid her in Oxford in summer 1994. Here follows Ramsey’s text: N.B. This comes in connexion with Broad’s doctrine that no prop[osition] about the future is true or false. Note on Time 2

Dr. Broad in Scientific Thought, the late McTaggart in The Nature of Existence vol II, and Mr. Dunne in An Experiment with Time have all found substantially the same difficulty in the fact that every event has (at different times) the three incompatible characteristics of pastness, presentness and futurity, and further that events change with respect to these characteristics from being future to being present and from being present to being past. Ordinary change is a change of objects in time, but this appears to be a change of time itself. To solve this difficulty3 Mr. Dunne has suggested a second time series, for4 our ordinary time series to change in, and a third for this second to change in and so on ad

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infinitum; Dr. McTaggart has declared that time is unreal and Dr. Broad has tried to save its reality by an elaborate theory. I should like, however, to suggest that there is no need for any such heroic solution since the initial difficulty5 is simply a mistake. What do people mean by “present”, “past” and “future”? By “the present time” a man means the time at which he is speaking, by calling an event present he means that it is at that time, or in other words that it is simultaneous with his speech, and past and future are defined as meaning respectively before and after the present. From this it is clear that the word “present” has a different meaning at every time at which it is used. When I used it yesterday, I meant6 what I now call yesterday; when I use it now I mean7 to-day. In this respect it is exactly like the word “mine” 8; which has a different meaning for every person who uses it. Every age or time calls itself the present, earlier ages9 past, later ages future. This is no more mysterious or difficult, than that every man calls himself I; the person he is talking to you and other people he. When a man10 changes from being I to being you in a conversation, this is not a change in his nature, but in what he is called. Just so events do not change their temporal relations, and then11 change from present to past is not a change in them at all, but merely in what we call them. (It is clear that this can occur; the number two cannot change but its name can change from duo to deux or two.) Events do not become present, it is the word “present” which comes to mean them; what changes is not the event but the meaning of the word. But you will say “the present” never changes in meaning, it always means “the time at which it is used”. But this is not its meaning, it is the law by which its meaning is on each occasion determined. Just so “I” means the speaker. But it does not mean that it always has the same meaning; if one man says “I did”, the other “I didn’t”, they are not contradicting one another, they mean different things and what each means can be determined from the rule that “I” means the speaker. We see that the fact might be better expressed by saying on each occasion on which it is used, “the present” means the time at which it is used, i.e. on each occasion it means something different. It is worth considering a little further how the mistake arises; in part it may be due to this ambiguity of the word present, but more, I think, to a source of confusion which arises when we try to imagine a temporal series of events. One way of doing this is to go through the events one after another in the order in which they happened, as when one rehearses a tune in one’s mind. But this method is often unsatisfactory as we want to have all the events in our mind at once in order better to see their relations, we then imagine them spread out before us along a line like the notes in a score. The defect of this method is that their time order is replaced by a space order, which does not share its “sense”; the difference between “before” and ”after” is lost. To overcome this we are apt to imagine each of the events spread out before us being lit up in turn by the bull’s eye lantern of presentness, and take presentness to be a real quality possessed by each event in turn12 as it moves down the series. 13We must either follow Mr. Dunne by taking this motion of presentness as being in another time system, or else we get landed in the fearful difficulty of each event having incompatible characteristics. Dr. Broad proposes to get over this by declaring the future non-existent, so that no event is ever future; on this view it is true that events do not have incompatible characteristics, but certain propositions seem still to be both true and false. e.g. [“] there is in the universe no such thing as the death of Queen Anne [”] was true up to 1714, false thereafter and the difficulty is not really removed. Bur clearly the whole difficulty is a mistake; the events are really in temporal order one before the other; each is present to or simultaneous with itself, future to the preceding

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ones past to the subsequent. The moving present is really the series of events themselves; only when the temporal series is replaced in imagination by a spatial series, do we try to restore its temporal quality by introducing presentness from outside. This is not to say that we cannot legitimately represent a temporal series by a spatial one, provided we are prepared to keep to it to allow (say) [“] to the left of [”] to stand by convention for [“] before [”] and not attempt simultaneously an imaginative realisation of the temporal relationship.

E DITOR ’ S COMMENTS ON R AMSEY ’ S NOTE Ramsey’s note features his particular way of addressing philosophical problems. On reading it through, one can see Ramsey’s intellect at work, that intellect that John Maynard Keynes in his obituary of Ramsey called “amazing” because of its powers and “easy efficiency” 14, and Dora Carrington in a letter to Lytton Strachey of 1923 depicted as so impressive as to deserve the title of “devastating” 15. When applied to Ramsey’s way of addressing philosophical problems, Carrington’s characterization is apt, for Ramsey literally jumps into the problem at hand and tries to dissolve it. In this enterprise, he is guided by a genuinely pragmatical approach, which leads him to look at problems from our perspective as human beings, acting according to our beliefs. This attitude is reflected by Keynes’ claim that “Ramsey reminds one of Hume more than anyone else, particularly in his common sense and a sort of hard-headed practicality towards the whole business” 16. It is precisely with such “hard-headed practicality” that Ramsey addresses the problem of time. Ramsey’s pages bear a strong resemblance to the second part of Chapter V: “Judgment and time [or? Time and the mind]” of On Truth. On the basis of this and other clues, the note (which is not dated) was probably written around 1928. Reference to McTaggart’s The Nature of Existence and Dunne’s An Experiment with Time, both published in 1927, obviously indicate that the note cannot have been written earlier. A further clue comes from Supplementary volume VIII of the Proceedings of the Aristotelian Society of 1928, collecting the proceedings of a symposium on “Time and Change”, with papers by J. Macmurray, Richard Bevan Braithwaite and Charlie Dunbar Broad. Ramsey’s note could be somehow related to that; he might have written it during or after the session of the Aristotelian Society, or before it, since there was the habit of circulating papers beforehand. Afterwards, he could have drawn from such notes the material for the chapter of the book he was writing. Of the three authors commented upon by Ramsey in his note, Dunne is likely to be almost unknown to the present day philosophical public. John William Dunne (1875-1949) is described as an “inventor and philosopher” in The Dictionary of National Biography (Missing Persons), 1993 Edition 17. Son of a general, he was born and brought up in South Africa, became an aeronautical engineer, and in that capacity designed a revolutionary type of monoplane with swept-back wings and no tail. The War Office employed him, with a view to the production of a prototype, but in the end his model was not accepted. His first

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book was a guide to dry-fly fishing (Sunshine and the Dry-Fly, London 1924). He won renown with the book mentioned by Ramsey, namely An Experiment with Time, first published in 1927 (third revised edition 1934), which became a best-seller, and was reprinted many times over a period of about fifty years. Other books by Dunne are The Serial Universe (London, 1934), meant as a continuation of An Experiment with Time; The New Immortality (London, 1938), Nothing Dies (London, 1940), Intrusions? (Published posthumously: London, 1955). An Experiment with Time attracted the attention of various writers, including John Boynton Priestley and Herbert George Wells, who praised Dunne in their writings and acknowledged his influence. Priestley, a well known novelist and playwright, devoted a chapter of his book Man and Time to Dunne’s “serialism”, and based on it his play Time and the Conways (1937). Dunne’s serialism originated from the consideration that certain dreams seem to foreshadow future experiences. Dunne called this phenomenon “displacement of time”, and set about explaining it in a somewhat positivistic spirit. He tried to transmit to his readers a truly experimental attitude, suggesting that they keep pad and pencil on their bedside table, to be able to record dreams immediately on awakening. In this way, they would eventually be in a position to experience the phenomenon in question, and be ready to appreciate his theory of time, meant to account for precognitive dreams. Dunne’s influence on his readers was such that talk of “Dunne’s dreams” became commonplace: probably a favourite topic of conversation at parties, but there must have been more to it, since the third edition of An Experiment with Time includes an Appendix with an extract from a letter of Arthur Eddington, which should count as evidence that the latter took Dunne’s theory of time quite seriously18. For the curious reader’s benefit, the gist of Dunne’s theory is a distinction between “Time length” and “Time motion”. While reaffirming the traditional distinction between past, present and future with respect to time length, Dunne claimed that time motion is to be seen as moving along time length. He then added that “motion in time must be timeable”, because if motion were everywhere in time length, it would not be moving at all. Dunne observed that in order to set the timing of time movement, another time is required, so the Time which times such movement needs to be a different Time, say Time2. In turn, the moving of Time2 requires a Time3 to be timeable, and so on. Accordingly, time change gives rise to a hierarchy of time series, which implies an “apparent series to infinity”19. This serial notion of time requires an analogous serialism with regard to observers, so that there is an Observer1 in Time1, an Observer2 in Time2 and so on. Dunne was not at all concerned by the infinite regress postulated by his theory. In his “Replies to critics”, published in the third edition of An Experiment with Time, he says that philosophers are wrongly suspicious of infinite regress, because “infinite regress is, after all, the proper and valid description of the mind’s relation to its objective universe” 20. By means of the conceptual machinery of serial time Dunne tried to explain precognitive dreams as follows. Take an Observer1 in Time1, and an Observer2 in

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Time2. Observer1 is immersed in a three-dimensional space, where he lives and makes experiences which are observed by Observer2. The latter, however, is located in four-dimensional Time2, where not only the past, but also the future are open to him. What happens is that while Observer1 is awake, he captures the attention of Observer2 who basically just registers the experiences of Observer1, but when the latter is asleep Observer2 is free to range freely between past and future, and occasionally this brings about precognitive dreams. Dunne’s theory is much more complex than described here, and includes a theory of the relationship between intelligence and the brain, consciousness and unconsciousness, mortality and immortality – for Dunne we are immortal beings, because death in Time1 does not involve death at Time221. Needless to say, Dunne’s theory is open to serious objections. For instance, one might demur that it presupposes a deterministic, pre-determined world since, if Observer2 can see the future, there has to be something out there to be seen. Well aware of this possible objection, Dunne anticipated an answer, ending up with a profession of idealism, according to which it is mere materialism to insist upon a physical world existing independently of observers. But this is at odds with other pieces of his theory, such as the tenet that Observer1 is in a position to educate higher order observers to interpret what they observe, precisely because the time and space constraints of Observer1 enable him to focus and sharpen his attention, so as to form a solid experience22. As already said, there is much more to Dunne’s theory of time; so much that it seems advisable to stop here. The other thinkers addressed by Ramsey do not need much presentation. John (McTaggart Ellis) McTaggart (1866-1925) was a well known British idealist, author of Studies in Hegelian Dialectic (1896) and Studies in Hegelian Cosmology (1901). The book mentioned by Ramsey, namely The Nature of Existence, was published in 1927. Concerning time, in 1908 McTaggart had already published a famous article in Mind, called “The Unreality of Time”, where he spelled out an argument, which was to become very influential, to the effect that there is no such thing as time. In a nutshell, McTaggart’s argument goes as follows. Events can be ordered in time in two different ways, namely according to a system of tenses or according to a system of dates. In the first case, the description of events includes mention of past, present and future, and gives rise to what he calls an A-series. In the second case, the description of events is not obtained by reference to pastness, presentness and futurity, being rather rendered by means of relations such as “earlier than”, “later than”, “simultaneous with”; in which case we have a B-series. McTaggart claimed that the notion of A-series is essential to the characterization of time, because time involves change and only A-series involve change, whereas B-series are immutable. Having argued thus, McTaggart went on to claim that the notion of A-series is contradictory, because the properties characterizing such series – namely presentness, pastness and futurity – are incompatible with one another, for the simple reason that the same event would be past, present and future. He then concludes that, the A-series being contradictory, time, which is based upon it, is unreal.

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Charlie Dunbar Broad (1887-1971) succeeded McTaggart as Fellow in Moral Science at Trinity in 1923. He wrote a number of influential books, such as Scientific Thought (1923), The Mind and its Place in Nature (1925), Five Types of Ethical Theory (1930) and Examination of McTaggart’s Philosophy (1933). Broad opted for a “tensed” theory of time, which takes the notion of “absolute becoming” as an irreducible feature of the world. Within such a theory, a pivotal role was assigned to “presentness”, seen as moving along the time series in a fixed relation. Contextually, Broad denied the existence of the future, on the basis of the consideration that judgments about the past and present can be said to be true or false, whereas the same does not hold for judgments about the future. To illustrate his view Broad discussed McTaggart’s example, also mentioned by Ramsey. In Broad’s words: “Let us take M’Taggart’s example of the death of Queen Anne, as an event which is supposed to combine the incompatible characteristics of pastness, presentness, and futurity. In the first place, we may say at once that, on our view, futurity is not and never has been literally a characteristic of the event which is characterised as the death of Queen Anne. Before Anne died there was no such thing as Anne’s death, and ‘nothing’ can have no characteristics”23. Against these authors, Ramsey takes an utterly original position, arguing that to associate time with the passage from future, to present, to past, is mistaken. In fact, if it is admitted that events change in this way, it is implied that pastness, presentness and futurity are characteristics of events, but this eventually leads to the contradiction that the same event would possess all of them, and further that events change when passing from being future to being present, and from being present to being past. On the contrary, Ramsey holds that “presentness” just means the time at which one is speaking, exactly as when using “now” one means that an event is “simultaneous with his speech” 24. Ramsey compares “the present” to other indexical terms, like “I” and “you”, that are assigned a meaning by a rule which fixes their meaning depending on the context in which they occur. Exactly as “I” means the speaker in a given situation, “‘the present’ means the time at which it is used”, and therefore means something different on every occasion. As claimed in On Truth, “presentness is not a quality at all, any more than ‘you-ness’ is a quality” 25. Having made this clear, Ramsey goes on to suggest that in order to represent time we imagine events “spread out before us along a line, replacing the time order by a space order” 26. Then a “sense” is imposed on the series from the outside by a convention, by which we agree that “to the left of” stands for “before”. Contrary to Broad, Ramsey regards the “moving present” as being “really the series of events themselves”, rather than a quality possessed by “each event in turn as it moves down the series” 27. Ramsey deems the whole idea of the A and B-series, as well as the claim that time is unreal, sheer “nonsense”. Ramsey’s denial that pastness, presentness and futurity are qualities of events and that change is something that happens to events having these qualities, leads immediately to a dissolution of the whole of McTaggart’s argument. As Ramsey puts it: “There is no more mystery in an

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event being both ‘present’ (when mentioned at one time) and ‘past’ (when mentioned at another) than in a man being both ‘I’ (when spoken of by one man (himself) and ‘you’ (when spoken to by another). To infer that the time relationship is unreal is like concluding that the relationship of conversation must be unreal because in it people have the incompatible characteristics of Iness and youness” 28. He concludes that “Really, the whole idea is so silly that it is hard to see what it makes it plausible” 29. But Ramsey does not stop here. He rather makes an attempt to analyse how the mistake affecting McTaggart’s theory arose, and this is the most original aspect of his account30. According to Ramsey, McTaggart’s mistake lies with the fact that he represents time series in two different ways at the same time, and then mixes them up when they should be kept separate. In Ramsey’s words: “the whole difficulty comes from combining two disparate modes of representation” 31. The first of such ways consists in imagining a temporal series of events, put one after the other in order, as “when one rehearses a tune in one’s mind”. The other occurs when we have all the events “in our mind at once”, and we “imagine them spread out before us along a line like the notes in a score”. In the second case, however, the difference between “before” and “after” is lost, and in order to restore it “we are apt to imagine each of the events spread out before us being lit up in turn by the bull’s eye lantern of presentness, and take presentness to be a real quality possessed by each event in turn as it moves down the series” 32. At that point, one has either to invent another time series to account for the motion of presentness, as done by Dunne, or “to adopt the less logical hypotheses of McTaggart or Broad” 33. However – Ramsey claims – there is no need for such tricks, once the mistake has been recognised. Ramsey’s account of time bears a strong resemblance to that of Richard Braithwaite. In the paper belonging to the symposium “Time and Change”, Braithwaite starts from an analysis of the notion of “presentness”, which is very close to that put forward by Ramsey, and reaches a similar conclusion. After embracing what he calls a “relational view of the present, past and future” he claims that “our knowledge of time is derived not from some subtle philosophy, but from direct experience”, adding that his “contention is that the reality of time and change necessitate no particular philosophy; any metaphysic is compatible with them except one (like McTaggart’s) which denies their reality”. Braithwaite’s conclusion is that “there is no paradox or antinomy or riddle or logical problem about time” 34 and his paper ends with the claim that “As philosophers we must take time seriously, but not too seriously” 35. The literature on time has been growing constantly since Ramsey’s times, and has become so conspicuous as to be beyond our reach. Therefore, no attempt will be made to compare Ramsey’s position with that of other authors who have contributed to the literature. Rather, this commentary will end with some remarks meant to explore the connections between Ramsey’s note and the remainder of his published papers. There are hardly any references to time in the bulk of papers published in The Foundations of Mathematics and Philosophical

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Papers, except for “General Propositions and Causality”, dated 1929, in which the asymmetry between past, present and future is discussed, and related to the asymmetry of the relation of cause and effect. In this connection, Ramsey claims that “It seems to be a fundamental fact, and widely agreed upon, that the future is due to the present, or more mildly, is affected by the present, but the past is not” 36, to which he adds that “it is not clear and, if we try to make it clear, it turns into nonsense or a definition”. Then, Ramsey spells out his solution to the problem of accounting for the asymmetry in question, which amounts to the following: “What is true is this, that any present volition of ours is (for us) irrelevant to any past event. To another (or to ourselves in the future) it can serve as a sign of the past, but to us now what we do affects only the probability of the future. This seems to me the root of the matter; that I cannot affect the past, is a way of saying something quite clearly true about my degrees of belief ” 37. Ramsey seems to be willing to derive the direction of time from the direction of the causal relation. Like the causal relation, which Ramsey construes as rooted in our being agents, time is a component of our nature as human beings, acting on the basis of beliefs. Indeed, in one of the notes published in the collection Notes on Philosophy, Probability and Mathematics, Ramsey held that time is an essential component of belief, and maintains that “belief presupposes time” 38. The volume Notes on Philosophy, Probability and Mathematics contains a number of references to time. Albeit fragmentary, they suggest that at least part of the importance ascribed by Ramsey to the notion of time is connected with defining what is meant by “subject”, and that time is seen as a component of consciousness, judgment and belief. In the note “Refutation of solipsism” we read that “Experience has essential a subject unless it is timeless; ‘now’ is the subject which knows about itself ” 39; and in the note “The subject”, Ramsey claims that “Now is a subject, which knows about itself. To deny the subject means to have only solipsism of the present moment, and indeed is not possible: e.g. a smell would be a one term fact; or could we divide it? Nowness is relational, in fact it is self identity” 40. The preceding remarks lead us to Ramsey’s conception of such topics as the subject, the self, self-identity, and the like. Once more, a discussion of such topics is left to more competent scholars. As the editor of Ramsey’s “Note on Time”, let me express the hope that his paper, together with the above commentary, will be of some use to all those interested in his extraordinary personality.

N OTES 1. 2.

See Russell (1996), Appendix II, pp. 587-91. The note “The “Long” and the “Short” of it or a Failure of Logic” had already appeared in American Philosophical Quarterly, 24 (1987), pp. 357-9. [Struck out:] Some, e.g.

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3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35 . 36. 37. 38. 39. 40.

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[Struck out:] the writers referred to have proposed different ([struck out:] made, very, various proposals) suggestions. [Struck out:] the first. [Struck out:] of all these philosophers. [Struck out:] that time; it contemporary with. [Struck out:] this time; contemporary with. [Struck out:] (and “now” is like “I”). [Struck out:] the preceding it calls the. [Struck out:] people. [Struck out:] when they become past. [Struck out:] possesses. [Struck out:] The notion of presentness. Keynes (1933, 1951), p. 240. “We left fortunately before his devastating intellect began, as I expect it did, to wreck the party” writes Carrington (1970, 1979, p. 256). Keynes (1933, 1951), p. 339. See p. 197. Dunne (1927, 1934), p. 215. Dunne (1927, 1934), p. 133. Ibid., p. 197. This is the topic of Dunne’s books The New Immortality (1938) and Nothing Dies (1940). For more on Dunne’s theory, the reader is referred to his books, or to Priestley (1964), Chapter 10. Broad (1923), pp. 78-80. Ramsey (1991a), p. 74. Ibid., p. 76. Ibid., p. 75. See the above “Note on Time”. Ramsey (1991a), p. 74; (parentheses in the quotation like in the original). Ibid., pp. 74-5. The originality of Ramsey’s account in this connection was pointed out to me by Jenann Ismael of the University of Arizona, whom I warmly thank for her cooperation. Ramsey (1991a), p. 75. See Ramsey’s “Note on Time”. Ramsey (1991a), p. 75. Braithwaite (1928), p. 172. Ibid., p. 174. Ramsey (1990), p. 157. Ibid., pp. 157-8. See “((What are the arguments against realism?))”, in Ramsey (1991b), p. 70. Ibid., p. 68. Ibid., p. 69.

R EFERENCES Braithwaite, Richard Bevan (1928), “Time and Change”, Proceedings of the Aristotelian Society, supplementary volume VIII, pp. 175-88. Broad, Charlie Dunbar (1923), Scientific Thought, London: Kegan Paul. Broad, Charlie Dunbar (1927), The Nature of Existence, Cambridge: Cambridge University Press. Reprinted 1968. Carrington, Dora (1970), Letters and Extracts from her Diaries, ed. by David Garnett, London: Jonathan Cape. Reprinted Oxford: Oxford University Press, 1979. Dunne, John William (1927), An Experiment with Time, London: Faber and Faber. Third edition 1934.

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Keynes, John Maynard (1933), Essays in Biography, London: Rupert Hart-Davis. Reprinted 1951. McTaggart, John (1908), “The Unreality of Time”, Mind, new series 68, pp. 457-74. McTaggart, John (1927), The Nature of Existence, Cambridge: Cambridge University Press. Priestley, John Boynton (1964), Man and Time, London: Aldus Books. Ramsey, Frank Plumpton, (1931), The Foundations of Mathematics, ed. by Richard Bevan Braithwaite, London: Routledge and Kegan Paul. Ramsey, Frank Plumpton (1978), Foundations, ed. by Hugh Mellor, London: Routledge and Kegan Paul. Ramsey, Frank Plumpton (1990), Philosophical Papers, ed. by Hugh Mellor, Cambridge: Cambridge University Press. Ramsey, Frank Plumpton (1991a), On Truth, ed. by Nicholas Rescher and Ulrich Majer, DordrechtBoston: Kluwer. Ramsey, Frank Plumpton (1991b), Notes on Philosophy, Probability and Mathematics, ed. by Maria Carla Galavotti, Naples: Bibliopolis. Russell, Bertrand (1996), Collected Papers, vol. X: A Fresh Look at Empiricism 1927-42, ed. by John G. Slater, London-New York: Routledge.

Department of Philosophy University of Bologna Via Zamboni 38 40126 Bologna Italy [email protected]

H ELEN E. L ONGINO

PHILOSOPHY OF SCIENCE AFTER THE SOCIAL TURN *

A word, first, about my title. Here, in Vienna, you might well ask, which social turn? Recently, scholars of logical empiricism and the Vienna Circle have been bringing us a different picture of logical empiricism than the one many philosophers educated in the ‘60’s, ‘70’s and ‘80’s in the United States encountered. I think here of Friedrich Stadler and Elisabeth Nemeth at this university and Nancy Cartwright, Jordi Cat, Richard Creath, Michael Friedman, Ron Giere, Alan Richardson, Thomas Uebel, elsewhere. Some have been trying to set the record straight while others are looking for a new model for philosophy of science and others some of both. The involvement of many Vienna Circle members in Red Vienna and socialist politics, the view of some, especially Otto Neurath, that the role of philosophy of science was to advance the integration of a scientific worldview and a democratic polity, gives the lie to the picture of a detached philosophy concerned only with logical structure and meaningfulness. And we are reminded that John Dewey in North America was also deeply concerned with the democracy enhancing potential of a properly reconstituted science. So, we might speak of a “social return,” or a revival of the social, that is, a reengaging with both analytical and socially normative questions about relations between science and society that characterized both philosophy in Europe and philosophy in North America before the ascendance of the North American form of logical empiricism. Of course, already in 1962, Thomas Kuhn was pointing to the importance of social factors, but the philosophy of science profession on the whole undertook to defend the integrity, objectivity, autonomy, and rationality of science from what it regarded as the irrationalism and subjectivism of Kuhn’s view. Since the 1990s, an interest in the challenges of feminism, in a critical science movement, in social-cultural studies of science, and in naturalism in philosophy, has encouraged some philosophers of science to shed their defensiveness and to think more constructively about the social dimensions of scientific knowledge. As the work of the scholars I mentioned above makes clear, there are deep resonances, areas of agreement and overlap between the concerns and approaches of the logical empiricists in their European, pre-diasporic, phase, esp. 167 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 167–177. © 2006 Springer. Printed in the Netherlands.

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those identified with the left wing of the Vienna Circle, and those of today’s philosophers, at least those partaking in this social (re)turn. At the same time there are significant differences. General philosophy of science today is still emerging from the hegemony of a stripped down logical positivism, as contrasted with the metaphysical and normative inclinations of pre-1920s philosophy. Even scientific realists work within parameters largely set by that form of logical positivism. The feminists and scholars in social and cultural studies of science who criticize those parameters are read as anti-science and anti-rational rather than opposed to a particular philosophical theory of science and rationality. So the rhetorical situation in philosophy is different. And the sciences have developed in status and achievement only dreamt of in the early decades of the century. The industrialized societies have created and inhabit a science and science-based technology saturated world. Nuclear physics gave rise to nuclear power generation and weapons capable of incinerating hundreds of thousands at a time. Genetics and molecular biology gave us insights into biological reproduction, inheritance, aspects of growth and development and cancer, as well as eugenics and the FlavrSavr Tomato. Transistors, materials science, and computing science transformed communication and data storage and processing. Scientists are consulted about policies concerning resource management, regulation of toxic exposure, food safety. Economists have gained unprecedented leverage over national policies, especially when they are basically capitalist, and the rubric “scientific” is a universally sought term of approbation. And so on. My point is that the material, as well as rhetorical, situation is different than it was. While it is both salutary and reassuring to see one’s views articulated in essays written 70 years ago, the differences in the rhetorical and material situations mean that we cannot just transfer their conclusions to the contemporary situation. The present situation has prompted a rethinking from the ground up of the social dimensions of scientific knowledge. This is the turn of my title. Philip Kitcher’s Science, Truth, and Democracy and my The Fate of Knowledge both respond to this turn. I would like to contrast the philosophical fundamentals of these two approaches and indicate the different directions each offers for articulating relations between the sciences and their sustaining societies. I will, of course, suggest that the approach I take is both a more adequate epistemology and a more adequate platform for the development of a social philosophy of science. Kitcher’s Science, Truth, and Democracy is a significant achievement and marks a significant shift for philosophy of science. He identifies a number of important questions about the value of science and its place in a democratic society that can be articulated and addressed from a relatively conservative epistemological position. It is a strength of his approach that at least some questions about the constructive role of values in science do not require a radical change of epistemology. Nevertheless, the epistemological conservatism of this work places

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significant limits on the kinds of investigations philosophers concerned with the social impact of science can pursue. Kitcher situates his position as the via media between constructivist debunkers of science on the one hand and the uncritical scientific faithful on the other. He begins by shoring up theses concerning scientific realism and objectivity familiar from his earlier The Advancement of Science against arguments he attributes to debunkers or to their philosophical authorities. Once realism and objectivity are secured, the excesses of the faithful can be moderated. In moderating these excesses, he accepts John Dupré’s view that languages, classification systems, are relative to our interests, so that there is no privileged system of natural kinds. There are multiple correct ways of representing reality. There may be different theories of a phenomenon answering to different practical or epistemic interests. In contrast to the argument of his earlier book, in Science, Truth, and Democracy there is no single overarching criterion of significance that enables the philosopher to evaluate alternative theories. Nevertheless, he claims, the multiple languages and classificatory schemes in which theories can be expressed, each correct relative to some set of interests, are and must be all consistent with each other.1 Where does any form of sociality enter? For Kitcher, scientific inquiry is contingently social, that is, it is pursued within and by communities of inquirers, and a scientific epistemology must take account of that fact. His models in Advancement of the distribution of cognitive labor and of the appropriate level of deference to cognitive authority were intended to bring the communitarian aspects of inquiry within the reach of mainstream individualistic epistemology. In Science, Truth, and Democracy, however, he is also considering the relation between scientific inquiry and a democratic polity. Thus, he asks to what evaluative norms can or must science be subject? Or as he puts it, can “collective research be organized in a way to promote our collective values in the most encompassing sense?” (p. 111) Since no apriori argument for what constitutes the objective common good can be provided, the answer is that research must be subordinated to enlightened democratic decision-making. His discussion of “well-ordered science” is an account of the deliberation that, in his view, would ideally determine choice of research projects to be pursued in a society. As long as the actual pattern of research agendas is the same as the outcome of ideal deliberation concerning such agendas would be, were such deliberation to take place, science is well ordered. But the arguments regarding realism and objectivity have provided the limits on the reach of such decision-making: it is the research agenda not the research process that is subject to democratic oversight. Are these limits justified? Let us take just the arguments concerning objectivity. Kitcher approaches the objectivity of science as a question about the balance of evidential vs. political or value-laden factors in choosing between rival theories. Here he clearly has in mind the use of underdetermination

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arguments by debunkers to support their view that scientific controversy is inevitably decided by non-epistemic values rather than by evidence. There are many ways to understand underdetermination and its implications. Kitcher chooses two. One, easily disposed of, concerns the possibility of empirically equivalent alternative theoretical formulations of the same formalism. These, for example the empirical equivalence of the Schrödinger and Heisenberg formulations of quantum mechanics, he says, may not admit of a systematic treatment. But the permanent underdetermination in such cases rests on particular features of the theories and cannot be generalized to scientific theories in general. The harder question concerns rival theories each claiming some common successes, some different successes, and some failures. Kitcher here calls on an example, the chemical revolution initiated by Lavoisier. While at the outset both the phlogiston theory and Lavoisier’s theory could each claim some successes, as time went on, more and more successes accrued to Lavoisier and more and more unsolved problems to the phlogiston theory. Since the scientific community eventually decided in favor of the theory that had more successes than unsolved problems, we can say that at least sometimes the scientific community over time resolves controversies on the basis of evidence. Thus is objectivity secured as a meaningful ideal for science. But this argument strategy does not take into account metaphysical differences that may underlie different ways of reading, selecting, and evaluating data. It accepts the debunker’s view that underdetermination, if not kept at bay, leaves scientific deliberation always at the mercy of values or politics. There is another way to see underdetermination than Kitcher does: not as a matter of empirically undecidable conflicts between two or more theories but as a matter of relations between theories and the evidence available for them. This way of understanding underdetermination sees it as a matter of the gap between what is presented to us for observation and measurement, whether in the kitchen and garden or in the laboratory, and the processes that we suppose produce the world as we experience it, between our data and the theories, models, and hypotheses developed to explain the data, On this view, underdetermination is a goad to inquiring what reliance on evidence amounts to. As long as the content of theoretical statements is not represented as generalizations of data or the content of observational statements is not identified with theoretical claims then there is a gap between hypotheses and data and the choice of hypothesis is not fully determined by the data. A familiar example from particle physics is provided by relations between claims about collisions and disintegrations of elementary particles and the data available to support such claims. Claims about the behavior of pions and muons and the other members of the “particle zoo” are not based on direct observation of the particles themselves, but on phenomena that can be observed – tracks in compressed gas, the sequence of ciphers on data tapes. For another example, correlation of exposure to or secretion of a particular hormone with a physiological or behavioral phenomenon is evidence that the hormone causes the physiological or behavioral phenomenon

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in light of an assumption that hormone secretions have a causal or regulative status in the processes in which they are found rather than being epiphenomenal to or effects of those processes. And more generally, the correlation of one particular kind of event with another is evidence that one causes the other in light of an assumption that the one kind has or can have a causal influence on the other. Nor do hypotheses taken singly specify the data that will confirm them. Data alone are mute and consistent with different and conflicting hypotheses. They require supplementation in order to be made evidentially relevant. The supplement required to establish a connection between hypotheses and data reports is provided by (background) assumptions. These include substantive and methodological assumptions that, from one point of view, form the framework within which inquiry is pursued and, from another, structure the domain about which inquiry is pursued. These assumptions are most often not articulated, but presumed by the scientists relying on them. They facilitate the reasoning between what is known and what is hypothesized. Some sociologists of science have used versions of the underdetermination problem to argue that epistemological concerns with truth and good reasons are irrelevant to the understanding of scientific inquiry and judgment. The point, however, should not be that observation and logic as classically understood are irrelevant, but that they are insufficient. The sociologists’ empirical investigations show that they are explanatorily insufficient. The philosophers’ underdetermination argument shows that they are epistemically insufficient. My view, spelled out in more detail in The Fate of Knowledge, is that rather than spelling doom for the epistemological concerns of the philosopher, the logical problem of underdetermination, taken together with the sociologists’ studies of laboratory and research practices changes the ground on which philosophical concerns operate. This new ground or problem situation is constituted by 1) treating agents/subjects of knowledge as located in particular and complex interrelationships in multiple and partially intersecting networks and 2) acknowledging that purely logical constraints cannot compel them to accept a particular theory. Those networks of relationships – with other individuals, social systems, natural objects, and natural processes – are not an obstacle to knowledge, but can be understood as a rich pool of resources – constraints and incentives – to help close the gap left by logic. The philosophical concern with justification is not irrelevant, but must be somewhat reconfigured to be made relevant to scientific inquiry. The reconfiguration I advocate involves treating justification not just as a matter of relations between sentences, statements, or the beliefs and perceptions of an individual, but as a matter of relations within and between communities of inquirers. In my 1990 book, Science as Social Knowledge, I supported this move by looking at strategies the sciences themselves employ to guard against the intrusion of personal or social values into the body of accepted results. (The conventions of peer review, reproducibility of experiments, etc.) To see these as part

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of scientific method we must expand the notion of justification. This expansion sees justification as consisting not just in the testing of hypotheses against data, but also in the subjection of hypotheses, data, reasoning, and background assumptions to criticism from a variety of perspectives. Establishing what the data are, what counts as acceptable reasoning, which assumptions are legitimate and which not becomes in this view a matter of social, discursive, interactions as much as a matter of interaction with the material world. Since assumptions are, by their nature, usually not explicit, but taken for granted ways of thinking, the function of critical interaction is to make them visible as well as to examine their metaphysical, empirical, and normative implications. The point is not that sociality provides guarantees of the sort that formal connections were thought to provide in older conceptions of confirmation, but that cognitive and epistemic practices have social dimensions. Acknowledging this cognitive and epistemic sociality has two consequences. In the first place, any normative rules or conditions for scientific inquiry must include conditions applying to social interactions in addition to conditions applying to observation and reasoning. A full account of justification or objectivity must spell out conditions that a community must meet for its discursive interactions to constitute effective criticism. I have proposed that establishing or designating appropriate venues for criticism, uptake of criticism (i.e. response and change), public standards that regulate discursive interaction, and what I now call tempered equality of intellectual authority, are conditions that make effective or transformative criticism possible. The public standards include aims and goals of research, background assumptions, methodological stipulations, ethical guidelines, and so on. Such standards regulate critical interaction in the sense of serving to delimit what will count as legitimate criticism. They are, thus, invoked in different forms of critical discussion, but most importantly, they are themselves subject to critical scrutiny. Their status as regulative principles in some community depends on their continuing to serve the cognitive aims of that community. The particular conditions of effective or transformative criticism that I have proposed (which Miriam Solomon has dubbed the norms of critical contextual empiricism or CCE norms) may not be the conditions ultimately settled on, but what I do contend is that something like them [conditions that establish the effectiveness of critical interaction] must be added to the set of methodological norms. Secondly, even though a community may operate with effective structures that block the spread of idiosyncratic assumptions, those assumptions that are shared by all members of a community will not only be shielded from criticism, but, because they persist in the face of effective structures, may even be reinforced. One obvious solution is to require diversity within the community to reduce the likelihood of reliance on assumptions that would otherwise be so shielded. Another is to require interaction across communities, or at least to require openness to criticism both from within and from outside the community. Here, of course, availability is a strong constraint. Other communities that might be able to demonstrate the non self-evidence of shared assumptions or to provide

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new critical perspectives may be too distant – spatially or temporally – for contact. Background assumptions then are only provisionally legitimated; no matter how thorough their scrutiny given the critical resources available at any given time, it is possible that scrutiny at a later time will prompt reassessment and rejection. Such reassessment may be the consequence not only of interaction with new communities but also of changes in standards within a community. So objectivity would not be a matter of the community settling on the theory that eventually comes to have greater evidential support. That any theory is judged to have greater evidential support than alternatives may be (usually is) a function of shared assumptions in the community that have made certain data salient or worthy of attention and/or that devalue or fail to make perspicuous other data or that frame problems in particular ways. Objectivity, insofar as it makes sense to speak of it, would instead consist in the critical scrutiny of data, reasoning, and assumptions, that is of the elements that go into the construal of evidential relations, by a scientific community that includes multiple perspectives and whose discursive interactions satisfy the norms of critical contextual empiricism. Let me note two further points of contrast between this approach and that of Kitcher. 1. The view of underdetermination and its solution that I advance means that pluralism is permanent possibility. This possibility is a consequence of the possibility that alternative defensible epistemological frameworks may serve as the public standards. These consist of rules of data collection (including standards of relevance and precision, standards of statistical significance, specification of objects and units of measurement), inference principles, and epistemic or cognitive values. They provide frameworks for addressing different kinds of (empirical) questions about the natural and social worlds. Other philosophers have advanced pluralism as a view about the world, i.e. as the consequence of a natural complexity so deep that no single theory or model can fully capture all the causal interactions involved in any given process. While this may be the case, the philosophical point I have taken pains to make is that a theory of knowledge should not presume either pluralism or monism. Thus I think such a theory should be as open to a strong form of pluralism as to monism. These are metaphysical positions, which should not be foreclosed by an epistemological theory. Kitcher agrees that it is a mistake to presume monism and also that such a presumption has vitiated a number of previous attempts to find an alternative to excessive rationalism and excessive skepticism. But he thinks we need only accept a “modest pluralism” according to which “the bits of nature we choose to represent accurately are a function of us, our capacities, and our interests.” These representations will per force be incomplete, and different interests will lead us to classify the objects of nature in different ways. No sense, however, can be made of a robust or less modest pluralism: the suggestion that equally successful representations may be irreconcilable or non-congruent. For Kitcher,

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all true statements, properly understood, are ultimately consistent with one another. I hold, on the contrary, that the multiplicity of defensible epistemological frameworks means that such a requirement is too restrictive. Partial accounts may adequately represent certain aspects of a complex system and contain statements inconsistent with those comprising another partial account of the same system. This is established case by case. 2. As just noted in the contrastive discussion of objectivity, the centrality of critical interaction to justification on this view brings social interaction into the heart of inquiry. In The Fate of Knowledge I offered additional arguments for the sociality not just of justification, but also of observation and of the specification of semantic success (what most call “truth”, but which I prefer to call “conformation”). These arguments are opposed to an individualist thesis something like the following: “empirical knowledge can be fully understood in terms of processes undergone by epistemically self-sufficient individuals.” Kitcher advances a view that I have elsewhere called Socialism Lite, on the other hand, which accepts a contingent version of Epistemological Sociality, i.e. that as a matter of fact scientists are located in communities and accept content as a result of their interactions with each other (or, in an alternative formulation, that some knowledge is produced by scientists working in groups or in institutions). Socialism Lite might acknowledge that the intricate and powerful knowledge produced by scientific inquiry as we know it is made possible by the community of scientists, but hold that such knowledge is the cumulative product of multiple instances of individual knowledge, which, as knowledge, can be understood without reference to social interactions. The process of research is thus, from the point of the community outside the scientific one, black-boxed. I argue, on the contrary, for a normative social element as part of the meaning of “knowledge”, i.e. that epistemic acceptability of content (or epistemically justified acceptance of content) presupposes the satisfactory performance of certain kinds of social interactions. The normative notions central to common understandings of “knowledge”, such as truth and justification or epistemic acceptability and conformation (in my preferred locutions), involve both traditional evidential norms and norms of effective critical interaction. Indeed evidential norms, properly understood, include those social norms. Why does this debate about knowledge matter? Consider an issue we might call upon the sciences to resolve: the health risk posed by exposure to a given substance. The point of such knowledge would be to set policy concerning maximum permissible limits of exposure to the substance. Heather Douglas has examined research and reasoning concerning the health risks of dioxin, a byproduct of paper production that is flushed into watercourses in the vicinity of paper mills. There are research communities who will produce the various results that support setting the exposure limits at some level and there the communities that will experience the exposures as well as the communities whose activities

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release the dioxin into the environment. Both these latter stand to be affected by where the permissible exposure levels are set, and thus, by the findings of the researchers that will be used to determine the maximums. The ideal of well-ordered science would treat the question whether the toxicity should be investigated as an agenda-setting question subject to democratic oversight (whether virtual or real). Once the question is deemed worth investigating, the details of the investigation should be left to the experts. However, in order that the scientific results be worthy of acceptance by those who have not participated in producing them they – the affected outsiders – must be assured that these results have been obtained by a reliable process. (Toxicity is generally determined through animal trials.) Douglas elaborates on the openness to (value) judgment of various stages of the relevant inquiry: setting standards of statistical significance, relative weighting of type 1 versus type 2 errors, protocols for interpreting borderline cases. The point is not that researchers bring an industrial or public health agenda into the research, but that the decisions, however motivated, have value consequences. And the trustworthiness of the risk estimates is a function of assurance that at those places of judgment one group’s interests have not been arbitrarily favored over those of another. On the CCE view, in order that scientific results be worthy of acceptance by those who have not participated in producing them, the users of consumers of knowledge must be assured that the results of inquiry have been secured through a process of critical scrutiny by a community diverse enough to include members who share or represent their interests. Consider also the increased privatization of knowledge production. Since the end of the Cold War, funding of scientific research, especially biomedical research in the United States, has been shifting from the public sector – the federal government – to the private sector. This shift has consequences for the organization of inquiry, the communication of ideas, and disciplinary eminence. Universities once partnered with the government now partner with private corporations, in some instances setting up jointly owned research facilities. Researchers maintain their sense of individual freedom by forming their own corporations. Intellectual property rights have replaced government secrecy as barriers to open communication and biology, especially molecular biology, has displaced physics as the frontier discipline. What should we make of this? Has a human gift of investigation and invention been hijacked? Or are these capacities always for rent? Is there something identifiable as science apart from the ways it is institutionalized and funded? Or are scientific practices so pervaded by their funding structures that there is no continuity from one funding regime to another? And now that science has become so central to so-called advanced society, what are the consequences of leaving the production of knowledge so largely in private hands? If the research process is black-boxed, then philosophy of science becomes powerless to fully explore these and other questions about the reliability and trustworthiness of scientific knowledge in different institutional forms.

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Philosophers in the non-social interregnum largely concentrated on the epistemological, conceptual, and metaphysical aspects of scientific inquiry, seeing there not an institution, but a 500 or 2500-year tradition of seeking knowledge of the natural world. The modern sciences, however, are not merely knowledge producers; they are also commodity producers, weapons producers, instruments of governance, ideology transmitters, engines of social and economic transformation. They are not just elements of a productive system, but also of a persuasive and communicative system. As noted at the outset, in the late 20th century and early 21st, the imprimatur, “scientific,” grants prima facie credibility to any proposal. One detaches the knowledge productive function from these other roles at risk of distorting one’s understanding of them all. Let me not be misunderstood: I’m not arguing that all philosophers of science should shift to thinking about science as a social institution. But philosophers of science should not ignore this, just as philosophers of science that take the social turn should continue to draw on and be in conversation with the philosophy that focuses on science considered in abstraction from its social milieu and forms of institutionalization. This work both illuminates the changes and intellectual achievements of Western science and philosophy and offers tools for the analysis of theories and research programs in contemporary science. A philosophy of science that does take the social turn, however, if it is to be genuinely social, must be accountable not just to the scientific practitioner but to the recipient of knowledge and bearer of knowledge’s benefits and burdens. In light of the various points at which scientific practice is open to judgment and/or must rely on assumptions that are not themselves empirically demonstrated, an insistence that the epistemic practices in the research process conform with the social norms of inquiry I advocate is at least a step towards that accountability. Philosophy of science should open up the black box of research rather than insulating it from social critique.

N OTES *

I am greatly honored by the invitation from the Vienna Circle Institute to give the Twelfth Vienna Circle lecture.

1.

More precisely, he says that all true sentences will be consistent with each other even when expressed in different classificatory schemes.

R EFERENCES Cartwright, Nancy, Jordi Cat, L. Fleck, and Thomas Uebel. 1996. Otto Neurath: Philosophy Between Science and Politics. Cambridge: Cambridge University Press.

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Douglas, Heather. 2000. “Inductive Risk and Values in Science” Philosophy of Science. 67, 4: 55979. Friedman, Michael. 1999. Reconsidering Logical Positivism. Cambridge: Cambridge University Press. Giere, Ronald and Alan Richardson, eds. 1996. Origins of Logical Empiricism. Minnesota Studies in the Philosophy of Science, Vol. XVI. Minneapolis, MN. University of Minnesota Press. Kitcher, Philip. 1993. The Advancement of Science. New York: Oxford University Press. Kitcher, Philip. 2001. Science, Truth and Democracy. New York: Oxford University Press. Kuhn, Thomas. 1962. The Structure of Scientific Revolusions. Chicago, IL: University of Chicago Press. Longino, Helen. 1990. Science as Social Knowledge. Princeton, NJ: Princeton University Press. Longino, Helen. 2002. The Fate of Knowledge. Princeton, NJ: Princeton University Press. Longino, Helen. 2003. “Reply to Philip Kitcher” Philosophy of Science 69, 4: 573-77. Nemeth, Elisabeth and Friedrich Stadler. 1996. Encyclopedia and utopia: the life and work of Otto Neurath (1882-1945). Dordrecht and Boston: Kluwer. Solomon, Miriam and Alan Richardson. Forthcoming. “Review of Helen Longino’s The Fate of Knowledge.” Studies in History and Philosophy of Science. Stadler, Friedrich. 2000. The Vienna Circle: Studies in the Origins, Development and Influence of Logical Empiricism. Vienna: Springer Verlag.

University of Minnesota 271 19th Ave. S. Minneapolis Minnesota, 55455 U.S.A. [email protected]

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NOTES ON THE ORIGINS OF FLECK’S CONCEPT OF “DENKSTIL” Ludwik Fleck’s Genesis and Development of a Scientific Fact (Entstehung und Entwicklung einer wissenschaftlichen Tatsache) is a work that resembles Wittgenstein’s Philosophical Investigations in several crucial respects. For example, at the time of their appearance, which in Fleck’s case means with the publication of the English translation, both books were considered to be without predecessors.1 Like the later Wittgenstein with the publication of the Philosophical Investigations in 1953, Fleck seemed to be an Athena emerging fully-grown from the head of Zeus when the book appeared in 1979. True, Polish philosophers were eager to claim him but they were not really able to illuminate anything about the origins of his chef d’oeuvre on the basis of their discussions of Polish analytical philosophy in the inter-war period.2 Moreover, the works explicitly cited by Fleck were not sufficient, even taken together, to account for the radical departure from conventional thinking about the nature of scientific knowledge that his approach to epistemology represented. The parallels to Wittgenstein can be extended even further. In Wittgenstein’s case it was becoming clear at the time of the rediscovery of Fleck that we found no predecessors because we did not know where to look. The assumption that Wittgenstein was an analytical philosopher prevented scholars (with a few notable exceptions) from posing fundamental questions about the origins of his views. In short, even if we looked to literary and religious precursors, we simply did not bother to look for philosophical predecessors elsewhere than in the traditions of analytical thought. The same has been true of Fleck. We have hardly looked beyond academic philosophy of science in our efforts to understand how he could have arrived at his radical, iconoclastic views about knowledge. Thus the conjecture that I want to advance here, namely that we should look to Spengler in search of a more profound understanding of Fleck, will surely seem shocking to many philosophers and historians of science. Just as we were shocked with the publication of Culture and Value (Vermischte Bemerkungen) in 1977 to discover that Wittgenstein considered himself to have been profoundly influenced by Oswald Spengler,3 the thought that a hard-nosed, no-nonsense practicing scientist like Fleck could have been influenced by a historicist metaphysician seems implausible or even outright absurd. However, just as subsequent research on the part of scholars like Rudolf Haller4 and Rafael Faber,5 to mention but two, has continually yielded insights into Wittgenstein’s development on the basis of a Spenglerian influence, the same could well be true of Fleck. 179 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 179–188. © 2006 Springer. Printed in the Netherlands.

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Indeed, in the course of my own researches into the connections between Wittgenstein and Spengler6 it occurred to me that there were certain parallels between Fleck’s intriguing notion of “thought style” and Spengler’s views about styles of knowing (der Stil des Erkennens, for example, the typical Baroque way of “looking at” and “seeing” pictures7) that might cast light upon Fleck’s development (not to mention the numerous parallels to Wittgenstein’s mature philosophy that we find in Fleck). Again, nobody ever thought of looking for a precursor or even parallels to Fleck outside of the circles of positivist and postpositivist (Popper, Kuhn etc.) philosophy of science; yet the parallels are there. Although I am aware that there are both general problems with the notion of influence8 and with attributing an influence upon Fleck to Spengler (see below), which cannot be ignored, I think there is, nevertheless, something to be gained by doing so. In that spirit I propose to offer a brief account of Fleck’s notion of Denkstil, then to consider what he might have taken over from Spengler and finally to consider briefly one alternative to a Spenglerian account of the origins of the concept of thought style. The place to start is with a brief recapitulation of the main lines in Fleck’s characterization of thought style. Fleck defines Denkstil as a readiness for directed perception of form that has been instilled into the practicing scientist in the course of his/her education to the point that the selective character of scientific observation cannot ever be explicitly recognized by the practicing scientist.9 More than any of his predecessors, Fleck emphasizes that the very precision, which scientific perception demands, requires that scientists be rigorously trained to see only certain complex aspects of what they observe while systematically ignoring others. Fleck’s view of scientific perception as selective vision as well as his seemingly unorthodox position with regard to what we have been accustomed to regard as problems of verification (or falsification) it entails is, on his own account, determined by his perspective as an immunologist. Even more than biological science itself his relation to medical research dictates the perspective he brings to the philosophical consideration of scientific knowledge. Here he speaks best for himself: A scientist looks for typical, normal phenomena, while a medical man studies precisely the atypical, abnormal, morbid phenomena. And it is evident that he finds on this road a great wealth and range of individuality of these phenomena which form a great number, without distinctly delimited units, abounding in transitional and limiting conditions. There exist no strict boundary between what is healthy and what is diseased, and one never finds exactly the same clinical picture again. But this extremely rich wealth of forever different variants is to be mastered [bezwungen] mentally, for such is the cognitive task of medicine.10

No small part of the radicality of Fleck’s account of scientific knowledge thus turns upon his realization that perception in medicine is inextricably linked to an intricate process of forming judgments. Making this sort of discerning perception possible is the goal of medical education, which is here taken to be especially

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illuminating with respect to the epistemology of science generally as the text cited clearly indicates. Precise discernment of what is normal in a complex set of specimens is possible because the researcher’s capacity to observe has been “stylized”. Fleck describes the thought style that emerges from rigorous scientific training as the Zwang (force, coercion, compulsion, control, restraint, obligation, pressure, but perhaps best here constraint; cf. ohne Zwang unconstrained) to such direct perception in a situation where said constraint is not forced but a matter of self-evident procedure (57, cf. 142). Scientific education must produce a scientist, who “sees” crucial differences quickly, clearly and easily in a situation where there are innumerable variants, i.e., where the question of what follows the rule and what constitutes an exception is always open. For example, Fleck describes a situation arising in the course of his experimentation with streptococcus where his team was confronted with 102 different specimens all varying in length and coloration. To the untrained eye, chaos, but to the trained eye, as Fleck argues, it was clear that there were 100 similar large yellowish, transparent specimens and two smaller, lighter more opaque ones. (119) The point is that the perceptions of trained scientists are so “stylized” as to observe only those differences which they have been trained to recognize as making a difference. This “stylization” forms their attitude to their work as well. Thus thought style is a Stimmung (mood or frame of mind) with respect to both the Gestalt that is perceived on the part of the scientific observer and the sort of experiential response that such a perception elicits. (130) Stimmung thus refers to a disposition and a constraint to perceive in a highly specific, selective way but also a disposition and a constraint to respond to a given perception in a disciplined way in word and deed. Thus a thought style has technical, behavioural and literary aspects. It determines our scientific needs and expectations as well as how we talk about them. Thought style forms the very framework for our investigations in ways that researchers themselves are not and cannot be aware of. It is, for those under its constraint, beyond criticism. The latter point tends to be one that sticks in the throats of philosophers of science raised on, say, Popper, who see the scientific enterprise as everywhere and always critical. However, those very philosophers of science who are sceptical with respect to Fleck’s claims here tend to overlook the fact that socialization in a scientific discipline means learning to incorporate, literally and figuratively, any number of methodological, and therefore scientific, presuppositions into our thinking – and acting – as scientists. This has tended to be overlooked, especially by those philosophers who have identified science with theory at the expense of ignoring scientific practice. Like scientific observations, the feelings they occasion are anything but impartial. This explains why Fleck found the notion of reducing scientific observation to so-called protocol sentences completely abstruse. (118) In short, the Stimmung that surrounds scientific observation is part and parcel of scientific knowledge and not something superadded to it.11 Be that as it may, thought styles develop in three stages. They originate out of vague and unclear everyday notions which Fleck terms Urideen or Präideen,

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which die hard, even under the pressure of becoming “stylized”. (36-9) The first stage or station is a matter of seeing something unclearly and inadequately. Then those observations are subject to what Fleck terms “concept-forming, style-transforming” (123-4) developments on the basis of skill and experience. He also insists that this development is “irrational” without explaining what he takes that to mean. Finally, there emerges an ability for developed, reproducible Gestaltseeing in conformity with an established pattern. Thus a fact originates as follows: first, as a curious, perhaps annoying, signal of resistance in the chaotic, initial stages of thinking, then as a certain anomalous constraint to thinking, and finally as an immediately recognizable form” (124). The result of the transformation is that something that was scarcely perceptible is now instantly recognized as obviously significant. In effect, a community of scholars has trained itself to see something that only it can see. Such seeing is in fact a case of “seeing as”, to speak with Wittgenstein. However, it cannot be recognized as such within the community of scientists trained to see that way; for, it is the only way that they can see at all. Such training equips the initiated with a set of spectacles that cannot be removed at will as it were. The constraint involved is not a matter of brute force because it is a self-constraint, like the conditioning exercise of an athlete or the musician’s practicing, which is voluntary and enables people to do things that they otherwise could not. Thus Fleck will speak about such “stylized” thinking as a “harmony of illusions” within a community, which is nothing other than the “inner harmony of the thought style” (114). However, unlike athletic discipline, the constraint involved becomes increasingly obscure to those who are subject to it, who cannot imagine the world in any other way and thus must react dogmatically without intention when their view of things (literally) is challenged. The very “stylizing” that makes precise, i.e., critical observation possible systematically obscures its own genesis by imposing a certain absolute, “necessary”, self-evident form on scientific perception, which makes its own relativity to established models of explanation unrecognizable (another parallel with Wittgenstein can easily be drawn here). However, it is a fact about science, indeed, the crucial philosophical fact about science, namely that it has a history: thought styles change. Because they change, it is possible – and necessary – to compare them. The first result of this comparison is to see something that is anything but obvious to the practicing scientist, namely that there are indeed different ways of perceiving (and representing what we perceive), which are relative to the development of the community of investigators in the field, i.e., what Fleck terms their “thought collectives”. The latter are defined by the way that they collectively perceive, reason and express themselves. However, the very discipline that enables members of the thought collective to perceive and think critically obscures their inability to see beyond the limits of the thought style. (122) Indeed, Fleck goes so far as to insist that the education of scientists is a matter of the constitution of a “closed system of opinion” (40) that offers constant

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resistance to anything view, which comes into conflict with it. Thus when he asserts that science is “stylized” thought Fleck maintains that: 1. what contradicts the system is unthinkable; 2. what fails to fit into the system goes unseen; 3. or is ignored, even if scientists are aware of it; 4. or is explained in a roundabout way that does not contradict the system; 5. and they proceed to observe, describe and illustrate what corresponds to the system even in the face of contradictory opinion. (40) This is what Fleck understands when he claims that science is a “harmony of illusions”. In the face of such a “tendency to tenacity” (Beharrungstendenz, cf. 40-53) at the core of scientific practice, the only mode of liberation for scientists is philosophical reflection in the form of a comparative epistemology (106, cf. Ch. 4 passim), which studies thoughts styles historically and sociologically, with a view to demonstrating how different conceptions of knowledge emerge from different thought styles or scientific paradigms, to employ the terminology that we have becomes accustomed to after Thomas Kuhn’s The Structure of Scientific Revolutions – a work that leans heavily upon Fleck’s insights, as we can appreciate now.12 In short, the crucial epistemological features of thought styles only become apparent when they are contrasted with each other or when their transformations are examined closely. How does this echo notions that we find in Spengler’s Untergang des Abendlandes? What is there in Spengler that might in the least illuminate Fleck’s ideas about thought styles? Spengler’s problems are on the face of it very different from Fleck’s but appearances can be deceiving. The simplest answer is that Spengler is one of the few philosophers to grant the notion of style epistemological pride of place in his exposition of crucial concepts for understanding cultural differences: “Knowing something about nature (eine Naturerkenntnis) is a function of cognition of a determinate style…. a natural necessity accordingly possesses the style of the pertinent mind (des zugehörigen Geistes – 502)”. Indeed, Spengler is one of the few for whom establishing such differences – and their consequences – is a central aim of philosophy (Book I, Ch 1, § 3, 79-81, et passim). In the first instance Spengler wants to disabuse us of the notion that culture is one thing that develops in a linear progressive manner (from the Renaissance, at least) as all “enlightened” liberals believed up to 1914 (21ff.). Instead of the model of European development that classifies the European heritage into its ancient, medieval and modern periods, more or less ignoring the rest of the world, Spengler distinguishes eight cultures that are in various stages of development from birth to growth and the attainment of maturity and on to aging and dying (259) – Spengler will speak of his task as one of writing cultural biography (36). It is crucial for Spengler that these cultures can only be studied comparatively (36 et passim).

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Cultures are defined in the basis of their style. Each culture is the collective result of socialization within the context of a particular habitat (to employ terms that are not Spengler’s – indeed, the quaintness of Spengler’s mode of expression continually tempts one to the dangerous, but necessary, practice of modern paraphrase). The process of becoming accustomed to the peculiarities of its proper landscape imprints a modus vivendi, incorporating an unreflective concept of its experience of the extension of space, upon the people who dwell there. That concrete response to its living space confers a basic sense of form (eine Formensprache) the thinking of its inhabitants. This is what Spengler terms a style of cognition. Spengler refers to the primary factor in determining a culture’s style its Ur-Symbol (226ff.). A culture’s ideals of natural order are derived from it. The Ur-Symbol is thus the key to understanding the practical metaphysics of that culture, asserts Spengler in a way that we have since been accustomed to from, say, the likes of linguists such as Benjamin Lee Whorf and Edward Sapir. However, the key to understanding Spengler’s notion of form is, as Spengler himself insists, to be found in Goethe, whose disciple he claims to be. Thus, quoting Goethe, Spengler insists, “Form is something in motion, something coming-tobe, something passing away, The doctrine of form is a doctrine of metamorphosis. The doctrine of metamorphosis is the key to all of nature’s symbols” (130-1). Form is thus decidedly dynamic for Spengler. The unity of a culture is thus explained on the basis of a shared picture of how things are that imbues all aspects of its life. For the Egyptians this primal symbol was the path or way (242ff.), for the ancient Greeks the individual body (228ff.), for the Magian or Semitic (Spengler typically refers to them as “Arabic”) cultures the world cave (847f.), for the modern occident infinite space (227f), for Russian culture the plain (259). Such root-metaphors13 derived from the way space is perceived in a particular environment thus literally confer a certain direction or orientation upon it inhabitants. (225ff.) That these distinctions bear upon our understanding of science, is a point that is easily overlooked in the Untergang des Abendlandes. Nevertheless, they most certainly have a central bearing upon how we should understand it. A few texts will make that clear: What we call statics, chemistry, dynamics, historical designations withouth any deeper meaning for today’s science, are the three physical systems of the Apollonian [Greek], Magian [Semitic] and Faustian [modern Western] soul, each grown to maturity in its culture, each restricted in its validity to one culture. Corresponding to them in mathematics are Euclidean geometry, algebra, and the calculus, and in art, the statue, the arabesque, and the fugue: If one wants to distinguish these three kinds of physics – for which every other culture again could have to and would have to add another – according to their respective conceptions of the problem of motion, one would have a set of mechanically ordered states, a set of hidden forces, and a set of processes. (492) …[modern western] science exists only in the living thoughts of large generations of scholars, and books are nothing, if they are not living and efficacious in people, who have

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mastered them. Scientific results are but elements of an intellectual [geistiger] tradition. (548)

Such texts are evidence that Spengler intended his analysis to clarify certain basic features about the culturally embedded nature of scientific activity. However, to return to his analysis of the genesis of styles of thought: the primal symbol from which the originate is not something abstract but something that as it were organically grows out of life in a specific environment. It is a sub conscious or pre-conscious mythical picture of how we have experienced nature that is incorporated in our ways of seeing, our gestures, our sense of melody and rhythm, our metaphors, our paintings and our architecture (382-3). The UrSymbol expresses what is basic to the habitus or “soul” of a culture in Spengler’s terms (cf. 382ff). Its characteristics are not clearly definable in logical terms because grasping a culture’s Ur-Symbol is a matter of seeing analogies. (4ff) It is the fundamental source of form and representation in a culture, which lends the culture what Spengler terms its “style” of cognition (Stil des Erkennens). That sense of style is what permits the historian to grasp the how a culture can be a dynamic unity-in-diversity. Thus Spengler insists that understanding style, i.e. a culture’s “language of forms” (Formensprache), is a matter of sensibility to an indeterminate feeling (ein unbestimmtes Gefühl) or mood (Stimmung), which pervades a culture’s ethos or mores. However, participation in the cultural myth that the Ur-Symbol determines prevents the participant from being aware of his own cultural style. (Thus the only way to come to understand how such myths function is through an historical and comparative study of cultural styles. Thus Spengler’s project is to show us on the basis of comparisons of analogies how the “souls” of the eight cultures he identifies become stylized. The comparisons in questions are studies in cultural physiognomy. The “face” that we learn to recognize is what is typical of the culture. We learn to recognize the “face” of one culture as we compare and contrast it with others. Moreover, the style of the culture permeates it entirely, even including its mathematics, which, Spengler insists, is more of an art than a science. However, Spengler distinguishes two aspects of culture, which are polar opposites and thus tend to confuse the superficial observer: its coming to be and its passing away. The later he terms the transition from “culture” to “civilization” (43ff.). This theme is crucial to rounding out our discussion; for it is, in effect an account of the relation between practice and theory. With a pathos that is not always easy for a contemporary reader to swallow, Spengler describes civilization as the “destiny” (Schicksal, 43) of every culture, i.e., an integral component of its life-cycle. It refers to what happens when a culture, which has hitherto been spontaneous and unreflective, grows to self-consciousness. Increasingly, Gesellschaft replaces Gemeinschaft (660ff). They city replaces the rural household as the center of social life. Words replace deeds; indeed, speaking (sprechen) becomes language (Sprache) as the drive to make itself explicit presses the

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culture to abstraction (248) with the result that education must be formalized by the introduction of the school (718). Style, which had previously a quality of action, becomes externalized in decorative ornament (353; cf. 702 et passim). The treatise replaces the saga: “Ornament ist – das Buch,” 740). Exchange, which was previously an personal interaction between two individuals, stamped by their particularity, becomes mediated by money and thus objectified. (46; cf., 670ff.) Thought, hitherto based upon analogy, becomes formalized in logic and the search for causal explanations. (4, cf. 153ff.) Specialists of all kinds arise to fulfil the priestly function literally and figuratively. In short, life becomes overlaid with ideology as culture begins to decline. (743) In effect, the culture seeks to protect itself from decline by inventing a symbolic order, which is impervious to decline but, in fact, a manifestation of it. The last stages of a culture’s development, then, it envelops itself in a brittle shell of formalisms as it expires – a highly dramatic picture, to say the least. The challenge to the philosopher is to capture all this comparatively. What, then, could Fleck have taken from Spengler, who says virtually nothing about the practice of science, which might have helped him to develop his notion of scientific “thought style”? Let us try to bring the elements of this discussion together by explicitly adumbrating them. First, the notion that what defines a community (culture) is a style of thinking, of which that community is not itself explicitly aware, is common to Fleck and Spengler. Second, the idea that stylized thinking is sensitivity to dynamic form and therefore a species of analogical rather than subsumptive thinking is common to both of them. Third, for both of them said sensitivity to dynamic form is inextricably link to feelings and a specific mood that form a frame of reference for thinking. Fourth, they agree that stylization derives from a relation to a certain Ur-Idee in ways that are less than obvious to everyone involved. Fifth, both insist that the resulting habitus that stylized thinking is also essentially linked to a certain set of aesthetic values: just as Spengler links the mathematics to the architecture of a culture, Fleck links the development of theories to modes of scientific illustration. Sixth, styles of thinking, like cultures, have a way of petrifying into a “harmony of illusions” in their resistance to change, so strong are their tendencies to tenacity. Finally, both Spengler (especially in connection with the notion of Menschenkenntnis) and Fleck are committed to the idea that the most basic form of knowing is what Michael Polanyi terms “tacit knowing”,14 a kind of practical knowledge that cannot be directly put into words but can be studied historically and comparatively. Briefly, for all their differences, both advocate a comparative epistemology on the basis of the stylized nature of knowledge. My claim is that all of these factors taken together provide evidence for considering that Fleck was influenced by Spengler. What counts against that view? The strongest objection stems from the fact that that Spengler is never mentioned by Fleck, who is not at all adverse to citing his sources. Fleck certainly could have cited Spengler if he wanted to but he does not. This clearly makes the kinds of claims I have been advancing problematic.

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There is no denying that it is possible that the similarities between them are purely co-incidental. Yet, an epistemology that centers upon style is something so unusual that the claim that Fleck learned from Spengler cannot be simple rejected out of hand. It is worth considering alternatives to a Spenglerian account of the origins of the notion of thought style. At the very least the contrast will help to highlight aspects of Fleck’s thought that we have perhaps overlooked. Where might Fleck have stumbled upon the idea, if not the term? We have already mentioned the crucial name: Goethe. In the Untergang des Abendlandes Spengler insists that all he is doing is applying the method that Goethe used to explain the morphology of plants to history. In fact, Fleck may well have got his method directly from Goethe’s notion of a graded, dynamic series15 bypassing Spengler entirely. Another possibility is that he may have encountered it in the writings on a commentator upon Goethe’s scientific writings such as Rudolf Steiner. This cannot be ruled out of court; it may be well worth our while to investigate that possibility. However, until further evidence compels us to alter our views, there is good reason to believe that Fleck came under the influence of Spengler (without in any way being compelled to ignore other possible sources of stimulation) in developing his revolutionary notion of thought style: philosophers of science interested in Fleck’s fascinating ideas neglect Spengler at their peril. N OTES 1. 2.

3. 4. 5. 6. 7. 8.

“…Wittgenstein’s new philosophy [after 1933] is…entirely outside any philosophical tradition and without literary sources of influence”, G.H. von Wright, “Biographical Sketch” in Norman Malcolm, Wittgenstein: A Memoir ( London: Oxford University Press, 1958), 15. See, for example, Jerzy Giedymin, “Polish Philosophy in the Inter-War Period and Ludwik Fleck’s Theory of Thought Styles and Thought Collectives”; Boguslaw Wolniewicz, “Ludwik Fleck and Polish Philosophy”; Wladislaw Markiewicz, “Lvów as a Cultural and Intellectual Background of the Genesis of Flack’s Ideas”, Cognition and Fact: Materials on Ludwik Fleck, eds. Robert S. Cohen and Thomas Schnelle (“Boston Studies in Philosophy of Science”, Vol. 87; Dordrecht: Kluwer, 1986), 179- 230. I cite this book in parentheses in the text for convenience. G. H. von Wright, “Wittgenstein in Relation to His Times”, Wittgenstein and His Times, ed. Brian McGuinness (Chicago: University of Chicago Press, 1982), 116. Rudolf Haller, “War Wittgenstein von Spengler beeinflusst?” Fragen zu Wittgenstein und Aufsätze zur österreichischen Philosophie, (“Studien zur österreichischen Philosophie”, Bd. 10, Amsterdam: Rodopi, 1986), 155-69. Rafael Ferber, “Wittgenstein und Spengler”, Archiv für die Geschichte der Philosophie Bd. 73, 2 (1991), 188-207. I have presented this in a lecture entitled “How Did Spengler Influence Wittgenstein?” at Roma Tre University in December 2003. See also Allan Janik Assembling Reminders (Paris: Presses Universitaires de France; forthcoming [in French]), Ch. 9, “The Morphological Turn”. Oswald Spengler, Der Untergang des Abendlandes: Umrisse einer Morphologie der Weltgeschichte (Münuch: DTV, 1972), 401. I refer to Spengler hereafter in the text in parentheses. I have discussed this matter in “Wie hat Schopenhauer Wittgenstein beeinflusst?” Schopenhauer Jahrbuch 73 (1992), 75-6.

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9. 10. 11.

12.

13. 14. 15.

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See Thomas S. Kuhn, Foreword, Ludwik Fleck, Genesis and Development of a Scientific Fact, Trans. Fred Bradley and Thaddeus J. Trenn (Chicago: University of Chicago Press, 1979), ix. Ludwik Fleck, “Some Specific Features of the Medical Way of Thinking”, Cognition and Fact, 39 (see n. 2). A certain similarity of usage between Fleck, Spengler and Martin Heidegger, in whose Sein und Zeit the notion of Stimmung is inextricably linked to our perceptions of the world, should be noted here. Whether the notion of Stimmung involved in Fleck’s concept of Denkstil owes anything to Heidegger’s usage in Sein und Zeit, (14 Aufl.;Tübingen: Max Niemayer, 1977) § 29; 134-40, is an interesting question; for there seems to be significant parallels in the ways that both Fleck and Heidegger, as well as Spengler, link the formation practical judgment to an ethos. See Thomas Kuhn’s Foreword to Fleck, n. 9. By the time Prof. Kuhn wrote this he was not particularly clear himself about the “influences” upon his classic The Structure of Scientific Revolutions (Chicago: University of Chicago Press, 1962) as it became clear to me in conversation with him in 1985. His graciousness in such matters precluded dissimulation. See Stephen Pepper, World Hypotheses (Berkeley: University of California Press, 1942). See Michael Polanyi, Personal Knowledge (Chicago: University of Chicago Press, 1964). See Ronald H. Bray, “Form and Cause in Goethe’s Morphology”, in Frederick Amrine, Francis J. Zucker and Harvey Wheeler (eds.) Goethe and the Sciences: A Re-appraisal (“Boston Studies in the Philosophy of Science” Vol. 97; Dordrecht: Reidel, 1987), 257-300.

The Brenner Archives Research Institute University of Innsbruck Josef-Hein-Straße 5 Innsbruck Austria [email protected]

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HANS REICHENBACH AND LOGICAL EMPIRICISM IN TURKEY* It has been really significant and a real pleasure for me to make a presentation at the Institute Vienna Circle within the framework of its ongoing activities, and this for more than one reason – firstly because it is a Society for the Advancement of the Scientific World Conception to which I am a sincere adherent; secondly because, and complementary to the first point, we are evidently so much in need, nowadays, of such a conception in the so-called “post-modernist” world of ours; third, because I, as a logical empiricist, have been given the chance of expounding my views on the state of logical empiricism in Turkey, and on philosophy in general; in the fourth place, I see myself as sort of “geographical” as well as methodological follower of Hans Reichenbach, apparently the foremost leader of scientific philosophy; fifthly and lastly, though not in the least to be sure, Vienna has been the city of the Circle, the beginning of that philosophical movement which, in my view, represents a true revolution, one of the greatest revolutions indeed, in the whole course of philosophical evolution. Understandably, all these points, my own involvement excepted, are interrelated as well as important because of their general relevance. I NTRODUCTION : A C RITICAL AS WELL AS D ESCRIPTIVE P RESENTATION Myself being, on the whole, a logical empiricist, and a critical follower of Hans Reichenbach in my particular way as a scientific philosopher, the present topic has expectedly been in my mind for some time. But the title here only occurred to me when I read that of Paolo Parrini’s talk in the same series about a year ago: “Italian Philosophy and Neopositivism”. I was not here during the activity, but judging by the short summary sent to the members of the Institute, it seems that my talk will be more or less parallel to his, with certain necessary modifications due to the special socio-historical if not a whole space-time setting. And although my title is apparently less comprehensive, to be able to give a more or less complete picture as regards my topic I will discuss the philosophical developments in Turkey not in a limited but interrelated, contextual manner; this is obviously reflected in the section headings of the presentation. Temporally or historically speaking, we might divide the period I will consider into three: before nineteen thirties, between thirties and seventies, and the last two decades. As we shall see, and however roughly, these periods are not arbitrary divisions but represent meaningful stages concerning my overall topic. As 189 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 189–211. © 2006 Springer. Printed in the Netherlands.

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such, a short account of the first period will be followed by a consideration of what has traditionally come to be known as the University Reform in Turkey, actually at the time of Reichenbach’s arrival in østanbul; this will certainly go hand in hand with a discussion on his achievements during his stay, and, also, afterwards. I shall then give an account of Nusret Hızır, his assistant, academic interpreter, and follower. The latter’s academic life coincides with most of our second period here, whose last two decades include a real interest in dialectical materialism in this country. Thirdly, as far as time or temporality is concerned, I will talk about the “rise” of scientific philosophy in Turkey, basically focusing on my work and philosophical conception as a close follower of Reichenbach, even if not in a temporally direct way. While doing all these, I will both present a more or less descriptive, historical account, in particular in the first parts of my talk, and discuss the overall topic later on in a methodologically evaluative, critical manner, particularly insofar as my own methodological comprehension of philosophy is concerned. P HILOSOPHICAL I NSTITUTIONS IN T URKEY IN THE LAST AND EARLIER IN THIS C ENTURY From a socio-professional point of view, we see that the first institution dedicated to scientific and philosophical studies was founded in 1820, that is, early in the last century in the Ottoman times; it was called, after the main district of the imperial capital østanbul at the time, The Scholars’ Group of Beúiktaú. This is also the first laic and national organisation in this country, using the latter word in a historically broad sense. In time, however, and not unexpectedly, this society was abolished, possibly having the fate of similar organisations earlier in the socio-political life of other countries in different times. And, again, as elsewhere I think, the intellectual and academic vacuum left in this sphere was later filled by other similar institutions under the impact of Westernization. In the period of roughly a quarter of a century in the beginning of the present one, until the time of the foundation of the Republic in 1923, the intellectual milieu was under the impact of French thought, American pragmatism and the work of Ziya Gökalp, apparently the most renowned Turkish sociologist in the first half of the century (with his more or less ideologically (“nationalistically”) tainted approach to social problems). Around 1920, it was Bergson’s élan vital and similarly dynamic “psychological” currents that had their sway on philosophy in this country. (Kaynarda÷ 1994) In the first years of the Turkish Republic, too, we see a similar if not the same tendency: this time, of combining the study of sociology and philosophy, a current reflected in the work of Hilmi Ziya Ülken, a leading sociologist and teacher of philosophy at Galatasaray Lyceum in østanbul (which, with French as its teaching language, is still one of the leading high schools in the country; and there is now a Galatasaray University). His attempts led to the foundation, in

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1928, of the first society of philosophy in the Republican era. Due mainly to what one might call “inner strife”, it was abolished, to be founded again in 1931 as the Philosophical Society. Ziya Ülken, the leading founder of this organisation as well, later made two interesting observations. On the one hand, he regards the Sociological Society, which he founded years later, in 1949, as a continuation of its philosophical counterpart of the early thirties. On the other hand, and more relevantly for us here, he sees the seminars and colloquia held in the Philosophy Department of østanbul University and begun by Reichenbach in 1933 as the continuation of the activities of the Philosophical Society. The latter, however, came to an end, ironically perhaps, with the University Reform realized in the same year, its active members having been appointed to other places. The attempt to found another society in 1934 was successful; unfortunately, however, all its papers were destroyed in a fire, apparently soon after its foundation. And Ülken’s renewed attempt in 1943 became abortive. (Kaynarda÷ 1994) T HE U NIVERSITY R EFORM AND R EICHENBACH My emphasis on “institutionalization” in the course of the development of philosophy in Turkey depends both on the incidental or specific fact that a related principal reference has been devoted to this aspect of our topic; and on the general fact that in principle it would apparently represent a significant part of the discipline’s evolution in any social setting. From what we might perhaps call a deeper academic point of view, however, apparently it is the university environment rather than the related socio-professional milieu, generally speaking, which seems to be worth studying; particularly, of course, so far as its education is concerned. There have been certain other radical attempts, following Atatürk’s death in 1938 and until recently, to realize significant changes in the structure and functioning of the Turkish universities, and these “for good or evil purposes” so far as the direction of the political intervention is concerned. However, it is the transformation in østanbul University in 1933, the only one at the time as a fullfledged institution of higher education, which comes to mind first in this country as the University Reform. I will make use of certain sources as references, which tell us, besides other related points, the background to this event. One is the “Atatürk University Reform”, actually the Turkish translation of a book in German, Exil und Bildungshilfe, written by a German professor of pedagogics, Horst Widmann, in 1973 (Widmann 1981). I am sure that this work is really worth reading for anyone interested in the history of higher education in the Turkish Republic. In the present context, I will briefly mention, so far as they concern us here, the main points of a report on the subject dated 29 May 1932 (Ataünal 1993, 175) and prepared by Albert Malche, a Swiss professor of pedagogics from Geneva (Hirsch 1997, 210). I intend to do so together with a very short

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consideration of the basic expectations of Kemal Atatürk of the university as a modern educational and research institution of utmost significance. Atatürk so frequently emphasized the importance of science, both basic and applied, as an indispensable activity in our time, the relationship between science and civilisation, and the significance of this activity as well as education for human life as a whole. And it was in compliance with his wish and directives that Professor Malche, who had also had administrative experience as a rector, was invited to Turkey to study the state of the østanbul House of Sciences, as it was called at the time (and expressed in the Ottoman language, “Darülfünun”). The latter had been founded in 1846 as an institution, with European universities of the time having been taken as examples. Due to the reactions on the part of the established religious schools, however, it took seventeen years for it to be an active institution; and, moreover, it was closed and re-opened twice later on, in 1871 and 1874, finally assuming a stabilised structure in 1880. In addition to this institution with an expected university function, there were schools of higher education founded in the last century as independent professional institutions in medicine, law, administration, fine arts, and so on, which were later incorporated into the structure of østanbul University. (And a school of engineering later formed the nucleus of the Technical University of østanbul.) (Ataünal 1993, 35) The House of Sciences was not able to follow the radical educational, political, economic reforms and great scientific, intellectual, social changes realized under the leadership of Atatürk in the first years of the Republic, in its first decade roughly speaking. Also, there was no indication that the teaching staff there could appreciate, for one thing, the new conception of history widely accepted in the country. And there were real complaints about this state of affairs coming from different sections of the society, above all, and as would be expected, from the intellectuals. This educational institution was, as it were, in a state of MiddleAge isolation from the rest of the society. And its 1932 budget was approved with the proviso that a foreign expert would be given the task of preparing a reform plan for it. Albert Malche was the expert mentioned in a related speech by the Ministry of National Education; he was invited to Turkey by Atatürk in person in 1932. (Ataünal 1993) The report of Professor Malche consisted of sixteen headings. One may classify these critical points as regards the insufficiencies and deficiencies of the House of Sciences in accordance with its duties, structure and functioning. And from among the main points of his overall and radical criticisms, we may mention here the following aspects/areas in relation to this institution, which was the counterpart of a university as it existed at the time: education-teaching, research, publications, the teacher-student interaction, academic cooperation, the relationship among the members of the teaching staff, their attitude toward their duties, and so on. It seems that the university or academic freedom with its scientific and administrative autonomy existing at the time (and already given in 1925) was not properly appreciated and observed by the teachers, with their continual strives and cliques. In Professor Malche’s view, no problem was more important

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for the future of the university than the choice and appointment of the professors. (Ataünal 1993, 37-38) Atatürk’s own views were quite in agreement with the criticisms mentioned by Malche in his report. He stressed the necessity of radical moves for the university as in the case of other projects of the Republic. And a year after the report, in June 6, 1933, the Turkish Grand National Assembly passed a law abolishing the “House of Sciences” and giving the Ministry of National Education the task of founding of a new university. Shortly afterwards, another one came into force which has been known as the University Law (the first of its kind since then). (Ataünal 1993, 38 and 508) (We might possibly omit here the consideration of two somewhat distantly relevant points, one being historically and the other indirectly related to the foundation of østanbul University in what we might call a formal manner. Speaking in terms of history, some people take the beginning of østanbul University, doubtfully if not quite unjustifiably I think, to the early times of the Ottoman settlement in the City when a religion-based school was founded. And at the time of the Republic, secondly, different single institutions of higher education have been founded in Ankara: the School of Law (1925), the Institute of Education (1926), the Higher Institute of Agriculture (1933) (Ataünal 1993, 38), and the Faculty of Medicine (1945). They were later brought together, except the second one mentioned in their historical order, to form the University of Ankara (1946).) Seen in a more comprehensive educational perspective, the 1933 university reform in Turkey was complementary to what had already been achieved so far in accordance with the Republic’s principle that at all its levels the national education should be unified, and all the religious and/or scholastic elements, a serious relic of the Ottoman Empire, should be eliminated from the educational domain. And this was the sine qua non or necessary condition for a social order and the conception of individuality to be based on rationality rather than belief, on scientific thinking and not on dogma. It is obvious that these are also necessitated, inevitably, by the ideas of Enlightenment, laïcism/secularism, and humanism, namely, the very foundations of the Republic from an ideological point of view. It seems interesting to me that Ernst E. Hirsch, a professor of trade law, and who came to Turkey in the same year as Reichenbach and spent almost twenty years in østanbul and Ankara, does not mention his name in his Memoirs on his Kaiser, Weimar and Turkey times. For the information I am going to share with you briefly here as regards Hans Reichenbach’s professional life and work, overall achievements, and contributions to Turkish philosophy and academic life, I have chiefly made use of the following sources: (a) the work of Horst Widmann, which I mentioned before; (b) the related texts of Arslan Kaynarda÷, a Turkish philosopher who has specifically been working on the history/evolution of philosophy in this country;

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(c) and the information material from the University of Pittsburgh’s Hans Reichenbach Collection, to which I had access some years ago through its parallel texts in the Philosophy Department of Konstanz University. I will begin with the latter reference. Reichenbach was forty-two years old when he came to østanbul. As some of you could possibly know, he had first studied engineering, but became interested, later on, in mathematics, physics, and philosophy; received his doctoral degree from the University of Erlangen; worked in the army, and then in the radio industry; attended Einstein’s first lectures on special and general relativity; taught philosophy of science, radio, and surveying in Stuttgart. In 1926, he received a professional appointment at the University of Berlin, with support from Einstein. During this time Reichenbach produced a series of works which deal with the problems of space and time as they are represented in the new physics, the best known of them being The Philosophy of Space and Time (1928); in this work, he sets out to reconstruct the related concepts from their most elementary counterparts, and relates them to the relativity theory. (Hans Reichenbach Collection) While in Berlin at the time of the rise of Nazism, Reichenbach had considered accepting a position at the German University in Prague, but decided to accept a more attractive teaching offer at the University of østanbul. This later proved to be less than satisfactory because it isolated him for five years from travelling or having important discussions with colleagues (outside Turkey). (I will touch on this point later on.) It was during this period, however, that he produced his major work on the problem of induction, namely, The Theory of Probability (1935), and his major epistemological work, Experience and Prediction (1938). After his term in Turkey was completed, Reichenbach accepted an offer from the University of California at Los Angeles, where he remained until his death in 1953. He produced here, two years before his death, his most popular work, The Rise of Scientific Philosophy (1951). And at this time, he had nearly completed his book, Direction of Time, published posthumously (1956), like his many other works, by his wife, Dr. Maria Reichenbach. (Hans Reichenbach Collection) As for an account of his time in østanbul, and as seen from within, so to say, I may summarize here the main points of an as yet unpublished article by Arslan Kaynarda÷; this is the text of his presentation at the meeting held in Ankara on the occasion of the one hundredth anniversary of Reichenbach’s birth. Kaynarda÷ speaks of Reichenbach, in this text as well as elsewhere, as “the famous German philosopher” who was among the group of about 200 German and Austrian cultural and scientific refugees fleeing from the Nazi regime. (Kaynarda÷ 1991) He also describes him as one of the most important members of the Vienna Circle; but I wonder if this is a correct observation, my reason being the difference in philosophical approach rather than because Reichenbach was teaching in Berlin and not in Vienna. Widmann, too, mentions Reichenbach as the internationally most renowned among the refugee philosophers, and, together with Rudolph Carnap and Carl Hempel, as one of the leading members of logical

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empiricists in general. (Widmann 1981) All three of them had been neo-positivists or logical positivists, to be sure, but in differing degrees as shown with their different degrees of contact and relationship with the Circle. Both Kaynarda÷ and Widmann point to the fact that Reichenbach was also a physicist, and the second author writes that he was invited to Turkey as a professor of positivist philosophy and mathematics. (Kaynarda÷ 1991; Widmann 1981) Reichenbach was apparently not known in Turkey at the time, and was noticed by the Turkish authorities because his name was among the Germanspeaking professors persecuted by the Nazis. There were, at that time, two main streams of philosophy in østanbul University clashing with each other: a predominantly metaphysical one which was under the impact of Islamic philosophy and the religious tradition in education; and the other having a Western direction with the positivism of August Comte predominating. And a philosophical language had not yet been sufficiently developed to meet the demands of philosophising. One could only expect, on the part of the traditional philosophical circles at the University, a reaction to the Berlin philosopher who had been appointed as ordinarius professor and head of the Philosophy Department – we must just think of his adherence to the new philosophical current, that is, neopositivism and logical empiricism. In defiance of the established non-discursive tradition and in spite of the rather poor quality of the academic work together with the low educational level of the students, Reichenbach showed efforts in his lectures, from the very beginning, to found his teaching on his scientific philosophy; expectedly, to the total exclusion of metaphysics and the traditional philosophical approaches generally speaking, and with great emphasis on logical analysis and the use of mathematical or symbolic logic. (Kaynarda÷ 1991) He gave lectures on logic, epistemology, and the history of philosophy, notably on Descartes, Hume and Kant. Kaynarda÷ has found out, thanks to his direct contacts with some students of his later on, that Reichenbach considered philosophical doctrines from the perspective of his scientific philosophy and with a critical attitude towards them. It seems that he was giving his lectures on the history of philosophy unwillingly, and after some time he suggested that Professor (Ernst) von Aster should be invited for this purpose. The latter came to østanbul in 1936, and in an article he wrote later, apparently at the time of Reichenbach’s departure, he was speaking with admiration about his contributions to mathematical logic and the philosophy of science in general terms, and to the teaching of philosophy in Turkey. (Kaynarda÷ 1991) (Von Aster assumed most of Reichenbach’s duties after his departure (Widmann 1981, 87-88).) Although most of Reichenbach’s students took notes in his lectures, these are not available today. Apparently, he has made use of the content of his lectures he gave in østanbul as the material of certain works that were published later. We may mention among them his Logistics, published and then translated into Turkish while he was there, and also the two major works I mentioned earlier in this section. (Kaynarda÷ 1991) Judging by the list of his overall works (Schriften), we see that so far as the publication of articles and other works is

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concerned, he was apparently no less productive during his stay in østanbul than before or after; these have appeared in Erkenntnis and other journals of philosophy and the philosophy of science. His presentations at the international congresses of philosophy in Prague, 1934, and in Paris, 1937, have been published in the respective proceedings of these meetings, as well as the one he delivered in the International Congress of Scientific Philosophy held in Paris in 1935 (Schriften). Interestingly, I think, we observe that in the 1937 Paris Congress Reichenbach made his presentation in French; and he wrote two articles, which were published in French journals of philosophy in the same year. Not less interestingly, perhaps, I may point out the fact that Reichenbach learned French in østanbul. And another interesting point might be that Reichenbach was the head of the Turkish delegation in the Prague Congress. (Kaynarda÷ 1991). He was active in the philosophical life of østanbul in other ways as well. He was one of the founding members of “The Turkish Society of Physical and Natural Sciences” (1934), which had a periodical of its own. He made several presentations on philosophy in the meetings of this society, and gave conferences at the University, which aroused great interest. The colloquium as a type of academic activity has been begun in this country by Reichenbach organised every three months, most of the professors in the University participated in them, as well as students in philosophy and some students from other departments selected by Reichenbach himself. All of them were eager; it seems, to take part in these discursive meetings. It was evidently a new phenomenon, a new sort of educational interaction in the University. And in his lectures, he was really trying to inculcate scepticism upon the students who were so much under the influence of the traditional learning by heart, and who had not been properly educated for discussion and research. The term “discipline” in the sense of academic / professional field had been introduced to the academic terminology at the time of the University Reform, and it was Reichenbach who particularly insisted on the requirement that the philosophy student should take courses from among the disciplines in the Faculty of Sciences. Philosophy could not do without the sciences. (Kaynarda÷ 1991) Hilmi Ziya Ülken, the sociologist-philosopher whose achievements I mentioned in the preceding chapter, was lecturing in the Philosophy Department as an associate professor when Reichenbach arrived. Ülken seems to have had a great admiration for the philosopher. He always expressed this; it seems, in his writings and activities, by pointing out his contributions, particularly to logical empiricism (Kaynarda÷ 1991) and the probability or multi-value logic (Widmann 1981, 86). He also attended Reichenbach’s lectures. It may be interesting to note that (Rudolf) Nissen, a professor of surgery, wrote that it was difficult for many people to understand what Reichenbach was talking about and that it was professors rather than students who made real use of his lectures. (Kaynarda÷ 1991) Reichenbach advised one of his female students, Nezahat Nazmi, to work on Carnap for her thesis, because the latter’s philosophy represented a midway position in logical positivism; and knowing that she was interested in psychology

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from the very beginning of her education, Reichenbach told her also to choose a subject related to this field. The final title of her thesis was “The Interpretation of Logical Behaviorism according to Carnap and Reichenbach”, possibly the last dissertation he supervised. (He also tried for the realisation of the appointment of (Wolfgang) Köhler as professor of psychology in østanbul; but for various reasons, the latter could not come. However, Reichenbach’s second attempt was successful, and (Wilhelm) Peters came and stayed in østanbul for years.) One of the main references of Miss Nazmi’s thesis was Experience and Prediction, published in America in 1938, the year Reichenbach went there. The doctoral thesis of Neyyire Arda, another female student of Reichenbach, had the following title: “The Concept of Problem in Different Sciences”. The topic had been chosen within the context of Reichenbach’s philosophy, and she had taken her related notes to America where the thesis was written. (Kaynarda÷ 1991) There may be a correlation between Reichenbach’s inclination to psychology and his pedagogics, the principles of which he apparently applied both to his students in the University and to his son and daughter (Kaynarda÷ 1991). His approach was the then rather new one of giving youth much more autonomy, respecting them as individuals, or candidates of individuals. His wife was a teacher, but there is no mention in Kaynarda÷’s reference whether or not she taught in østanbul; so far as one can judge by his text, she probably did not. Reichenbach was also active in sports. He took the university students to sportive activities; particularly fond of mountaineering and skiing, it was he who discovered the skiing opportunities at Mount Olympus, near Bursa, and not far from the Southern coast of the Marmara Sea. (Kaynarda÷ 1991) Evidently, he loved Turkey and the people. So, why did he not stay? The main reason seems to be that he could not get his right to retirement, this being due to hard-to-believe bureaucratic formalities. Although he was apparently paid well, there was no guarantee for his and the family’s future. So, he saw no choice but accept the invitation from the University of California at Los Angeles. (Kaynarda÷ 1991) At all events, and overall, his earlier choice as regards østanbul may not perhaps have proved “less than satisfactory”, as is mentioned in the historical note on his life and work in the Pittsburgh University’s Library (Hans Reichenbach Collection), and which I referred to above. It must be true, however, that the Turkish philosophical and scientific atmosphere in his time was apparently not ripe enough for a wider or full appreciation of his work; and, also, that he and his colleagues did indeed contribute to the development of a scientific and cultural atmosphere during their stay (Kaynarda÷ 1994). So far as human contact is concerned, and leaving aside the unjustifiable obstacles of bureaucracy, what Reichenbach experienced seems to have been, possibly, more than satisfactory. As recounted by Nezahat Arkun, a lady who knew him well as a psychology student at the time, he donated his personal library to his Department in østanbul where he had worked five years. He wanted, following his departure, to continue his contacts with his students, and to know what they were doing; but the

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intervening war years, particularly, did not give him this possibility. And it seems that while in America, Turkey was not infrequently in his mind. (Kaynarda÷ 1991) A N I MMEDIATE F OLLOWER : N USRET H IZIR , AND HIS R OLE IN L ATER D EVELOPMENTS In an earlier study, which is on the evolution of Turkish philosophy, Kaynarda÷ has more systematically considered the contributions of Reichenbach to this process generally, as well as his direct, more specific role he played in the University during his stay in østanbul. In my attempt to give here a short account of Nusret Hızır’s role as his closest follower, I will rather make use of both of his related texts, one published in 1983 and the other presented in 1991, together with his 1994 work on the institutional development of philosophy in this country. Both in accordance with my own philosophical methodology and in terms of a general and/or “neutral” analysis, the superlative adjective “closest” used in this context signifies a direct continuity in time rather than similarity in philosophical approach between the two thinkers, the teacher and the student. I think this point will be clear as we proceed in this section. Reichenbach has been particularly influential on later developments in the philosophy of science in Turkey (Akdo÷an 1994). So far as Hızır is concerned, and although he was not a philosopher of science in the more or less technical sense of the term, he was apparently closer to Reichenbach in understanding in this field than he was in philosophy generally speaking. We shall see this when I give here a short account of his two published works. I will also consider, later on and rather briefly, how he saw his position in philosophy as well as his role in relation to Reichenbach and the Vienna Circle. The two hard-working women students of Reichenbach I mentioned above later became his assistants, as well as interpreters in his lectures. There were also male assistants who were at the same time his interpreters. And among them, we see Nusret Hızır (1899-1980), who was seen in Turkish academic life as the person who carried the scientific philosophy of Reichenbach, together with mathematical logic, to Ankara University and the philosophical circles in Ankara. From 1942 until his retirement in 1968, and with the exception of a two-year break between 1960 and 1962, he lectured at the Faculty of Language and History-Geography of Ankara University (Hızır 1985, 11). As Ziya Ülken writes, he was the most capable of Reichenbach’s students (Widmann 1981, 86), and later became one of the leading figures among the first-generation of philosophers in (the Republican) Turkey (Kaynarda÷ 1991 and 1994, 14-15). He gave lectures on philosophy at the Ecole Normal Superior in Paris in 1963; and, following his retirement, he taught philosophy and logic in different faculties of three universities in Ankara for short periods of time, notably in the Middle East Technical University (for two and a half years). From 1971 until his death that is

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for about ten years he continued to give courses in his home to small groups interested in philosophy (Hızır 1985, 11), and in his overall and immense cultural background; I was an occasional participant in these non-formal but professionally interesting activities. And one may say that overall, Hızır has been more influential on the general, enlightened public eager to learn more about philosophy and science by direct contact, so to say, than within the philosophical circles of the university, that is in a basically academic atmosphere. Nusret Hızır had studied physics, mathematics and philosophy in Germany, and, returning home, became an assistant in the Philosophy Department of østanbul University in 1934, one year after Reichenbach’s appointment there (Hızır 1985, 11; Kaynarda÷ 1983, 773). Further among his non-university activities, Hızır worked as an “expert” in the Turkish Historical Society between 1937 and 1942; he was involved, between 1941 and 1948, in the translation activity of classical works of philosophy (carried out by the Ministry of National Education), and himself made translations from different philosophers such as Erasmus, Leibnitz and Nietzsche (Hızır 1985, 11). As for Hızır’s own productivity in philosophy, the most striking fact to be mentioned about him is that he was always an oral person, so to say, rather than a writer. In a way, this is perhaps to be expected, given, for one thing, his inclination to teach in an informal manner rather than with an academic concern in mind; and, also, his fondness for “philosophical chatting” while considering the problems of philosophy and trying to give his own answers to them, rather than discussing their solutions in a multidimensional context through writing. At all events, and to the best of my knowledge, he has two books, one of them having been published four years before his death and the other five years thereafter. Their titles are, respectively, “Philosophical Writings” and “Philosophy in the Light of Science”. The former consists of completed notes or texts of presentations, edited by two “friends” as Hızır calls them, one of them being an earlier female assistant. The latter is a compilation of his articles published in different journals and/or texts of presentations made on different occasions, edited, again, by the same female philosopher. From an academically formal point of view, none of his writings, perhaps, is a “scientific” article, with a true systematization of the material and a satisfying list of references, and so on; they may possibly be regarded as philosophical essays, in the more or less traditional sense of this form of writing. So far as their content is concerned, however, they do reflect Hızır’s philosophical views in a clear, and what we might call undiluted manner. His posthumous work truly sounds “positivistic” or “logical positivistic”, or, more justifiably perhaps, logical empiricistic. And indeed, in the foreword of his earlier book, he gives a short, personal account of his philosophical stance. He says that during his years of assistantship in østanbul he was very close to Hans Reichenbach and the Scientific Philosophers of the Vienna Circle. He was, years later, still rather close to them in understanding. And he adds, interestingly, that he owes to Reichenbach and to the Circle the ability to see philosophy as an analytical activity and to cherish certain theses of the Anglo-Saxon analytical

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philosophy, which are not in conflict with dialectics. (I will discuss these two points, namely the relation of dialectics to his philosophy and the term “analytical philosophy”, in the penultimate and last sections, respectively.) However, many views of the Vienna Circle seemed to him, later, as too narrow and stiff; and his writings in his book were significant for him because they showed that he turned away from a rather orthodox Viennese position to a more moderate and more liberal “logical empiricism”. On the other hand, the aim of the publication of his book was to help people think rather than to inform them on various topics of logic and philosophy. (Hızır 1976, 6-7) As for the topics in this work, I may mention here such titles as the following: “Romanticism in Philosophy”, “The Meaning and Significance of the Philosophy of Science Today”, “Pascal – one of the Messengers of Existentialism”, “A Christian Existentialist: G. Marcel”, “Is Existentialism a Philosophy?”, “Phenomenology and Logic”, “The Young Nietzsche”, “Fichte and the Thinking of our Time”, “The Personality of Machiavelli”, “Kant and Einstein”, “A View in Vogue in Science: Structuralism”, “The Importance of the Concept of Probability for Knowledge”, “Natural Science and History”… (Hızır 1976) As we see, Hızır was, as a thinker in general and a philosopher in particular, a person of wide interests; and reading the texts will reveal that he has an originality in the elaboration of the topics he treats. So far as professional depth in philosophy and philosophising are concerned, however, we see that he somewhat lacks logical rigour, conceptual dynamism, and the academic dimension of giving rationales at the conceptual level, so far as can be done, as supports for one’s arguments. On the other hand, in my view, some of the titles show us that the variety in his choice of topics go beyond the usual, philosophically or methodologically “formal” limits of neo-positivism. We observe that from the viewpoint of logical empiricism and scientific philosophy, his analyses are not sufficiently systematic and critical, and somehow represent a “colourfully” original personal approach to certain classical or traditional philosophical and near-philosophical topics. Thus, his writings obviously show intuitive insight but not sufficient logical analysis. Among the writings/essays in his second and posthumous work, he discussed such topics of interest in our context as “Philosophy vis-à-vis Sciences”, “On the Evolution of Science and Scientific Disciplines”, “Classical Physics and Heisenberg”, “For Albert Einstein”, “Thoughts on the Formalisation of Logic”, “The Concept of Laïcism in the West”, “German Universities and National Socialism”, and so on (Hızır 1985). As is the case in his first work, this book’s title does not correspond to that of any essay in it. My main points of concern and criticism as regards his earlier work are equally or, perhaps, almost equally valid for the second one as well. We may say that as a university teacher and thinker Hızır was indeed instrumental in the propagation, so to say, of rationality in general as well as in philosophical thought in this country, and so far as a scientific conception of the world is concerned. It seems that, interestingly, he was also influential, perhaps

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to a lesser extent though, in the development of philosophy in this country in another channel as well, which will be discussed in the very beginning of the next section. Lastly in this one, and in relation to our overall topic, I may mention that Reichenbach’s wish as to the continuation of his philosophy in his own Department in østanbul could not be realised – his colleague to whom he suggested this, (Richard E.) von Mises, professor of mathematics in østanbul at the time, did not accept this proposal. And Hızır appears to be the philosopher who realised this in another academic setting in Turkey, although he was not the only young person within the academic circle close to Reichenbach in østanbul. His colleagues who stayed there were active in one or more particular area, perhaps above all in modern logic. S IXTIES AND S EVENTIES , AND THEREAFTER : D IALECTICAL M ATERIALISM ON THE S CENE The other channel through which Nusret Hızır has had an influence on the intellectual and philosophical life of Turkey is dialectical materialism. So far as I can make a judgement, this was particularly the case in his activities following his retirement. And in so far as both my own observations and the opinion of certain other observers are concerned, he was far from being a “true” or “typical” Marxist, using the term in an unbiased manner. One might say that his philosophical approach was to a certain extent materialistic, and even dialectical materialistic in some respects. At least, one aspect of his philosophy and overall intellectual conception of the world was Marxist in a general way. And although he was certainly not a “street” Marxist with a methodologically superficial conception, and too pragmatic an approach to philosophy, science and the society, I think that here, too, he had the same difficulty of an insufficient consideration of the related conceptual and scientific (and ideological) points in depth. Possibly, from an overall technical-academic point of view, and to repeat, his influence in this area may not have been so powerful when compared with his role in the development of logical empiricism in this country. The political scene in Turkey in the sixties and seventies seems, generally speaking, to have had real similarities to what the Western Europe also experienced during this period; the student activists of 1968 had basically the same kind of demands in the political and socio-economic area as well as in the field of university education. That the most recent Turkish Constitution, that of 1961, had opened the way to a more comprehensive democracy would understandably be worth mentioning here as a socio-political factor in this country so far as our topic is concerned. In the present context, however, what really concerns us is certainly the philosophical scene itself and the relationship of dialectical thought to the development of philosophy in this country; and this, however politically oriented and founded the Marxist philosophy may be.

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On this matter, it is in Kaynarda÷’s paper on the Evolution of Philosophy in Turkey (Kaynarda÷ 1983) that I have found, personally, the most relevant information. Interestingly, and not quite coincidentally I think, it is roughly the same period, which he considered, in the way I have done here, to be the most representative one for the fruition of Marxist philosophy in Turkey. As he wrote quite justifiably, for a long time certain philosophical circles in this country behaved as if Marxism and the philosophy of Historical Materialism did not exist; they have even abstained from pronouncing the word “dialectics”. In reality, however, the beginning of the studies in historical and dialectical materialism goes back too much earlier decades in this country, with the publication of books and articles on related topics. What we might call the classic works of Marx and Engels has been translated in a growingly intensive manner until the time of the conservative, rightist military coup in 1980. The overall efforts in this area also included, expectedly, the works of contemporary Marxist authors such as Lukacs, Garaudy, Althusser and others, not to mention the seemingly classic work of Georges Politzer on the (so-called) principles of philosophy. And overall, among the philosophical currents, it is on Marxism that the highest number of publications in philosophy has been made since the very first years of the Republic. And there has been a general tendency in these works, essays, books, dissertations and so on, to consider dialectical thought since its beginnings in Herakleitos and others in Antiquity. (Kaynarda÷ 1983) For the rest of this chapter, I intend to make use of an unpublished and not too short letter of mine, which I sent, more than a year ago, to the bimonthly periodical, Radical Philosophy. Published in Britain and run by an editorial collective of sixteen members working on a voluntary basis, it is evidently a serious and respectable philosophical journal. Whether, or to whatever extent, it may also be regarded, as an academic journal would certainly depend on how you would define the adjective “academic” with special reference to philosophical periodicals, and to publications in philosophy generally speaking. I shall make here, basically from my own logical empiricist perspective to be sure, a critical evaluation of the contents of the 86th issue of this journal published in November/December 1997. It must be understandable that the reason why I do so is my observation and belief that the material of such an analysis would be quite representative of the Marxist approach to philosophy in Turkey as well, for the past forty years or so; and this must indeed be the case in the world at large. One should certainly add, however: “though with certain modifications in place as well as in time”. Let me now give you a brief description of my observations and impressions on the issue of the journal in question. The more or less complete eye in the upper part of a human face, to which most of its front cover has been dedicated, has evidently a message – the message, it seems, of deep thoughtfulness and serious concern about human affairs. And considered together with some photographs and one or two drawings dispersed in the texts, the cover design seems to be an introduction, as it were, to the overall understanding underlying the concept of

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radical philosophy, at least as it is represented by the visual contents (of this issue) of the journal – a pistol divided into two, diseased and/or tortured human legs, a naked black man drinking milk, two young naked black men sitting side by side and with one eye covered with one of their hands… And a picture showing busts of Karl Marx meaningfully completes the picture, not just as a visual device representative of an ideology and doctrine, but so far as philosophical methodology is concerned as well. Understandably, Radical Philosophy is first and foremost if not exclusively devoted to a Marxism-oriented political philosophy, which is certainly in keeping with its textual content. I may just touch upon another basic point here without elaborating it: What is “Radical Philosophy”, from a methodological standpoint, as the concept underlying this publication? The subtitle of the journal has more than an implication in this regard, if not, possibly, a full answer to this question: “a journal of socialist and feminist philosophy”. The inside of the front cover is a Call for Papers on the theme of “evil”. Interestingly, and contrary to what we would ordinarily expect perhaps, but evidently in compliance with the basic approach of the Journal, no mention is made, in that context, of the so-called “religious studies” among the related disciplines invited for the investigation of this basically religious moral concept. On the other hand, and quite in keeping with the main orientation of Marxist philosophy as well, one would be reminded here of the “humanities” approach to philosophy in the Anglo-Saxon universities. As is shown in the latter’s academic division and activities generally, this evidently reflects the widespread conception of philosophy, not only in these countries but in the world at large – that philosophy is a humanisticly oriented activity; and this, in spite of the enormous development in this century in the philosophies of logic and mathematics, and those of physics, geology, biology, and so on. Marxist philosophy, and the Marxist doctrine in general, are certainly man-centered in their very essence, however “materialistically” they may have been founded. At all events, generally speaking and so far as one can judge by the content of just one issue, Radical Philosophy appears to be a professionally reasonable journal with its apparently balanced emphasis on political philosophy and technical philosophising. And this makes it more vulnerable, in a positive sense, to methodological criticisms of the sort I have in mind as a scientific philosopher; and, on the face of it, the expectations of critical readers from it in general would necessarily be high. Marxism is a philosophically based, historically oriented, socio-political, and, most characteristically perhaps, self-sufficient doctrine. It begins with materialistic philosophy as its overall conceptual framework; proceeds with dialectical materialism as an allegedly scientific basis; comes to a climax with historical materialism as a socio-economically based political ideology. As we all know, it has a very strong commitment to the undertaking of power to revolutionize all the states of affairs in human societies, mainly by putting an end to socioeconomic and, apparently derivatively, every sort of exploitation. It is “self-sufficient”, in the sense that it allows no other philosophical (or any other) school,

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view, or approach for a critical evaluation of its claims, and this from almost any point of view, philosophical, scientific, historical, moral… This is just because, obviously, it is, in the first and last analysis, a political doctrine; the attitude and behaviour of Marxist/socialist thinkers, or socialists in general, are almost always political – just like in political life in general, they would never really be “beaten” by their opponents in any debate, except, possibly, by force. And just like any belief system, whether heavenly or worldly, it is holistic, however materialistic, non-idealistic, and secular it may claim itself to be. In this sense, and as a particularly relevant point in philosophy and in the present context, it seems to be quite justifiable to compare it to the speculative philosophical systems of rationalist thinkers, above all Plato, Descartes, and Kant, as has been very aptly discussed by Reichenbach in The Rise (27-49, 71-72, 121-122). Even further, a young Marxist wrote to me in one of his letters from prison that you would or could either accept Marxism in its totality, or otherwise you should reject it altogether; there could be no other way, or, as it were, a mid-way, in its consideration. In accordance with the doctrine’s greatly pragmatic aspect, the whole truth is on your side if you are a Marxist; if you are not one, what you would have is the whole non-truth, so to say, apparently in almost all the possible senses of such a term. In other words, an absolute belief both in his own rightness and in the wrongness of his debaters and opponents seems to be inevitable for the ordinary or orthodox Marxist, who appears to be actually a believer so far as a “universal” and “all-knowing” doctrine is concerned. In his work on Power, Russell devotes a chapter to “Power Philosophies” and gives the philosophy of Fichte, pragmatism in some of its forms, Bergson’s Creative Evolution and the ethics of Nietzsche as more or less typical examples (Russell 1960, 172-177). And Marxist philosophy is certainly a “power philosophy” in this sense; not only, however, because it is strongly pragmatic in its essence but also, and more directly, as it constitutes the philosophical component and the conceptual ground of a basically political doctrine to be actualized, ultimately, through “revolutionary power” (which Russell discusses in a separate chapter; pp. 72-81). I will not, understandably, consider Marxist philosophy or dialectical materialism in any detail here (and I am not in a position to do so without preparation specifically for such a purpose). As for the situation in Turkey, and to repeat by way of emphasis, it is quite possibly not too different from what one would witness elsewhere in the world, both in philosophical outlook and political thought, and as an ideological tool. Under what I would call the democratic pressure of the 90’s, Marxist philosophy (side by side with Marxist politics) is seemingly being “revised” now in the intellectual milieu of the society at large. I do wonder, however, to what extent the ideological, political-international and intellectual atmosphere created by the so-called New World Order would allow this, as an extreme situation, and challenging the doctrine.

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T HE L AST TWO D ECADES : S CIENTIFIC P HILOSOPHY AND THE “T RADITIONAL ” R EACTIONS Interestingly in my view, in two publications of the UNESCO on philosophy which appeared within the same decade, Turkey was regarded among the Asian and Pacific countries in one and as a European country in the other (Kuçuradi 1986 and 1993). The author of the related sections in these publications is among the third generation of the philosophers in Republican Turkey (together with A. Kaynarda÷), and has been the Chairperson of the Turkish Philosophical Society for years, became the Secretary General of the International Federation of Philosophical Societies, and is now the latter’s President. On the other hand, during the concluding session of the conference held in Ankara in 1991 on the occasion of the one hundredth anniversary of Reichenbach’s birth, she commented on his philosophy by saying that they organised the meeting not because of any real merit of his work but because he had spent some time in Turkey. I am just referring to this observation here without making any comment on it. The only point that I can add in the present context would be that we must see such remarks as regards scientific philosophy not as exceptional evaluations but as “ordinary” reactions on the part of traditional philosophers (as has been aptly emphasized by Reichenbach in The Rise). Philosophy as an academic activity has developed, essentially, along Western lines in Turkey, with all its ramifications having been represented (Örs 1998b). And as admitted by a Turkish historian of science who is highly critical of logical positivism, Reichenbach “started a new and revolutionary movement within Turkish philosophical circles” (and) “found a following in Turkey”, particularly, of course, in the philosophy of science (Akdo÷an 1994). At this point of my presentation, I think I may be entitled to give a short account of my own development and contributions in scientific philosophy, for it seems that as far as Turkey is concerned I am apparently the only one in this area whose name can be mentioned. For about twenty years following my graduation from the medical faculty in 1960, I read philosophical texts, above all Russell. Seen retrospectively, this was basically an unsystematic reading on the part of an intellectual interested in the general, abstract, conceptual aspects of human endeavour, and a quest to know the world in its general outline. From roughly 1980 onwards, I began to get involved in philosophy in a more academic and, if you like, professional way. The institutional academic milieu for this was the Philosophy Department of the Middle East Technical University in Ankara (where the teaching language is English). And following a one-semester term as a special student, I began, in 1982, my doctoral studies there, which I completed in 1991, after all the possible extensions, with the defence of a dissertation on the topic: “Is the ‘Biological’ Reducible to the ‘Physical’ – An overall critical analysis of the concept of reduction in biology”. Cemal Yıldırım, who translated The Rise in 1981 (see Reichenbach 1966), was my advisor during the period of special studentship, and Teo Grünberg has been my supervisor throughout the whole

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course of my doctoral studies. Being among the 3rd generation of philosophers in Turkey, they have been retired for some years now; and both have been regarded more or less as followers of Reichenbach, particularly so far as the philosophy of science is concerned. I think, however, that in actual fact I am, as their student, more closely related to him from the viewpoint of philosophical conception and methodology than they really are. The opponents of neo-positivism and logical empiricism are inclined to see the followers of these philosophical currents in Turkey as “the disciples” of Hans Reichenbach. This must be an established attitude in the traditional philosophical circles all over the world, particularly, I think, in the West, to scientific philosophers, and to logical empiricists in general. But it is not a right and justifiable attitude, I believe, because contrary to most currents in philosophical evolution, above all the rationalist systems, the “new philosophy” of the Vienna Circle and the new empiricism as a whole is not comparable to a tenet, or creed, as it were; it has, as one of its great characteristics, the quality of being open to criticism and self-criticism, hence, in principle, to change. This is due, first of all, to the fact that, like science, it is performed as a piecemeal activity. And it is nondoctrinal. It does not aim, as has been frequently emphasized by Reichenbach, towards the attainment of absolute knowledge, or towards anything absolute indeed. A disciple in any area is as a rule a “true”, basically uncritical follower of the master or the “great” man, as is readily observable in philosophy in the case of Plato, Kant, Marx, for instance, and many others. A follower of scientific philosophy, and the new empiricism generally speaking, is in principle equally critical of every philosophical work, including his own, and whether it is close to or distant from the latter. The reason why such an attitude cannot be appreciated by the traditionally-minded majority in the philosophical arena must arise, above all, from the fact that they cannot see one of the most essential points in the new philosopher’s approach to philosophical activity – that philosophy should, and can, be freed, to a great extent, from its traditional or established man- and individual-centeredness. My position in the new philosophy, and in philosophy generally speaking, is certainly very much related to my intentions and aims, to my “academic mission” if you like. To put it briefly, I have been trying to develop scientific philosophy in a certain direction – that of an overall methodology. The term “methodology” used in the present context signifies an endeavour, a quest for an answer, or rather answers, to the three basically simple but interrelated and rather comprehensive questions – “What?”, “Why?”, and “How?”. (At least two others, perhaps, may be added to these, namely, “How did it develop?” and “What is its overall significance?”.) I think these questions must be asked, and answered in however a tentative manner, in the case of all the major human activities, such as science and sciences; the applied fields of medicine, health professions in general, and branches of engineering; architecture, the arts, and so on. The quest for an answer to the first question would be directed to the subject matter (or “whatness”) of any serious human activity; the second one to its overall purpose or aim

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(and differently from a personally teleological “What for?” question); and the third question to the problem of what relates the first to the second, that is, the method and/or techniques to be applied while working on the subject matter in question for the purpose specified – this is usually what is meant by the term “methodology” in a narrow sense. In the light of such a “methodological” quest, the core phrase of my definition of philosophy will be: “a critically logicosemantic and conceptually analytical activity, an interpretation, aimed at contributing to the understanding and explanation of the world (in an indirect manner)”. There are, of course, so many different philosophical conceptions due to the widely differing methodologies or basic meta-philosophical approaches concerning this activity. So, this is what and/or how philosophy should be in accordance with my methodological view, rather than reflecting a generally accepted definition, let alone one widely agreed upon. My own and possibly more or less special emphasis as regards the basic points or properties of philosophy mentioned in this context would be on its conceptuality and semantic aspect. Philosophy thus becomes, in my view and in its essence, a critically semantic conceptual activity. The basic question a scientific philosopher has to ask in connection with his/her activity would then be, “What do I, you, or they mean by this or that expression?”, as the case may be. But this must not taken to be either a linguistically oriented or rationalistically philosophical question – the semantic aspect or core involved here assumes its function and significance within a framework which is at one and the same time conceptual and prepositional / judgemental. And this is the case whether the expressions in question are synthetic propositions, as in sciences for instance, or analytic propositions, as in pure mathematics and symbolic logic, or, still, judgemental and similar utterances, as we see in the case of moral and aesthetic evaluations. There could also be an overall methodological question, which we could justifiably ask in the case of philosophical activity as well: “What sort of an activity is it?” This should apparently be dividable or analysable into the three questions, at least, mentioned above. In all events, if philosophical activity is scientific, it should be self-corrective like science, and opposed to metaphysics and speculation. And it should also be functional in the sense that it must throw some light on a “philosophical”, or scientific, social, moral, aesthetic, or similar issue in a way that philosophers and non-philosophers alike could in principle see the point, however complex and specifically technical the underlying concepts and terminology may be. So far in this area, what I have been able to realize, in its main outline and worth mentioning in the present context, is the following: Twelve articles on Philosophy, published consecutively in Felsefe Tartıúmaları (Philosophical Discussions) between 1990 and 1996, and later compiled in one volume, In the Light of Scientific Philosophy (Örs 1998a). More recently, I began to write a book in English in the beginning of last year, The Limits and Limitations of Philosophy, with a subtitle, An inquiry into philosophical power; unfortunately, however, my intervening activities, though mostly philosophical in a general sense, have not

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given me the possibility of continuing that work for more than six months now. While it would not be possible for me to undertake the second enterprise if I did not write, above all, those twelve articles earlier, the work in English has been planned, developed, and written, in part, as an entity on its own. Among other activities of mine worth mentioning in the present context is a text, which I prepared upon a call from a lady philosopher in østanbul University (namely, in the Department Reichenbach worked). She has been working, apparently with her younger colleagues, on a three-year project entitled “Philosophy in Turkey”, supported by her University and expected to be completed by the end of this year. Part of the project has been devoted to first-hand information on the part of the philosophers, teachers of philosophy in the universities and the historians of the field in Turkey. What they were expected to do to contribute to the idea is mainly to write a text stating their academic background and work, their conceptions of philosophy and their views as to the state of philosophy as an academic discipline with its research/inquiry aspects and teaching. My own text bears the title “From Science and Philosophy to Scientific Philosophy”. We are expected to update our texts and give further information on later significant developments in our academic life. I shall do so, and send an additional text to her, hopefully soon, on further developments in my philosophical career. I would like to mention two more points at the end of my talk, one on my most recent areas of interest, and the other as regards certain meta-philosophical issues which I see as important from my own methodological stance. In the nineties, we have witnessed the development of the inter- or cross-disciplinary field of Philosophy and Psychiatry, whose number-one responsible person is Professor K.W.M. Fulford. A Fellow of the Royal College of Psychiatrists, he is teaching, mainly in the philosophy and ethics of mental health, in the Medical Faculty of Oxford University and the Department of Philosophy, University of Warwick. It is now an internationally developing academic field thanks to his efforts and certain others in the United States, Italy, France, Germany, and so on. I may be said to represent this new academic and inter-professional movement, if you like, in Turkey, above all in the psychiatric circles of Ankara. The new discipline is methodologically based on the intersections between philosophy, abnormal psychology and medicine, in particular, of course, psychiatry. Vienna, as the City of Freud as well as the Circle’s, could be, in my view and potentially speaking, one of the most convenient venues for its further development. I have also begun to take a real interest in the Ethics of Philosophizing as a so far unduly neglected and almost non-existent subdiscipline of the field of ethics. It is methodologically to be related to how, or on what grounds, philosophers do philosophize. It must be regarded as a field possibly comparable to the ethics of any of the academic activities in general, with responsibility being its core moral concept. What is significant for us in this regard is whether the philosopher is capable of giving the logical, semantic, definitional and/or other rationales in whatever he/she produces as a philosopher; this would apparently have the same

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methodological status as the empirical or empirico-mathematical operations in the sciences. (See Örs 1996). Besides, I have been more and more involved, in recent years, in the Concept of Evolution, a topic I have been working on, not continuously though, for about twenty-five years now. I am also a member of a small, interdisciplinary group of academics, mostly in Ankara, who have to give a fight, so to say, on both the scientific and ideological fronts, for the defence of the evolutionary theory against the reactionary circles in Turkey with their connections abroad, predominantly in the States. (One is inevitably reminded here of the most perfect conceptual or philosophical analysis of Reichenbach, who has devoted a chapter to Evolution in The Rise (Reichenbach 1966, 191-214).) If I had time to consider certain key concepts in the meta-philosophical domain, I could perhaps discuss, from a methodological-definitional-semantic point of view, such terms as “analytical philosophy”, “metaphysics”, or “the history of philosophy”. Now, I might perhaps do so during our discussion. At all events, such terms seem to be important within the context of the activities of the Institute Vienna Circle as well, because they are frequently mentioned in its programs, activities, calls, and so on, as well as in similar texts by other philosophical institutions such as university departments. This would be of great conceptual value, because methodological analysis would always be the first and foremost means to clear the “philosophical” ground. As just one example, let me quote here a sentence from the Hans Reichenbach Collection text in the University of Pittsburgh’s Libraries I referred to several times above: “During this time (at the University of California) he produced The Rise of Scientific Philosophy (l951), in which he recounts the evolution of philosophy as viewed by a logical empiricist.” If someone who does not know the work of Reichenbach reads this sentence, he/she would take it to mean that this logical empiricist philosopher wrote a dynamically oriented book on the overall evolution of philosophy. Actually, however, Reichenbach has written a superb, unmatched book on the methodological-conceptual clarification of philosophy with its evolution as a comparative background for a developmental analysis of the activity. I think we should all be as brave as Reichenbach for a radical reckoning with the traditional ways of thinking in philosophy. Then, I think, we will be mostly free from making such obvious “meta-philosophical” (or, in my terminology, “methodological”) mistakes. Acknowledgements. I am thankful to Prof. Dr. Ayhan O. Çavdar, President of the Turkish Academy of Sciences, for giving me a copy of the text of her presentation, “Atatürk and Science”, held at Ankara University on the occasion of the sixtieth anniversary of Atatürk’s death, 10 November 1998; and to Prof. Dr. Süleyman Çetin Özo÷lu, one of her chief advisers at the Academy, for his sincere help in providing me with the basic material and a summary of the 1933 Turkish University Reform and thereafter. I also owe thanks to Hafize Öztürk, M.D., a capable third-generation doctoral student at her thesis stage in

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Deontology and Medical History; thanks to her observations on my philosophical work and her suggestions to me, she has been influential, however indirectly, in the realisation of the present text.

N OTE *

Based on the text of a presentation made at the Institute Vienna Circle with the same title, on 12 April 1999.

R EFERENCES Akdo÷an, Cemil 1994. The Philosophy of Science in Turkey; Proceedings of the 3rd International Symposium of Philosophy of the Balkan Countries: Philosophy in Balkan Countries Today, Athens, pp. 247-251. Ataünal, Aydo÷an 1993. Cumhuriyet Döneminde Yüksekö÷retimdeki Geliúmeler (Developments in Higher Education in the Republican Era); Directorate General of Higher Education (of the Ministry of National Education), Ankara, pp. 27-52; 176-229. Hans Reichenbach Collection, in the Special Collections Department of the University of Pittsburgh Libraries. Hirsch, Ernst E. 1997. Anılarım. Kayzer dönemi, Weimar dönemi, Atatürk ülkesi, transl. into Turkish from the German original, Aus des Kaisers Zeiten durch die Weimarer Republik in das Land Atatürk’s – eine unzeitgemäße Autobiographie; Schweitzer Verlag, München, 1982, by Fatma Suphi, and publ. by TÜBøTAK, the Scientific and Technical Council of Turkey. Hızır, Nusret 1976. Felsefe Yazıları (Philosophical Writings); Ça÷daú Yayınları, østanbul. Hızır, Nusret 1985. Bilimin Iúı÷ında Felsefe (Philosophy in the Light of Science); writings compiled by Füsun Akatlı; Adam Yayınları, østanbul. Kaynarda÷, Arslan 1983. Türkiye’de Felsefenin Evrimi; Felsefe Çalıúmaları; Cumhuriyet Dönemi Türkiye Ansiklopedisi. (The evolution of philosophy in Turkey; Philosophical Studies, in: The Turkish Encyclopaedia of the Republican Era), øletiúim Yayınları, østanbul, vol. 3, pp. 762-774. Kaynarda÷, Arslan 1991. Filozof Hans Reichenbach’ın Türkiye’deki yılları ve etkileri. (Philosopher Hans Reichenbach’s years and influences in Turkey.) Paper presented at the commemorial meeting on the occasion of his one-hundredth anniversary, organised jointly by the German Cultural Center and the Turkish Philosophical Society, Ankara, 11-12 November 1991. (I thank the author for sending me his manuscript upon my request, to be referred to particularly for the present occasion. As the text was not yet complete with its references and so on, I have only given Kaynarda÷’s presentation as reference.) Kaynarda÷, Arslan 1994. Bizde Felsefenin Kurumlaúması ve Türkiye Felsefe Kurumu’nun Tarihi (The Instıtutionalization of Philosophy in Turkey and the History of the Turkish Philosophical Society); Türkiye Felsefe Kurumu, Ankara. Kuçuradi, Ioanna 1986. Turkey, in: Teaching and Research in Philosophy: Asia and the Pacific; UNESCO, pp. 298-322. Kuçuradi, Ioanna 1993. Turquie, in: La Philosophie en Europe, R. Klibansky and D. Pears (eds.); in coop. with UNESCO, Gallimard, pp. 467-484. Örs, Yaman 1996. The Irresistible Rise of Scientific Philosophy – Philosophism and the Ethics of Philosophizing; Synthesis Philosophica 22: 447-460. Örs, Yaman 1998a. Bilimsel Felsefenin Iúı÷ında (In the Light of Scientific Philosophy); Öteki Yayınevi, Ankara. Örs, Yaman 1998b. Psychiatry and Philosophy in Turkey – Godotian Expectations? (Regional Report); Philosophy, Psychiatry and Psychology 5: 267-271.

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Reichenbach, Hans (1951) 1966. The Rise of Scientific Philosophy; University of California Press, Berkeley and Los Angeles. (Bilimsel Felsefenin Do÷uúu (1981); transl. by Cemal Yıldırım, Remzi Kitabevi, østanbul). Russell, Bertrand (1938) 1960. Power; Unwin Books, London. (Die) Schriften Hans Reichenbachs, the list at the Philosophy Department of Konstanz University. Widmann, Horst 1981. Atatürk Üniversite Reformu, transl. into Turkish from the German original, Exil und Bildungshilfe – die deutschsprachige akademische Emigration in die Türkei nach 1933, mit einer Bio-Bibliographie der emigrierten Hochschullehrer im Anhang; Herbert Lang, Bern and Peter Lang, Frankfurt/M., 1973, by Aykut Kazancıgil and Serpil Bozkurt, and publ. by Cerrahpaúa Medical Faculty of østanbul Univ., on the occasion of the one hundredth anniversary of Atatürk’s birth.

Department of Deontology Akdeniz un. Medical Fac. Dumlupinar Bul., Kampüs Antalya, 07070 Turkey [email protected]

REVIEWS

STEVE AWODEY & CARSTEN KLEIN (eds.), Carnap Brought Home: The View from Jena. Full Circle: Publications of the Archive of Scientific Philosophy. Volume 2. Chicago: Open Court, 2004. viii + 387pp. 34.95 US$. ISBN 0-81269551-8 (pbk.). This volume offers 16 essays, most of which originated in papers presented in late September of 2001 at a conference in Jena, Carnap’s intellectual birthplace. It was in Jena, where Carnap attended university and received his Ph.D. in 1921, that he took his first steps towards philosophical maturity. While the title of the collection suggests a single interpretative theme of the importance of Carnap’s Jena origins, most of the essays have little to say about this period of Carnap’s intellectual development. Instead, the aim of the editors is to ‘bring home’ or emphasize how important Carnap’s philosophy was and how important it still should be. Thus, in the first essay that acts as an introduction, Gottfried Gabriel insists, “that Carnap is a much subtler and more sophisticated philosopher, on many more fronts, than was generally suspected even a few years ago” (3). The danger of such an approach is that it could blind an interpreter to the weaknesses of her subject. I am glad to say that none of these essays errs in this direction, although there is a decidedly pro-Carnap feel to many essays. In the end, we find 16 high-quality essays that convincingly make the case both that Carnap is a philosopher of first-rate importance and that Carnap scholarship has reached a new stage of rigor and thoroughness. Although the essays are not divided up into parts by topic or theme, I will impose such a division in this review. I begin with a group of five essays that consider Carnap’s place in his broader philosophical and intellectual context. Gabriel’s “Introduction: Carnap Brought Home” argues for the importance of Dilthey’s Lebensphilosophie in shaping Carnap’s attitudes towards traditional, theoretical metaphysics. Dilthey argued that different metaphysical systems had their roots in the opposing attitudes towards life of the metaphysicians. Gabriel claims that Dilthey’s conception of metaphysics influenced Carnap directly and via Carnap’s friendship with Herman Nohl, an exponent of Dilthey’s views at Jena. The evidence offered here includes Carnap’s own autobiographical reflections as well as Carnap’s use, in the 1932 essay “Overcoming Metaphysics”, of Nohl’s linkage between musical composers and metaphysical theories. Gereon Wolters extends this picture of Carnap’s deep engagement with his broader intellectual context by isolating Carnap’s philosophical style from his contemporaries in “Styles in Philosophy: The Case of Carnap”. Wolters presents

213 M. C. Galavotti (ed.), Cambridge and Vienna: Frank P. Ramsey and the Vienna Circle, 213–236. © 2006 Springer. Printed in the Netherlands.

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Carnap’s style as above all collective and objective, and opposes this to the individual and subjective approaches often attributed to German Romantic philosophers such as Novalis and Schleiermacher. Opposing this, Carnap presents philosophical activity as an activity that can and should be cooperative and whose conclusions can be debated objectively, and not resolved simply as expressions of feeling or emotion. While Wolters praises these aspects of Carnap’s style, he completely rejects Carnap’s noncognitivism about value statements, which removes practical questions from the realm of collective and objective theoretical resolution. Moving beyond the world of academic philosophy, Hans-Joachim Dahms examines the intellectual sympathies between the Vienna Circle and modernism in art and architecture. His “Neue Sachlichkeit in the Architecture and Philosophy of the 1920s” builds on Galison’s earlier work by offering important new information about the personal connections between Franz Roh, Carnap and Neurath. Dahms relates how Roh, the author of the “decisive manifesto” (361) of the Neue Sachlichkeit movement, not only knew Carnap from his early days at Jena, but even helped Neurath in the turbulent post-World War I period and later introduced Carnap to Neurath. The philosophical connections between Carnap and Husserl are the focus, in somewhat different ways, of the essays by Jean-Michel Roy and Michael Beaney. Roy argues against Carnap’s own suggestion in the Aufbau (section 3) that his constitution system is linked to Husserl’s “mathesis of lived experiences”. The basis for this skepticism is the claim that the main goal of the particular constitution system outlined in the Aufbau is the reduction of scientific concepts to the given, where this is interpreted in terms of easily accessible immediate experiences. Husserl must reject both this starting point and the wholly formal logical tools that Carnap uses to constitute his objects. According to Roy, Husserl sought to provide a foundation for formal logic itself based on his ultimate given, and so cannot take formal logic for granted as Carnap does in his constitution system. Michael Beaney’s essay “Carnap’s Conception of Explication: From Frege to Husserl?” explores a different link between Carnap and Husserl: Carnap’s notion of explication and its connections to Husserl’s use of the same term. In his Logical Foundations of Probability Carnap had indeed acknowledged Husserl when he used the term “explication”, but after a careful analysis of Carnap’s practice Beaney concludes that “no genuine influence” (141) of Husserl on Carnap can be found. Instead, Beaney traces back the philosophical roots of the need for explication to the lectures by Frege that Carnap attended at Jena and the need to solve the paradox of analysis. A second group of five essays in the volume focuses more narrowly on Carnap’s philosophy and its origins in the interactions between Carnap and the other philosophers that he worked with directly. Erich Reck’s “From Frege and Russell to Carnap: Logic and Logicism in the 1920s” presents the case that Carnap’s work in logic and the philosophy of mathematics in the 1920s, while based

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squarely on the work of Frege and Russell, superseded both Frege’s and Russell’s versions of logicism in several important respects. What made Carnap different was his appreciation of the importance of the formalist approach to mathematics, and his attempt to take the strengths of the formalist program and combine them with logicism. Reck also helpfully points out how this work complicates any rigid division between what is sometimes called the “universalist” philosophy of logic of Frege and Russell and the more contemporary model-theoretic conception of logic of Hilbert and Tarksi. We move into the Vienna Circle and its warring factions in Thomas Uebel’s “Carnap, the Left Vienna Circle, and Neopositivist Antimetaphysics”. Uebel presents Carnap’s opposition to metaphysics as strongly linked, throughout his philosophical development, to the rejection of any theory of truth, especially correspondence theories. It is this opposition to theories of truth, and not any verificationist dogmas, that tie Carnap’s work to the members of the left Vienna Circle: Frank, Hahn and above all Neurath. In the course of the protocol sentence debate, Carnap then understandably sides with the left Vienna Circle, and against Schlick, when Schlick moves closer to a correspondence theory. Later, in his semantic phase, Uebel describes Carnap’s views on truth as “disquotational” (271), and so as still remaining within this generally antimetaphysical camp. Perhaps the most technical essay in the collection is Thomas Mormann’s “A Quasi-analytical Constitution of Physical Space”. Mormann is eager to defend Carnap’s procedure of quasi-analysis in the Aufbau against Quine’s criticism. Quine objected that when Carnap constitutes physical space he uncritically adopts a primitive “is at” relation between perceptual qualities and points of physical space. Mormann responds by outlining how to constitute physical space and this relation using more restricted means than Carnap actually employed. Technical issues aside, it is less than perfectly clear whether or not Mormann’s constitution is Carnapian in spirit, as he claims it is. For Mormann argues that Carnap’s strategy of first constituting physical space and then embedding qualities in it is bound to fail without investigating why Carnap took this route. A brief moment in the philosophical relationship between Carnap and Gödel is the focus on Bernd Buldt’s “On RC 102-43-14”, which refers to the archive number of Carnap’s notes of a conversation with Gödel in July of 1931. Carnap records his own and Gödel’s remarks about Hilbert’s recently proposed Ȧ-rule in the context of Carnap’s own work on the foundations of logic that eventually became the Logical Syntax of Language. After a detailed examination of the technical and philosophical background to their conversation, Buldt proposes an interpretation of Carnap’s remarks that are considerably more charitable than what Carnap initially appears to be saying. An important innovation here is Buldt’s reconstruction of what Carnap would like an Ȧ-rule to do in his Language I, and of how this goal differs from Hilbert’s likely conception of an Ȧ-rule. Carnap and Gödel remain the focus in “How Carnap Could Have Replied to Gödel”, jointly authored by Steve Awodey and A.W. Carus. Awodey and Carus are concerned with Gödel’s later unpublished criticisms of the “syntactic”

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philosophy of mathematics that Gödel saw in Carnap’s Logical Syntax of Language. They maintain that Gödel’s criticisms are unfair, and rest on a misunderstanding of Carnap’s position. The essential difference between Gödel and Carnap is that what Gödel saw as absolute, theoretical claims about, for example, mathematics, Carnap presented as proposals for languages, for example, proposals for how to relate mathematical terms to the rest of the language of science. Thus, Awodey and Carus contrast Gödel’s platonistic attitude towards the continuum hypothesis, as a claim with a pre-established truth-value, with the more tolerant, open-ended Carnapian attitude. In any volume on Carnap we would expect to find some discussion of his most famous philosophical partner and opponent, Quine, and here we find two contributions by experts on this complex relationship. Thomas Ricketts, in “Frege, Carnap and Quine: Continuities and Discontinuities”, builds on his previous work on the Carnap-Quine controversy by linking Carnap’s and Frege’s approach to truth and contrasting this shared tradition with Quine’s alternative approach. Ricketts sees Carnap’s Logical Syntax of Language, with its emphasis on correct operations with formal languages as the “analogue and successor” (195) to Frege’s conception of the laws of logic as the laws of truth. Against this, Ricketts presents Quine as accepting the ordinary conception of truth as unproblematic, and argues that this leads to Quine’s distinctive focus on ordinary language. In “Carnap’s Program and Quine’s Question” Richard Creath articulates Carnap’s conception of philosophy in the Logical Syntax of Language and outlines a defense of this approach as “more durable” (292) than Quine and many others anticipated. For Creath, Carnap’s philosophy involves making proposals for how to do mathematics and science and an associated pragmatic principle of tolerance allowing for various competing proposals to be worked out. Creath then presents Quine’s objections to Carnap as a demand that we be able to tell, using very restricted empirical means, whether or not ordinary practice fits one of these proposals. Rejecting this demand, Creath concedes that Carnap must still offer some way that we can empirically determine which proposal is being implemented, if not in ordinary language, then at least in rigorous scientific disciplines. Rounding out the volume are four essays that present Carnap’s philosophical projects as currently viable or at least worthy of serious consideration today. “Tolerating Semantics: Carnap’s Philosophical Point of View”, by Alan Richardson, emphasizes the importance of the principle of tolerance for correctly interpreting the role of semantics in Carnap’s overall philosophical program. Linking his interpretation with earlier work by Creath, Richardson dubs Carnap a “conceptual engineer” (74) who articulates a proposal for how to think about logic, mathematics and science that does justice to the success of these disciplines, but who is not motivated by any overarching philosophical commitment such as empiricism. Richardson argues that there are no constraining matters of fact for Carnap prior to the adoption of a linguistic framework, and so there are no limitations on the linguistic frameworks that Carnap can adopt.

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Michael Friedman seeks to extend another aspect of Carnap’s philosophy into a viable contemporary position in his “Carnap and the Evolution of the A Priori”. Friedman argues that Carnap’s distinctive conception of the a priori as relativized to a choice of language had its roots both in Carnap’s work on physics and geometry in the 1920s, and later, after the Aufbau, in logic and mathematics proper. Carnap’s original problem was to see how to relate the abstract, mathematical structures needed for general relativity theory to the concrete experiences that we actually have. Unlike Schlick, who solved this problem by coordinating the abstract with the concrete, Carnap’s constitutional system “is already attached to the empirical world from the very beginning” (110). Even though Carnap went on to abandon these epistemological concerns, and replace them with problems from the “logic of science”, Friedman suggests that Carnap’s epistemological program has benefits over Quine’s alternative influential conception of epistemology. Clashing somewhat with many other contributors to this volume, Carsten Klein’s “Carnap on Categorical Concepts” places Carnap in a tradition of philosophers who sought to describe the fundamental metaphysical categories of the world. Klein first summarizes the proposals offered by Frege, Russell and Wittgenstein for how to articulate categorical concepts and see how they apply. Wittgenstein’s Tractatus had argued that claims about categories are illegitimate, and Klein relates how Carnap appears to respond to Wittgenstein in Logical Syntax. He goes on to complain that Carnap’s solution in unacceptable, though, as it involves a rejection of an “absolutistic” (312) conception of language presupposed by the search for fundamental categories. Finally, A.W. Carus, making his second appearance in the volume, deploys Carnap’s philosophy to undermine the work of Sellars, and by extension the work of those such as Brandom and McDowell who trace some of their ideas to Sellars. Carus focuses on Sellars’ conception of the “manifest image”, i.e. our everyday reasoning about the world, and its relation to the image of the world presented by science. Unlike Carnap who offered maximal flexibility in his pragmatic attitude towards the selection of linguistic frameworks, Sellars is presented as overly intellectually conservative and out of step with the analytic tradition. Thus, unlike many analytic philosophers, and incorrectly according to Carus, Sellars thought there must be something that a correct philosophy will preserve from traditional philosophy. These short summaries fail to do justice to the arguments, both historical and non-historical, found in these contributions, but they hopefully convey the wideranging nature of this volume and its importance for Carnap scholars and for those working on logical empiricism more generally. I would add that I expect the remaining volumes in the Full Circle series to further bolster the range and depth of scholarly work on Carnap’s philosophy. I end with a brief point of concern. If there is anything like a single theme running through many of the essays, it is Carnap’s wish to move beyond traditional philosophy, and his eventual appeal to the principle of tolerance in order to obtain these anti-philosophical goals.

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While many contributors note that the principle of tolerance has deep philosophical implications, often bordering on transcendental idealism, very little space is devoted to explaining exactly how such a philosophically loaded principle can be used to transcend traditional philosophy. Hopefully this is an issue that supporters of Carnap’s philosophy will turn to with greater focus in the future. Christopher Pincock (Purdue)

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Bergmann, Gustav, Collected Works Vol. I: Selected Papers I, edited by E. TEGTMEIER, Frankfurt/Lancaster: Ontos-Verlag, 2003. ISBN 3-937202-17-X, pp. 350, hardcover € 99,00 (€ 67,00 subscription). Logical Positivism, the Linguistic Turn, and the Reconstruction of the Questions of Ontology This volume makes available 17 papers published by Gustav Bergmann (1906 – 1987) during the years 1946 – 1958. The edition of Bergmann’s works in three volumes by the publisher “Ontos-Verlag” (www.ontos-verlag.de) is now complete. Volume II contains papers from 1960 – 1981, volume III contains Bergmann’s book Realism from 1967. Bergmann was born in Vienna (Austria) in 1906. When he received his doctorate in mathematics from the University of Vienna in 1928, he had already been invited to join the Vienna Circle, where he was especially influenced by Schlick, Waismann, and Carnap. He went to Berlin to work as an assistant to Albert Einstein and then returned to Vienna. In 1938 he left Austria as a Jewish refugee from the Nazi era. He soon obtained a position at the University of Iowa, where he was a member of both the philosophy and the psychology department for more than forty years. In this volume we find Bergmann’s great programmatic essay of 1953 “Logical Positivism, Language, and the Reconstruction of Metaphysics”, which lays out the core doctrines of logical positivism. Bergmann explains what branches of the movement there are and what his own position is. All logical positivists, says Bergmann, accept the linguistic turn, which Wittgenstein had initiated in the Tractatus. They pursue “linguistic philosophy or philosophy of language” (146), they philosophize “by means of” language. Philosophy, employing linguistic analysis, has “the task of elucidating common sense, and not of either proving or disproving it”. That is, it does not attempt to develop and defend true theories about the world, say about properties or about the human mind, or at least it does so only through investigating our language. According to Bergmann, the logical positivists fall into two groups, the ideal linguists and the analysts of ordinary usage. Among the ideal linguists there are formalists, like Carnap, and reconstructionists, like Bergmann himself. “What the reconstructionists hope to reconstruct in the new style is the old metaphysics.” (147) Bergmann finds that philosophers use language in a peculiar way, saying things like that there are no physical objects, which taken in their ordinary sense are absurd. One reaction to this would be to say that philosophers should stop saying such things. For Bergmann, however, this difference between ordinary discourse (including the discourse of science) and philosophical discourse is part of his philosophical program. According to his philosophical method, the reconstructionist linguistic turn, philosophical discourse is ordinary, or commonsensical, discourse about an ideal language (151). By contrast, the method of the ordinary language analyst is ordinary discourse about ordinary language, and the formalist’s method is just to develop the ideal language.

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“The ideal language is an interpreted syntactical schema” (155), that is “an idealization of our natural language” (84). It must fulfil two conditions. First, it must be complete in that it accounts “for all areas of our experience” (155). For example, it must contain the way in which scientific behaviourists speak about mental contents, but also the way in which one speaks about one’s own experience. Secondly, it must be such that, “by means of ordinary discourse about it” (155), “all philosophical problems” can be solved. Bergman believes that there is such an ideal language. He believes that, for example, we can discover the categorial structure of the world through discourse about an ideal language because he believes “that the categorial features of the world reflect themselves in the structural properties of the ideal language” (84). As a reconstructionist Bergmann differs from the other logical positivists in that he does not hold that the old questions of philosophy, or their answers, are meaningless. He does not reject metaphysics and ontology but reconstructs the old questions, such as whether properties are universals or whether ordinary things persist through time, and answers them with his new method. So he agrees with the other positivists in that classical philosophy is to be rejected, but he differs from them in that he thinks that the old questions can be reconstructed in the spirit of the linguistic turn. One view on Bergmann’s project is that through his “reconstruction” he clarifies the old questions and brings out what they should be getting at. Another view is that Bergmann proposes new philosophical questions which look in a certain way similar to the old ones, calling the new ones the “reconstruction” of the old ones, and that he fails to answer the old ones. For example, Bergmann reconstructs the old question whether there are universals, that is, whether things in themselves have ontological constituents of a certain type, as the question whether “the ideal language contains no undefined descriptive signs except proper names” (155). To illustrate, this is the sort of philosophical method, which David Armstrong in his book Nominalism and Realism (1978) rejects when he writes: “[T]he identification of universals with meanings (connotations, intensions) […] has been a disaster for the theory of universals. A thoroughgoing separation of the theory of universals from the theory of the semantics of general terms is in fact required.” (xiv) This volume helps us to understand the difference between philosophy before and after the linguistic turn, and it helps to see the relation between the linguistic turn and the methods used in today’s philosophy. The editor, Erwin Tegtmeier, writes enthusiastically in the Introduction: “Bergmann’s positions are diametrically opposed to those of mainstream analytical philosophy, especially to materialism and nominalism. […] There will occur no renewal of ontology proper and on a par with the old ontology before the writings of Gustav Bergmann are studied more closely.” (13) From another point of view, however, it appears that Bergmann was not so different from the other logical positivists because he too rejected “classical philosophy” (178) and made the linguistic turn, although he differs from them through his claim that we need to do ontology. So if you are a metaphysician influenced by the linguistic turn,

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then you will benefit from reading Bergmann because you have much in common with Bergmann and he has contributed much to the kind of ontology you might be looking for. If, on the other hand, you are (like me) an antilinguistic-turn philosopher, then you will benefit from reading Bergmann because it will help you to understand the method of mainstream contemporary metaphysics and the influences of the linguistic turn. Here is a survey over the papers contained in this volume. The first two papers try to show how positivism can preserve the common sense core of epistemological realism. Bergmann wants to “reconstruct realistic common sense within a positivistic frame of reference” (39). The first paper, “Remarks on Realism” (1946), argues against some positivists that experience has to be founded on existence. For this purpose Bergmann defends a meaning criterion that assumes, against other positivists, that something is verifiable because it is meaningful, rather than vice versa. In the second paper, “Sense Data, Linguistic Conventions, and Existence” (1947), Bergmann criticizes A.J. Ayer’s suggestion that existence is to be defined in terms of direct apprehension and that thus “esse” is a synonym of “percipi”. For this he uses arguments G.E. Moore stated in his “Refutation of Idealism”. In the article “Russell on Particulars” (1947) Bergmann discusses sense data analyses. By a sense data analysis he means “an attempt to describe all percepts […] by means of a language whose simplest or basic sentences are of the kind exemplified by ‘this is green’ or ‘this is later than that’, where the descriptive universals ‘green’ and ‘later’ have their ordinary (phenomenal) meanings, and where the referents of ‘this’ and ‘that’ are objects of the sort many philosophers call simple momentary givennesses or sense data” (63). He criticises Russell’s sense data analysis, which avoids reference to particulars and refers only to universals. Russell analyzes ordinary things (or rather the percepts corresponding to them) in terms of bundles of universals. “On Non-perceptual Intuition” (1949) is a short, interesting argument against nonanalytical necessity statements. Is (1) “Everything that is green is extended” adequately transcribed as (2) “For all x, x is green ĺ x is extended”? Bergmann considers whether (1) is to be transcribed, alternatively, as (3) C(gr, ext), where “C” stands for “essentially connected” or “necessarily coinherent”. He argues, however, that transcribing (1) by (3) leads to the same difficulty as transcribing (1) by (2). The difficulty Bergmann means is that as (1) is certain the proponent of (3) has to maintain that it is certain that (3) ĺ (1), in the way in which analytic statements are certain. But this is not certain because only analytic statements and statements containing only names of particulars and simple predications (such as “gr(a)”) where we are “acquainted with what they express” (81) are certain. Bergmann indicates that there is a similar argument against causal connections. Remarkable about this paper is its assumption that (1) is certain (in the sense in which analytic statements are certain) and that (3) if it were a transcription of (1) would have to be certain too. This invites the objection that there is no need for the defender of (3) to assume that (1) and (3) are certain.

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Next, we find in this volume a “Note on Ontology” (1950), comparing Bergmann’s conception of the ideal language with Quine’s. “Bodies, Minds, and Acts” (1952) and “Intentionality” (1955) discuss the mind-body problem. In order to solve it Bergmann investigates which “descriptive inventory of the ideal language” (107) is needed with regard to the mental. In “Two Types of Linguistic Philosophy” (1952) Bergmann compares the formalist linguistic philosophy, as represented by Carnap’s “Logischer Aufbau der Welt” and Goodman’s “Structure of Appearance”, and the antiformalist linguistic philosophy, as represented by British analysts like Ryle. He agrees with both parties “that all philosophical problems are verbal” (112), but criticises the formalists for playing mathematical games that are philosophically irrelevant, and the antiformalists for being too much occupied with idiom. One of Bergmann’s main themes is sameness and diversity. In “The Identity of Indiscernibles and the Formalist Definition of ‘Identity’” (1953). The problem is in his view not whether the principle of the identity of indiscernibles is true but whether it is analytic. Here he offers only an analysis of the principle. “Particularity and the New Nominalism” (1954) criticises Quine’s and Goodman’s nominalism. The claim of “Some Remarks on the Ontology of Ockham” (1954) is that for Ockham a thing’s qualities are particulars, “tropes” as we call them nowadays. In “Professor Quine on Analyticity” (1951) Bergmann criticises Quine for overestimating the relevance of science for philosophy. Russell’s reconstruction of Leibniz’s ontology is discussed in “Russell’s Examination of Leibniz Examined” (1956). In “The Revolt Against Logical Atomism” (1957) Bergmann defends, against Urmson, Logical Atomism, i.e. the doctrine consisting of the picture theory of language and the verification theory of meaning combined with the philosophical method of “reductive analysis by means of an ideal language” (293). “Frege’s Hidden Nominalism” (1958) criticises Frege for not recognising the full ontological status of functions. In the last paper of this volume, “Sameness, Meaning, and Identity” (1959), Bergmann distinguishes two ordinary uses of “same”. First, the basic use, where “it makes no sense to search for a criterion by which to decide whether or not two existents are the same” (346). Secondly, “same” is applied to words and phrases and their meanings in the sense of “analytically equivalent”. Sameness in both senses is different from identity, which is defined through Leibniz’s formula “two things are identical if and only if whatever can be said of the one can be said salva veritate of the other” (346). Daniel von Wachter (Munich)

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FERRARI, MASSIMO: Ernst Cassirer – Stationen einer philosophischen Biographie. Von der Marburger Schule zur Kulturphilosophie, Meiner: Hamburg, 2003 (German translation of Cassirer. Dalla Scuola di Marburgo alla filosofia della cultura, Florence: Olschki, 1996) With Ernst Cassirer – Stationen einer philosophischen Biographie there is now available in German a study of Cassirer that was originally published in 1996 under the title Cassirer – Dalla Scuola di Marburgo alla filosofia della cultura. Its author, Massimo Ferrari, is a well-known scholar of neo-Kantian philosophy, who in the last two decades has published a series of articles on philosophical movements that fall under that umbrella term. Ferrari’s interest in Cassirer has evolved out of his preoccupation with this once predominant philosophy in Germany, which collapsed in the 1920s. As the sub-title suggests, and the book itself confirms, Ferrari’s ambitions are broader than a study concentrating on Cassirer alone. The structure of the book, the repeated reference to Kantian-sounding questions, and the way Cassirer’s theory of symbols is approached make it clear that the author is not primarily interested in exploring the influences on Cassirer’s philosophy. He treats the philosophy of Cassirer as an instance of neoKantianism long after its decline as a common movement with an officially shared core of philosophical theses. The book, in effect, aims at a general reevaluation of the philosophical situation in Germany in the first half of the 20th century. Massimo Ferrari pursues these aims by telling the story of Cassirer’s intellectual development in his own terms, mentioning a variety of questions and topics that became interesting to Cassirer in the course of his studies. There is much to be gained from this narrative approach. One gets to know Cassirer’s own assessment of the works of Leibniz, Einstein, Herder, Humboldt, Goethe, and Croce. Above all one sees the significance of Immanuel Kant for Cassirer throughout his life. The reader also sees that Cassirer’s recognition as one of the “last universal scholars of the 20th century” (Jürgen Habermas) is fully justified. In the first half of the book Ferrari addresses questions concerning Cassirer’s attitude to Kant and his positioning inside the Marburg School of neoKantianism. He brings out the extent to which Cassirer’s writings on the history of knowledge (1906), his monograph on Kants Leben und Lehre (1918), his study Freiheit und Form (1916), and his remarks on Cohen’s and Natorp’s interpretation of the Critique of Judgement all make clear how much Cassirer’s positioning of his own philosophical agenda was based on the so-called ‘free’ interpretations of Kant. Ferrari speaks here of the ‘liberalization strategies’ espoused by Cassirer’s teacher Hermann Cohen and by Paul Natorp. Even in his early writings, Cassirer takes Kant to task for his ‘rigid’, ‘undynamic’ understanding of the a priori, which runs counter to a possible explanation of future scientific insights. In this, he follows the position of Cohen and Natorp. The verdict was that Kant’s system did not do justice to the postulated

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development and transformation of the ‘fact of science’ (p. 16). The conclusion drawn was that a new understanding of the Kantian a priori is needed: a ‘dynamic, flexible categorical structure’ that would allow for the ‘continuity’ and ‘universality’ of scientific knowledge (p. 16f.). Ferrari documents with a wealth of material the debate on the interpretation of relativity theory, and the difficulty of combining transcendental idealism with the idea of changing constitutive principles in the light of scientific developments (Chapter 4). Reichenbach and Schlick, for instance, did not go along with the claim that such principles are knowable a priori. In opposition to Cassirer and other neo-Kantians, the Logical Empiricists rejected the “unrevisable” or “fixed for all time” understanding of the a priori and the more general idea that a philosophical investigation completely independent of experience can lay down necessary conditions for all possible experience (pp. 125-135). Ferrari’s interesting documentation of the correspondence between Cassirer, Reichenbach, Schlick, and Einstein shows that for the Logical Empiricists the idea of a ‘dynamic a priori’ needed to be understood as no more than the idea that there must be some constraints on empirical content. But on that view the necessary conditions for empirical claims are to be understood as products of our decisions and choices (pp. 125-135). Schlick and Reichenbach consequently offered Cassirer the choice between psychologism and the view that the function of the constitutive principles is fulfilled by conventions. As we know, Cassirer chose neither of these options, but instead began to develop what he became most famous for – his theory of symbolic forms. The second main part of the book, consisting of five chapters (‘The Foundation of the Geisteswissenschaften’, ‘Symbol and Expression – Leibniz’s sources in the Philosophy of Symbolic Forms’, ‘Logic of Origin and Philosophy of Language’, ‘A ‘dangerous’ Library’, ‘Davos 1929’) is devoted to the period between Cassirer’s call to Hamburg in 1919 and his emigration in 1933. Here the author takes up a number of issues: Aby Warburg’s extraordinary collections of books and materials in Hamburg, the influence of Leibniz, Humboldt, Goethe and Croce on Cassirer’s thinking, and the famous debate between Heidegger and Carnap in Davos in 1929. Ferrari attaches great importance to the impact of Warburg’s library on Cassirer’s formation of the theory of symbolic forms as well as to the debate with Heidegger, and the discussion on relativity. The last chapter (‘Cultural Philosophy – from Transcendental Method to Anthropological Philosophy’) touches on the final years of Cassirer’s life in Sweden, England, and the United States, and on his cultural philosophy. Particularly significant in Ferrari’s description of Cassirer’s development is his continued insistence on the transcendental function of signs, symbols, and myths. There is a wealth of material and stimulus here for further studies on Cassirer. But there remains a question, whether the author’s aims – to show the significance of neo-Kantian philosophy for Cassirer, and to elevate him from a minor to a major figure in the 20th century philosophy – are fully achieved. In terms of

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the history of philosophy, “the basic thesis of this book”, that “the mature Cassirer” remains committed to his neo-Kantian roots (p. xiii), depends on the extent to which the different approaches subsumed under this heading can be grasped as a single uniform critical continuation of Kantian transcendental philosophy. In Ferrari’s narrative approach, major differences among the reasonings employed by Kant, Cohen, Natorp, and Cassirer for the foundation of the objectivity of science tend to be ignored, as well as differences in their respect to Kant’s notion of necessity. The first four chapters, for example, (‘Genesis and Structure of the Problem of Cognition’, ‘Freedom, Idea, and Form’, ‘Cassirer and The Critique of Pure Judgement’, ‘The Interpretation of the Relativity Theory’) give the impression that there was no more to neo-Kantianism than the attempt to isolate a core of transcendental philosophy whose concern with the conditions of the possibility of knowledge got directed to ‘the fact of the development of science’. Consequently, unlike Klaus Köhnke (Entstehung und Aufstieg des Neukantianismus, 1986) or Michael Friedman (A Parting of the Ways – Carnap, Cassirer, and Heidegger, 2000), Ferrari never takes up the questions of the neo-Kantian distortion of Kant’s main philosophical notions. Ferrari seems too devoted to the views of Cohen and Natorp to have pursued questions about the objectivity of science still embedded in a distinct Kantian framework. The last chapters also employ this same conception, presumably out of attachment to Cassirer. Ferrari describes thus the mature Cassirer in contrast to John M. Krois (Cassirer – Symbolic Forms and History, 1987) as having merely expanded the goal of the Kantian investigation to include the development of language, art, science, history, and philosophy. He mentions, but does not account for, the fact that Cohen saw in Cassirer’s “Freiheit und Form” a decisive break with neo-Kantianism, and that Cassirer took ideas from Hegel to ‘accomplish’ his understanding of a ‘dynamic a priori’. What is therefore unfortunate in Ferrari’s treatment is that he does not really trace the effects these ‘influences’ might have had on the overall position whose nature they are supposed to explain. Cassirer’s philosophy of symbolic forms holds out the promise that what remained no more than an assumption in his early work – the idea of one principle governing the possibility of all understanding – can finally be specified by the recourse to actual human activities. Having hit upon the Warburg Library in Hamburg in the early 1920s, Cassirer became more and more interested in language, myth, and the usage of symbols in art. It was through these studies that he eventually found in the notion of a symbol what he called “original expression” of human beings, which at the same time is the object of human activity and is created by it. Ferrari rightly emphasizes the key role ‘symbol’ plays for Cassirer in being simultaneously ‘spiritual’ (geistig) and ‘sensible’ (sinnlich), thus providing an understanding of science, art, religion, and culture as the results of acts of free, self-determining human individuals. In addition,

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Cassirer believed he had found present in these expressions of human beings the unity of intuition and concept that Kant had arrived at by a priori reasoning. Cassirer’s pursuit of the idea that the investigation of the properties of symbols is the key to understanding the conditions of experience was meant to ‘integrate’ historical studies of art, and science, and the study of different cultures. As for his philosophical speculations about the function of symbols and ‘symbolic forms’, Cassirer did not return to Kant but to the very teleological idea he had been criticized for by Cohen. For Cassirer the idea of an organic form that determines as a ‘whole’ the development and orders of its various ‘parts’, was used to elucidate the possibility of experiences. ‘Symbolic forms’ are accordingly for the early and the mature Cassirer expressions of the “process of life” in which he saw “the mental energies of knowledge unfold” (p. 189f., passim). Ferrari, repeatedly, points out Cassirer’s fascination with Goethe’s idea of the “primal plant” which Cassirer regarded as “instructive” for an “analysis of the basic forms of world understanding in a general sense” (p. 59ff., passim). In adopting a “Kantian-Goethean network”, he is said to have overcome the science-orientation of neo-Kantianism, the passivity of the mind according to the Logical Empiricists, and the anti-humanism of Heidegger, and to have achieved a ‘subtle completion’ of Kant. Ferrari’s conviction of Cassirer’s theory of symbolic forms as reconcilable with an “unlimited allegiance to transcendental method” (p. 106) tend to leave untouched many fundamental questions that were raised in the Schilpp Volume on Cassirer (1949), and in several recent conferences. The Kantian question of the conditions of the possibility of having objects in experience, loses its point when Cassirer, (according to Ferrari) inspired by Wilhelm von Humboldt, eventually is said to have defended a “critical dissolution of the concept of the object.” (p. 193). Ferrari here claims that the idea that the function of a symbol is to enable all understanding of objects implies a breakdown of the distinction between symbols and objects. But if this were true, the investigation of this very function could no long longer be understood as legitimizing our beliefs in objects. Whether Cassirer regarded the world as the sum of the symbolic forms or as something that merely enables this sum is crucial for understanding Cassirer’s overall philosophical position. If the latter were so, Cassirer’s epistemological investigations rest on metaphysical assumptions that he himself thought would not work out. If the former is true, and Cassirer did not distinguish between thinking or symbolizing and what can be thought or symbolized, the role of his cultural philosophy as prima philosophia is in question. Perhaps Cassirer’s recourse to metaphors like Goethe’s ‘primal plant’ was finally due not to the wish to show human activity as ‘dynamic’, ‘expressive’ and so on, but due to his inability to legitimate any judgement about the function of ‘symbolic’ forms.

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The publication of Ferrari’s book, which is a collection of reworked articles, some of them published two decades ago, comes at a time of wide scholarly attention to Cassirer as well as in the philosophy of neo-Kantianism. Alike other authors, Massimo Ferrari is interested in neo-Kantianism and Cassirer for not just philosophical-historical reasons. His interest in these philosophical movements is an expression of his conviction that questions of the conditions of the possibility of science, morality, and knowledge in general, reveal a fundamental desire of human beings to understand ourselves. But his attempts to prove Cassirer to be an author who offers answers to these important questions cannot conceal the dissatisfaction one experiences with the foundation of Cassirer’s approach. If Ferrari’s portrayal of Cassirer is adequate, Cassirer’s originality consists mainly of his sensitivity to questions of art and morality, his references to a wide range of authors, and his ability to develop stages and systems in history, science and philosophy on the basis of a combination of Kant’s and Hegel’s philosophy, using historical and scientific material as well as rich metaphors. By clearly bringing out that diversity, Ferrari’s Ernst Cassirer – Stationen einer philosophischen Biographie offers a valuable complement to studies by authors such as Krois, Köhnke, and Friedman. One is nonetheless finally inclined to agree with the verdict of Edmund Husserl written in a letter to Paul Natorp in 1922. Lauding Cassirer for having written much “historically illuminating material”, Husserl sums up Cassirer’s philosophical efforts as “vicarious experience of someone else’s originality” rather than philosophical efforts in its own right. Ferrari’s book on Cassirer gives little reason to revise that judgement. Gabriele Mras (Vienna)

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RICHARD C. JEFFREY, Subjective Probability: The Real Thing, Cambridge University Press, 2004. RICHARD C. JEFFREY, After Logical Empiricism/Depois do Empirismo Lógico, English edition with Portuguese translation by António Zilão, Lisbon: Colibri, 2002. ‘This is my last book (as they say, “probably”)’, wrote Dick Jeffrey in the preface to Subjective Probability. For those who were fortunate to know him, this preface evokes many memories of Dick’s inimitable style, wit, warmth, scholarship and humour. Dick had circulated early drafts of what became Subjective Probability in 1995, if not earlier, under the light-hearted working title Bayes Ways. Dick continued working on this draft, and several other new projects, throughout an arduous course of chemotherapy to treat his lung cancer. Other projects during this period included papers with Mathias Risse and me on probability, on higher-order beliefs in game theory and on social choice theory. Dick pushed these projects forward with an unfailing energy and enthusiasm. When asked about his prognoses, he would never allow himself to slide into the traditional all-or-none framework that he berates as ‘dogmatism’ in the first paragraph of the preface to Subjective Probability. Instead, he would ironically remind us in the language of probability of the upside and give us reason to hope. Subjective Probability is a very personal book. Along with After Logical Empiricism, it is a public testament of Dick’s triumph in the biggest test in a person’s life. In his preface to Subjective Probability, short as it may be, Dick leaves a literary document of how one of the most eminent philosophers of the twentieth century confronted death. Although professional philosophers in his circle rarely reflect publicly on such defining elements of human existence, the reader here catches a glimpse of Dick’s love for his wife Edith, his family and friends. Supported by his loved ones, Dick was finding consolation also in his philosophy, as witnessed by the very existence of this book written in the most difficult of times. As a man of letters, he carefully avoids any pathos. Instead, his farewell, tellingly headed ‘acknowledgments’, shows his care for his loved ones whom, amidst the expression of deepest feelings, he wants to make smile with his trademark banter: Dear Comrades and Fellow Travellers in the Struggle for Bayesianism! It has been one of the greatest joys of my life to have been given so much by so many of you. (I speak seriously, as a fond foolish old fart dying of a surfeit of Pall Malls.)

I think Dick would have welcomed the comparison with Epicurus whose last letters are filled with the same care for his friends and the same poised clarity in the face of the inevitable. The philosophical discussion of the chapters that follow Dick’s preface is of the same clarity and determination, leaving aside what

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in Dick’s eyes must have been unnecessary complications and presenting his own philosophical outlook. Subjective Probability is indeed the ‘real thing’ promised by the subtitle. It invites the reader on a captivating philosophical journey that brings to life the great topics with which probabilists have wrestled for generations. This journey takes place in a slim volume of little over 120 pages, with introductions to probabilities and expectations and chapters on the confirmation of scientific theories, learning from experience, statistical inference, and decision theory. The book is an easy read, but by no means a light read. Elegantly presented, it introduces its readers, beginner students and professionals alike, to probability theory and its Bayesian interpretation through explanations, exercises and examples. From these lowlands, it swiftly ascends to higher vistas usually reserved to few advanced scholars. A book like this was sorely needed and advanced scholars may well grumble at the effort they themselves had to take to reach this perspective without the assistance of Dick’s latest book. From my experience with its previous drafts, the book makes an excellent starting point in both the undergraduate and graduate curriculum and prepares students for the intricacies and mathematical as well as conceptual technicalities they will encounter in their supplemental readings. Yet, the book is more than the usual ‘Introduction To …’. The book summarizes the development of the Bayesian framework through Dick’s own work and that of other scholars. Dick’s mastery in this slim volume lies both in his deceptively simple presentation and in his selection of the material included. That is to say: It is just as telling to see which material Dick chose to include and which material he chose to leave aside. The notion of an ‘objective probability’, for instance, makes no appearance in the index and is dealt with on four pages in the speedy discussion of the principle of direct probability (‘homecoming principle’). Similarly, there is none of the expected discussion on the selection of prior probabilities. Instead, Chapter 2 deals with the issue through the use of odds factors – without the novice reader ever sensing any turbulence along the journey. Finally, there is no mention of the as-if interpretation of probabilities and utilities that is popular among economists. Instead, subjective probabilities are from the beginning presented as ‘a mode of judgement’. All of these selections reflect Dick’s considered judgment for which he offers ample arguments in his other writings. Here, the fruits of these earlier labours are brought within easy reach. After Logical Empiricism records Dick’s Petrus Hispanus Lectures in Lisbon in December 2000 in little over seventy pages (not counting the Portuguese translation). More so than Subjective Probability, this essay develops a probabilistic worldview on some of the most long-standing epistemological questions of philosophy. Dick’s answer to the sources of knowledge is a ‘radical probabilism’ that he here restates with clarity and brevity:

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What I call ‘radical probabilism’ is the view that probabilistic judgment need not be rooted in underlying dogmatic judgments: it can be probabilities all the way down the roots.

To arrive at this position, he attacks empiricist epistemology on the grounds that experience cannot be reported in the form of sentences or propositions (observation reports) because […] my current experience is (1) not a proposition in the domain of [your old probabilities], but (2) a particular existent – your current experience in full detail – (3) which is definable ostensively but not purely descriptively.

To take the place of propositions, Dick defines ‘probasitions’, basic probability judgment that are induced by experience: The terminological conceit is: just as a proposition is a set of complete truth valuations val of the sentences of L, so a probasition is a set of complete probability assignments to the sentences of L.

On this account, once experience gives rise to probasitions (in a process that is not explained any further), they transform current, prior, probability judgements into updated, posterior, probabilities via Dick’s rule of Generalized Conditioning. This position – Dick calls it a ‘softcore empiricism’ – agrees with the central tenet of logical empiricism that judgments are grounded in experience. Dick’s empiricism differs, however, in the absence of a bedrock of certainty on which these judgments are build and in the mechanisms by which experience leads to updated beliefs. After Logical Empiricism abounds with quotes from the literature that show the same reasoned bias as Subjective Probability. Most of all, the style of After Logical Empiricism, with humorous and provoking headings like ‘InnerOuter Hocus-Pocus’ and ‘Mad-Dog Subjectivism’, lets us once more see Dick’s passion as a teacher and debater. This is how I first met Dick, as my teacher and in passionate debate; this is how I want to remember him. Matthias Hild (Charlottesville)

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PATRICK SUPPES, Representation and Invariance of Scientific Structures, CSLI publications, Stanford, California (distributed by Chicago University Press). After being in preparation for many years, the latest result of Patrick Suppes’ work has come to light with the book Representation and Invariance of Scientific Structures, published in 2002. The book collects significant achievements of Suppes’ work, both as a practising scientist in many disciplines (from quantum mechanics to experimental psychology), and as a committed philosopher who has contributed to foundational analysis of various branches of science. Many contemporary philosophers of science cite Suppes as one of the most significant influences on the semantic view of theories, a new way of defining the nature of scientific theories, breaking with logical positivism’s linguistic view of theories. As the title of the book clearly points out, representation and invariance are the concepts around which Suppes centers his analysis of science: he argues that the language of representation and invariance is the correct way to rationalize scientific theories when adopting a foundational point of view. The first step in characterizing a scientific theory is to provide a representation of it. More precisely, according to Suppes’ methodology, a theory must be analyzed starting from its structure, represented in terms of models of the theory, i.e. the possible realizations in which the theory is satisfied. The representation of a scientific structure is achieved in terms of these models, especially the ones expressed within a set-theoretical framework. Suppes stresses in many different passages that to axiomatize a theory is to define its set-theoretical predicates, as opposed to the usual approach of adopting a syntactic characterization, where first-order logic is the formal language of description for the primitive concepts of the theory. Suppes’ preference for a set-theoretical approach mainly has the purpose of maintaining the complexity of scientific theories, avoiding the sometimes too abstract description provided by the syntactic view, where a scientific theory is considered as a logical calculus with some correspondence rules. Suppes clearly acknowledges that set-theoretical models serve as tools for thinking about the foundations of a science, while in carrying on the same science from a practical point of view more detailed models are needed, not just for representation, but also for empirical predictions. In order to study the models by means of which to analyze the structure of a scientific theory, representation theorems have to be stated, since “the best insight into the structure of a complex theory is by seeking representations theorems for its models” (p. 51). The framework under which the explication of a scientific theory is performed is not complete without considering the concept of invariance. Intuitively, invariant is what is constant in the representation of a structure, when the contextual features vary. How invariance is connected to the explanation

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of scientific structures relies, again, on the process of representation. In order to axiomatize a theory, it is necessary not only to define its set-theoretical models and to prove representation theorems about the theory, but also to individuate the fundamental properties that are invariant with respect to some important transformations. Such individuation means to seek the “objective” meaning of a phenomenon, so that “objective” becomes identified with “invariant with respect to a given framework of reference”. If a representation theorem is devoted to identifying the fundamental properties of a theory and serves to isolate a significative subset among the models in order to work on such subset, the correlating invariance theorem states the uniqueness of a representation. The book covers a great deal of material on foundational issues in science; throughout it, representation and invariance do not only play a major role for the internal (in the sense of the structure) characterization of a theory, they also function as unifying principles of Suppes’ diverse foundational investigations. It is well known that Suppes has worked in several different areas of research, proving fundamental results such as his axiomatization of classical particle mechanics, or probability theory. By means of the concepts of representation and invariance, in this book we can see these results from a more unifying point of view. For the first time in Suppes’ vast bibliography, Representation and Invariance of Scientific Structures aims at explicitly illustrating the overall perspective of Suppes’ thought on science, while discussing some of its major issues. Still, this unified methodology in dealing with scientific theories does not entail, as it has sometimes been alleged, a unified philosophical stance towards science. Pluralism in science is one of the core concepts of Suppes’ philosophy of science, together with the idea that epistemology must be carried on in a genuine empiricist spirit. The detailed analysis of science, which derives from Suppes’ practice as an experimental scientist, plays a central role in his philosophical enterprise. In this perspective detailed has to be intended as a style for reflecting upon a scientific realm: to investigate a scientific theory is necessary to know how it is practically “implemented” in real scientific contexts, inside the real laboratories. This implies a work of reconstruction of the theory from its empirical bases that is tortuous and much less precise than the straight path of reason idealized by many philosophers. This down to earth approach might seem to contrast with Suppes’ advocacy of formal methods in the philosophy of science; however, empirical structures are central tools of investigation as much as theoretical structures, in his view. Which approach we should adopt depends on the specific scientific problem at hand. It is appropriate to invoke both formal and informal methods when explaining scientific knowledge and the nature of some scientific concepts. In general it is useful, mainly for reasons of clarity, to embrace formal methods when possible, at least for that part of a science (i.e. foundational studies) that can benefit from them; however, with a very pragmatic attitude (which is one of the other traits of Suppes’ thought), we should not rely too much on the rigorous

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nature of the formal approach as a way to reach certainty. Phenomena are, in the end, inextricably messy. But if truth or certainty are not up for grabs, this does not mean that science is absolved from its duty in leading to knowledge. And this is the reason why Suppes believes that probability is one of the best tools in practicing science. It is not surprising, then, that the central and longest part of the book, Chapter 5, is dedicated to the discussion of the nature of probability. To represent the standard formal theory of probability, Suppes uses Kolmogorov’s axioms, based on the notion of probability space expressed in a set-theoretical notation. Starting from them, he states representation theorems for each of the important views: the classical one, the relative-frequency one, the logical one, and the subjective theories amongst the others. What is invariant is the settheoretical notion of probability space, while an explicit formulation of the probability function is determined by each of the different theories of probability. Hence, for every probability theory it is possible to demonstrate a representation theorem stating that the models of the particular theory are also models of Kolmogorov’s axioms. Even if representation and invariance constitute the central perspective for discussing probability, Suppes is very determined to stress also the pragmatic use of probability in physics, where scientists exploit probability concepts without any concern about foundational problems. Space-time is another concept whose representation is fundamental in many scientific areas of science. In Chapter 6, Suppes provides different ways of thinking about this representation, in so far as “different disciplines concerned with spatial and temporal phenomena pose problems that require different approaches” (p. 266). Even while stressing the plurality of approaches, nevertheless Suppes is lead to the basic assumption that both classic and relativistic structures of space-time are special cases of affine structures. In fact, analyzing the invariant properties in both approaches, Suppes underlines that many of these (such as linearity of inertial paths and conversation of their parallelism) are invariant under a general affine group of transformations, and that the Galileo transformation in classical physics and the Lorentz transformation in special relativity are both subgroups of the affine group. Once again the study of representation and invariance gives a valuable contribution to the foundations of science, in this case of physics, foundations that are too often neglected, according to Suppes, by many philosophers. In the same chapter, Suppes gives an example of how representation of space can bring insight in perceptual and psychological problems, such as the problem of establishing if visual space is Euclidean. These results are less definitive than those in foundations of physics, yet they still provide valuable heuristics for future experimentation. Suppes delves much deeper into the foundations of physics in Chapter 7, where we find a representation in terms of vectors of a real affine space in

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classical mechanics, followed by invariance theorems on conservation of momentum and energy. Suppes selects this example because it is mathematically simple for the reader to grasp, while at the same time rich enough to show the importance of philosophical foundations and of systematic applications. When discussing quantum physics, Suppes demonstrates representation theorems for hidden variables, i.e. common causes; the research for common causes for a set of empirical data is a fundamental goal of every empirical science, but it is of particular interest in quantum physics, where the nonexistence of hidden variables is one of the disconcerting outcomes of the foundational efforts in the field. Suppes does not mention any invariance theorem regarding quantum physics, he offers instead other important examples of invariance in physics concerning temporal reversibility for causal chains. The final chapter of the book, Chapter 8, illustrates different representations of language, presenting both well-known results and new research directions that show Suppes’ interests in psychology and linguistics. Representation theorems are stated to describe how grammars of a given type correspond to automata of a given strength. He follows this with a discussion of the work on machine learning of natural language, in order to evaluate whether it is possible that association and conditioning may, in principle, be adequate to give the reason for complex linguistic phenomena. In the final part of the chapter, then, we find Suppes’ latest work on language in terms of brainwave representations: the idea is to collect data on what is going on in our heads while performing some cognitive tasks; the hope is to find invariances in these data showing useful information about internal process related to the use of language. Here no representation theorem is proved, since the work is still in progress; however, experimentally found invariances are discussed, giving evidence of some invariance in internal representations across different people. Aside from its possible consequences related to the philosophical debate on representation and associationism, this part of Suppes’ work is also very interesting from a methodological point of view. It exemplifies the interplay between experiments and theory formation, where the process of collecting and analyzing data and the formulation of a theoretical framework are shown in their tight interplay. From a more general point of view, the very diversity of this book is highly stimulating, and it is helpful to have a single reference for the vast body of Suppes’ work. Moreover, inbetween the most technical parts of the work, large sections are dedicated to historical overviews of some of the topics (from axiomatic methods, to mental representations and the nature of the visual space). Interesting and provoking philosophical considerations, for instance about reductionism in physics, or associationism in psychology, are spread all over the book. Unfortunately, Suppes does not seem interested in an organic presentation of these ideas, nor in a comparison with other contemporary mainstream views

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in philosophy: it seems clear that this would result in a refreshing analysis of these views, but is not part of the scope of this book, and we can only guess some possible conclusions from his words. Suppes is difficult to categorize in the current debates about the role of models in science, mainly for his lack of explicit discussion of them. Nevertheless, it is fair to say that his view has promoted research on the role of models in science, leading the process that has ended in the shift from the syntactic view towards the model-centered view that characterizes so much contemporary philosophy of science. Recent developments, such as Ronald Giere’s, Mary Morgan’s and Margaret Morrison’s and Paul Teller’s work1, apparently distant from Suppes’ perspective, are in fact descendants of it, and Representation and Invariance of Scientific Structures clearly proves the milestone role of Suppes’ ideas. While on the surface he appears to offer some hope to those who value unificationist approaches in philosophy of science, his philosophy is much closer to that of someone like Nancy Cartwright or Arthur Fine. His emphasis on formal methods notwithstanding, the pragmatist streak and pluralist commitment evident in his work place him as much closer to the latter; the drive towards solving foundational issues in science, coupled with the refusal to address metaphysical issues of any kind of detail, in many ways render him a role model of Fine’s NOA scientist, if not an explicit advocate. The many technical sections of the book can be intimidating, in particular for the bulk of non-specialist readers the book deserves, especially amongst students of philosophy of science. The reader can sense a lack of homogeneity. As we have said, a level of uniformity across the different parts of the book is gained by adopting the concepts of representation and invariance as guidelines; however, even if the several representation and invariance theorems are clearly stated and summarized at the end of the volume, the conceptual contribution of these theorems inside the respective science or from a philosophical point of view are not always easily identified. For this purpose it could be useful to follow the indications provided by Suppes himself in the subsection “How to read this book”. Here Suppes indicates how to get the most out of this book without the need of committing to a cover-to-cover reading: “As in love and warfare, brief glances are important in philosophical and scientific matters. None of us have the time to look at all the details that interest us” (p. 15).

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Ronald Giere, Explaining Sciece: A Cognitive Approach. University of Chicago Press, Chicago, 1988. Mary Morgan, Margaret Morrison, Models as Mediators. Cambridge University Press, Cambridge, 1999. Paul Teller, “Twilight of the perfect model model”. Erkenntnis, 55, 393-415.

Claudia Arrighi (Stanford) Viola Schiaffonati (Milan)

ACTIVITIES OF THE INSTITUTE VIENNA CIRCLE

A CTIVITIES 2004 International Workshop Sigmund Exner – Physiologie, Psychologie, Ästhetik und empirische Kulturforschung Location: Department of Contemporary History, University Campus Date: March 5–6, 2004 Lecturers: Herta Blaukopf (Vienna), Karl Clausberg (Lüneburg), Deborah Coen (Harvard), Peter Geimer (Berlin), Michael Hagner (Zurich), Anke te Heesen (Berlin), Veronika Hofer (Wien), Christoph Hoffmann (Berlin), Franz Lechleitner (Wien), Gerda Lechleitner (Wien), Michael Stöltzner (Bielefeld), Paul Ziche (Munich) International Symposium Paul Feyerabend (1924–1994). Ein Philosoph aus Wien Location: Universität Wien, Universitätscampus, Hof 1, Kapelle Date: June 18–19, 2004 Lecturers: Paul Hoyningen-Huene (Hannover, D), Kurt Rudolf Fischer (Vienna, A), Juliet Floyd (Boston, USA), Reinhold Knoll (Vienna, A), Erhard Oeser (Vienna, A), Hans Sluga (Berkeley, USA), Friedrich Stadler (Vienna, A), Karl Svozil (Vienna, A) Fifth International Fellows Conference of the Center for Philosophy of Science Recent Developments in the History and Philosophy of Science Organized by the Center for Philosophy of Science (Pittsburgh), Department of Philosophy (University of Cracow) and the Centre of Philosophy and Philosophy of Science (University of Konstanz), co-sponsored by the Institute Vienna Circle (Vienna) Location: Cracow (Poland) Date: May 26–29, 2004 Fourth Vienna International Summer University Scientific World Conceptions (VISU-SWC) “The Quest for Objectivity” Location: Vienna, University Campus Date: July 19–30, 2004

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Lecturers: John Beatty (University of Minnesota, USA), Michael Friedman (Stanford University, USA), Helen Longino (University of Minnesota, USA) Scientific World Conception and Art Art, Theory of Art and Studies in Art in the Scientific Discourse Coordination: Martin Seiler Presentations: Barbara Boisits (Vienna): Der Einfluss der österreichischen Philosophie auf die Musikwissenschaft; Katharina Scherke (Graz): Die Wiener Schule der Kunstgeschichte und die Warburg Schule im Vergleich. Einige wissenschaftssoziologische Betrachtungen

Publications Induction and Deduction in the Sciences Ed. by Friedrich Stadler. Dordrecht–Boston–London: Kluwer, 2004 (Vienna Circle Institute Yearbook, vol. 11) Österreichs Umgang mit dem Nationalsozialismus. Die Folgen für die naturwissenschaftliche und humanistische Lehre Friedrich Stadler (ed.) together with Eric Kandel, Walter Kohn, Fritz Stern and Anton Zeilinger Vienna–New York: Springer, 2004

Library and Documentation Expansion of primary sources and research literature on the Vienna Circle and its influence. Acquisition of estates and archival material in Austria and abroad. Robert S. Cohen Collection and Archives: Robert Sonné Cohen (born 1924) is an American philosopher, scientist and historian of science and philosophy who has been editing the Boston Studies in the Philosophy of Science and organizing the Boston Colloquium for the Philosophy of Science for many decades. The Robert S. Cohen Collection contains correspondence, unpublished and published manuscripts and typescripts, reprints, journal issues, news clippings, photographic prints, sound recordings, memos and notebooks. A substantial portion of the Robert S. Cohen Collection is being made available for use by educators and researchers at the Institute Vienna Circle as the Robert S. Cohen Archives. The Institute Vienna Circle will provide access to full-sized photomechanical reproductions of documents selected from the Collection that offer insight into the development of Logical Empiricism.

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Adolf Grünbaum Archives: The institute plans an acquisition of the private archives of Adolf Grünbaum. Adolf Grünbaum (born 1923) is one of the most important American philosophers and philosophers of science. His writings deal with the philosophy of physics, the theory of scientific rationality, the philosophy of psychiatry, and the critique of theism. Apart from his contributions to the philosophy of space and time he has dealt with psychoanalysis in the light of philosophy of science and with a critique of religious belief. He is the founder and chairman (director until 1978) of the Center for Philosophy of Science at the University of Pittsburgh. Currently, he is Andrew Mellon Professor of Philosophy of Science, Research Professor of Psychiatry, and Chairman of the Center for Philosophy of Science, all at the University of Pittsburgh. In April 2003, he resigned from the Department of Philosophy there, while retaining his Mellon Chair and all his other appointments. He is a member of the American Academy of Arts and Sciences. Currently, he is President of the International Union for History and Philosophy of Science, Division of Logic, Methodology, and Philosophy of Science. He is the recipient of Yale University’s Wilbur Lucius Cross Medal for outstanding achievement. The Adolf Grünbaum Archives will be made available for researchers at the Institute Vienna Circle, University of Vienna (University Campus). Eugene T. Gadol Library: The research library of Eugene T. Gadol was dedicated to the Institute Vienna Circle in 2002 by his heirs and is accessible for research.

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P REVIEW 2005 Fifth Vienna International Summer University Scientific World Conceptions (VISU/SWC) “Chance and Necessity” Location: University Campus Vienna, Court 1, Kapelle, and Institute for Contemporary History Date: July 18–29, 2005 Lecturers: Ted Porter (University of California, Los Angeles, USA), Wolfgang Spohn (University of Constance, Germany) Assistant Lecturers: Deborah R. Coen (Cambridge, Mass., USA), Franz Huber (University of Constance, Germany) In co-operation with the Austrian Ludwig Wittgenstein Society: 28. Internationales Wittgenstein-Symposium / 28th International Wittgenstein Symposium “Zeit und Geschichte / Time and History” Location: Kirchberg am Wechsel Date: 7-13 August, 2005 Scientific direction: Friedrich Stadler (University of Vienna, Institute Vienna Circle) and Michael Stöltzner (University of Bielefeld) International Conference Neurath’s Economics in Context Location: University Campus Vienna Date: September 29–October 1, 2005 Lecturers: Peter Boettke (George Mason University, Fairfax), Guenther Chaloupek (Wien), Robert S. Cohen (Boston), Albert Jolink (Rotterdam), Thomas König (Wien) and Karl Rieder (Wien), Robert Leonard (Montreal), Ortrud Leßmann (Hamburg), Juan Martinez-Alier (Barcelona), Peter Mooslechner (Wien), Elisabeth Nemeth (Wien), John O'Neill (Lancaster), Hermann Rauchenschwandtner (Wien), Günther Sandner (Wien), Roman Stolzlechner (Wien), Thomas Uebel (Manchester), Nader Vossughian (New York) Moritz Schlick Project Moritz Schlick (1882–1936): Critical Edition of the Complete Works and Intellectual Biography First phase 2002–2005 In co-operation with Universität Rostock (D) and Universität Graz, Institut für Philosophie and Forschungsstelle für österreichische Philosophie Publication of the first three volumes at Springer Verlag (Vienna–New York): Moritz Schlick, Allgemeine Erkenntnislehre, ed. Hans Jürgen Wendel

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Moritz Schlick, Raum und Zeit in der gegenwärtigen Physik / Über die Reflexion des Lichtes, ed. Fynn Ole Engler und Matthias Neuber Moritz Schlick, Lebensweisheit – Fragen der Ethik – Sinn des Lebens, ed. Matthias Iven

Publications Cambridge and Vienna. Frank P. Ramsey and the Vienna Circle Ed. Maria Carla Galavotti Dordrecht–Boston–London: Kluwer 2005 (Vienna Circle Institute Yearbook 12/2004) Paris – Wien. Enzyklopädien im Vergleich. Elisabeth Nemeth und Nicolas Roudet (eds.) Vienna–New York: Springer, 2005 (Veröffentlichungen des Instituts Wiener Kreis, Bd. 14) Paul K. Feyerabend: Ein Philosoph aus Wien. Anläßlich der 80. Wiederkehr seines Geburtstages und des 10. Todestages Kurt Rudolf Fischer und Friedrich Stadler (eds.) Vienna –New York: Springer, 2005 (Veröffentlichungen des Instituts Wiener Kreis, Bd. 15)

DONALD DAVIDSON: A BRIEF MEMOIR I first met Donald Davidson in 1955, when I was spending an academic year at Berkeley; there were regular joint meetings of people interested in logic from Berkeley and Stanford. In the 1960s I made several visits to Stanford as a Visiting Professor, and there I got to know Donald extremely well. We became close friends and remained so ever afterwards. I did not share his enthusiasm, or his capacity, for difficult physical skills such as surfing, though I admired his ability to perform such feats. We were also far apart in our attitudes to religion. But I think that the liking for another person which generates friendship does not depend on sharing attitudes to these things. Of the three closest friends outside my family that I have had, one of whom was Donald, and another of whom is also dead, all have been atheists, which I am not. Referring to Donald as an atheist is a bit misleading. I think his attitude to religion was like that of the man who preceded me in line when I joined the British Army in 1943. We were questioned for what was to go on our identity discs, and I heard the following dialogue: Name? Smith. Initials? D. A. Religion? What’s that? Well, Church of England, R.C., Other Denominations. Oh, none of that. Right, C. of E. But friendship, or the liking that underlies it, probably demands a sharing of some attitudes. I think it was much the same with our approach to philosophy: we differed over much, particularly over Donald’s firm adherence to classical logic and my sceptical attitude towards it; yet we shared a basic approach to philosophy, in a common belief that the structure of thoughts can be analysed only through an analysis of the means of their expression in language. Of everyone whom I have met, it was with Donald that I found it easiest and most fruitful to discuss philosophy. For some reason, the ideas and arguments of each of us resonated with the other: I immediately understood what he said, and he immediately understood what I said; and to each of us the other’s remarks struck him as completely to the point. The most striking manifestation of this occurred during a seminar on the philosophy of language that he and I gave together during one of his visits to Oxford. We alternately read papers, continuing the discussion from the previous session, and then the other would reply. We had not at all planned

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that it would go as it did, but in fact virtually no one said anything during the eight sessions of that seminar save the two of us: it was a sustained dialogue lasting over sixteen hours; we ought to have paused to allow the other people attending to participate, but neither of us could stop. As everyone knows, Donald’s death was utterly unexpected, and shocked all who knew him. He had reached a creditable age, but everyone had taken for granted that he would live for many years more: he was still physically energetic and mentally active. He had an imaginative and stimulating mind; he was tolerant and had a sense of humour and an ability to establish rapport with many people very different from himself. He had strong feelings, occasionally prickly but never malevolent. He contributed much to philosophy, but was also a very nice man and a very good friend. I miss him very much. It is a great pity that he could not be the Vienna Circle Lecturer for 2003. I greatly regret that illness has prevented me from being present at this memorial session for Donald Davidson. With sorrow I honour his memory. Michael Dummett

O BITUARY OF P ROFESSOR DONALD DAVIDSON (1917 – 2003) On the 30th August 2003, Donald Davidson, a leading American philosopher, died. He was 86, having been born on 6th March 1917. Yet his friends were stunned by his death, which was completely unexpected. He had been very fit, save for a routine operation on his knee: he was dedicated to keeping fit, and still took a good deal of physical exercise. He continued, as he had done for years, to travel across the world, giving lectures and attending conferences, for which he composed fresh new papers; he was expected in October this year to attend and speak at a conference in Vienna on the work of Frank Ramsey, a brilliant Cambridge philosopher whose contributions were very important to Davidson, and who died at the age of 27 in 1930. Probably Davidson’s friends expected him to reach 100, like the German philosopher Gadamer, whom he knew and admired. Davidson studied as an undergraduate at Harvard; he majored in English for his first two years, and then switched to philosophy. He attended a course and a seminar given by Whitehead, and was invited by him to his afternoon teas. He later decided that his encounter with Whitehead had set him back philosophically for years. He went on to become a graduate student, and made an acquaintanceship which was to prove far more fruitful, with W.V. Quine. From Quine he learned some mathematical logic, but, more importantly, a new attitude to philosophy. He had been interested in it as a part of the history of ideas; for the first time he became imbued with a desire to attain the truth about philosophical questions. His friendship with Quine and respect for his philosophical views lasted the whole of Donald’s life. In several respects he could be regarded as a disciple of Quine’s; but his importance in the subject derives from ideas that were original with him. Davidson’s graduate studies were interrupted by the war. He joined the Naval Reserve, and was demobilised in 1947. He was fortunate to obtain a post as an instructor at Queen’s College, New York, before he had completed his dissertation for Harvard; that would surely be impossible nowadays. The chairman of the philosophy department was John Goheen, an old friend of Donald’s from Harvard. In 1950 Goheen went to Stanford, in northern California’s Bay Area, to become chairman of the department there. Invited to become Assistant Professor at Stanford, Davidson followed him. McCarthyism was at its height. Donald had received an intimation that his left-wing political views would prevent him from obtaining tenure at Queen’s; so he was glad to be able to escape to California. He was to remain at Stanford for sixteen years; although he was later at several other universities, it was at Stanford that he attained his full stature both as a teacher and as an original thinker: it was Stanford that made him.

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At Stanford Donald Davidson lectured on a great variety of philosophical subjects. He also held classes for graduate students in his beautiful house high in the hills above the University. He became the favourite teacher among the graduate students in philosophy. In his classes he usually took some book to study week by week, often a book of collected essays by different hands. He displayed two excellent characteristics. If any of the graduate participants said something silly, Donald would reinterpret it as an interesting and sensible remark, attributing the reinterpreted question or statement to the confused speaker. Secondly, he did not doggedly hang on to views he had himself expressed, but was very willing to yield to any telling objection that had been made. He often invited visiting professors to these classes; the graduate students surely learned a great deal from them. It was not until a much longer time into his career than holds good for most academics that Donald Davidson started to publish on any considerable scale. Until then, his name was known only at Stanford and at nearby Berkeley; elsewhere, other philosophers had not heard of him. In 1957 and 1959 he had collaborated with Patrick Suppes and others on work on decision theory; otherwise his name had appeared only in footnotes to books by Quine saying, “I owe this point to Donald Davidson”. In the 1950s he contributed an essay to the Library of Living Philosophers volume on Carnap, which was not published until 1963; in any event, not much notice was taken of this. But in the 1960s he discovered something that made his name known. It surely was not how to write philosophical articles; it looks more like how to submit them to learned journals. Probably it was an access of resolution: he had not previously felt the pressure, and perhaps not the confidence, to write for publication. In 1965 he wrote “A Theory of Meaning for Learnable Languages”, and in 1967 the first article that made him famous, “Truth and Meaning”. It was a great step forward to make his ideas accessible to the community of analytical philosophers at large. Unfortunately, it had one bad effect. Cook-Wilson had refused to publish all his life, on the ground that, if one did so, one would be tempted to defend one’s published views instead of revising them in the light of further reflection. Davidson now became a fierce defender of views that he had published, and was sometimes angered by those who criticised them, in contrast to his earlier readiness to accept criticism. But he was still willing to modify his views in response to his own pondering of the philosophical issues. These early publications in the philosophy of language encapsulated the original version, subsequently modified, of the salient idea which was to become central to his whole philosophy. The idea was dual. First, the way to answer the question “What is meaning?” is to determine the form that a theory of meaning for an arbitrary natural language must take. A theory of meaning need not itself employ the notion of meaning: rather, it displays those features possessed by the words and sentences of the language that constitute their having the meanings that they have. Secondly, the way to arrive at a theory of meaning for a natural language is, first, to construct a Tarskian truth-definition for the statements of

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that language, and then to turn that definition on its head. (A statement was, for Davidson, a triple of a sentence, a speaker and a time; for the formal languages considered by Tarski, a sentence will do, since formal sentences contain no indexical expressions such as “here” and “yesterday”.) Tarski attempted to define truth for the sentences of a formal language, taking their meanings as given. By turning on its head a definition of his type for the statements of a natural language, Davidson intended to take the notion of truth as given, and so give a theory – not a definition – of meaning for the language. From this basis Davidson developed many arguments for theses to which he subscribed: for instance, the thesis that beliefs, and, more generally, thoughts, are possible only for those who have a language, and thus not for infants or for (non-human) animals. One can have a belief only if one has grasped the possibility that it may be mistaken: it is integral to beliefs that they may be right or wrong, true or false. But from where do we obtain the notion of a mistake? From language, Davidson argued: the notion of a mistake arises from the experience of a mismatch between the condition for the truth of a statement and its being taken to be true. Towards the end of his career, various commentators claimed resemblances between Davidson’s thought and that of philosophers well outside the analytic tradition, such as Derrida and Heidegger. Perhaps the most characteristic tenet of analytic philosophy, as it has been traditionally practised, is that the best means of attaining a philosophical analysis of thoughts – their contents rather than the psychological process of grasping them – is to give a philosophical analysis of the linguistic means by which we express them. Davidson’s view was more radical than this: thought is not possible for beings who lack the linguistic means of expressing it. He cannot be denied to have been a prominent member of the analytic school. To give a Tarskian truth-definition for a natural language, it is necessary to analyse the sentences of that language in such a manner as to render them amenable to such a definition – more exactly, to a definition of the Tarskian notion of satisfaction. It is notorious that natural language contains many devices that are hard to represent in the notation of first-order quantification theory that Tarski assumed for his formal languages. Davidson struggled with two of these. One was the category of adverbs and adverbial phrases, of the type that are said in grammar-books to qualify the verb-phrase rather than adjectives or other adverbs, and whose deletion from a true sentence does not affect its truth. Davidson proposed that we should understand these as containing a hidden existential quantifier over events, so that the adverbial phrase becomes a predicate applying to the bound event-variable: this would explain why adverbs and adverbial phrases can be multiplied almost indefinitely (saying when the event occurred, where it occurred, in what manner it occurred, etc.). This attractive theory led him into explorations of the notion of causality, construed as a relation between individual events. Another difficulty is provided by substantival clauses beginning “that” following verbs such as “said” and “believes”. Davidson rejected Frege’s theory

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that, within such clauses, the words denote what in ordinary contexts are their senses. He propounded instead the “paratactic” theory, namely that a sentence such as “Galileo believed that the earth moves” should be read as: Galileo believed that: The Earth moves. where the word “that” is understood as a demonstrative referring to the following sentence. This theory has been far less popular than his analysis of adverbs. By no means all Davidson’s philosophical views were connected with his conception of a theory of meaning. An example is his response to the mind/body problem, namely his theory of anomalous monism. Many analytic philosophers of a materialist bent have proposed that what we think of as mental events – a twinge of jealousy, the making of a resolution, the rejection of a former belief, the increase of a sensation of pain – are strictly identical with various happenings within the brain. Davidson believed the same; but he repudiated the standard presentation of the view. On the standard presentation, any given type of mental event is identical with a specific type of event within the brain: this is called ‘type/type identity’. Davidson denied this. For him, every mental event was identical with some physiological event, but, if the event is classified by its psychological characteristics, there is no classification in physiological terms of the physical event with which it must be identical. This is ‘token /token identity’, or anomalous monism: Davidson believed that he had in Spinoza a predecessor in advancing this theory. In 1967 Davidson transferred to Princeton, and in 1970 to Rockefeller University in New York, essentially a research centre with a few peripheral graduate students. After Rockefeller closed down its philosophy section in 1975, he moved to Chicago, and then, in 1981, to Berkeley, where he was still teaching when he died. He loved travelling, and gave the six John Locke lectures in Oxford in 1971, in which he summarised almost his whole philosophy as it then was. They would have made an admirable book, but he never published anything but collections of articles. For a time Oxford was full of Davidson disciples among the graduate students. He travelled to almost every country of the world. In 1984 a conference on his work was held at Rutgers, New Jersey: this was to be the first of many such. He loved music; he also loved many sports – skiing, surfing, flying, gliding and tennis. By Virginia, Donald Davidson’s first wife, whom he married in 1942, he had a daughter, Elizabeth, his only child. He was very proud of Elizabeth, and kept in touch with her all his life; she became a social and political activist. But the relationship between Donald and Virginia soured, and in about 1970 they separated. In 1975 he made a very successful marriage with Nancy Hirshberg; a professor of psychology; but in 1979 she died of lung cancer. The progress of her illness was emotionally shattering for Donald; for some time he could speak to any of his friends of nothing else, reliving the agony. It took him a full two

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years to recover from it. In 1984 he married Marcia Cavell, with whom he lived in cheerful contentment until his death. Michael Dummett

MEMORIES OF DONALD DAVIDSON I arrived at Stanford in August 1950 having just finished my PhD at Columbia University in New York City. Donald Davidson arrived just a few months later in January 1951. Our arrival just about doubled the number of full-time instructors in philosophy at Stanford. When Don showed up, we had already started an informal reading seminar in logic and philosophy in the fall, and in that January of 1951 we had just begun reading the first volume of Hilbert and Bernays’ Grundlagen der Mathematik 1. He joined in with enthusiasm. There is a typical aspect of Don that this example brings out. His interests ranged far and wide. Not much later one of Don’s most popular courses at Stanford was on philosophy and literature – in this context ‘literature’ means what it means in Departments of English in American universities, a subject matter very far from Hilbert and Bernays’ reflections on the foundations of mathematics. For reasons I can’t remember in detail now, rather early Don, the logician J.C.C. McKinsey, who had also joined the department in 1951, and I began discussing the theory of value in philosophy, concurrently with studying the theory of expected utility in game theory and economics. This led to our first joint publication: Davidson, McKinsey and Suppes, “Outline of a formal theory of value, I” (1955)2. The writing was actually completed in 1953, shortly after McKinsey’s death in that year. Certainly no later than the fall of 1953 or the winter term of 1954, Don and I began discussing how to think about experimentally measuring expected utility. We were, at that time, both naïve about running experiments. Neither of us had done so before, and neither of us had taken the kind of graduate courses that teach students how to do it. I am thinking here especially of students in psychology. So we got the cooperation of Sidney Siegel, who was at that time a graduate student in psychology at Stanford, to join us in designing and carrying out some experiments. Don and I also spent time on the theory of measurement needed as a background for empirical measurements of utility and subjective probability. This theoretical work led to our 1956 paper in Econometrica, “A finitistic axiomatization of subjective probability and utility” 3. The intuitive ideas were very much those set forth much earlier by Frank Ramsey (1931)4. But the details were different, because of the finitistic requirement for experimentation that we imposed. So in 1954 we conducted several experiments on measuring expected utility. A full report was given in our 1957 book with Siegel, Decision Making: An Experimental Approach 5. The work was completed by sometime in 1955. This was the last collaborative published effort by Don and me, although we continued to talk about new projects that never got off the ground.

252

MEMORIES OF D ONALD D AVIDSON

Let me end with some remarks on collaborating with him. The first, and perhaps most important, remark is that by and large we worked in a very congenial and easy way. I think it is fair to say that many people thought, probably correctly, that Don had a rather prickly personality. But at least not so in these early years. The collaboration with me was the most extensive in terms of published research of any such efforts during his long academic career, and so I can speak with some authority about what it was like to work with him. We argued a lot, but in the intellectual spirit of clarifying things that initially neither one of us understood well. We were exploring territory new to both of us and we instinctively recognized that we ourselves had different intellectual backgrounds, which could enable us to make separate but essential contributions to the research underway. Don’s thinking about our experiments was as careful and systematic as those of you who knew him would expect. Also, as the Preface to the 1957 book notes, we got help from a large number of persons, and I think we appreciated equally well how important this assistance had been to our work. In later years our conversations did not ever turn to an in-depth analysis of our early years of collaboration. But I have tended to assume, in conversations with others about Don’s later influential ideas in many areas of analytic philosophy, that those three or four years of intensive work on subjective probability, utility and decisions played a role in his development of new and original ways of looking at belief, desire and meaning. N OTES 1. 2. 3. 4. 5.

David Hilbert / Paul Bernays, Grundlagen der Mathematik, Vol. I. Berlin: Springer 1934. Donald Davidson / John C.C. McKinsey / Patrick Suppes, “Outlines of a formal theory of value, I”, in: Philosophy of Science, 22, 1955, pp. 140-160. Donald Davidson / Patrick Suppes, “A finitistic axiomatization of subjective probability and utility”, in: Econometrica, 24, 1956, pp. 264-275. Frank Plumpton Ramsey, “Truth and Probability”, in: Richard Braithwaite, (Ed.), The Foundations of Mathematics. London: Kegan Paul, Trench, Trubner & Co. 1926/1931. Donald Davidson/Patrick Suppes / Sidney Siegel, Decision Making: An Experimental Approach. Stanford, CA: Stanford University Press 1957.

Patrick Suppes

INDEX OF NAMES Not included are: Figures, Tables, Notes, References

Akdogan, C. 198, 205 Allais, M. 140 Althusser, L. 202 Arda, N. 197 Aristotle 94f., 101, 141, 156 Arkun, N. 197 Armendt, B. 56 Armstrong, D. 220 Arrow, K.J. 140, 142, 144-147 Aster, E. von 195 Atatürk, K. 191-193, 209 Ataünal, A. 191-193 Awodey, S. 213, 215f. Ayer, A.J. viii, 221 Bain, A. 51 Baker, L. 9f., 13-17 Barrow, J.D. 146 Bayes, T. 58f., 62, 64, 149, 151, 228f. Beaney, M. 214 Becker 21, 25 Bell, J. 26 Bendixson, I.O. 130 Bergmann, G. 219-222 Bergson, H. 190, 204 Berkeley, G. 4, 100f. Bernays, P. 92, 96, 106f., 156, 252 Bernoulli, J. 46, 57 Black, M. viii Boden, M.A. 151 Bohnert, H. 100, 102 Bolzano, B. 93f., 100f., 107 Boole, G. 62, 95 Boolos, G. 92, 110 Borel, F.E.J.E. 130 Bosanquet, B. 156 Bradley, J. 156 Braithwaite, R. viii, 5, 12, 17, 26, 35, 67, 83, 155, 158, 162 Brandom, R.B. 217 Brentano, F. 4 Broad, C.D. 20, 156-158, 161f. Brouwer, L.E.J. 25, 51, 93, 107, 110, 156 Browning, R. 2 Buldt, B. 215 Burali-Forti, C. 31 Campbell, N. 37 Cantor, G. 83, 92f., 95, 107, 124, 130 Carlyle, T. 2

Carnap, R. vi-viii, 22, 57, 67, 77f., 91, 93f., 96-105, 107-109, 194, 196f., 213-218, 219, 222 Carrington, D. 158 Cartwright, N. 167 Carus, A.W. 215, 217 Cassirer, E. 223-227 Cat, J. 167 Cavdar, A.O. 209 Cavell, M. ix, 249 Church, A. 92, 96, 98 Clark, P.J. 92 Cohen, H. 223 Cohen, R.S. 238 Comte, A. 195 Cook-Wilson, J. 246 Cornford, J. 26 Craig, W. 67f. Creath, R. 167, 216 Croce, B. 222f. Dahms, H.-J. 214 Dahrendorf, R. 143 Damasio, A. 139, 141, 144, 147-151 Davidson, D. ix-x, 43, 243-252 Davidson, E. 248 Davidson, V. 248 Dedekind, R. 31, 92-94 Degen, W. 99 Demopoulos, W. 72 Denby, E. 13, 15 Derrida, J. 247 Descartes, R. 108, 195, 204 Dewey, J. 167 Diaconis, B. 56 Dilthey, W. 213 Dodgson, C.L. 95 Domotor, Z. 41 Douglas, H. 174f. Drury, M. 26 Dummett, M. ix-x Dunne, J.W. 156-160, 162 Dupré, J. 169 Eccles, W. 22 Eddington, A.S. 83, 159 Edwards, P. viii Egidi, R. 24 Ehrenhaft, F. v Einstein, A. v, vii, 194, 200, 219, 223f.

254

INDEX OF NAM ES

Eliot, T.S. 20 Elphinstone, D. 11 Empson, W. 26 Engelmann, P. 27 Engels, F. 202 English, J. 72 Epicurus 228 Erasmus 199 Euclid 233 Exner, S. 237 Faber, R. 179 Farkas, J. 60 Fechner, G.T. 38 Feigl, H. vi, 22, 67 Fermat, P. de 105 Ferrari, M. 223-224 Feyerabend, P. 237 Fiche, J.G. 200, 204 Fine, A. 235 Finetti, B. de 43-46, 51, 56, 103, 144 Fischer, K. ix Flaherty, L. 15 Fleck, L. 179-187 Fraassen, B. van 63 Fraenkel, A. 25, 92, 96, 109 Frank, P. 111, 215 Frege, G. 23, 25, 30, 51f., 91-96, 98, 100f., 105-108, 123, 125f., 128, 130, 135, 214217, 222, 247 Freud, S. 6, 12, 49, 156, 208 Freedman, D.A. 56 Friedman, M. 167, 217, 227 Fulford, K.W.M. 208 Gabriel, G. 213 Gadamer, H.-G. 245 Gadol, E.T. 233 Galavotti, M.C. x, 23f., 49, 55 Galileo, G. 233, 248 Galison, P. 214 Garaudy, R. 202 Geach, P.T. 20 Gibbon, E. 4 Giere, R. 167, 235 Gintis, H. 145, 147 Gödel, K. v, 29f., 91f., 95-97, 99-102, 104106, 108-111, 126, 130f., 134, 146 Goethe, J.W. von 184, 187, 215f., 223f., 224f. Goheen, J. 245 Gökalp, Z. 190 Goldstein, M. 63 Good, I.J. 57 Goodman, N. 222 Graves, P. 64 Grünbaum, A. 239 Grünberg, T. 205 Habermas, J. 223

Hahn, H. v-vi, 6, 97, 100, 102, 215 Haller, R. 179 Hardy, G.H. 37 Hare, J. 26 Harrington, L. 105f. Harsanyi, J.C. 142, 148 Hayek, F.A. von ix Hegel, G.W.F. 96, 160, 224 Heidegger, M. 103, 223 Heine, E. 130 Heisenberg, W. 170, 200 Helmholtz, H. von 74f., 79 Hempel, C.G. 67, 194 Henkin, L. 128 Herder, J.G. 223 Hertz, H. 25 Hicks, J.R. 143 Hilbert, D. 25, 32, 51, 70, 93, 98f., 100, 105-108, 110, 128, 130, 133, 156, 215, 252 Hirsch, E.E. 191, 193 Hirshberg, N. 248 Hizir, N. 198-201 Hölder, O. 37 Horkheimer, M. viii Hughes, H.S. viii Humboldt, W. von 223f., 224 Hume, D. 4, 39f., 48, 50f., 101, 135, 156, 158, 195 Husserl, E. 214, 227 Jeffrey, D. ix, 56, 64, 228-230 Jeffrey, E. 228 Jensen, R. 64 Johnson 156 Kaila, E. v Kaldor, N. 143 Kant, I. 75, 86, 100, 102, 104, 107, 156, 195, 200, 204, 206, 223-224 Kaufmann, F. 102, 109 Kaynardag, A. 190f., 193-199, 202, 205 Keynes, G. 22 Keynes, J.M. v, viii, 5, 11-14, 19, 21f., 27, 35f., 45f., 56f., 155f., 158 Kienzler, W. 23f. King, J. 26 Kitcher, P. 168-170, 173f. Klein, C. 213, 217 Kneale, M. 93 Kneale, W. 93 Köhler, E. x, 147 Köhler, W. 197 Köhnke, K. 227 Kolmogorov, A.N. 233f. Kraft, C.H. 45 Kraft, V. v Krantz, D.H. 38, 43 Kraus, K. 20, 25

INDEX OF NAM ES

Kreisel, G. 130 Krois, J.M. 227 Kucuradi, I. 205 Kuhn, H.W. 139 Kuhn, T.S. 167, 180, 183 Lane, D.A. 56 Laplace, P.S. 46, 111 Lavoisier, A.L. 170 Leavis 26 Lee, D. 26 Leibniz, G.W. 92, 94f., 100f., 108, 129, 199, 224 Leinfellner, W. 142, 144f., 147, 149, 151f. Lenin, W.I. viii Lewis, D.K. 86 Lewis Carroll 95 Lincoln, A. 151 Locke, J. 248 Loos, A. 20 Lopokova, L. 14, 22 Lorentz, H.A. 233 Luce, R.D. 38, 43 Lukacs, G. 202 Mach, E. viii, 4, 20, 105 Machiavelli, N. 200 Macmurray, J. 158 Majer, U. 24, 155 Malche, A. 191-193 Marcel, G. 200 Marion, M. 24 Marschak, J. 144 Marx, K. 201-204, 206 Maxwell, G. 67, 76, 78f., 81, 86 Maxwell, J.C. 39, 111 McCarthy, J. 245 McDowell, J. 217 KcKinsey, J.C.C. 251 McTaggart, J. 156-158, 160-162 Mellor, D.H. ix, 20, 55, 155 Mendel, G. 73 Menger, C. v-vi Mill, J.S. 48-51 Mises, R. von 102, 201 Moore, G.E. viii, 12, 16, 19-21, 27, 156, 221 Morgan, M. 230 Morgenstern, O. vi, 139, 142-144 Mormann, T. 215 Morrison, M. 230 Munier, B.R. 144 Myhill, J. 131 Nasar, S. 139 Nash, J. 139-143 Natorp, P. 223f., 227 Nazmi, N. 196f. Nemeth, E. 167 Neumann, J. von vi, 92, 96, 139, 142-144

255

Neurath, O. viii-ix, 101, 103, 167, 214f., 241 Newman, M.H.A. 75f., 80-82, 85 Newton, I. 12, 41 Nietzsche, F. 199f., 204 Nissen, R. 196 Nohl, H. 213 Norton, B. 102 Novalis 214 Ockham, W. of 97, 100, 222 Ogden, C.K. 4, 12, 20 Örs, Y. 205, 207, 209 Özoglu, S.C. 209 Öztürk, H. 209 Pareto, V. 146 Paris, J. 105f. Parrini, P. 189 Parsons, C. 110f. Parsons, T. 145 Partridge, F. 10, 16, 20, 26 Pascal, B. 200 Paul, G. 1 Paul, M. v, ix, 1-3, 9, 11, 16, 156 Peano, G. 92, 94, 100, 104-107 Peirce, C.S. 45, 47f., 50f., 156 Penrose, A. 12 Penrose, L. 5, 17 Peters, W. 197 Petrus Hispanus 229 Picardi, E. 24 Piccoli 26 Pigou, A.C. 141-143, 145 Plato 95, 100-102, 104f., 107, 156, 204, 206 Poincaré, H. 94f., 99f. Polanyi, M. 186 Politzer, G. 202 Popper, K.R. ix, 180f. Pratt, J.W. 45 Prawitz, D. 128 Priestley, J.B. 159 Purves, R.A. 56 Putnam, H. 56, 79f. Pyke, M. 6-9 Quine, W.V.O. 32, 92f., 96-98, 101f., 104, 216f., 222, 245f. Raiffa, H. 57 Ramsey, Agnes 1, 7, 9f., 13f. Ramsey, Arthur S. 1, 9, 14 Ramsey, Bridget 1f. Ramsey, Frank P. v-x, 1-165, 245, 251 Ramsey, Jane 13-15 Ramsey, Lucy 14 Ramsey, Margaret ĺ Paul, M. Ramsey, Michael 1f., 10, 13, 17 Ramsey, Sarah 16 Rawls, J. 142f., 145-147 Reck, E. 214f.

256

INDEX OF NAM ES

Redhead, M. 86 Reichenbach, H. 102, 189-209, 224 Reichenbach, M. 194 Reik, T. vi, 6-8 Reidemeister, K. v Rescher, N. 55, 155 Rhees, R. 26 Richard 92, 97, 104 Richards, I.A. 3 Richardson, A. 167, 216 Ricketts, T. 216 Rickman, J. 6 Risse, M. 228 Roh, F. 214 Roy, J.-M. 214 Russell, B. v, vii-ix, 5, 12, 19-21, 23, 25, 27, 29, 33, 37f., 67, 74-76, 79, 81-83, 86, 91-100, 104f., 107, 109f., 123-126, 128, 130-132, 134f., 155f., 204f., 214f., 217, 222f. Rylands, D. 26 Ryle, G. 25, 222 Sahlin, N.E. 55, 155 Samuelson, P.A. 143 Sapir, E. 184 Savage, L.J. 43, 51, 57 Schilpp, P.A. 223 Schlaifer, R. 57 Schleiermacher, F.D.E. 214 Schlick, M. v-vii, 6, 14, 21-23, 70f., 86, 100, 102, 109, 215, 217f., 224, 241f. Schopenhauer, A. 103 Schröder, E. 101 Schrödinger, E. 170 Schulte, J. 21 Schuster, P. 150 Schütte, K. 134 Scitovsky 143 Seidenberg, A. 45 Sellars, W. 217 Sen, A. 27, 142, 144-147 Shakespeare W. 2, 26 Shimony, A. 103 Shin, H.S. 59 Siegel, S. 243 Sigmund, K. 150 Skinner, B.F. 26 Skolem, T. 101, 156 Smythies, Y. 26 Solomon, M. 172 Spengler, O. 25, 27, 103, 179f., 183-187 Spinoza, B. 241 Sprott, S. 6, 8 Sraffa, P. 25-27 Stadler, F. 167 Stebbing, S. vii Stegmüller, W. 91

Steiner, R. 187 Stelzer, J.H. 41 Strachey, A. 6, 19 Strachey, J. 6, 12, 19 Strachey, L. 158 Sudderth, W. 56 Suppes, P. ix-x, 38, 43, 139, 142f., 231-235, 239, 443 Szilárd, L. 111 Takahashi 128 Takeuti, G. 128 Tarski, A. 47, 97f., 105, 107, 215 Tegtmeier, E. 218, 220 Teller, P. 56, 236 Thackeray, W.M. 1f. Thirring, H. vi Tolstoy, L. 20 Townsend 26 Trevelyan, J. 26 Tulving, E. 144 Tversky, A. 38, 43 Uebel, T.E. 167, 215 Ülken, H.Z. 190f., 196, 198 Urmson, J.O. 222 Venn, J. 95 Waismann, F. vi, 21-23, 25, 109, 219 Wang, H. 100, 110 Warburg, A. 224 Waterlow, S. 27 Watson, A. 12, 27 Weibull, J.W. 145, 147 Weierstrass, K. 93 Wells, H.G. 159 Weyl, H. 25, 70, 74f., 79, 156 Whitehead, A.N. viii, 95, 111, 123, 130, 245 Whorf, B.L. 184 Widmann, H. 191, 193-196, 198 Wiener, N. 37f., 40 Wilder 105 Williamson, T. 32 Winnie, J. 77 Wittgenstein, G. 3, 5f., 19f. Wittgenstein, L. v-vii, ix, 3-5, 8, 14, 16, 19- 27, 42, 99f., 102-104, 134f., 155f., 179f., 182, 217f. Wolters, G. 213f. Woodger, J.H. vii Woolf, L. 22 Woolf, V. 20, 22, 27 Worrall, J. 67, 79-81 Yildirim, C. 205 Zabell, S. 56 Zahar, E. 67, 79-81 Zanotti, M. 45 Zermelo, E. 92, 95-97 Zinnes, J.L. 139, 142

VIENNA CIRCLE INSTITUTE YEARBOOK The Vienna Circle Institute is devoted to the critical advancement of science and philosophy in the broad tradition of the Vienna Circle, as well as to the focussing of cross-disciplinary interest on the history and philosophy of science. The Institute’s Yearbooks provide a forum for the discussion of exact philosophy, logical and empirical investigations, and analysis of language. Each volume centers around a special topic which is complemented with a permanent section with essays arising from the scientific activities at the Institute and reviews of recent works in the history of philosophy of science or others with a particular relation to the tradition of logical empiricism.

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F. STADLER (ed.), Scientific Philosophy: Origins and Developments. 1993. ISBN 0-7923-2526-5

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D. GREENBERGER / W.L. REITER / A. ZEILINGER (eds.), Epistemological and Experimental Perspectives on Quantum Physics. 1999. ISBN 0-7923-6338-X

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M. HEIDELBERGER / F. STADLER (eds.), History of Philosophy of Science. New Trends and Perspectives. 2002. ISBN 1-4020-0509-1

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