Aristotle's Theory of the Unity of Science

MALCOLM WILSON

Aristotle's Theory of the Unity of Science

Aristotle's Theory of the Unity of Science

Aristotle was the first philosopher to provide a theory of autonomous scientific disciplines and the systematic connections between those disciplines. This book presents the first comprehensive treatment of these systematic connections: analogy, focality, and cumulation. Wilson appeals to these systematic connections in order to reconcile Aristotle's narrow theory of the subject-genus (described in the Posterior Analytics in terms of essential definitional connections among terms) with the more expansive conception found in Aristotle's scientific practice. These connections, all variations on the notion of abstraction, allow for the more expansive subject-genus, and in turn are based on concepts fundamental to the Posterior Analytics. Wilson thus treats the connections in their relation to Aristotle's theory of science and shows how they arise from his doctrine of abstraction. The effect of the argument is to place the connections, which are traditionally viewed as marginal, at the centre of Aristotle's theory of science. The scholarly work of the last decade has argued that the Posterior Analytics is essential for an understanding of Aristotle's scientific practice . Wilson's book, while grounded in this research, extends its discoveries to the problems of the conditions for the unity of scientific disciplines. MALCOLM WILSON is an assistant professor in the Classics Department at the University of Oregon.

PHOENIX Journal of the Classical Association of Canada Revue de la Societe canadienne des etudes classiques Supplementary Volume xxxvrn Tome supplementaire XXXVIII

MALCOLM WILSON

Aristotle's Theory of the Unity of Science

UNIVERSITY OF TORONTO PRESS Toronto Buffalo London

@ University of Toronto Press Incorporated 2000 Toronto Buffalo London Printed in Canada ISBN 0-8020-4796-3

Printed on acid-free paper

Canadian Cataloguing in Publication Data Wilson, Malcolm Cameron Aristotle's theory of the unity of science (Phoenix. Supplementary volume ; 38 = Phoenix. Tome supplementaire, ISSN 0079-1784; 38) Includes bibliographical references and index. ISBN 0-8020-4796-3 1. Aristotle - Contributions in methodology. 2. Aristotle - Contributions in ontology. Science - Philosophy. 1. Title. II. Series: Phoenix. Supplementary volume (Toronto, Ont.) ; 38. B48SWS4 2000

185

C99-932973-1

University of Toronto Press acknowledges the financial assistance to its publishing program of the Canada Council for the Arts and the Ontario Arts Council. University of Toronto Press acknowledges the financial support for its publishing activities of the Government of Canada through the Book Publishing Industry Development Program (BPIOP).

CONTENTS

ACKNOWLEDGMENTS ABBREVIATIONS

INTRODUCTION

vii

ix

3

CHAPTER 1: GENUS, ABSTRACTION, AND COMMENSURABILITY 14 Demarcating the Genus 15 Abstraction 29

I. Speed of Change 39 2. Value 41 3. Animal Locomotion 47 CHAPTER 2: ANALOGY IN ARISTOTLE'S BIOLOGY Problems with Analogy 53

I. Fixity of Analogy 60 2. Difficult Cases 67 3. Analogues and the More and Less 69 4. An~logues and Position 69 5. Analogy of Function 72 6. Genus as Matter 74 A Solution 77 A Challenging Case 83 Analogy and Abstraction 86

53

vi Contents CHAPTER 3, ANALOGY AND DEMONSTRATION

89

Analogy in APo; Passages and Discussion 91 Analogy in the Biology 99 Analogy and the Scala Naturae 109 CHAPTER 4, THE STRUCTURE OF FOCALITY

116

Focality and Pcr Se Predication 122 The Limits of Focality in the Biological Works 129 CHAPTER 5, METAPHYSICAL FOCALITY

134

The Genus of Being 136 Categorial Focality in Metaphysics Z 144 Demonstration in the Science of Being 158 The Wider Focal Science ?f Being 165 CHAPTER 6, MIXED USES OF ANALOGY AND FOCALITY

Matter and Potentiality 177 The Good 194 CHAPTER 7, CUMULATION

207

Souls 208 1. The Analogical Account 210 2. The Cumulative Account 214

Friendship 224 1. Eudemian Ethics and the Problems of Focal Friendship 225 2. The Nicomachean Version 231 The Place of Theology in the Science of Being 235 Conclusion: Analogy, Focality, and Cumulation 239

BIB L lOG RAP H Y I N D E X L 0 COR U M GENERAL

INDEX

243 255 265

175

ACKNOWLEDGMENTS

My first thanks go to my teachers at Berkeley, T any Long, John Ferrari, and Alan Code, who supervised the dissertation from which this book arose. Mary Louise Gill and James Lennox also kindly read my entire dissertation and provided encouragement and advice. Friends and colleagues have read and commented on various parts in various stages of completion: Andrew Coles, William Keith, John Nicols, Scott Pratt; and my wife, Mary Jaeger, who conquered 'philosophy-induced narcolepsy' to read the entire manuscript more than once. Two anonymous reviewers for the University of Toronto Press provided much detailed and general comment useful in improvement. Finally, I should also like to thank Ancient Philosophy for permission to use ma terial published in 'Anal ogy in Aristotle's Biology: Ancient Philosophy 17 (1997) .

......................------

ABBREVIA nONS

Works of Aristotle

APo APr Cat. DA DC DI EE

EN GA

GC HA IA Juv. Long. MA Met. Mete.

MM PA Phys. PN Pol. Resp. SE Sens.

Somn. Top.

Posterior Analytics Prior Analytics Categories

de Anima de Caelo de Interpretatione Eudemian Ethics Nicomachean Ethics Generation of Animals Generation and Corruption

History of Animals Progression of Animals On Youth, Old Age, Life and Death On Length and Shortness of Life Movement of Animals Metaphysics Meteorologica Magna Moralia Parts of Animals Physics Parva Naturalia

Politics Respiration

Sophistical Refutations Sense and Sensibilia de Somno Topics

x Abbreviations

Other Works LSj H.G. Liddell and R. Scott. A Greek-English Lexicon. Revised and augmented by H. jones. Oxford: Clarendon Press, 1996. ROT j. Barnes. The Complete Works of Aristotle. The Revised Oxford Translation (Bollingen Series LXXI.2). Princeton: Princeton University Press, 1984. Acronyms and Summary of Per Se Relations IPO SGA WP

is predicated of species-genus-analogy wholes-parts

per se (1) predicate: is contained in the definition of its subject, e.g., linear is predicated of triangle. per se (2) predicate: contains its subject in its definition, e.g., female is predicated of animal. per se (3) is self-subsistent subject, e.g., man. per se (4) predicate: is predicated of something on account of itself, e.g., dying is predicated of being slaughtered.

Aristotle's Theory of the Unity of Science

INTRODUCTION

Aristotle is renowned for having been the first to create autonomous

sciences and independent disciplines. By distinguishing physics, political science, and many other areas of study, he circumscribed and identified some of the most important modern scientific fields. His reasons for separating such sciences and their subject matters were not the social and

practical reasons familiar today. He did not worry about the limitations of the individual human mind faced with the explosive growth of knowledge and the consequent drive towards ever-increasing specialization . Quite the

contrary, he thought humans were naturally capable of fulfilling their desire for understanding and he did not view the sheer amount of knowledge as an impediment to this end. His concern lay instead with the form that

that understanding takes. He denied that all of our knowledge falls into a single undifferentiated domain, a single universal science, and he developed a solution, the subject-genus, which served to separate and isolate each subject matter.

But his solution created problems of its own. J shall contend that the isolating force of the subject-genus was so powerful that additional techniques were required to provide for the legitimate causal and explanatory links between sciences and subject-genera. To effect the happy compromise between universal science and genus-isolation, Aristotle developed four techniques of connection: subordination, analogy, foeality, and cumulation,

of which the last three are the special concern of this book. J intend to study these techniques both at a specific and a general level. J am first of all interested in the use Aristotle makes of them. The specific passages in which he explicitly puts these techniques to work are among the most controversial in the Aristotelian corpus. They concern such fun-

damental questions as the unity of the science of Being and metaphysics,

4 Aristotle's Theory of the Unity of Science the definition of the soul, the organization and nature of goods, and the

kinds of friendship. In treating each technique in turn and with an eye to the larger picture, I shall offer new interpretations of specific areas of Aristotelian philosophy. At a more general level, I gather these techniques together and provide a single comprehensive theory for them. This theory arises out of my reflections on recent developments in Aristotelian scholarship. One of the most important trends of the last several decades has been the realization that Aristotle's theory of science contained in the Posterior Analytics is not an abstract ideal without practical application, but in fact is used in important ways in the special sciences, especially in the biological works.

Many of the basic concepts of Aristotle's formal scientific methodology, like demonstration and definition, have been found to inform the practice and presentation of specific sciences. This research has been very fruitfuL but

it has focused primarily on the single isolated genus. There is good reason for this focus. While the APo does discuss the subordination technique at some length, it only briefly notes analogy and never mentions focality or cumulation at all. And yet these are important organizational tools in the several sciences. In view of the success in applying the APo's single-genus theory to Aristotle's scientific practice, I want to reverse the hermeneutic

process, as it were, and ask whether the widespread use of analogy, focality, and cumulation in the special sciences can be given any theoretical account within the terms of the APo. I believe that this is possible, and shall adduce evidence and argument to show that Aristotle had the APo in mind when

he formulated these techniques. I shall also argue that this fact yields important results. Not only do we obtain a theoretical account of these techniques, but we also discover that, far from being a random assortment

of tools of various vintages scattered haphazardly throughout the corpus, they perfonn interlocking and complementary functions. Moreover, they

are all logical developments of the most important concepts in the APo, per se and qua predication. This fact both confirms our belief in the relevance of the APo for these techniques and also allows us to provide a general and unified account of them, for they are variations on a Single logical theme.

Finally, by describing these techniques in terms of the central concepts of the APo, we can provide a richer and more powerful account of Aristotle's theory of science, one that is more funy integrated into all aspects of his scientific practice. Such an interpretation is founded on an assumption hermeneutically

confirmed that Aristotle's philosophy forms a basically consistent unity, and that there are few radical changes in his views. The unsuccessful attempts of this century to impose a chronology on Aristotle similar to

5 Introduction

the one that 5,0 successfully applies to Plato lead me to view the historical question as less interesting than the philosophical question concerning the logical organization of concepts. It would be absurd to deny that . any philosopher underwent intellectual ' development, but I am inclined to believe that Aristotle's development is more like the articulation of basic ideas than the repeated creation and destruction of whole systems of thought. The story begins with Aristotle's objections to a single universal science. These objections arose out of the historical context of debates with his older contemporaries Plato and Speusippus, heads of the Academy. It was a common supposition of ancient Greek epistemology that we know something when we know how it is related to other things we know. This relational view of knowledge manifests itself in two patterns. First, Plato held that we know the particulars best (to the extent that we actually can know them ) when we understand how they imitate the Forms, and since we understand the particular in virtue of the universaL Plato exalted the Form or universal and depreciated the sensible particulars. Since we ·can understand only what is common and universal among the particulars, the variations among them are relegated to the shadowy realm of opinion. With the quip that Meno was providing a whole swarm of virtues, Plato's Socrates compelled him to avoid examples, like manly virtue and womanly virtue, and state instead the single definition of virtue that covers all these cases. For virtue, Socrates claimed, must be the same whether it is present in a man or a woman (Meno 71e-73a) . Likewise, in the Republic he supposed tha t justice will have the same nature wherever it is found, and as a result, he argued, justice in the soul will be the same as justice in the state (368c-369a). In the drive for the universal definition, Plato often overlooked genuine ambiguities in terms. For Aristotle, detecting and disarming these ambiguities became something of a philosophical obsession. He faults Plato on the grounds that justice exists properly as a relation between two people, and exists between the parts of the soul only by a metaphorical extension (EN V.111138a4-b14). Similarly, Plato's universalization of virtue, which is manifested in the Republic's inclusion of women in the leadership of the state (4S1d-e), prompts Aristotle to distinguish between men's and women's tasks and therefore between their virtues (Pol. II.S 1264b4-6). For Plato, then, the possession of any common characteristic among particulars was a sufficient condition for positing a Form and universal, and as a result he failed to detect other more subtle relationships. The preference for the universal over the particular is recapitulated in the preference for the more general Form over more specific Forms, as is clear in the example

6 Aristotle's Theory of the Unity of Science of Meno's virtues, in which man's virtue, even though a universal itself, was rejected as too particular. As a result, important demarcations between

fields and sciences were blurred, and in the Republic all knowledge became an articulation of the unified politico-philosophical super-science of the Good, in which the Form of the Good made all other Forms intelligible. [n his later work, plato studied a second form of relational knowledge. [n the Sophist the Forms themselves are known through a process of division by their participation in Sameness and Difference with respect to other Forms. Here, the relations among the Fanns themselves are the source

and ground of knowledge. Plato's nephew, Speusippus, while rejecting the Forms, elaborated this system of division and used it to drive even harder in the direction of scientific unification. He argued that all knowledge is relational, and that everything is known in virtue of its sameness and difference from all other things. [n order to know anything, therefore, one must know everything l Knowledge is articulated through a universal scheme of division, and a thing just is its relational position within this universal scheme.

As a member of Plato's Academy and as a philosopher in the Platonic tradition, Aristotle was engaged in this common quest for systematic understanding, but he was suspicious of both the generalizing and unifying tendencies he found there. On several grounds he argued the inadequacy of the Academic project. He claimed that there was no universal subject matter to provide an object for a universal science; there was, that is, no one genus of Being. And even if there were, he claimed, this general science

would tell us nothing about the manifold nature of reality. Nor would it be useful, since we do not even need it in order to know about specific

pieces of reality. As Aristotle presented it, plato identified Being and Unity as the highest genera of things, under which all Forms fall. He also identified Being and Unity as the elements of things, since he supposed that the Forms were somehow constituted out of them. Being and Unity, then, were at

the same time both principles and the highest genera (Met. B.3 998b9-21). For Plato, the more universal a thing was, the more of a principle it was and the greater its generative and explanatory power. Aristotle, by contrast, argued that there was a limit to the degree of universalization attainable

among all objects . Neither Being nor Unity, he thought, form a genus with a Single unambiguous definition, and therefore neither can be a principle

for a universal science (998b22-28).

1 According to Aristotle (APo II,13 97a6-19). See my 1997a.

7 Introduction Aristotle was also concerned about the epistemological etiolation that attends increasing universalization. The more one grasps at what is com· man, the less one retains of the particular kinds. And yet what a thing is spe"cifically is as much a part of its Being as what it is at a high level of generalization. For being biped is as much, if not more, part of the Being of a man as being a substantial unity, the actuality of a potentiality. This is not to say that Aristotle rejected general understanding altogether, but he did not think that we know something solely in virtue of its membership in a genus. Nor did he believe that the genus always provides the cause and explanation for a thing. He preferred instead the constitutive element and the various kinds of cause as explanatory principles, and in his theory of science the genus comes to denote the extension of the explanation, rather than the explanation itself. Aristotle also took issue with the Academic doctrine that all knowledge forms a single science. He made the observation - hardly original conSidering Socrates' frequent appeal to it - that there were experts who understood their own field but not others. It was clearly not necessary to know everything in order to have expertise in a single field.' Nor was it necessary to know the most general science. Plato, for his part, had been scandalized that the mathematicians simply accepted the principles of their science without investigating its foundations. He supposed that their hypothetical principles could be perfected by an unhypothetical science, philosophical dialectic, which would remedy the deficiency of mathematics and indeed all hypothetical sciences. Only the philosopher, then, could legitimately lay claim to true knowledge of the special sciences. Aristotle, though he recognized a first philosophy that examined the first principles of the special sciences, thought it right and proper that the special sciences should merely presuppose and not examine their own first principles. Accordingly, Aristotle sought to redress the imbalance apparent in the Academic prejudice towards the universal. He attended more equally to both the specific and the general levels of inquiry and studied the causes of things in addition to their similarities and differences. These new concerns found logical expression in his theory of scientific understanding, whose foundation is the demonstrative syllogism. A syllogism is composed of at least three terms, a major (e.g., having wings), a middle (e.g., fliers), and a minor (e.g., birds), arranged in at least two premisses and a conclusion; for example, 2 See PA I.l, where Aristotle draws the distinction between the specialized expert and the generaUy educated layman. Also Balme 1972, 70, on the connection with Plato and Speusippus.

8 Aristotle's Theory of the Unity of Science having wings is predicated of (henceforth, IPO) fliers fliers IPO birds therefore, having wings IPO birds J In order for a syllogism to be demonstrative, the relationship between the terms of its premisses (e.g., 'having wings' and 'fliers') must be necessary.4 This necessity is understood in terms of essential, definitional relationships: in order for 'having wings' and 'fliers' to be terms in the same demonstrative premiss, 'having wings' must appear in the definition of 'flier' or vice versa, e.g., wings are by definition the instrumental part for flying. s When

terms are so related, they are said to be per se (Ka8' aim5) or essentially related. Only essentially related terms may be joined in a demonstrative premiss, and a string of such premisses wi1l form a string of essential relations. Terms that are not essentially related are said to be accidentally related, and cannot be connected in a demonstrative premiss. In addition to this per se requirement Aristotle introduces the rule that terms in a demonstrative syllogism must be proved of the subject as such and universally, indicating this criterion by the use of the relative pronoun Ti (qua). The effect of this requirement is to restrict further the terms admissible to a demonstration and therefore to a science. A triangle, for

example, can be demonstrated as having interior angles equal to two right angles (following the custom, I shall call this the 2R theorem), because it possesses this property as or qua triangle. By contrast, a demonstration that proves this attribute of isosceles triangle is defective because the property does not belong to isosceles triangle qua isosceles, but qua triangle. Such

a proof is said to be an accidental proof, because 2R does not belong to isosceles triangle qua isosceles. The term 2R, then, belongs in the science of triangle and not in the science of isosceles triangle. These two restrictions on the admission of terms to a demonstration constitute the identity conditions of a science and provide the foundations

for the autonomy of disciplines. Since not all terms are per se related to one another, and since they are different in their qua designations, they 3 This syllogism is frequently presented differently by modem commentators: birds are fliers fliers have wings birds have wings. This is not, however, Aristotle's presentation, and it will be most convenient for our purposes to adhere to his chara([eristic fonn. 4 These issues will be discussed in greater detail in chapter 1 below. S In relating tenns within definitions Aristotle allows for some paronymy, Le., flying for flier.

9 Introduction cannot all be included in one universal science. Each science has a subject or a subject-genus. This is what the science is about and the subject of which the predicates are predicated. A science is the sum of the demonstrative syllogisms that concern the same subject.' The subject of the science is indicated by the qua expression, and the per se criterion for including other terms in a science implies that each science is autonomous and has its own and unique set of principles. When these restrictions are violated, when there is an attempt to introduce a term that is not per se and qua related to the other terms into a demonstrative syllogism, the result is an error, which Aristotle calls I'ETa/3arJ'lS or kind-crossing, and this will destroy the demonstrative power of the syllogism and the cogency of the science. In contrast to Plato's and Speusippus' universalizing and inclusive tendencies, Aristotle's theory of demonstration is a powerfully isolating force. The qua requirement especially entails that understanding occurs within a single subject-genus, and not in relation to other genera through an analysis of sameness and difference.' Each science will be specialized and isolated from every other except by incidental connections, and there will be no communication between disciplines. Each subject-genus, bound by necessity solely to its own principles and predicates, will form an island in the sea of Being. The view of the world that this theory of science represents will be that of a heap of subjects, in which one genus is only incidentally related to another. It is clear, however, that Aristotle never advocated such a degree of isolation. In fact there are a multitude of ways in which sciences are connected with one another and share principles. The axioms, like the principle of non-contradiction, are common to all sciences, and are the precondition for any understanding at all. More elaborately developed within the APo is the connection between a more abstract, superordinate science and a less abstract, subordinate science. A superordinate science, usually a branch of mathematics, supplies principles and explanations for a fact or conclusion found in a distinct and subordinate natural science, for instance, harmonics or optics. Since this technique and its place in the APo has been well studied

6 I am deliberate in avoiding the claim that a science is the sum of demonstrations which

have the same minor term for reasons which will be discussed in chapter 4. 7 No doubt, division remains an important part of Aristotle's epistemology, but it plays a preliminary role in establishing the extent of the subject-genera and the attributes that are coextensive with them. It is not the primary form of understanding. See Ferejohn 1991, who places division in the 'framing' or pre-demonstrative stage of science. See also chapter 2 below.

10 Aristotle's Theory of the Unity of Science by the secondary literature, I shall not treat it in the same depth as the three other techniques· It will proVide, however, a useful stepping-stone to those techniques . In the first chapter of this book I shall begin by laying out in more detail the conditions for a unified subject-genus and what makes two subject-genera different. I shall then consider subject-genera that are related to one another through abstraction, but that nevertheless are separate and autonomous. Abstraction is a feature of Aristotle's philosophy familiar from his theory of mathematics. According to Aristotle, mathematical objects are ontologically dependent on their physical substrate, but can be mentally abstracted from that substrate so that they maintain absolutely no conceptual connections (Le., per se relations) to it. Mathematics and physics, then, are a pair of subject-genera related by pure abstraction. I shall argue that abstraction has a much broader application than merely to mathematics and, more importantly, that there are several degrees of abstractability, depending on the nature of the subject matter. I shall focus on several pairs of subject-genera in which the conceptual abstraction is not absolute, cases in which there are per se relations between the abstracted genus and its substrate. I call this situation 'semi-abstraction.' The superordination technique will proVide us with the first step along this road. It is precisely in the realm of abstraction and semi-abstraction, in which two subject-genera can be treated as autonomous and yet maintain per se connections to one another, that analogy, foeality, and cumulation operate. Analogy, strictly speaking, is a proportional relationship between four terms (A is to B as C is to 0), that expresses a common relation between each of the two pairs. The formal structure of the relationship does not dictate the content, and an analogy can express any commonality from an exuberant metaphor of poetry to a trivial numerical identity. Nevertheless, I argue that Aristotle has a more specific function in mind for analogy, one closely related to demonstration. Analogy arises between subject-genera. Where genera are different, their qua designations are different, and there are no per se connections between them. As a result they cannot be treated by a common science. In the face of the injunction against metabasis or kind-crossing, analogy provides us with the means of treating subjects that are generically different in a parallel way. In the Parts of Animals, for example, Aristotle discusses the analogous parts, wing and fin. These parts are predicated respectively of bird and fish in virtue of the final causes or functions, flying and swimming. Bird, wing, and flying have obvious universal and per se connections; so also do fish, fin, and swimming. We

8 See e.g., Lear 1982, McKirahan 1978, CartWright and Mendell 1984, and Lennox 1986.

11 Introduction can prove that wing is predicated of bird by using the proper principles of the subject genus, bird; similarly with the fish's fin' In spite of the independence and autonomy of the demonstrations, there is a parallel in the proofs, an analogical identity of relation: as wing is to bird, so fin is to fish. This identity, however, cannot be abstracted from, and must always be per se related to, the subject-genera in which the demonstrations take place. This is a result of the fact that the subjects, bird and fish, determine the qua level at which the attributes and causes are treated. At the same time, behind the generic difference there is the intimation of a more abstract subject-genus to which both bird and fish are related. This subject-genus arises from the fact that flying and swimming are forms of locomotion, and that wing and fin are instrumental parts of locomotion. The second and third chapters of this book will be devoted to explaining how analogy facilitates this limited degree of unity among different scientific subjects. The second object of our investigation, the focal relationship, is a method for drawing together in a single subject matter objects that are of different genera lO According to Aristotle's favourite example, the term 'medical' applies to many different kinds of objects. For instance, we call an operation medical, a doctor medical, a scalpel medical, not because they possess the same attribute, medical, but because they are all related to the thing that is called medical in the primary sense, the medical art. The other medical things are so called because they are the work of the medical art, the possessor of the medical art, or the instrument of the medical art. The definitions of these derivatively medical things contain in themselves the primary term or its definition. Chapter 4 will be devoted to analysing the focal relationship in terms of -Aristotle's theory of science and showing that medical is predicated of the derivative medical things in virtue of a variety of per se relations. Although all the medical objects do not form a single genus, in the sense that they are not of the same kind or similar to one another, the definitional relations among them show how they form a genus in another important sense of the term, objects related by per se connections to a single subject-genus.

9 This is Aristotle's standard pattern of demonstration in the PA . We perceive that a bird has wings from obseJVation, but to know in the fullest sense we must know why, and this knowledge comes from relating the cause to the fact in a demonstration. We cannot prove that a bird has wings from observation, because only demonstration provides proof. 10 G.E.L. Owen (1960) first provided the current English translation of 7rpor tV A.EyOP.EVOV as 'focal meaning.' It is also known as 'relational equivocity.' Most recently Shields 1999 has called this (as well as cumulation) 'core dependent homonymy.'

12 Aristotle's Theory of the Unity of Science The most important ·consequence of this interpretation of the focal relationship in terms of the APo theory is a reassessment of Aristotle's famous application of focality, the science of Being (ov). This will be the task of chapter 5. Though they do not form a single genus, Beings can be treated under a single science because they are all per se related to a single primary term, substance (ovcria). The focal relation has traditionally been treated as a very special case, found only in exceptionally difficult circumstances like the science of Being. But the fact that the focal relation is basically a per se relation suggests that focality should be viewed instead as a simple application of the logical and causal relations of normal Aristotelian demonstrative science. The terms (subjects, attributes, causes) of demonstrative premisses are bound together by necessary, definitional relations, whereby one tenn (or its definition) is included in the definition of another. This is the structure of any ordinary Aristotelian science, and the binding relations found in ordinary or normal science are of the same kind as those by which focal science, including the focal science of Being, is constituted. In the sixth chapter I shall consider groups of objects that Aristotle treats both analogically and focally. These cases have a long history of controversy. Aquinas, for example, made analogy invariably into a relation between prior and posterior, assimilating it to focal and serial schemes, which he called 'analogy of attribution.,ll More recently, G.E.L. Owen sharply distinguished analogy and focality and tried to set them in a chronological sequence within Aristotle's philosophical development. 12 Neither, however, studied analogy and focality in terms of per se relations and demonstrative science. And though Owen was right to reject the terms of Aquinas's assimilation of the techniques, there are other and deeper structural connections that have escaped the notice both of Aquinas and the moderns. In this chapter I shall argue that, far from being independent or even incompatible means for the unification of a subject-genus, focality is logically prior to analogy and a necessary precondition for it. Analogy and focality are two basic ways in which Aristotle treats different genera in conjunction with one another. But there is another 11 Summa thcologiac 1.13.6c: 'In the case of all names which are predicated analogously of several things, it is necessary that all be predicated with respect to one, and therefore that that one be placed in the definition of all. Because "the intelligibility which a name means is its definition," as is said in the fourth book of the Metaphysics, a name must be antecedently predicated of that which is put in the definitions of the others, and consequently of the others, according to the order in which they approach, more or less, that first analogate.' For passages and discussion see Klubertanz 1960, 68-9. 12 Owen 1960.

13 Introduction important means that employs elements of focality and analogy to create a series of similar objects. I call this method 'cumulation,' and it will be the subject of the final chapter. l3 It is a special form of a series, which is arranged in order of priority and posteriority, and is used in Aristotle's discussions of souls and friendships. It is also important for determining the place of theology within metaphysics. The prior members of the series are logically and ontologically contained in the posterior members, as for example the nutritive soul is contained in the sensitive soul. The latter cannot exist without the former, and the latter contains the former in its definition potentially. Members of cumulative series do not form standard genera, but they all share some essential attributes with one another, as analogues do; they are also per se related among themselves, since the definition of a later member contains the definition of a prior member, just as focally related objects do. In spite of the features of cumulation that are common with foeality, cumulative objects cannot form a focal genus. The reasons for this will emerge in my interpretation of the soul series. The chapter will be filled out with an examination of Aristotle's two discussions of friendship and an argument that he abandoned the focal analysis of friendship he provided in the Eudemian Ethics for a cumulative view in the Nicomachean Ethics because of the intractible difficulties in applying focality in this context. Finally, I shall use the lesson of cumulation and focality to shed light on the problem of the place of theology in the science of Being. Together, analogy, focality, and cumulation provide Aristotle with the means to balance the claims of the universal science advocated by the Academy and the isolation of the subject-genera, which arises within the logic of his own theory of science. This solution, by preserving the autonomy of sciences without creating a chaotic heap of subject matters, allows each subject to be treated separately while still maintaining its place in the intelligible architecture of the world.

13 Grice 1988, 190--2, has called this 'recursive unification.'

Genus, Abstraction, and Commensurability

In this chapter I shall first discuss two issues preliminary to 'semi-abstraction.' I shall begin by presenting in more detail the per se and qua relations, and show how they make a subject-genus a single subject-genus distinct from other subject-genera. Aristotle illustrates these relations by the familiar 2R example and the proof for alternating proportionality. In both cases the per se and qua relations provide an adequate set of criteria

for identifying and demarcating subject-genera. Next, I shall introduce abstraction (&'aipfCH<) through Aristotle's theory of mathematics, and analyse this concept in terms of per se and qua relations. Abstraction will provide a means of moving or shifting between qua levels and between subject-genera, not just among mathematical and physical objects, but wherever two subject-genera are related.

These preliminary discussions provide the background for semi-abstraction, and allow for a distinction between semi-abstraction and pure abstraction. In pure abstraction, such as the abstraction of mathematicals from their physical substrates, the abstracted subject-genus maintains no per se connections to the substrate from which it was abstracted. In semiabstraction, by contrast, the abstracted subject-genus does maintain some per se connections to its substrate. I shall argue that, precisely because these per se connections are maintained, the lines of demarcation between a semi-abstracted subject-genus and its substrate cannot be sharply drawn. As a result ambigUity arises in determining which subject-genus is under consideration, the semi-abstract or its substrate. We shall see this problem first arising with the proof for alternating proportionality, and then more acutely in the 'mixed' or subordinate sciences, like harmonics and optics. In these latter cases more than one subject-genus is involved in the same proof, and therefore proofs in such sciences do not occur clearly within one or the other subject-genus, but rather occur in both.

15 Genus, Abstraction, and Commensurability There are different degrees of semi-abstraction. By enlisting commensurability as a sign of generic unity (i.e., objects in the same genus can be compared directly with one another, while objects from different genera cannot) I shall examine abstraction and resistance to abstraction in several graduated cases. While mathematicals can easily be abstracted from their physical substrate and be compared as quantities, some other objects resist abstraction to a greater or lesser extent. I shall consider three such objects . . First, kinds of change cannot be abstracted from their substrate and cannot be compared one with another. Next, the exchange value of manufactured goods can be abstracted from the proper function of the goods sufficiently to allow commensuration for the purpose of exchange and trade. Finally, causes of animal locomotion can be abstracted from the instrumental parts of locomotion to the extent that at the upper reaches of abstraction there remain no per se connections with the specific -instruments. But each level of abstraction from the pans allows for commensuration within that level. By establishing the possibility of semi-abstraction and degrees of abstractability and by describing them in the theoretical terms of the Posterior Analytics, I shall have identified the fundamental concepts in Aristotle's theory of relations among subject-genera.

Demarcating the Genus A demonstrative science is constructed out of demonstrative syllogisms. A demonstrative syllogism, in turn, is constructed out of terms that are organized into premisses and a conclusion. The terms of the premisses are related to one another by necessity. In order to explicate the notion of necessity, Aristotle introduces three relationships between terms in a demonstrative syllogism: Demonstration, therefore, is deduction from what is necessary. We must therefore grasp what things and what sort of things demonstrations depend 00. And first let us define what we mean by holding in every case (Kanl 7TaVn:lS') and what by in itself (peT se; Ka8' a;'To) and what by universally (Ka80Aov) . (APo 1.4 73.24-27;

modified Revised Oxford Translation [ROT]) Necessity, then, is explicated in terms of the relations holding in every case, holding in itself, and holding universally. It is not clear from this passage whether each of these relations by itself is a sufficient condition of necessity, or whether they are sufficient only as a group. However, they appear to be arranged in order of increasing stringency and, to some extent, inclusion. We may, therefore, leave at least the holding-in-everycase relation (KarCz. 1TavTo~) safely aside, on the grounds that it is subsumed

16 Aristotle's Theory of the Unity of Science under the other forms of necessity. OUf main interest lies with the in itself

(or per se as I shall refer to it;
demonstrative premisses. But the fourth use of per se, that which belongs to each thing on account of itself (Ilt' aUTO, 73b10-16), clearly involves predication. Aristotle cites as an example death (cinoaau"u ) belonging per se to slaughter (
relevant to predication, all involve definitional relations. Only the fourth case is problematic in this respect, since it has, sometimes been taken to

refer to a causal rather than a definitional relationship. According to the causal interpretation, something dies because it is slaughtered or sacrificed.

1 This list may be compared to Met. 6 .18, which arguably covers all the four kinds of APo 104. For detailed discussions of these relationships, see Ferejohn 1991, 75-130, and McKirahan 1992, 80-102. 2 Aristotle later qualifies this form (1.6 74b8-l 0) by saying that these predicates are opposites. There is some controversy whether so restricted a relation is useful. I agree with McKirahan (1992, 90) that the more general formulation of 1.4 captures the important aspects of this relation.

17 Genus, Abstraction, and Commensurability But since ()(p(hUCTea~ can simply mean 'to be killed,' and since a:7To8av€lV also admits of that meaning, they may be synonyms or close synonyms, and one may be implied in the definition of the other. 3 Moreover, even if 0"&.(w 1I.2 and 3; a1foOzryiO'Kw II, as passive of a1fo/CTdvw). See also Goldin 1996, 1-14, for an overview of some of the problems involved in definitional inclusion. 4 Aristotle adds that /Cae' aim, and VaUTO are the same, and supplies examples (73b26-32): point and straight belong to line /Cae' airr~v (for they belong to it Vline) . McKirahan 1992, 97-8, argues that the VaUTO requirement does nOt add the distinctive feature of universality. This feature is instead described in 73b32-3: 'something holds universally (Ka80>..ov) whenever it is proved of a chance case and primitively.' Although Aristotle does not identify this feature with the Va1iro requirement here, they are identified at 1.5 74a12-13: 'I say a demonstration is of this primitively and as such when it is of it primitively and universally .' It is also Aristotle's practice everywhere to indicate this feature by the V expression. See Mignucci's thorough discussion (1975, 81-4), which attenuates the force of the identification . Barnes 1994, 118-19, argues briefly for the identification.

18 Aristotle's Theory of the Unity of Science virtue of the definition or the account in accordance with the subject's

name (in the language of the Categories, h6yo< KOro. rovvoJ.W.). This is an intensional condition and provides an imr0rtant restriction, since it is not

identical with the extensional condition. For as Aristotle points out (1.5 74al6--17), if there were no other kind of triangle besides isosceles, the 2R predicate would seem to belong to isosceles qua isosceles, because all and only isosceles triangles would have interior angles equal to 2R. But, in fact, it would not, since the definition of isosceles triangle includes having two sides equal, and it is not in virtue of this fact that the 2R predicate holds. The distinctive differentia of isosceles triangle is irrelevant to the predicate. That two of those sides are equal in length is not the part of the definition in yirtue of which 2R holds. As a result, even if 2R, triangle, and isosce les triangle were coextensive with one another, nevertheless 2R

would not belong to isosceles qua isosceles· So far, then, the terms of demoflstrative premisses must be both per se and qua related. But as yet I have made no comment about the relation

between the terms of a demonstrative conclusion. Whereas the terms of a premiss are related by definitional inclusion, the terms of a conclusion are not. For the conclusion is what is proved from the definitions of things. For example, 2R is predicated of triangle as a conclusion, but 2R is not present in the definition of triangle (APo 1.9 76a4-7; Met. Ll..30 1025a30-32). In the strict sense of definitional inclusion, then, 2R cannot be predicated per se of triangle. However, as the same 2R example makes clear, the predicate in the conclusion of a demonstration is predicated qua the subject, and so is commensurately universal with the subject?

5 On this issue I side with Lennox 1987a and McKirahan 1992 against Ferejohn 1991 that the qlfa requirement has an intensional aspect. There are variations on these positions. Ferejohn (70-1; 149n9) claims that qlfa itself is an 'essentially extensional requirement: While he grants that it is not always purely extensional, he claims it is in APo IA. He cites as evidence the bronze isosceles triangle example, which shows that commensurate universals are the only concern. Lennox (92) claims that both per se and qua requirements are intensional. McKirahan (102) agrees, claiming that the qua requirement derives its intensionality from its connection with per se. 6 Compare a similar passage at Met. Z.l1 1036a26-b3 using as an example a bronze circle. Here the abstraction must be made between the circular fonn and the bronze material, rather than between two mathematical fonns. 7 The examples cited by Bonitz 1961 all point in this direction. There are no cases to my knowledge in which 2R is said to be a per se accident of isosceles triangle. Met. 6. .30 1025a30-32 cites 2R predicated of triangle as an example. APo 1.7 75a42-bl strongly suggests that the per sc accidents must be within the same genus as the subject. Most clear is Met. B .2 997a21-22: 'to investigate the per Sf accidents of one subject-genus, starting from one set of beliefs, is the business of one science' (modified

19 Genus, Abstraction, and Commensurability We have a situation, then, in which the tenns of a legitimate scientific proposition are qua related, but not per se related . Aristotle seems to recognize such a class of connections called per se accidents (Ka8' aUTO. rrop./3
the subject:' 2R IPO (per se / qua) having angles around the apex of the triangle = 180· having angles around apex of triangle = 180· IPO (per se / qua) triangle 2R IPO (per se accident / qua) triangle So long as we keep the distinction between premiss and conclusion in

mind, these qualifications to the theory present little difficulty. But there is another form of argument, important for analogy, called an 'application argument,' in which certain tensions arise between the per se and qua criteria. 9 In such an argument a predicate can be proved to belong to the

ROT); explicitly too in the context of qua, Me t. M.3 1078a5-8 (d . PA I.1 639a15-19). Phys. II.2 193b26-32 clearly mentions mixed sciences as dealing with per se accidents. APo 1.22 83bl9-20 comes the closest to extending the formulae to all necessary concomitants, but it is unclear, and even if it does, it seems to connect only a string of genus tenns. 8 Per se accidents (/Cae' aiml OlJf'j3lj3'1Kora) such as 2R predicated of triangle are not under consideration in APo 1.4, where Aristotle is only concerned with immediate connections (73a24-25), which indeed must be either per se or accidental. He is not talking about conclusions, though, admittedly, 2R, which is not an immediate predicate, is discussed in this context. At Met. 6..18 Aristotle seems ·to grant a per se accidental conne(:tion an unqualified per se status: a man is alive per se, because the soul is a part of the man, and in it primarHy is life (1022a31-32). This example, however, is fou nd together with a dear case of per se (2) predication. A stronger claim is made at APo II.4 91al8-21: 'if A belongs to every B in what it is (Ell T~ Ti EOTl), and B is said universally of every C in what it is, necessarily A is said of C in what it is.' The question of the status of per se accidents and how they are to be fit into Aristotle's classification of per se is fraught with difficulty. Tiles 1983, 13-14, and Ferejohn 1991, 123, for example, place th em among per se (4) predicates, on the grounds that they cannOt be placed under per se (1) or (2) fonns, since the per se accident is not de6nitionally included in a direct way with its subject. McKirahan 1992, 169-71, by contrast, argues that conclusions are per se (1) predications, supposing' that definitional inclusion is a transitive feature. He tends to minimize the importance of all per se relations except (1) and (2) (164). 9 For application arguments, see McKirahan 1992, 177-87, who coined the term. Lennox 1987a, 92-3, earlier identified the application argument as Type A (I have modified his fonn somewhat), and the argument proving the predicate universally of the subject-genus as Type B. For an in-depth treatmem of the problem of syllogizing the 2R theorem, see McKirahan 1992, 151-5.

20 Aristotle's Theory of the Unity of Science subject through per se premisses, although it does not belong qua the subject: 2R IPO (per se I qua) having angles around apex of the triangle ~ 180" having angles around apex of triangle ~ 180" IPO (per sel qua) triangle triangle IPO (per se) isosceles triangle 2R IPO isosceles triangle The peculiarity of this demonstration lies in its third premiss. Triangle is predicated of isosceles triangle by the per se (1) connection, since triangle is present in the definition of the isosceles triangle. Indeed, in general, the per se (1) connection admits predicates that extend further than the subject, for example, the genus of the subject. And since other predicates, like the essence and properties of the genus, belong to the genus per se and qua the genus, these also can be proved to belong to its species in the same manner as the example above. 2R clearly belongs necessarily to isosceles triangle in the sense that all isosceles triangles have 2R, but it does not belong to isosceles qua isosceles. Such proofs apply wherever there are invariably concomitant features of a subject whether coextensive or not. Now, Aristotle did not seem to have a name for these kinds of predication. He clearly denies that they are predicates of the subject qua the subject. Nor can they be per se predications in the strict sense, since per se is an immediate definitional relationship. We might, therefore, characterize them as non-coextensive (non-qua) perse accidents. lO As we shall see, they form an important class of predication in th e context of abstraction. A demonstrative science is constructed out of demonstrative syllogisms, and the terms of a demonstrative syllogism are per se and qua related in the manner described above. When the terms of the science are so related, the science is unified with respect to its genus or subject-genus. ll

The subject-genus is the underlying subject matter of a demonstration, that which is identified by the qua expression. It is the subject of which the attributes are proved (APo 1.7 7Sa39- b2), the minor term of the demonstrative syllogism. But it may also be extended to include all those predicates that are immediately predicable of the subject matter per se and universally, and ultimately to all those predicates that can be proved of th e subject qua what it is through immediate premisses, since, as Aristotle 10 Cf. Met. ~.2 1014al-3, where Aristotle says that classes that include (711 7r~Pt£XOV1'o. ) the accidental causes are causes, e.g., animal is the cause of the sta tue, because Polyditus is a man, and man is an animal. 11 For an excellent discussion of the significance of the genus, see McKirahan 1992, 50--63.

21 Genus, Abstraction, and Commensurability says, 'it is necessary for the extreme and the middle terms to come from the same genus' (APo I.7 7SblO-ll). Aristotle explains in more detail·how the identity of a science is determined by the genus: A science (f7TLUT~,U:1J) is one if it is of one genus (EVO~ yivov!O) - of whatever things are composed from the primitives and are parts or attributes of these in themselves (.!Cae' aimi). One science is different from another if their principles depend neither on the same things nor the ones on the others. There is evidence for this when one comes to the non-demonstrables; for these must be in the same genus as the things demonstrated. And there is evidence for this when the things that are proved through them are in the same genus and of a kind. (APo 1.28)

It is an important point made clear in this passage that this sense of 'genus/ the identity condition of a science, is not the same as the sense in which a group is divided into species by differentiae. This' genus' includes a subject, its principles, its parts, and its attributes. Many of these will not be in the same divisionary genus, and will not even be in the same category as the subject itself. Whereas members of a divisionary genus like animal are all similar and share some characteristics, members of a scientific genus are related to one another by per se relations. 12 The terms of a single science, then, all belong in the same genus, because they are related per se and qua the subject. Conversely, terms that are not related per se and qua the subject do not belong in the genus. What is not related per se is incidental (APo 1.4 73b4-S), and since it is impossible to demonstrate anything with incidental premisses, one can only demonstrate with terms from the same genus. Each thing must be proved from its own principles (A Po 1.9 7Sb37-38), and the principles used must be coextensive with the subject. Aristotle repeatedly warns about breaking this rule: what is proved must not be proved of a subject narrower in extension than the predicate: One cannot, therefore, prove anything by crossing from another genus (E~ aAAOV yivovS' flETaj3a.vTa) - e.g. something geometrical by arithmetic ... For this reason one cannot prove by geometry that there is a single science of opposites, nor even

12 For further comments, see McKirahan 1992, 61-2. The senses of the tenn are hardly exclusive, and as Andrew Coles has pointed out to me they are central to two moments of a single inquiry. The first, the divisionary moment in which subjects are connected with attributes at various levels of generality, requires that a genus be divisible into species. After this stage each level becomes a genus-subject of demonstration. See especially Lennox 1987a.

22 Aristotle's Theory of the Unity of Science that two cubes make a cube, nor can one prove by any other science the theorems of a different one, except such as are related to one another that the one is under the other - e.g. optics to geometry and harmonics to arithmetic. Nor can one prove by geometry anything that belongs to lines not as lines and as from their proper principles - e.g. whether the straight line is the most beautiful of lines or whether it is contrarily related to the circumference; for that belongs to them not as their proper genus but as something common. (APa 1.7 75a38-39; 75b12-20)

Aristotle calls this error metabasis. Further elucidation of the problem involved comes later: Since it is evident that one cannot demonstrate anything except from its own principles if what is being proved belongs to it as that thing, understanding is not this - if a thing is proved from what is true and non-demonstrable and immediate . (For one can conduct a proof in this way - as Bryson proved the squaring of the circle.) For such arguments prove in virtue of a common feature which will also belong to something else; that is why the arguments also apply (i.cpapiJ.OTTOvUW) to other things not of the same kind. So you do not understand it as that thing but accidentally. (APa 1.9 75b37-76a2)13

Again, if we use a general proof for a specific subject and suppose that we are proving the attribute of that subject as such, we commit metabasis and prove the attribute only inCidentally. The per se and qua requirements for predicates demand that attributes and proofs be adapted to their appropriate genus (icpap!lOTTEW hr' TO YEVO,) and not cross to another kind (y.,m/3aiv,w Ei, ail.il.o yEVO,). It is clear from the examples Aristotle provides that, practically speaking, metabasis does not usually occur between unrelated genera, since it is unlikely that we would look for principles among irrelevant objects. Instead the danger of metabasis is most acute between closely related genera, like a sub-group and a more extensive genus (e.g., straight lines and beautiful things). Although they are closely related, the sub-group forms a different genus from that of the larger 13 There is a long-standing difficulty with the case of Bryson. Heath (1949, 47-50) discusses the possibilities and despairs of a solution. More recently, Mueller 1982 supports Proclus' interpretation that Aristotle's objection stems from Bryson's not providing a constructive proof to correspond to the intuition that the circle has the same area as a certain polygon intermediate between the i.nscribed and circumscribed polygons. In short, Bryson moved from premisses to conclusion without using the immediate premisses. But it is not clear on this explanation how Bryson then is proving in virtue of a common feature. Mueller admits that this is a weakness in Prod us' interpretation (160-4).

23 Genus, Abstraction, and Commensurability group. The suh-group may be a species of the more extensive genus, as isosceles is a species of triangle, or it may not, as straight lines are beautiful things, but are not species of beauty. In either case the genera must be

kept separate, and metabasis is forbidden. This is not to say that we cannot prove that straight lines are the most

beautiful or that the isosceles triangle has 2R. We can prove that straight lines are the most beautifuL but not qua lines.14 Beauty, even if it is an inva riable concomitant of straight lines, does not belong to lines qua lines nor qua geometrical entities. Beauty belongs to straight lines because they are a particular set of beautiful things. Beauty is common to many other things besides, namely to beautiful things qua beautiful, a genus with its

own principles. In order to prove that straight lines are beautiful, we need an application argument. As we saw, this applies a predicate that is proved of a gen us to a species or instance of that genus. It must have one more premiss than the argument that proves the attribute of the genus qua the

genus. The application argument for straight lines being beautiful might be something like the following: . beauty IPO intelligibility intelligibility IPO symmetry symmetty IPO straight line beauty IPO straight line The first two premisses are sufficient to prove that symmetrica l things

generally are beautiful and the third premiss merely applies the general conclusion to the species. This is a perfectly legitimate proof. But if we tty to prove straight lines beautiful without the intermediaty of symmetty, we shall have committed metabasis. 15 14 The contrary relation of straight line and circumference may be an allusion to DC 1.2 268h17-19, which sta tes that they are the only simple motion s. This, then, will be a physical rather than a geometrical proposition. 15 Aristotle provides an interestingly different analysis of thi s situation at Met. M.3 l 078a31-b5: 'Now since the good and the beautiful are different (for the fonner always implies conduct as its subject, while the beautiful is found also in motionless things), those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a very great deal about them; for if they do not expressly mention them, but prove attributes which are their results or their formulae, it is not true to say that they tell us nothing about them. The chief fonns of beauty are order and symmetry and defin iteness, which the mathematical sciences demonstrate in a special degree. And since these (e .g. order and definiteness) are obviously causes of many things, eVidently these sciences must treat this so rt of cause also (Le. the beautiful) as in some sense a cause.' Mathematics

24 Aristotle's Theory of the Unity of Science Aristotle recognized that errors frequently occur because the appropri-

ate steps of proof are not followed, and this happens when we misidentify the appropriate qua-level for demonstration and produce a mismatch between the subject and the property proved of it. Sometimes these errors occur through carelessness, sometimes because of the difficulty of the problem involved. Aristotle discusses one especially difficult case: And it might seem that proportion alternates for things as (i1) numbers and as lines and as solids and as times - as once it used to be proved separately, though it is possible for it to be proved of all cases by a single demonstration. But because all these things - numbers, lengths, times, solids - do not constitute a single named item and differ in sort from one another, it used to be taken separately. But now it is proved universally; for it did not belong to things as lines or as numbers, but as (n) this which they suppose to belong universally. (APo 1.5 74a17-25)

Aristotle introduces this case as a parallel to the triangle / isosceles-2R case, but one in which there was no obvious universal corresponding to triangle

over the particulars kinds of triangle. Formerly the law of alternating proportion (if A:B::C:D, then AC::B:D) had to be proved separately for each of the species to which it applied, because these species did not appear to constitute a single universal genus. This general kind escaped notice,

Aristotle says, because it did not have a single name. The definitions and proofs for alternating proportionality had to be couched in terms of the specific magnitude, length a or time b or volume c. Because of the lack of a common name the laws of proportionality masqueraded as a problem re-

quiring multiple parallel solutions, though in fact it was a generic problem and required a general solution. For, as Aristotle says, the general proof was subsequently discovered. 16

Aristotle was familiar with the general proof that had been developed by Eudoxus, a friend of Plato and member of the Academy.l7 Subsequently, Euclid incorporated Eudoxus' di?coveries along with the earlier, seems to provide some of the causal material for the science of beauty. It explains why a straight line is symmetrical. Other principles will be necessary to show why symmetry is beautiful, i.e., what symmetry, order, and definiteness have in common, say, intelligibility, which makes them all beautiful. This passage also makes clear that one science may say a lot about another science without being the same as that science. 16 But even for Aristotle the general kind, though constituting a common nature, does not have a general name. By the time Euclid composed the fifth book, however, the general teon JlfYf.8os was in use. 17 For the professional activities of Eudoxus, see Heath 1981, I, 322- 7.

25 Genus, Abstraction, and Commensurability

less-developed work on proportion into two books of the Elements, book V on general magnitude and book VII specifically on number.18 As a result we can compare the general treatment of alternating proportion with one of the specific treatments, and make observations regarding the appropriate per se and qua predications. We find that the error in proving a theorem on the specific level rather than the general is not so clearly an error in this case as it was in the case of 2R proved of isosceles rather than of triangle. This is because there are legitimate proofs both on the general and the specific levels, and as a result the predicate, proportionals alternate, belongs at both qua-levels, though in different ways. This case provides a good introduction to situations in which qua-levels of predicates are not perfectly demarcated. In his introductory definitions to the two books Euclid provides both a general and a specific definition for 'part': V. def. 1: A magnitude is a part of a magnitude, the less of the greater, when it measures the greater. VII. def. 3: A number is a part of a number, the less of the greater, when it measures the greater. The term 'part' is defined in different ways in each case. If we apply Aristotle's language of necessity to these definitions, the terms in the definition are related to the definiendum, part, by the per se (1) relationship. As a result, in V def. 1 a part is magnitudinal, and in VII def. 3 a part is numerical. 19 It is dear, then, that the per se relationships of the general and the specific sciences are different, and although Euclid has preserved for us the specific science governing only discrete quantity, it is easy to see how the definition can be modified to be appropriate for time and so on: A time is a part of a time, the less of the greater, when it measures the greater.

The subject-genus is different in each of the specific sciences, and the terms that enter into the demonstrations concerning the subject-genus

18 See Heath 1956, II, 112-13; Mueller 1970a. For the general proofs of Eudoxus, see Produs, In primum Ellclidis 67, 3- 5: 7rPWTM TWV Ka86.\ov Ka.\ov}J.EvWV 8€wpruuiTwv TO 7J'.\i180S' 'YJU{'YJfT€v.

19 So also V. def. 2: 'The greater is -a multiple of the less when it is measured by the less,' and VII. def. 5: 'The greater number is a multiple of the less when it is measured ·by the less.' Translations from Heath 1956.

26 Aristotle's Theory of the Unity of Science must be defined in a correspondingly restricted way. Since the term 'part' has different definitions, it is ambiguous, and yet the ambiguity is far from random . The meanings of part correspond to one another: the role that a part-number plays in the genus of number corresponds to that of a part-time in the genus of time, and so on. This arrangement in which terms are adapted to a specific subject-genus is comparable to Aristotle's remarks about another class of scientific principles, the axioms: Of the things they use in the demonstrative sciences some are proper to each science and others common - but common by analogy, since things are useful in so far as they bear on the genus under the science. Proper: e.g. that a line is such and such, and straight so and SOi common: e.g. that jf equals are taken from equals, the remainders are equal. But each of these is sufficient in so far as it bears on the genus; for it will produce the same result even if it is not assumed as holding of everything but only for the case of magnitudes - or, for the arithmetician, for numbers. (APo 1.10 76a37-b2)

Comparison with a passage at APo 1.11 77a26-35 shows that the common items discussed here are axioms, one of the three kinds of principles in demonstrations, and that without which no learning is possible (1.2 72aI617). Though these axioms, such as the 'equals taken from equals' axiom, are common to many genera (or common to all genera in the case of the principle of non-contradiction), they are not used in their common form within a specific genus. Instead they are adapted to the genus in which they operate.'o When there is a multiplicity of such adaptations in many different genera, the axioms are analogically the same, since they perform corresponding functions in each genus. The issue is similar in the case of alternating proportion. Each proof is conducted within its own proper genus, but each part of one proof corresponds to that of another. Prior to Eudoxus analogy was the nearest one could come to a general proof among this group of subject matters . The substitution of the appropriate terms in order to adapt the definienda of one specific-genus to another specific genus seems to be fairly trivial. The general science of proportionality, however, accomplishes far more than merely introdUCing a general term that will adequately cover all the specific cases. Eudoxus developed a science that holds good for irrational 20 Ross 1949, 538: 'other {principles are} common, but common in virtue of an analogy, since they are useful just in so far as they faU within the genus studied.' Cf. Met. r .3 1oo5a26--27: 'men use [common axioms} JUSt so far as to satisfy their purposes; that is, as far as the genus whose attributes they are proving extends.'

27 Genus, Abstraction, and Commensurability quantities as well as rational, and in order to accomplish this he had to modify some definitions fundamentally. Take, for example,

V. def. 6: Let magnitudes which have the same ratio be called proportional, where being in the same ratio is defined as V. def. 5: Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order. We are instructed to multiply the first and third quantity by any equal factor, and multiply the second and the fourth quantity by any other equal factor. If the quantities stand in proportion, then, no matter what factors we use, the first and third will always be likewise smaller than, equal to, or larger than the second and the fourth respectively. This definition is expressly formulated in terms of equimultiples in order to overcome the challenge of incommensurability, which arises in the environment of irrational quantities. For this reason the definition requires neither a rational relationship between the first and the second term, and the third and the fourth, nor between the two pairs of magnitudes. Compare this with VII. def. 20: numbers are proportional when the first is the same multiple or the same part, or the same parts of the second that the third is of the fourth, which assumes that all the members of the proportion are commensurable rational numbers. For the single theorem Aristotle is referring to, that if A:B::C:D, then A:C::B:D, Euclid's proofs are parallel in broad outline, both depending on finding some means of measuring the first quantity by the third. They accomplish this in different ways: V. prop. 16, the general proof, uses equimultiples to establish the proportion between A and C, and Band 0, while the theorem for discrete number, VII. prop. 9, can show this more directly, since A is the same part of B that C is of 0 , and wholes with the same number of parts have their parts proportional with their wholes.

28 Aristotle's Theory of the Unity of Science Euclid's presentation tells us a great deal about the relationship between the gene ral and the specific science, but not about the relationship between specific sciences. Unfortunately we are prevented from comparing two special definitions or proofs, because we only have the special science of numbers. But there is nothing in VII prop. 9 that would prevent a simple substitution of number for time, area, and so on, so long as irrational quantities are avoided. This theorem is the same by analogy for all genera of quantity. This passage teaches that the law of alternating proportion appeared at one time to be capable of only analogical proof. In fact, this was never so, it only appeared so. If, however, there had not been the more general genus, magnitude, the legitimate proofs would have been analogical. As it is, the legitimate proof for alternating proportion is to be found at the general level, since alternating proportion belongs to magnitude qua magnitude. This does not, however, make the specific proof, such as we find in Euclid VII, illegitimate, since it is specifically adapted to discrete quantity and depends upon the nature of discrete quantity to make its proof. But it would be illegitimate to prove the general theorem in the context of discrete quantity qua discrete quantity or to prove the specific theorem in the context of magnitude generally. For discrete quantiry, there are now two legitimate proofs for alternating proportion, the original specific proof, and a proof through an application of the general proof. Though Aristotle does not recognize the possibility of two legitimate proofs in the passage from APo 1.5, he does later: Why do proportionals alternate? For the explanation in the cases of lines and of numbers is different - and the same: as lines it is different, as having such and such an increase it is the same . (APo 11.17 99a8-10)

Furthermore, just because one theorem is the same by analogy does not mean that all the theorems in a genus will have analogous proofs in the other ge nera. Most of the definitions in Euclid's two books on proportion are peculiar to their own science. For example, VII. def. 6: I An even number is that which is divisible into two equal parts' is true and relevant only on the supposition that we are dea ling with discrete numbers. It has an analogue neither in the general science nor in the specific sciences of continuous quantity. Likewise VII . prop. 2, 'Given two numbers not prime to one another, to find their greatest common measure,' which depends upon commensurability of quantities, has no analogue in the general science. Eudoxus' discove ry of the general science of proportion did not, therefore, completely eliminate the need for the specific sciences.

29 Genus, Abstraction, and Commensurability Only certain theorems could be proved at the general level. Others still had to be treated specifically. Still others, as we just observed, could be treated both ways. The question 'In what genus is the theorem of alternating proportion proved 7' does not have a single unambiguous answer. Rather it is proved in two genera in two different ways. As a result, numerical proportion, for example, cannot be treated within a single genus, but instead some theorems must be proved in a more general genus, others in a more specific. This is a very frequent occurrence in Aristotelian science as well. Abstraction Confusion in determining the correct qua-level for a demonstration arises most frequently among qua-levels that are related to one another by abstraction (acpatpftTls). We can move from one qua-level to a more general qua-leve l when we abstract certain features of the object under consideration . For example, to move from isosceles triangle to triangle we abstract the general triangular nature and ignore the fact that it has two sides equal. Similarly, from the straight line we may eliminate all of its geometrical nature, including its genus, line, and leave only a necessary accident, its beauty. As this last example makes clear, the process of abstraction occurs not just among the qua-levels of mathematics, but among objects more distantly related as wel l. In fact, Aristotle's most famous application of the process abstracts mathematical entities from their physical substrates: Just as the universal part of mathematics deals not with objects which exist separately, apart from magnitudes and from numbers, but with magnitudes and numbers, not however qua such as to have magnitude or to be divisible, clearly it is possible that there should also be both formulae and demonstrations about sensible magnitudes, not however qua sensible but qua possessed of certain definite qualities. For as there are many formulae about things merely considered as in motion, apart from the essence of each such thing and from their accidents, and as it is not therefore necessary that there should be either something in motion separate· from sensibles, or a separate substance in the se nsibles, so too in the case of moving things there will be formulae and sciences which treat them not qua moving but only qua bodies, or again only qua planes, or only qua lines, or qua divisibles, or qua indivisibles having position, or only qua indivisibles. (Met. M.3 l077b17-30j

According to Aristotle mathematical objects are ontologically dependent on natura l substances. We abstract the quantitative nature of substance and

30 Aristotle's Theory of the Unity of Science

en

treat it as if it were separate XWPLtJ'Tov) from substance, even though it is not (Phys. II .2 193b22-194a12; Met. M.3)21 Although quantity is dependent on substance, we can mentally separate it (Tn VO~
'Since in each genus what belongs to something per se and qua the genus belongs to it necessarily' (modified ROT 1.6 75a28-29), it follows that not only is mathematics a different genus from natural science, but triangle is 21 Aristotelian mathematical theory has recently received a great deal · of attention. See e.g., Mueller 1970b; Annas 1976; Lear 1982; Cleary 1985 and 1995; and Graeser 1987. I take the per se view, that all per se connections to natural substance are ignored or abstracted away from. That the imperfection of natura~ things cannot be at issue in mathematical abstraction is shown by the fact that mathematics provides the causes in mixed sciences, such as optics, and the mathematics in these sciences is laid out in strictly mathematical fonn. 22 So Phys. n.2 193b32-33: 'nor does [the mathematicianI consider the attributes indicated as the attributes of such [narural1 bodies.'

31 Genus, Abstraction, and Commensurability a different genus from isosceles triangle. And since 'a science (E7TlCTT~lq ) is one if it is of one genus' (1.28 87a38), it follows that these genera will also form different sciences. If it seems strange to say that the study of triangles and isosceles triangles are different sciences, we shall have to wait until we can provide a fuller explanation in the context of focality. Aristotle distinguished this conceptual abstraction, in which the abstracted genus maintains no per se relations to its ontological substrate, from the concrete attribute, emblematized by the 'snub: which is defined as curvature in the nose. 23 The name snub (UL,uOV ) contains nose in its definition, and insofar as we are treating snub, nose will always be a per se part of it. We may certainly study snub without the nose, but we shall no longer be studying snub qua snub, but rather snub .qua curved in its abstracted geometrical nature. This same fact can be expressed in another way: once we have abstracted mathematicals from their natural substrate and developed the science of mathematics, we can play the process of abstraction in reverse, and add (7rPOCTTL8EvaL ) the mathematics back into the natural substance. We maYI as it were, add the CUIVe back to the nose in order to get the snub. The contrast is drawn at DC I1I.1 299a13-17, where Aristotle says that mathematics deals with abstracts (Tel E~ a.c/JaLpEIIEw,), physics with concretes (Ta EK 7rpoII8E"EW, ).24 The science of optics for Aristotle is analogous to the snub nose (phys. 11.2 194a7-15). Lines and points, the stuff of geometry, when added to the optical subject matter, become rays and eyes. Similarly with nature in general (194a12-15): Since two sorts of things are called nature, the form and the matter, we must investigate its objects as we would the essence of snubness, that is neither independently of matte r nor in terms of matter only.

23 So also DA 1.1 403a25-b19; Met. E .1 1025b30-1026a6. 24 In fact, the contrast is extended to the barest logical applications in Met. M.2 l077b4-11, according to which white is logically prior to white man, because it is by the addition (EK 7fpou8iufwr) to the white that we speak of the white man. In a dIfferent formulation, Aristotle says (Me t. A.2 982a25-28): 'Those [sciences] which involve few er principles are more exact than those which involve additional principles (b: 7fpo
32 Aristotle's Theory of the Unity of Science The 'snub' serves metonymically to refer to a broad variety of terms that might be called 'embedded: It is the general character of the embedded term that it is a predicate (snub) applied to its subject qua that subject (nose). Some embedded terms are also necessarily (and perhaps per se) related to other, abstract, objects that serve as subject-genera themselves (curved) . The abstract subject-genera are, however, not coextensive with the embedded term or its substrate, and so cannot be included in the science of the embedded term and its subject. 25 In short, there is a tension between the per se requirement of definitional inclusion (for an element in a definition can extend beyond the definiendum) and the qua requirement, which demands coextension. When we abstract from one kind of object we are usually abstracting some named feature common to many other kinds of objects as well. Sometimes, however, the common feature, while having a common name, also has a name peculiar to the specific genus from which it is abstracted. So, for example, in abst racting the geometrical curve from the snub nose, we abstract a feature that is common to many things besides noses. But so long as the curve is in the nose, it goes by the name snub, and until snub is abstracted into curved, it cannot be treated as something common. Only a nose may be snub and only a leg may be bandy. Snub and bandy cannot be treated together in a common science, since they are per se attributes of different subjects: For 'concave' has a general meaning which is the same in the case of a snub nose, and of a bandy leg, but when added, in the one case to nose, in the other to leg, nothing prevents it from meaning different things; for in the fonner cannexion it means snub and in the latter bandy. (SE '31 181b37- 182a2)

It is within this context that Aristotle recognizes one legitimate kind of m etabasis, that between general and specific sciences, in which the principles of a superordinate and abstract science are used to provide a proof in a subordinate and concrete science: If this is not so [if the attribute and middle are not in the same genus as the subject], then the theorems are proved as harmonical theorem s are proved through arithmetic. Such things are proved in the same way, but they differ; for the fact falls under a different science (for the underlying ge nu s is different), but the reason 25 Bahne 1987b, 311, arrives at the same conclusion through a different path, noting that snub is properly a description of nose-flesh in a ce rtain state, rather than a quality abstracted from nose-flesh.

33 Genus, Abstraction, and Commensurability under the higher science under which fall the attributes that belong in themselves. Hence from this too it is evident that one cannot demonstrate anything simpliciter except from its own principles. But the principles of these sciences have the common

feature. (APo 1.9 76a9-15) In this passage, Aristotle discusses the so-called mixed sciences, in which a branch of mathematics and a branch of natural science are mixed together. In other passages Aristotle considers a similar mixing between solid geometry and mechanics, between mathematical and nautical astronomy, and between geome try and optics. 26 In these cases the conclusion of the demonstration, which is the fact to be proved, comes from a natural science, while the reason or cause, the middle term, is located in a mathematical science. Two different genera are operative within the same demonstration and the same science. As such these sciences are different from a simple science like mathematics, in which only one genus is involved. This form of metabasis is important for the present purposes, because the understanding in one genus directly bears on the understanding in an-

other, and there is not the ·tidy separation of genera we find with triangles and isosceles triangles or with mathematicals and natural objects. It is one

of a group of cases I shall consider in which the autonomy of genera becomes weaker and the demarcations less clear. It has been common to characterize these mixed sciences as forms of application argument, in

which the gene ral conclusion proved at a higher, mathematical qua-level is applied to a natural species or instance. On this interpretation the general conclusion can be immediately applied to the specific instance without any

further premisses or explanation. I shall argue, however, that the general attribute cannot be immediately applied to the specific genus, but that this connection itself requires proof, and that the predication of the general attribute requires that some explanatory work be done at a specific level. On this interpretation the mixed science combines explanatory elements

from both subject-genera, rather than merely applying the explanation of one to the other. In order to understand how one science can provide the explanation or reason for a fact that is found in another, we may once again turn

to a comparison of Aristotle and Euclid. To the extent that Euclid provides clarification for points Aristotle is making, we may use him for corroborating evidence. We may start by turning to the proofs for optical phenomena found in his Optics, which at once clarify Aristotle's discussion

26 APo 1.7 75bl4-17; 1.12 77a40-b6; 1.13 78b32-79a16.

34 Aristotle's Theory of the Unity of Science of mixed sciences and raise the further questions I have mentioned. Of course, Euclid's proofs are not arranged as syllogisms, but they start with a statement of a proposition, which corresponds to an Aristotelian fact or conclusion of a syllogism. For example, proposition 23 begins: When any sphere is seen by a single eye it will always be seen as less than a semicircle and that very part which is seen will appear bounded by a circle. 27 The proposition clearly contains optical terms (e.g., eye, seen) and as such belongs in the science of optics. There follows in Euclid's proof the setting out (heECTL'), which ~rovides a bridge from the optical proposition to the geometrical solution. 8 The eye, for example, is hypothesized as a point. Thereafter, the proof (cbr61\"t,,) is conducted purely in geometrical terms, and the conclusion finally relates the geometrical proof to the optical fact. To make the distinction between optics and geometry in a Euclidean proof is fairly straightforward, since they are separated in the stages of the proof. In an Aristotelian demonstration, however, it is much more difficult, since the requirement for immediacy in the premisses is so strict. But we get some clue how this is done by examining Aristotle' 5 treatment of various meteorological phenomena in Mete. 111.2-6 29 He begins his explanation of the shape of a halo in the following way (III.3 372b34--373aS): The visual ray is reflected from the mist that forms round the sun or the moon, and that is why the halo is not seen opposite the sun like the rainbow. Since the reflection takes place in the same way from every point the result is necessarily a circle or a segment of a circle; for if the lines start from the same point and end at the same point and are equal, the points where they form an angle will always lie ' on a circle. 30

As with Euclid there follows a purely geometrical proof: Let ACB and AFB and ADB be lines each of which goes from the point A to the point B and forms an angle. Let the lines AC, AF, AD be equal and those at B -

27 My translation of Hayduck's edition of Euclid. 28 For the ElCeffItS see Heath 1981, I, 370. 29 Lennox 1986 has pointed out the importance of this passage for these issues, and my discussion relies heavily on his. 30 ROT translates oo/tS as 'sight' instead of 'visual ray.' lowe the correction to an anonymous reader.

35 Genus, Abstraction, and Commensurability viz. CB, FB, DB - equal too. Draw the line AEB. Then the triangles are equal; for their base AEB is equal. Draw perpendiculars to AEB from the angles; CE from (, FE from F, DE from D. Then these perpendiculars are equal, being in equal triangles and all in one plane; for they are all at right angles to AEB and meet at the single point E. So if you draw the line it will be a circle and E its centre. (373a6-16)

Aristotle concludes with some principles that allow us to interpret the geometrical proof in optical and natural terms: now B is the sun, A the eye, and the circumference passing through the points CFD the cloud from which the visual ray is reflected to the sun. (373al6-19)

SuperfiCially it is easy to see just what kind of explanation Aristotle has in mind when he says that geometry provides the cause for the optical fact. One common and plausible interpretation argues that in the context of a demonstrative syllogism, the major and middle terms of the demonstration will come from geometry, while the minor term will be optical, and the minor premiss will state that the optical phenomenon falls under the geometrical explanation.31 Consequently, the demonstration will have the same sort of structure as that applying the general 2R theorem to the specific case of the isosceles triangle, an application argument. But isosceles is a species of triangle, and the application of the genus and its properties to the species does not require any further explanation, since the genus-species connection is immediate. By contrast, the connection between optics and geometry is not immediate and requires explanation. 32 I should like to suggest that, because of the presence of embedded terms in the proof, this mixed science cannot be a case of simple application argument. First of all, at Phys. II.2 194al-12 Aristotle clearly places mixed sciences among those that behave like the snub. In this same passage he claims that, 'while geometry investigates natural lines but not qua natural, optics investigates mathematical lines, but qua naturaL not qua mathematical.' The difficulty in setting a determinate qua-level for such demonstrations is illustrated by his contradictory claim that 'neither

31 This is the interpretation given by McKirahan 1978, 201, and Lennox 1986, 48. Lennox 1987a, 94, notes the similarity between 2R-isosceles and mixed science, but rightly does not identify their structure. 32 McKirahan 1992, 178, 184, recognizes that application arguments need not be to species, but does not deal with cases where the application may not be immediate.

36 Aristotle's Theory of the Uniry of Science [optics nor harmonics] considers its objects qua light-ray or qua voice,

but qua lines and numbers' (Met. M.3 1078a14-16). At what qua-level optical phenomena are to be proved is clearly in doubt. By contrast, 2R is clearly proved of isosceles triangle qua triangle. Optics cannot be studied purely qua geometry (i.e., those mathematical proofs that apply to optics), since then we should merely cull proofs from the Elements, and without

adapting their terms in any way, call them optics. No reference could be made to rays or eyes. Obviously, neither Aristotle nor Euclid does this, since this would not make clear how they explain optical phenomena. Alternatively, we might cull proofs from the Elements and briefly apply them to optical instances by identifying, for example, point A as centre of a sphere, B as eye, and so on. Again, neither Aristotle nor Euclid does this, since it would still not be clear what we were trying to prove, namely, why this optical phenomenon exists. Instead, in both authors we begin

with an optical phenomenon to be explained. 33 Optical nature is deeply embedded in the explanation in a way isosceles nature is not embedded

at all in the explanation of 2R. It is clear, then, that optics studies optical phenomena but makes use of geometry in its explanations. How is this the case? We have already seen both the setting out of Optics 23 and the manner in which Aristotle in Mete. III.3 begins his explanations of halos. It is

clear that geometry is not the only explanatory factor in these explanations. Instead, part of the explanation is optical and part is geometrical. In demonstrative form we may represent the explanation for halos as

follows: forming a circle IPO equal lines falling from one point equal lines falling from one point IPO a halo forming a circle IPO a halo But this is not yet a demonstration, since neither premiss is immediate. Between .the major and the middle term we must 'pack' or insert further

geometrical premisses. Equally, between the middle and the minor terms we require packing of premisses containing optical terms in order to explain why optical terms can be described in geometrical terms. These premisses

might be something like the following: 33 Cf. PA 1.1 639b5-10, where Aristotle asks whether the procedure in biology should be similar to that in astronomical mathematics, in which the astronomical mathematician first makes the obselVations and collects the phenomena, and then supplies the cause.

37 Genus, Abstraction, and Commensurability equal equal equal equal

lines falling from a point IPO equal rays falling from a light source rays falling from a light source IPO equal rays falling from the sun rays falling from the sun IPO equal rays reflected by mist to the eye rays reflected by mist to the eye IPO halo.

These premisses will be explanatory of why halos exhibit this particular geometrical nature. We now have an explanation of how these mixed sciences may have

both geometrical and optical explanatory components, and as a result it will not be possible to say that the explanation resides either at the qua-level of geometry or at the qua-level of optics: it resides at both. In a corresponding way we can redescribe Euclid's Optics 23 in a schematic demonstrative fashion: smaller than the diameter IPO circle at the tangent from a point circle at the tangent from a point IPO appearance of sphere from one eye smaller than the diameter !PO appearance of sphere from one eye Again the cone shape of the optical field will serve as a principle to explain the connection between the middle and the minor terms. As Lennox has rightly pointed out, the form of explanation in these 'mixed' sciences differs from the application of 2R to isosceles in that halos are not species or determinate forms of circles. 34 In fact, circle is not

even part of the definition of halo. For this reason, the transference of per se attributes of common features (geometry) to the instance (halo) is not an immediate fact, but itself requires explanation. Aristotle describes the situation in terms of facts and causes, because he is interested in

the reason why the halo takes a circular shape, rather than why it fall s under geometrical analysis at alL Nevertheless, the example illustrates that where the subordinate science is not a species of the superordinate science, the subordinate science makes a genuine and unique contribution to the

understanding of why the major term belongs to the subordinate subject. In proving that halos are circular, we are studying halos qua halos, that is, we are studying what belongs to halos in virtue of their halo nature, but we are proving attributes that extend beyond halos, attributes that are non-coextensive per se accidents. Owing to the inconcinnity between the per se and qua requirements, the distinction between the mathematical

34 1986,41.

38 Aristotle's Theory of the Unity of Science genus of circle and the natural genus of halo cannot be sharply drawn in this case. The mathematical component of mixed sciences is treated as snub, that is, as unabstracted from the natural substrate. But that mathematical component can also be completely abstracted and treated as pure mathematics. Such is the nature of mathematical entities. Other objects are susceptible to abstraction in different ways and lie somewhere in between embeddedness and complete abstraction. These objects [ call 'semi-abstracts.' The degree of abstractability depends on both the subject matter from which the abstraction is made and the abstraction itself. Some abstractions simply cannot be made, in which case demonstration can only proceed within a single genus. Other abstractions can be made but only to the most limited degree; still others, while not complete like mathematical abstractions, for most explanatory purposes leave their concretes behind.'5 A study of these cases is important, because they illustrate the basic principles of scientific unity, focality and analogy. [n the examples we shall now consider we are helped in determining the limits of abstraction by the presence or absence of commensurability. It is a peculiar feature of quantified things that they can be compared as less and greater. 36 This is true, however, only if we are making comparisons within a single genus or subject matter, for instance, one nose may be more snub than another, but a nose cannot be more snub than a leg. So long as the discourse concerns snub and bandy, there can be no com parison and no commensuration between them, 'for things which differ in genus have no way to one another, but are too far distant and are not comparable' (Met. 1.4 1055a6-7). [t is only as abstracted mathematicals, i.e., qua curved, that . they form a single subject, a new genus, and so can be compared. Aristotle makes the same point in the context of the parts of animals: parts of animals in the same genus differ only by more and less (HA 1.1 486a21-23). Such differences are contrarieties of affections or incidental attributes (naerj.uaTa 486b5). Excess or defect of these contrarieties does not affect the essential nature of their substrate, and the per se attributes remain undisturbed by

35 Aristotle's example of snub has an ambiguous status in this scheme. Inasmuch as snub is an accident of nose, it behaves as a predicate of the subject-genus nose. As such, it is completely embedded. But inasmuch as it is emblema tic of fonn in a "matter-fonn compound, it behaves as a semi-abstract, since, like soul and the form of natural objects generally, it can be abstracted to the extent that it forms a subject of discourse with its own per se predicates. 36 Cat. 6 6a19-25 claims that quantities themselves do not admit of the more and the less, i.e., one three cannot be more three than another three.

39 Genus, Abstraction, and Commensurability

changes in the affections. A wing may be longer or shorter without ceasing to be a wing. Commensurability, then, is a mark of genus. Aristotle recognizes degrees of abstractability according to how easily the proposed object can be removed from the per se connections that bind it to its substrate and how easily this new object forms a commensurable genus. Let us consider three cases drawn from a wide range of contexts, which illustrate the varying degrees to which semi-abstracts maintain per se connection with their substrate . 1. Change is impossible to abstract, and so does not even qualify as a semiabstract. What it is to be a change is completely embedded in the specific instance, its primary recipient. One cannot remove change from its per se and qua connections to its substrate. This is indicated by the fact that change is only commensurable within the genus of its substrate, and different kinds of change, such as alteration and locomotion, are incommensurable with each other. 2. The value of manufactured goods is only slightly easier to abstract. Manufactured goods cannot form a single genus, because they perform a great variety of functions. Their value is dependent on their function, and so value is per se and qua related to each specific kind of good. But their exchange value in barter must be commensurable if exchange is to occur. Nevertheless, exchange value, though common, is not conceivable apart from the specific goods to be exchanged. Value is commensurable, but it is dependent upon the specific goods, and cannot be abstracted even conceptually from their manifold specific variety. 3. In the case of animal locomotion there is a series of abstractions that fall short of mathematical completeness, but are more separable than change or exchange value. Because the series of abstractions never leaves the natural domain, each new abstraction remains a hylomorphic compound, but they become increasingly general and increasingly focused upon the form. Accordingly, the abstracts always serve as causes for the substrate, although their per se relations with the substrate become less direct. As the qua-level changes, the basis for commensuration also changes.

1. Speed of Change In one of the more important and searching passages for issues concerning abstraction, Physics VIl.4, Aristotle argues that the forms of change (alteration, locomotion, etc.) must be specifically identical in order to be commensurable. The chapter begins with an aporia: is every change

40 Aristotle's Theory of the Uniry of Science (K,vrycn<)commensurable? Aristotle approaches the problem from the issue of equality, because commensurability depends on the notion of quantitative identiry. He begins with the hypothesis that if a circular and a linear motion are equal, then the circle and line must be the same. Before coming to a definite conclusion on this question, he cites a case of obvious incommensurability: there can clearly be no comparison between

locomotion and alteration, for line and affection would have to be equal and that is impossible, since only quantities can be equal. 37 Aristotle compares such cases to cases of radical homonymy like 'sharp' in wine, pen, and pitch. 38 The term 'quick' as used of linear and circular motion is just a more

subtle form of homonymy, and other terms, like much, equal, and one, are similarly homonymous. Aristotle distinguishes these terms from 'double: which means the same thing when applied to air and water, though air and water are incommensurable. Since it is a term of proportionality, it can be used to mark identical relations without being proper to the genus. Like motion, quick and similar terms are bound per se and universally (qua) to their substrates.

As a result, even if some general formulation of speed of change is possible, there may be homonymy lurking among the variables (249a21-25): So we now have to consider how motion is differentiated; and this discussion serves to show that the genus is not a unity but contains a plurality latent in it and distinct from it, and that some homonymies are far removed from one another, some have a certain likeness, and some are nearly related either generically or analogically, with the result that they seem not to be homonymies though they really are. 39

Again (248b17-19): In fact there are some terms of which even the definitions are homonymous; e.g. if 'much' were defined as 'so much and more', 'so much' would mean something· different in different cases; 'equal' is similarly homonymous; and 'one' again is perhaps inevitably homonymous.

37 Aristotle directly calls on the fact that these changes are not in the same category at Phys. 1Il.1 200b32-201a3. 38 Cf. Top. US l07b13-18: 'See if tenns cannOt be compared as more or less or as in like degree, as is the case (e.g.) with a dear sound and a clear argument, and a sharp £lavour and a sharp sound. For neither are these things said to be dear or sharp in a like degree, nor yet is the one said to be dearer or sharper than the other. Clear, then and sharp are homonymous. For synonyms are always comparable. For they will always hold either in like manner (o,iJ.oiw~), or else in a greater degree (}.diAAOU) in one case.' 39 The analogical relation probably refers to the £onns of change in different categories (e.g., substantial change and alteration), generic relation to different form s of alteration, etc.

41 Genus, Abstraction, and Commensurability The general tenn and definition only appear to be common to the various forms of change. In fact, since they have different per se connections in

each case, they will be ambiguous. The reason for the strict standards on commensurability is the fact

that the affection or kind of change cannot be abstracted from the primary recipient, what the change occurs in. Three elements are present in the

definition of speed of change: the time in which it takes place, the affection, like white or health, and the substrate, like surface or man (249a29-b26). Speed is measured by the amount of the substrate changed to the affection in a certain time: 10 square feet of surface changed to white in 40 seconds. The affection and substrate must be related to one another per se and not incidentally.'" Therefore, the affection and the substrate must both be specifically the same in the cases compared, and equality of amount will be denominated in amount of substrate. Thus the white of dog and the white of horse are commensurable because both dog and horse have surface, and surface, not dog or horse, is the primary recipient of white. The surface becomes the single subject that allows for commensuration, and we are not

comparing dogs and horses. Speed of change is bound by its necessary relations to be treated at the same qua-level as its affection and primary recipient. Because these

things differ from change to change, and change is defined in terms of them, change is necessarily ambiguous, and there is no one definition in accordance with its name. The confusion ari ses because the re is a single

name, change, which suggests that there will be a single definition, and a Single commensurable genus. But, in fact, the re is no abstract change apart

from the specific changes. Therefore, speed of change, too, is unabstractable.

2. Value The concept of value admits of a greater degree of abstraction than change, but remains nevertheless bound to its substrate. Aristotle's discussion of

this subject at Politics 1.9 1257a6ff. is aimed at showing how wealth properly speaking must always be bound to its substrate, property, which fulfils some specific function for its owner: Of everything which we possess there are two uses (XP7jffl:tS'): both belong to the thing as such (KaO' aUTO). but not in the same manner, for one is the proper (oLKEia), and the other is not the proper use of it (OVK OLKEla). For example, a shoe is used for wear, and is used for exchange; both are uses of the shoe. He who gives a shoe

40 Cf. Cat. 6 Sa38-bIO.

42 Aristotle's Theory of the Unity of Science in exchange for money or food to him who wants one, does indeed use the shoe as a shoe (1J7Too~J.lan ii inroolU.l,a), but this is not its proper use, for a shoe is not made to be an object of barter. The same may be said of all possessions, for the art of exchange extends to all of them, and it arises at first from what is natural, from the circumstance that some have too little, others too much. Hence we may infer that retail trade is not a natural part of the art of getting wealth. (1257a6-18;

modified ROT) The first problem is to provide an account for the apparent confusion of terms, according to which a per se (Ka8' aim)) use of an object, one in which the object is used qua that named object, is, however, not proper (olKda). It is clear that the wearer of the shoe is using the shoe as a shoe. But the exchanger is not wearing the shoe; he is instead using it for exchange. This is not the proper use of it, because the shoe was not made for the purpose of exchange. This, however, cannot be the whole story, because nothing prevents the cobbler from making shoes expressly to exchange them. In spite of the confusion in the technical expression, Aristotle's thought seems to be this: 41 there is a natural circumstance in which some have too much and others too little of some natural good (1257al4-17), and this is caused by the practice of the crafts. The cobbler makes shoes. He wears them (a per se and proper use of shoes). But he keeps on making them, because he is a cobbler and cobblers make shoes to be put on feet. But now he has too many, and other people are unshod. In trading his shoes he is treating his shoes qua shoes, and they are achieving their per se use, because they are protecting feet, the reason the cobbler made them in the first place. But in the act of exchange he is also treating them as exchange goods to fulfil his own natural needs other than shoes. This is not the purpose for which they were made (OUK oiKfia), but they serve this purpose because others need them and he needs what they have more of. The exchange comes to an end when everyone has what they need. The shoe can serve as an exchange good precisely because it is being treated as a shoe and is needed as such, for otherwise it would have no exchange value. The retail trader, by contrast, is neither interested in shoeing the world as the cobbler is, nor in fulfilling his natural needs. He buys shoes not .to wear them, but to sell them again at a profit, and since he sells them neither to supply himself with other necessaries nor in accordance with the art of seeing people shod, he is neither using the shoe as a shoe nor using it in one of its two per se uses.

41 lowe this interpretation to Meikle 1995, 68-81.

43 Genus, Abstraction, and Commensurability Natural wealth cannot be abstracted from the specific good and the purpose for which it is intended. That is what makes it natural wealth: the wealth is derived from the inherent purposes of the objects. And even when the shoe is being used for exchange, it is being treated qua shoe, since it is fulfilling a natural need, and this is what gives it value in exchange. The exchange value cannot be abstracted from the natural need. The same object is at one and the same time treated both as a shoe and more generally and abstractly as an exchange good 42 This is as far as one may abstract and still be concerned with natural wealth. Exchange within the context of natural wealth is possible, but Aristotle does not discuss how it occurs in the Politics. We can instead draw on his treatment of rectificatory justice in EN V.5. It is clear from here that some form of equality must be established in order for exchange to take place." But since the goods are of different kinds, absolute equality is impossible. Instead rectificatory justice, like distributive justice, must be expressed by proportional analogy: Now proportionate return is secured by cross-conjunction. Let A be a builder, B a shoemaker, C a house, D a shoe. The builder, then, must get from the shoemaker the latter' s work and must himself give him in return his own . If, then, first there is proportionate equality of goods, and then reciprocal action takes place, the result we mention will be effected ... And this proportional will not be effected unless the goods are somehow equal. All goods must therefore be measured by some one thing, as we said before. Now this unit is in truth need {)(pita) , which holds all things together ... but money has become by convention a sort of representative

of need. (113307-29; modified ROT) Now in truth it is impossible that things differing so much should become commensurate, but with reference to need they may become so sufficiently. There must, then, be a unit, and that fixed by agreement (for which reason it is called money); for it is this that makes all things commensurate, since all things are

measured by money. (1133bl8-23; rnodined ROT) In contrast to distributive justice, in which different people receive different amounts of goods in proportion to the difference in their excellence, 42 Cf. EE VIL13 1246a26-31 for the gruesome example of the eyeball in its proper purpose and in its beitig sold or eaten. 43 Meikle 1995, ch. 1 and 2, has denied that Aristotle provides a positive theory of commensuration in this chapter. He takes 1133b18--20 as a denial of 'epistemic' commensurability. See Judson 1997, 158n21, for an argument contra.

44 Aristotle's Theory of the Unity of Science rectificatory justice depends on each party receiving equal shares. But in

the analogy, housebuilder:cobbler::house:shoe, it is difficult to see just what the relationship between the housebuilder and the cobbler is so that they could have a proportion of one. As Meikle has pointed out, for Aristotle their most natural relationship is mediated through the political art, which situates each craft within the activity of the polis." But that relationship cannot be described by analogy, since, as we shall see, it is the job of the focal relationship. Likewise, because houses are not shoes, a simple commensuration and equation between them is impossible. Yet the relationship

between the cobbler and the housebuilder must be some form of equality for exchange to take place. We might think to express the relationship as follows: the claims of and demands on the cobbler are equivalent to those of the housebuilder. 45 But considering Aristotle's suspicion concerning equal-

ity in the context of change, he is likely to be wary of this formulation, since the demands and claims of the exchanging partners are opposite

to one another (the cobbler claims a house, the housebuilder a pair of shoes). Since need is bound to its object Aristotle puts strong emphasis on the commensurating power of money, which mediates and measures

the goods exchanged. In the Politics Aristotle aids this commensurating power by making exchange a per se use of a good, thereby essentially joining the common function with the specific good. The EN manifests a similar tension. The commonality between goods of exchange is posited

hypothetically (i~ inroe€cr,ws), a matter of convention rather than nature. Need w,ia) as measured by money provides the equation between the craftsmen and between the goods. While there is a natural analogy, housebuilder:house::cobbler:shoe (as artisan is to artefact), this analogy does not express the commonality necessary to effect an exchange. This can only

be achieved when we treat the goods as objects of need:" t

44 Meikle 1995, ch. 4. 45 Judson seems to concur (1997, 168-69): 'the ratio of the strength of their needs for the goods in question .' 46 I am in fundamental disagreement with Meikle's basic views on commensurability. It is the basic thesis of his book that Aristotle's economic theory was not that of neo-c1assical utilitarianism, according to which goods in exchange can be fully commensurated through the 'satisfaction a subject derives from possessing or consuming an object' (38). So intent is he on shOwing that Aristotle viewed goods only in their proper use, that he denies that Aristotle intended a quantitative commensurability at all, declaring 1133h18-20 as an 'unambiguous' denial of commensurability (35-6). The problem with his analysis, as I see it, is that though he is trying to support Aristotle's economics with an Aristotelian 'metaphysics' of substantial ends, he should also have considered Aristotle's theory of science, and especially the role of the universal, the pcr sc, and

t.

45 Genus, Abstraction, and Commensurability Let A be a house, B ten minae, C a bed. A is half of 8, if the house is worth five minae or equal to them, the bed, C, is a tenth of B; it is plain, then, how many

beds are equal to • house, viz. five. (EN V.5 1133b23-26) The analogy now yields to something more common. When the goods are treated as units of value, that is, qua minae, they can be commensurated. But this is not to say that value has been entirely abstracted from the specific goods. There are two ways in which the exchange value remains per se related to the specific goods. First, in the exchange different goods must be exchanged. One does not trade shoes for shoes. 47 Commensuration to the point of absolute identity would destroy the exchange, since housebuilder and cobbler are not trading units of exchange value (minae), but goods they need. The exchange can occur only if the exchange goods are different in kind, but the same in value. Second, the exchange occurs only when the parties are in need (EV xpfi~ 1133b7) of each other's goods. One is in need when one lacks a component of natural wealth. Opportunities for such exchange frequently occur, as the Politics says, because there are naturally circumstances in which one person has too much, another too little of something. In both these ways, then, the value of something in exchange is necessarily related to the specific goods being exchanged and cannot be abstracted from them. But their value is commensurable and therefore abstractable to a greater degree than change. How goods may be incommensurable and commensurable at the same time is suggested in the passage quoted above: 'now in truth, it is impossible that things differing so much should become commensurate, but with reference to need (7I'pOS TTl" xp,iav) they may become so suffiCiently.' It is clear that in their proper uses they are no more commensurable than changes are. But when we treat them as .relative to their xp,ia (which notwithstanding is a per se predicate of them), and this xp,ia holds the exchange together as if it were some one thing (iiv Tl ov 1133b7), xpfia has both a specific nature and a common abstraction, to which he grants only passing mention (54-5) . That manufactured goods have specific purposes and ends does not, as Meikle claims, immediately preclude them from having some common nature as well . There is no need to preserve the 'metaphysics' of purposes at the COSt of making exchange virtually impossible. There was never a con Oiet in the first place. 47 Cf. EN V.5 1133a16-18; EE VII.tO 1243b30-35: 'For how is a cobbler to have dealings with a farmer unless one equates the work of the twO by proportion? So to all whose exchanges are not of the same for the same, proportion is the measure, e.g. if the one complains that he has given wisdom, and the other that he has given money, we must measure first the ratio of wisdom to wealth, and then what has been given for each.'

46 Aristotle's Theory of the Unity of Science nature. 48 Just what that common nature is is not made dear, but Aristotle suggests that it is expressed analogically: as five shoes are in the fulfilment of the house builder' s natural needs, so one house is in the fulfilment of the cobbler's natural needs. The analogical structure allows Aristotle to treat as a limited commonality what must be treated as generically different" And yet there are more abstracted ways of dealing with wealth. Aristotle views retail trade and usury as successive deviations from natural wealth-getting, and as a result he does not recognize them as abstracted subject matters that have a per se existence. Although he does recognize

48 Cf. Judson 1997, 171, for a rather different view: 'Aristotle means that, if one considers "houses and shoes in isolation from human needs, there is simply no fact of the matter as to what a house is worth. This is quite compatible with thinking that there can be such a fact of the matter when houses and shoes are considered as objects whicl;l satisfy human needs.' 49 A similar analogical relationship is discussed at GC II.6 (333a20--34), where Aristotle is criticizing Empedocles for holding that the elements are commensurable and non-transfonnable:

'If it is meant that they [the elementsI are comparable in their amount, all the comparables must possess an identical something whereby they are measu red. If, e.g., one pint of Water yields ten of Air, both are measured by the same unit; and therefore both were from the first an identical something. On the other hand, suppose they are not comparable in their amount in the sense that so much of the one yields so much of the other, but comparable in power of action (a pint of Water, e.g., having a power of cooling equal to that of ten pints of Air); even so, they are in their amount, though not qua amount, but qua having power. Instead of comparing their powers by the measure of their amount, they might be compared as tenns in an analogy: e.g., as x is hot, so Y is white. But "as," though it means equality in quantity, means similarity in quality . Thus it is manifestly absurd that the bodies, though they are not transformable, are comparable not by analogy, but by a measure of their powers; Le. that so much Fire is comparable with many times that amount of Air, as being equally or similarly hot. For the same thing, if it be greater in amount, will, since it belongs to the same kind, ha~e its ratio correspondingly increased.'

If the elements cannot undergo mutual transfonnation, then they can only be compared by analogy. There seem to be tWO kinds of analogy under consideration, one that allows for commensuration by quantification on the basis of measure of power, and one that does not (as x is hot, so Y is white), since there is no similarity of the qualities. Though the elements are not transfonnable, they may still be capable of eHecting some common thing in a similar manner, and on that basis a ratio may be established between the amounts necessary to bring about the similar effect. The commensuration of the elements in question cannot be separated from the elements they are, since we are not trying to commensurate cooling power, but the elements that bring about the cooling. Commensuration through analogy is possible when some common attribute is shared by different subjects, and can be partly abstracted from the subjecrs it is found in.

47 Genus, Abstraction, and Commensurability discrete crafts, like retail sale and usury, governing each, he clearly thinks these crafts are perversions. And yet as a result of the close connections between the crafts of exchange and retail, he says, some people confuse the different forms of wealth-getting (Pol. 1.9 1257b35). Usury is for him the most unnatural form of wealth-getting just because it makes a gain from money itself, rather than from the natural object of wealth (1.10 1258a38-b8). It is unnatural because it has become completely conceptually separated from the only source of value per se, the manufactured good. For Aristotle the subject matter of economics is natural wealth, and other things, like money, may be included in the study to the extent that they are relevant to natural wealth. Money is included because it measures the need for natural wealth and therefore is per se related to natural wealth. But it has no legitimate function apart from its relation to natural wealth. And yet we see how easily usury and even capitalism can be made to fit into Aristotle's scheme of abstraction. We are more inclined today to view usury as part of the art of finance, and would consider it as a more completely abstracted craft. The subject matter of finance is capital and its properties, and these properties are different from those of shoes. Banking is more abstract too in the sense that it gives principles to the manufacturing arts, like those of capital investment or deficit finanCing. But Aristotle did not abstract finance from manufactured goods, because he did not conceive of value abstracted from some fairly primitive natural needs of man. Value maintains its per se connections to the specific genus of good, and a commensurable commonality is attainable only by analogy and the convention of money. 3. Animal Locomotion

In the case of animal locomotion, Aristotle treats a series of subjects related to one another by abstraction as he proceeds from the PA to the lA, MA, and DA. Though these subjects are more abstractable than the arts of wealth-getting, the abstraction is never as great as with mathematics, and the per se connections to less abstract levels are not abandoned: the form, no matter how abstract, is always conceived of as part of a hylomorphic compound, and is always in a causal relationship, however distant, with the lowest concrete object. so The PA studies the parts of animals and their causes. The investigation takes place at a concrete material level, and the treatise supplies reasons

50 See Peck's (1983, 8-10) comments on the organization of the biological treatises.

48 Aristotle's Theory of the Unity of Science for the material nature of the parts. 51 Broadly speaking, these reasons

are couched in terms of function (form) and constraints (matter). The treatise is organized largely part by part starting with the head and moving down, and each greatest genus, like bird and fish, is treated more or less separately. Aristotle does not devote much energy to the instrumental parts of locomotion in the PA, but he does, for example, say that birds have a pair of wings because it is part of their nature to be able to fly (IV .l2 693blO--13) . Wings in their material constitution are commensurable among themselves: rapinous birds have unusually large wings, other birds have smaller wings. As such, they form a genus. Fishes' fins form another genus, commensurable among themselves, but incommensurable with birds' wings. Aristotle explains the differences among wings by reference to the differences in the way of life (/3io<) of the several kinds of birds (693b26-694a12). The fun ction and {3io, are introduced only to the extent that it is necessary to explain the part and its variations. The subject of the treatise, after all, is parts, not functions. Explanations are adapted to the qua-level of the subject-genus, and for this reason a general account of locomotion is not provided, though the ' four-point' theory is used.52 Like the PA , the fA is still concerned with parts and has not abstracted from them; not all parts now, but only those useful for movement in place. These parts are no longer being treated separately according to genus of part and whole animal, but together as a group governed by common principles. 53 At the beginning of the work Aristotle announces that he intends to explain first

why each part is such as it is and to what end [a nimals] possess them, and second, the differences between these parts both in one and the same creature, and again by comparison of the parts of creatures of differen t species with one another. (1 70435-9) 51 Lennox 1987a has done much to clarify the relationship between the PA and the HA. According to him, the HA is a pre-demonstrative historia that collects facts into divisionary groups according to commensurate universals, thus facilitating the process of discovering the middle tenn. The PA begins the work of demon stration with a consideration of the material and final cause. The GA continues with a study of the moving cause. Though these trea tises are distinguished by the causes they treat, there is nothing in the requirement for generic unity that demands their separation. Indeed both causes do belong in the same genus, since the efficient cause is subsumed under and is for the sake of the final cause. 52 Indeed. IA seems to be presupposed by the PA (IV.11 690bl4-16). 53 Cf. PA I.l 639a29-b3: 'Very possibly also there may be othe r characters which, though they present specific differences, yet come under one and the same category. For instance, flying, swimming, walking, creeping, are plainly speCifically distinct, but yet are all fonns of animal progression.'

49 Genus, Abstraction, and Commensurability

The IA is a problem-based inquiry. As in the PA the problems are material, concerned with the instrumental parts, but now at a general level. Certain facts are clear from the HA and this treatise must provide the cause (1 704b9-11 ). The questions concern the number of points of motion (some animals have more, others fewer), the convexity or concavity of limbs, and the way in which the limbs move. The point theory of movement is a common explanatory principle and must account for the different features of various animals taken now as a group. Features of locomotion are still correlated to the broad divisions used in the PA (sanguineous animals move at four points, birds have convex legs, and so on), but since the IA chooses a different basis of comparison from the PA , the various genera of animals become commensurable. Whether the locomotions of animals are commensurable is not a question Aristotle explicitly addresses in the IA. It arises instead at Phys. VilA in the context of determining the commensurable substrate tor change: {Locomotion is specifically differentiated} also accordingly as the instrument of the locomotion is different: thus if feet are the instrument, it is walking, if wings it is flying. Or is that not so? Is locomotion different only according to the shape of the path? (Phys. VII.4 249a17-19)

Aristotle hardly gives an unequivocal answer in this passage, but he clearly leans towards commensurability, instrument of locomotion not making a specific difference. We can say, then, that birds move faster than dogs (as the crow flies). Commensuration is possible, but what is commensurated here is obviously different from what we find in the PA. The genus has changed from wing to locomotion. But in the IA Aristotle is not interested in the quantitative aspects of locomotion, since these problems extend more widely than animal locomotion, and belong in physics rather than biology. At the end of the IA Aristotle claims that after having investigated the parts, we must move to investigating the soul (19 714b20-23).S4 But, in fact, it is clear that the MA, not the DA, is methodologically the next treatise, since it begins with an explicit statement that seems to assume the IA: Elsewhere we have investigated the movement of animal s after their various kinds, the differences between them and th e causes of their particular characters (for some animals fly, some swim, some walk, other move in various other ways); 54 This reference may suggest that the MA was not written at the time of the reference. Cf. Nussbaum 1978, 27.3-4.

50 Aristotle's Theory of the Unity of Science there remains an investigation of the common cause animal movement whatsoever. (1 698al-7)

(ICOW7}S-

alTius) of any sort of

Aristotle shows in the first chapter that there must be a point of rest in the animal that is the origin of motion. In addition there must be something outside it that is absolutely at rest (ch. 2). This is a fact that extends beyond animals even to physics in general, and is treated as useful for the present science. 55 The MA will also consider how the soul moves the body. Accordingly there is a brief discussion of the practical syllogism (7701a7-bl), which provides the psychological part of the answer. The corporeal part of the answer is found in the expansion and contraction of the connatural spirit (a1JJ.'CPVTOV '1TVEvJ.'a) located in the origin of movement (i.e., the soul) which pushes and pulls and thus causes other movements in the instrumental parts. Absent from this common treatment is any mention of the specific kinds of instrumental p~rts. Instead we learn about some common material conditions for movement in general (not just locomotion), the internal and external unmoved, and the joint; and some common formal conditions, desire and the practical syllogism; and that which mediates between formal and material, the connatural spirit. How and in what way the soul is moved is the subject of the DA (MA 6 700b4-6). In the treatment of movement in the DA all material considerations are absent on the grounds that examination of it falls within the province of the functions common to body and soul' (!IUO 433b19-21). Instead the DA asks what part or parts of the soul are responsible for movement. No one faculty by itself is sufficient, Aristotle avers, but appetite initiates the movement and together appetite and thought or imagination suffice. In general. then, the DA merely considers which faculties of the soul are responsible for movement and the nature of the conflict between various desires and faculties. These four treatises, then, are organized in order of increasing generality and formality, away from what is specific and material towards what is common and forma1. 56 Each step in the abstraction provides a I

55 Cf. Nussbaum 1978, 107-14, who argues that the MA is 'a deliberate and fruitful' (113) departure from Aristotle's strictures on metabasis; Kung 1982 correctly replies that this does not constitute metabasis in any usual sense, that it is assimilable to the subordinate-science model. 56 In organizing a subject matter, Aristotle sometimes identifies two levels of principles, the first of which might roughly be characterized as internal to the subject matter, the second as external. Patzig referred to this technique in the context of metaphysics, which he called a 'doppelt paronymische Wissenschaft' (1961, 196). Here all being depends on substance and cannot be separated from substance. Substance is, as it

51 Genus, Abstraction, and Commensurability new genus and qua-level, and new per se predicates. And yet for two reasons abstraction of the mathematical kind is never attained. First, never

does Aristotle suggest that the ·abstraction of the soul faculties from their material substrates can be fully effected in definition. Soul faculties must always be defined as actualities of material potentialities. And yet it is clearly legitimate to consider appetites and imagination separately from the instrumental parts of locomotion in a way it was not appropriate for money to be considered separately from specific exchange goods. Whereas value is always tied to the specific good of exchange, the material conditions of locomotion become increasingly abstracted and generalized from their specific manifestations as Aristotle generalizes the formal components. The increasingly abstract formal sequence, flying, locomotion, motion, desire, is per se and qua related to the increasingly abstract material sequence, wing, limb, joint, potentiality for desire. 57 Second, the more abstract and formal subject matters provide the causes

for the more concrete, and for this reason they remain necessarily connected to the more concrete. The soul provides a principle of animals (DA L1 402a6-7) in several ways, being the formal, final, and moving cause of living things. The instrumental parts are ultimately explained by reference to the faculties of the soul, though they are not the subject of the DA. The examples we have considered in this chapter develop the notion of scientific autonomy. The case of 2R belonging to triangle is the simplest case of 'pure generic autonomy,' in which a per se predicate is proved to belong to a subject qua that subject. Alternating proportion shows that the same predicate can be proved of two subjects of different extension

through generically different causes. This is a case of 'mixed autonomy,' since the proof in each genus is autonomous and independent of the other.

The case of optical proofs and mixed science introduced the notion of the 'mixed genus,' in which two different but related genera were active within

a single proof. The genera are no longer treated as autonomous, but both contribute to the same proof. were, an internal cause. But in addition, god is the first substance and an external cause of all other substances. Similarly, general and internal causes of the organs of locomotion are considered, then the external causes of their motion. For desire and perception are not part of the wing, etc., but instead are present in the heart. So also Met. A.10 1075al4-15: 'For the good [of the army] is in the order and in the leader, and more in the latter: for he does not depend on the order but it depends on him.' 57 Cf. Met. H.3 1043a34-37, which by using the example of animal rather than man or horse, implies that different levels of generality in form imply different levels of generality in matter and composite. See Loux 1991, 163.

52 Aristotle's Theory of the Unity of Science

Speed of change, value, locomotion, and mathematics form a graduated series of sciences, which illustrate the issue of autonomy from a different perspective. Instead of a reduction in autonomy as two genera become fused into 'Jne, this series marks the degrees to which autonomous genera can be abstracted from the mixed genera in which they reside. In different contexts, certain aspects of the natures of things can be more or less abstracted so as to form new subject matters . In the case of speed there is nothing common that can form a subject matter over the various speeds. In the case of mathematics, we can completely abstract the quantitative nature of objects and treat it as if it had no per se connections with its substrate. Since mathematics loses its per se connections to its substrate, it forms a science independent from physics. It genuinely has its own principles and per se attributes. In the case of locomotion, and to a lesser extent value, common features can be abstracted, but not to the extent that they lose all their per se connections to their substrate. Such semi-abstract subject matters do not form wholly independent sciences, even though their subject-genera have different per se and qua relations from those of their substrates. Semi-abstract subject matters are related to the science of their substrate, and are really parts of the science of the substrate. To this extent, as we shall see, they embody the principles of focality. At the same time, in those cases where either abstraction or semiabstraction is possible (value, locomotion, mathematics), related terms exist and function both at concrete and at abstract levels. The concrete term is logically embedded in a specific genus, the wearing of a shoe, the flight of a bird, the sn ubness of a nose. But they are all instances of more abstract terms which are not embedded in the specific genus, though the degree of the abstraction varies in each case: exchange value, locomotion, curve. Where there are two or more terms that embed the same abstract concept in different subject matters, those terms will be considered analogous, as the snub is analogous to the bandy.

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2

Analogy In Aristotle's Biology

Problems with Analogy In this chapter I turn to analogy and its role in Aristotle's biological works. The biological works serve as a good introduction to analogy, since the concept and the term are most frequently and systematically used here l I ·shall first review some of the prominent interpretations of biological analogy, and then provide some observations on its use derived from a thorough examination of the evidence. These observations will form the foundation for a new interpretation, one that fits analogy into the most basic organizational schemes of Aristotle's biology, the genus-species scheme and the r ho!e-parts scheme. This interpretation exploits the t~nsion between the 'per se and qua requirement and shows how this tension operates to bind together discrete genera of objects. The clearest exposition of the role of analogy in biology is provided in the first chapter of the HistoriaAnimalium:

or animals,

some resemble one another in all their parts, while others have parts wherein they differ. Sometimes the pa rts are identical in form, as, for instance, ::me man's nose or eye resembles another man's nose or eye, flesh flesh, and bone bone; and in like manner with a horse, and with all other animals which we reckon to be of one and the same species; for as the whole is to the whole, so each to ~ach are the parts severally. In other cases the parts are identical, save only for a

1 The biological works represent 26 per cent of the Bekker edition. The uses of avclhoyol1 / avahoyia. in these same· works represent 36 per cent of the uses. The other extensive use of the tenn is in the discussion of justice in the ethical works (EN and MM, 12 per cent).

54 Aristotle's Theory of the Unity of Science difference in the way of excess or defect, as is the case in such animals as are of one and the same genus. By 'genus' I mean, for instance, Bird or Fish; for each of these is subject to difference in respect of its genus, and there are many species of fishes and of birds. Among them, most of the parts as a rule exhibit differences through contrariety of properties (TGS Ti;w 7Ta(fryj1.aTwV €VavnwO'Hs-), such as colour and shape, in that some are more and some in a less degree the subject 0'£ the same property; and also in the way of multitude or fewness, magnitude or smallness, in short in the way of excess or defect. Thus in some the texture of the flesh is soft, in others firm; some have a long bill, others a short one; some have abundance of feathers, others have only a small quantity. It happens further that, even in the cases we are considering, some have parts that others have not: for instance, some have spurs and others not, some have crests and others noti but as a general rule, most parts and those that go to make up the bulk of the body are either identical with one another, or differ from one another in the way of contrariety and of excess and defect. For the more and the less lJ,tnAAov KaL 11nov) may be represented as excess and defect. There are some animals whose parts are neither identical in form nor differing in the way of excess or defecti but they are the same only in the way of analogy (KaT' avaAoytav), as, for instance, bone is only analogous to fish-bone, nail to hoof, hand to claw, and scale to featheri for what the feather is in a bird, the scale is in a fish. (HA 1.1 486al4-b22)

Though this system of identity - £lOO~-yEvos-d.vaAoyia - seems intuitively apt for biological phenomena, 2 it present us with two challenges. The first has to do with the meaning of genus in this context. This challenge is .one my account faces because I have treated genus strictly as subjectgenus, while here Aristotle is talking about a divisible genus. The second challenge, the one that has most occupied scholars and will be the starting point for my own interpretation, has been to justify 'more and less' as a consistent demarcation between genus and analogy. The last chapter focused on genus in the sense of subject-genus, which I distinguished from the genus that is divisible into species. In the former context species of a genus are relevant only in application arguments, and their differentiae, that which makes them species, are not considered. Instead, the differentiated species are treated as different subject matters from their divisionary genus. As we saw, the differentiated species (like isosceles triangle), when treated as a subject of demonstration, becomes a

2 See Thompson's (1961) chapter on the theory of transformation, esp. p. 273 .

55 Analogy in Aristotle's Biology subject-genus in its own right. In light of recent research, there is little dispute that the HA and PA make use of such subject-genera. These works are organized according to subject-genera, and Aristotle is seeking coextensive universals to join in demonstration. 3 There remains, however, a great

deal of dispute concerning the technical terms genos and eidos. Eidos is extensively used in the biological works and has been a source of confusion and perplexity. Balme was the first to argue that Aristotle's genus -species system was not a precursor of the Linnaean taxonomic system, and that

Aristotle's use of the terms, outside of what he called the 'programmatic passages' (like the one above) was not consistently taxonomic. In fact,

Balme so despaired of finding a hierarchical use for these terms that he opted for the etymological sense of genos as lineage group and eidos as appearance, and he dismissed as later additions the 'programmatic' passages, in which eidos, genos, and analogia are placed in a clear hierarchy.4 Pellegrin thought that he could discern a consistent order in Aristotle's use. 5 Genus and species were not fixed levels of generality, but were relative to one another. The same group of objects could be considered both as a genus and as a species. The difference was that the genus is divisible into species, and the species are determined by differentiae. Both scholars produced their work before the insights of the Posterior Analytics were widely applied to the biological works, and so, for all the progress in their battle against the taxonomic view, they never completely abandoned the concept of genus as divisible. If, however, we distinguish the use of the term in the HA and the PA, and especially if we distinguish the first book of the PA from the other four books, we find some remarkable results . It is reasonable that we should make this distinction, for, as Lennox has shown, the HA provides the facts of biology, an enumeration of the kinds and sub-kinds of animals together with their coextensive attributes. PA !I-IV takes these facts and provides demonstrations for them. PA I is a treatise on general biological method, and so is different in character from both HA and the rest of the PA. Now, eidos is hardly used at all in PA ll-IV, just six times, and on four of those occasions it clearly does not mean a determinate kind, but, as Salme remarked, means appearance. 6 In two cases it arguably means species, but in neither of these cases is it found in the context of a biological demonstration. Rather, on these

3 See especially the work of Lennox (1987a). 4 Programmatic passages include HA I.1 486al4-b22 (quoted above), 1.2 488b29-32, 1.6

491.14-19, PA 1.4644.16-23, .nd 1.5 645b20-28. 5 Pellegrin 1986a, 1987.

6 665b8; 680.15; 687b6; 692b13.

56 Aristotle's Theory of the Unity of Science occasions Aristotle is introducing discussions of the great kinds, testacea and crustacea, and 50 is recapitulating the findings of the HA? By contrast, genas is widely used in PA II-IV and frequently in demonstrative contexts. In short, genos, as we would expect, is the only term used in the context of demonstration in the PA. When we turn to the HA, we find both terms in fre~uent use. This is to he expected in view of the purpose of that treatise. The HA is pre-demonstrative. Since it establishes genera, divides them into species, and identifies coextensive attributes for both levels, it is natural that in this context we should find extensive use of eide as species into which a genas is divided. This divisionary stage is followed by the demonstrative stage in the PA. We take each group of whatever extensi
57 Analogy in Aristotle's Biology the possibility that analogues share any properties and restrict analogical Similarity to identity of function. This might be called the orthodox, realist, or functionalist position.

A second interpretation, that of the relativists or formalists, holds that species and genus constitute a coherent pair of concepts by themselves to

which analogy has nothing genuine to contribute. David Balme and Pierre Pellegrin are the principal advocates of this view 10 They have emphasized that Aristotle's use of the terms genus and species in the biological works is not the same as the Linnaean, taxonomic use of genus and species, and that Aristotle is not interested in constructing a taxonomy based on fixed levels of generality. For our purposes it is important to note that Balme extended his argument to analogy: since Aristotle frequently claimed that the same groups both differ by more and less and are analogically identical, the distinction between genus and analogy is just as confused as that between species and genus. To cite one of Balme's more difficult examples: 'oo-ToBv and xovopo, are "vaAoyov at P.A. 653b36 ... but differ Tcr P.UAAOV Kat ~TTOV at 655a32.' Moreover, Balme thought - if rather inconsistently -that analogy was wholly dependent on the genera of whole animals, so that any similarity in part or function between animals of different genera, say, birds and fish, was ipso facto an analogue. Pellegrin, by contrast, argued that the biological use of species and genus was consistent with their hierarchical use elsewhere in the corpus: species and genus are only fixed relative to one another, and are tools of analysis that can be applied

of analogy, p. 87). He explicitly calls the more and less a criterion of generic identity (73-4). According to Gotthelf (1985, 48), the distinction between a part and its analogue is precisely one between two parts with (essentially) the same function but which differ in material constitution and structure, and do so by more than 'the more and the less'; d. a similar description in Lennox 1987b, 341n8, who rightly stresses that the function is the same at a very abstract level. Also see Ross 1949, 670. Cf. Nussbaum 1978,83: 'When [Aristotle] so frequently users] the phrase "the x or its analogue" [he is] emphasizing that we are interested in a functional state of the organism, which is realized in some suitable matter or other. An artificial pump might perform the heart's function, whereas a non-functioning heart would be only homonymously a heart.' This position is supported by Cohen 1992, 59, and Charles 1990, 157, who holds that the genera are based on distinctive modes of discharging some function. 10 Balme 1962; also important for issues in this chapter are Balme 1961 and 1987a. Pellegrin 1986a, 88--94. The English edition contains extensive revisions of his section on analogy, and so I omit reference to the original French edition (La Classification des animaJlx chez Aristote: Statllt de fa biologie et unite de l'aristotelisme. [Paris: Les Belles Lemes, 1982]) . For a quick summary of most of the main issues in his book see Pellegrin 1987. Balme 1987a, 79n8, said that he came to agree with Pellegrin on the issue of analogy.

58 Aristotle's Theory of the Unity of Science to groups of objects of any extension. Analogy completes the series by allowing Aristotle to compare man, who forms the standard of biological intelligibility, with other genera on the lower rungs of the scala naturae. In general, the relativists have focused their attention on the relationship between genus and species and as a result tend to trivialize the role of analogy to the extent that it merely recapitulates the function of genus. It simply becomes a higher order of generality than genus and can easily be transformed into a genus if we generalize in the appropriate way. Still a third interpretation has provided a deep 'scientific' reason for demarcating generic from analogical identity. On the grounds that species of a common genus develop out of a common physical matter, some scholars have argued that this matter will provide the criterion of generic identity. According to the embryological interpretation, there is some point

early in their development when all embryos of a genus have a common form which later becomes differentiated into the various specific forms. This common form is the matter for further differentiation, and will be different for each genus. Thus, all and only birds are generated from bird matter, all and only fish from fish matter and so on. If this were true, then generic boundaries could be determined by a thorough study of the embryos. Analogues, then, would be parts that perform the same function, but come from animals of different generic matter. Lloyd, Rorty, and, at one time, Lennox have supported this interpretation,l1 Like the orthodox interpretation it is functionalist, but it grounds generic difference, not in the more and the less, but in facts of embryological development. Like the position of the relativists, it has the consequence of making all transgeneric similarities into analogues. All three positions share the assumption that analogy is an interpretative problem. Aristotle nowhere provides a clear and extended treatment of analogy, and we are forced to piece his theoretical remarks together with his actual practice in order to produce a coherent account. The functionalist interpretation is prima facie most plausible, not least because it is most closely based on the text, but its supporters have done little to defend it against attack. Indeed the major stumbling block to maintaining analogy as a Significant part of the system of identity has been the fact that the distinction befween analogy and the generic 'more and less' simply cannot be maintained without further qualification. For, as has been repeatedly and correctly remarked, analogues frequently differ by more and less in many ways. Though Aristotle does not call them analogues, the beak in

11 Lloyd 1962; Rorty 1973; Lennox 1980, and for his revised position see 1987b.

59 Analogy in Aristotle's Biology birds and the lips and teeth in humans are surely beyond differences of degree, and yet Aristotle transforms one into the other in a remarkable passage (PA II.16 659b23-27): For supposing that one were to cut off a man's lips, unite his upper teeth together, and similarly his under ones, and then were to lengthen out the two separate pieces thus formed, narrowing them on either side - then we should at once have

a bird-like beak. 12 In fact, differences of more and less are pervasive throughout all levels of generality. Within a single species one animal is taller, darker, and thinner than another. And even within an ~ndividual animal variations are found, for instance, in the temperature of blood, the lower parts being cooler than the upper pans (PA IL2 647b29-35). Difference of degree is, therefore, not

sufficient in itself to distinguish generic from any other form of identity. It was precisely by seizing on this problem that the relativists extended their argument. Balme began with the observation that species and genus had no hierarchical sense, and then pointed out that analogues too differed by the more and the less, and so could be treated as belonging to the same genus. The confusion that started with species and genus spread to genus and analogy. It was likewise in response to this problem that the embryologists invoked the material from which organisms develop as the basis for drawing generic lines. For they realized that the 'more and less' could not be trusted as a steadfast criterion, and cast about for a more secure foundation for generic distinctions. The functionalists for their part, since

they deny that analogues are similar, have sidestepped the problem. My own interpretation will attempt to combine the virtues of these three accounts: remaining close to the text and respecting analogy as a significant part of Aristotle's system of difference (as the functionalists do), embracing the more and less of analogues (as the relativists do), and providing a theoretical framework in hylomorphism and qua-levels that will account for the fixity of analogy (as the embryologists do). But before proceeding to that positive step, I shall argue against the relativists that (1) 12 Cf. also Pol. V.3 1302b33-1303a2: 'Political revolutions also spring from a disproportionate increase in any part of the state. For as a body is made up of many members, and every member ought to grow in proportion so that symmetry may be preserved. but it loses its nature ($8f'pfTal) if the foot is four cubits long and the rest of the body two spans; and, should the abnormal increase be one of quality as well as of quantity, it may even take the fonn of another animal; even so a state has many parts, of which some one may often grow imperceptibly; for example, the number of poor in democracies and in constitutional states.'

60 Aristotle's Theory of the Unity of Science they are inconsistent in claiming that analogy is a relative designation, and

that (2) in spite of a couple of difficult cases, the analogues are fixed and do not vary. I also wish to show, against the functionalists, that (3) analogues, in a certain sense, are related by the more and the less, that (4) relative position is of fundamental importance in assigning analogical status, and that (5) identity of function in different matter cannot be a criterion for ana-

logues, because there are analogues of function as well as of parts. Finally, (6) I shall provide some arguments against the genus-as-matter position.

1. Fixity of Analogy In the passage quoted above Aristotle describes analogy as a form of identity in a descending scale together with generic and specific identity. But in one important respect analogy is quite different l3 Whereas whole animals can be specifically and generically identical, analogical identity applies only to the parts of animals14 For analogy depends on two objects being compared as parts of two different systems, in this case whole animals. But inasmuch as Aristotle groups analogy together with specific and generic identity, he invites comparison between them. And to make

them comparable he presents all three kinds of identity in terms of the parts of animals. Indeed in this passage he draws an explicit correlation between parts and wholes and claims that as the parts are to the parts, so the whole is to the whole (486a20-21). But while whole animals can only be specifically or generically identical, parts can be specifically, generically, or analogically identical. Although Aristotle says here that there is a correlation between the levels of analysis, it is by no means perfect. Speaking of generically identical animals, he says, 'as a general rule, most parts and those that go

13 In addition to the three common kinds of difference in animals - specific, generic, and analogical- Aristotle adds several others: position, arrangement, possession/lacking. These are not often included in the standard list because they do not fit logically into that series. They are similar to analogy in that they deal prinCipally with parts rather than wholes. So, for example, in viviparous quadrupeds teats may be found in the breast or dose to the thighs (HA I.1 486b24-487a1). Identity of relative position is almost always a condition for analogical identity. 14 Muskens 1943, 33. There is only one case where Aristotle calls whole animals analogous. At GA 1II.1l 761a24-32, testacea and plants are said to be analogous (T~V 4>ucnu a.uaAoyov iXH) because the nature of testacea is to be in such a relation to water as plants are to earth, as if plants were, so to say, land shell·fish and shell· fish water plants. In this case the analogy is between the organisms and their environment, rather than between pans a~d whole organisms.

61 Analogy in Aristotle's Biology to make up the bulk of the body are either identical with one another, or differ from one another in the way of contrariety and of excess and defect' (HA 1.1 486bl4-16). Among generically identical animals, then, Aristotle says that some of their parts are either the same or differ by excess or defect. Although fewer than fifteen lines before he had said that whole animals are related as their parts are, here he qualifies his previous statement and divides the parts of generically identical animals into three categories, those that are the same, those that are present in some and absent in others, and those, the majority, that differ by more and less. We can envisage cases like the following: among species A,B,C,D of a genus, A and B may have a certain part the same, which C has to a lesser degree and D has not at all.15 Generic attributes that are exactly the same represent the limiting case of more and less, and so long as not all members of the genus share the same attribute to the same extent, the more or less distinction stands, because it holds good for the most part. At either end of the generic scale there will be attributes that are so little distinct between two animals as to be exactly the same, or so much distinct that they are possessed to a negligible degree by some members, and indeed are completely absent from them.'6 Evidence from the text overwhelmingly shows that some parts are more widely distributed than others and that between two animals of the same genus not all their parts need have exactly the same degree of difference. Indeed, this fact can be observed in the organization of the PA, for while the internal parts of blooded animals are treated in common, their external parts are treated separately for each greatest genus (p.€YWTOV yiVD', viviparous quadrupeds, oviparous quadrupeds, birds, fishes). Not only within a genus are some parts more similar than others, some greatest genera simply display a greater degree of internal similarity than others. Aristotle's paradigm cases of genera, birds and fish, have by far most of their parts the same or differing by more and less. This is especially so with birds: The differences of birds compared one with another are differences of magnitude, and of the greater or smaller development of parts. Thus some have long legs, others short legs; some have a broad tongue, others a narrow tongue; and so on with the other parts. There are few of their parts that differ, taking birds by

15 Pellegrin prOVides a similar analysis in 1986b, 151. 16 This is suggested by Met. I.4, where the various fonns of opposition are arranged in an order: contradictories, posseSSion/privation, contrariety, and relatives. The limiting case of contrariety is possession/privation. See Pellegrin 1986a, 59-60.

62 Aristotle's Theory of the Unity of Science themselves. But when birds are compared with other animals the parts present differences of form also (Tfj flOp<j>fj TWV flopiwv). (PA IY.12 692b3-9)

Other genera, like viviparous quadrupeds, do not show this same degree of internal unity. At HA 11.1 497b6-12, Aristotle says that some organs and parts are

common to all animals, and some common only to a particular genus: With regard to animals in general, some parts or organs are common to aU, as has been said, and some are common only to particular genera ... For as a general rule all animals that are generically distinct have the majority of their parts different in form; and some of them they have analogically similar and diverse in genus, while they have others that are alike in genus but specifically diversei and many exist in some animals but not in others. 17

This passage clearly implies that if generically identical species can have parts that are specifically the same, vary by degree, or are missing from some members altogether, some parts of generically distinct animals will be more closely related than others (e.g., the eyes of fish and birds are more closely related than their scales and feathers)'8 Likewise, a part of an animal in one genus may simply not have an analogue in an animal of another genus. For example, cephalopods simply do not have analogues of hair; testacea do not have analogues of lungs. Alternatively, a certain

17 The last part of the passage reads: UXEOOV yap oa-a y' fUTl yivEt Eupa TWV '~WV, Kat TO. 7TAftt1Ta rwv P.fPWV (Xft EUpa Tip dOft, I(al TO. ,!.tEV l(aT' avaAoyiav aOta.cpopa p.Ovov, Tlf yivEt o· EUpa. Til Of T~ yivEt }lfV TaVra r~ f!'Oft 0' fUpa. 18 The passage is nOt without controversy. In comparing it with HA 486al4--b22 quoted above, Balme took issue with those who interpret them together and claim that generically distinct animals have some partS generically distinct, others specifically distinct (1962, 91): 'Thompson, ad loe.: "In the opening sentences, which must be read together with those of Book I. brevity leads to a certain appearance of confusion: we are reminded that a generic difference between two animals carries with it generic difference between certain parts as wdl as specific difference between many others." But the words which I have italicized are nOt in accord with I. 486316f. (above) . yivEt Eupa are, for example, opw~ and 'XOvs (486a21 ). Their pans are to be compared ouu fWEt OUTE KaO' inrfPOX~V I(al (hAEt",'V, ahAa I(ar' ava,).,oyiav ... 0 yap f V opvt8t 7TTfpOV. ToilTO fV ;''X!JVl fO"T ~ hf1Tls. KaTa. ,!.tfv o~v .uDPla a. fXOtXnv (lC.aO"Ta TWIJ (~WIJ. TOVTOV roy rpinrov fUpO. fO"Tll(a~ mimi (486bl8-23). The expression fUpa T
63 Analogy in Aristotle's Biology part shared by animals in two different genera may not be analogically, but generically the same, for example, blood, which is shared by man, viviparous quadrupeds, oviparous quadrupeds, and fish.19 In general, then, the relations of similarity among parts are fixed and primary, and the similarity among whole animals is dependent upon these. Since different parts have different extensions, there may be some ambiguity in assigning identity status to groups of whole animals. Since Balme was concerned with problems of whole animal taxonomy, he tended to devalue the importance of parts in determining identity status. Pellegrin, by contrast, took the parts as primary. When a certain generic part is uncler consideration, he argued, the animals which have that part form a genus, and when a modification or species of that part is under consideration the animals which have that part form a species. It follows that the same animal group may be a species or a genus depending on which part is under consideration. So, considered as an animal having a liver, birds form a species of the genus blooded animals, but as having wings they are a genus. The identity status of whole animals depends on the identity status of parts, and these must be fixed. So, if a group of animals is called a species, it is because the part that these animals have is a species, a determination of a type; if they are called a genus, the part that they have is a genus, a determinable type. To some extent, then, the passages we have discussed corroborate Pellegrin's controversial thesis concerning Aristotle's 'moriology: the claim that the parts of animals are ontologically

19 There is one statement which suggests that analogies are ubiquitous, since all similarities between genera are analogues: TOVTO ~E 7rOLt:tV i1rl1TdCTul au pq.~tDlr TO. yap 'lTo.\M (~a ava..\oyolJ wf:rrov8f:v (PA 1.4 644a22-23). Peck translates: 'It is not easy to do this in all cases, for the corresponding analogous parts of most groups of animals are identical.' This is a rather difficult construal of the text, but he seems to mean that in most animals (Le., between mOSt animals groups, however you take them) the proportional relation is really identity (i.e., not analogy). So, e.g., as wing is to sparrow, so wing is to finch, and the relationship, even if set in analogical form, is really identity. That is why it is. difficult .to find genuine analogies, because most of them are really identities. If this is what Peck has in mind, it strains the meaning of the words. The ROT translation ('It is not easy to do this in all cases; for in most animals what is common is so by analogy'; W. Ogle) makes good sense of the last sentence, but it does not seem to fit the context. The TOVTO 11"Otf:IV almost certainly refers back to the beginning of the chapter, meaning that it is difficult to comprehend two groups into a single kind (so Balme 1972, 121), and since it is difficult, presumably the common lot of men have not done it, and they were right not to do so. The implication of the passage is that it is difficult to find a common nature among distinct groups (animals that breathe do fonn such a common nature). Among such groups analogy is a much more common relation. This passage, then, does not constitute evidence that every transgeneric Similarity is an analogy.

ravTo

64 Aristotle's Theory of the Unity of Science and epistemologically basic and that whole animals, species or genus, are derivative.'o But when Pellegrin discusses analogy, he fails to apply this scheme consistently and ignores the fact that analogy is a relationship that exists between parts only, and not, as species and genus, between both parts and wholes. While he rightly makes the genera of wholes dependent upon their parts, when he treats analogy, he reverses the order of dependency and makes the identity status of parts dependent on whole animals. He cites the example of bone (to which I shall return) in order to show that under one description a group of parts (bone and cartilage) may be considered only analogically identical, while under another they may be generically identical. He claims that there is no simple answer to the question whether bone and cartilage are related analogically or by difference of degree, since the contexts in which Aristotle talks of analogical difference are quite different from those in which he talks of more and less. Inasmuch, he says, as 'we have two genet .bony animals and cartilaginous animals,' there is 'between them an analogical relation,,2l For Pellegrin, the determination 20 I cannot follow him in his argument regarding the use of the tenns genos and ddos outside the programmatic passages for the reasons given at the beginning of the chapter. Here Balme is basically correct: eido5 as used of whole animals very rarely designates the technical 'species,' and the text does not support his claim that gene are ne<:essarily divisible into cide, for suh.groups that are explicitly determinations of more extensive groups are very frequently called gene {to provide just three examples from the HA, which can easily be multipled: HA IV.1 523b27-29, all octopuses have a double row of suckers, save for one genos; IV.8 534b12-15, the remaining gene of animals have been divided into four gene (which is quite impossible on Pellegrin's reading); VI.12 566b12-13, many say that the porpoise is a genos of the dolphins). Throughout his discussion (1986a, 94-106) Pellegrin's interpretations of the text are unconvincing. 21 1986a, 88. I quote the summary from his 1987, 328-9: 'Might one find in the notion of analogy - which does not designate a class of animals - the fixed point which would permit attributing to Aristotle at least the outline of a project of taxonomic construction? What we have seen of this notion with respect to the logical usage of concepts would seem to indicate that the answer must be "no", since analogy is a way of going from one genos to another genos, and genos denotes classes of variable level. Nevertheless one finds in Aristotle a doctrine which, in the biological corpus, opposes analogical difference to difference "according to the more and the less" . .. But in the Aristotelian conception, as we have seen, such a fixing is logically impossible. Thus as I have just said analogy ought to be just as variable as genos. For, from the Aristotelian point of view, it is impossible to say that the analogy feather-scale fixes the genos at the level of "bird" or "fish ", but we must understand that feather and scale can be called analogous as soon as one has decided to take "bird" and "fish" as gene. But if the level called genos changes, which by definition it can do, analogy also changes level. That is shown by a comparison of two passages, noted by Salme, located a few pages apart in the Parts of Animals:

65 Analogy in Aristotle's Biology of genus ' is largely a matter of decision: 'from the moment one decides to take' these groups as genera, parts common to both become analogous?2 But from a different perspective, he says, Aristotle considers the nature and function of skeletons in general, and from this perspective 'bone and cartilage are now two different "species" of material used by nature as "support.'" Pellegrin's comments are brief and not altogether clear.23 He The animals which do not have [boneJ have something analogous: in the fishes, for example, in some there are spines, in others cartilage (11.8 653b35, after P.P.) The nature of cartilage is the same as that of bone, but they differ according to the more and the less. (11.9 655a33, after P.P.) 'Is there between cartilage and bone an analogical difference or a difference of degree? That is not an Aristotelian ques tion. In the first case we have two gene, bony animals and cartilaginous animals, which have between them an analogical relationship; but in the second case the point of view is not the same. Chapter 9 studies the nature and function of the skeleton: from this perspective bone and cartilage are two different "species" of matter employed by nature as "suppOrt" of the body ... Within the genos constituted by "parts" assuring the "support" of flesh, there are variations of degree, particularly according to size and hardness, which relates, among others, to the difference between bone and cartilage. And one may find other examples of these changes in perspective which have the effect of "declassing" the analogical relationship, even if these examples are less explicit from a terminological point of view. Compare two texts : In some animals the parts are not of the same ddos and do not differ by excess and defect, but differ by analogy: that is the case, for example, of bone in relation to spine, of nail in relation to hoof .. . (HA I.l 486b17, after P.P.) We have here an example very close to the doctrine which we found above at PA 644a16 [not quoted here]: that which is nail for genos A, is hoof for genos B. But as in the example given above, the point of view can change: There are some parts which to the touch resemble bone, for example nails, hoofs, claws of lobsters, horns, beaks of birds. All these parts at e possessed by animals for their defense. (PA 11.9 655h2) Although he does not say so explicitly, Aristotle now considers these different parts as

eide of the genos "organs of defense", and from this perspective nail and hoof are no longer analogous. One may even suppose that when a little later Aristotle reminds us that these parts are all composed of earth (655bll), that is a way of saying that they form one genos: 22 1986a, 88: 'A logical examination of the concepts of genos and analogia shows us . that feather and scale can be said to be analogues from the moment one decides to take "bird" and "fish" as gene.' The italics are Pellegrin's. 23 The immediate context of the passage he quotes for this second perspective, PA 11.9 655a32-34, discusses the use of bone and cartilage in the same animal (i.e., in addition to bones, we have cartilage which supports our ears and nose) .

66 Aristotle's Theory of the Unity of Science seems to be aiming at a contrast between the way parts are treated when they are considered as parts of animals of different genera (analogues) and when they are considered as a group of parts that perform the same function (members of a genus). Considered just as flesh support they differ by the more and the less, harder and softer, and as such they are species of a genus. But inasmuch as they discharge the same function in different genera of animals, they are analogically related. Taking another example, Pellegrin claims that the organs made of nail stuff, including teeth, can be considered as species of the genus 'organs of defence,' so making analogous organs fall into a single genus (EVTOlmp ni> YEVEl 655b8). But inasmuch as they appear in different animal genera they are considered analogous. This cannot be right. For while nail, horn, hoof, claw, and bird beak are clearly made of a similar material necessitated by their being defensive organs, Aristotle never says they are all analogues. In fact, only nails, hooves, and claws are.24 For Pellegrin a solution lies ready at hand. It is one of the central theses of his book and later work that the identity status of whole animals depends upon the identity status of their parts. 25 Thus if we decide to take a certain part as a genus, it will logically follow that the animals that have this part will form a genus. This whole edifice falls unless it is based upon the fixed identity status of parts, and for this reason Pellegrin should not have abandoned this principle when dealing with analogy. According to his general argument, Pellegrin should say that bony and cartilaginous animals are placed in different genera only if the parts they have, bone and cartilage, are generically different. He should remain faithful to this general principle and claim that just as genus applies primarily to parts, and derivatively to whole animals, so also analogy applies to parts first and foremost, and is not something that logically follows from a predetermination that ' two groups of whole animals constitute different genera. This position is more in accordance with the spirit of his interpretation and the evidence from the text. So, from the general argument provided by Pellegrin, we can see that the relativists, since they are relativists only in regard to whole animals and not in regard to parts, have no need to insist on the relativity of analogy. Analogues are fixed at the level of parts, a wing just is an

24 Aristotle says (PA II.9 65Sb2-4; HA IILll 517b21-26) that nail etc. are the same as bone with respect to hardness or to the touch, but at HA III.9 517a6-10 he goes $0 far as to say that though these parts do not have the same nature, it is not too far removed from that of cartilage and bone. 25 Pellegrin 1986a, 1987.

67 Analogy in Aristotle's Biology analogue of a fin, hair of scale, and so on. Pellegrin is generally correct about the primacy of parts in determining group affiliation in the HA and the PA. HA I- IV and PA II-IV are, after all, about parts, so it is natural that the animals should be discussed in these terms."

2. Difficult Cases Though the relativists, in order to maintain their basic thesis concerning the primacy of parts over wholes, must"concede that the identity relation

between analogues is absolutely fixed and unchanging, there are several cases in

which the demarcation between analogy and genus seems far from

fixed. For example, the distinction between flesh (TCipt) and its analogue usually follows that between blood and its analogue (PA III.5 668a25-27; HA 1.4 489a23-26). But on one occasion Aristotle divides among blooded animals, and makes the division correspond to bone and fish-spine, thus

making fish-flesh only analogous to other blooded flesh rather than generically identical (HA II1.16 519b26-30). Likewise, there are variant accounts about chests (aTijea,). On the one hand, 'all animals have a part analogous to the chest in man, but not similar to his; for the chest in man is broad, but that of all other animals is narrow. Moreover, no other animal but man has breasts in front; the elephant, certainly, has two breasts, not however in the chest, but near it' (HA I1.1497b33-498a2; d. HA 11.12 503b29-32). The

difference in the arrangement of the elements of the parts and the shape of the whole parts are sufficient in this case to make the parts analogous. Since the breasts are the major component of the chest in man, and this is a major part of what chest is, without the breasts 'chest' can only deSignate a position.27 Alternatively, when all perfect animals are divided in three

parts, the middle is called the chest in the largest animals, and in others it is the analogue Uuv. 2 468a13- 17). In this context, the chest is invoked

26 For good reasons we need not, and should not, follow him in his ontological claim: Aristotle clearly says that the whole individual C!idos is primary (PA I.4644a23-27). Moreover, pans are often the explananda, not the explanantia, and so ultimi'!!ely may not form pan of the definition of the animal. While pans are methodologically the first way of looking at animals, they are not the last or best way. Cf. also G.E.R. Lloyd 1990. 27 Cf. HA I.12 493a12-16, which mentions the breasts as the only component of the chest: 'Next after the neck in the front part is the chest, with a pair of breasts. To each of the breasts is attached a nipple, through which in the case of females the milk percolates; and the breast is soft. Milk is found at times in the male; but with the male the flesh of the breast is tough, with the female it is spongy and porous.'

68 Aristotle's Theory of the Unity of Science as the seat of the nutritive faculty. Thus, the demarcation between chest

and its analogue can be drawn either (i) between man and other animals, or (ii) between big perfect animals and other perfect animals. Again, there are two quite different levels of analogy among wombs. Copulating female insects frequently have a part that is extended into the male, and this is called an analogue of a womb (GA 11.4 739a18-20). In what is obviously a remoter analogy, an eggshell is also called an analogue of the womb (GA 111.2 753b35-754a3). Some analogues even extend beyond animals. Without giving explicit examples Aristotle says that mouths among animals may be analogous (HA 1.2 488b29- 32), but more remotely, the roots of plants are analogous to the mouth in animals (Juv. 1 468a9-12). It is clear from these examples that analogical distinctions can be made

at different levels, and that there is no precise degree of similarity that characterizes analogous parts. As a result, Aristotle is sometimes not clear whether the relationship is

one of analogy or something closer. Urchins have black fonnations attached to the starting point of the teeth. Other animals like tortoises, toads, frogs, and cephalopods have something like this or analogous (rowvrov i) .lv/IAoyov HA IV.S S30b31-33). We may compare this to the case of fish-flesh above, which may be considered either analogously or generically related to the flesh of other blooded animals. These cases present an important challenge to the fiXity of analogy and genus, and suggest that the distinction is universally interchangeable or relative. However, most analogues do not admit of these variations, and there are good reasons why these cases are peculiar. Each part has a definition in accordance with its name (AOYOS- Karel TOVVO/la), and for most parts the essential features of the definition are clear enough. But with some parts, and especially those with nameless analogues, it is often difficult to set a demarcation with exact precision, and sometimes essential features

float in and out of the definition according to the demands of grouping and explanation. So chest may be defined either as the place where breasts are located or as the seat of nutrition. Because named analogues like wing and

fin pick out clearly defined objects, there is never a question whether these are analogues or form a genus. A nameless analogue, however, is invoked

because, though it corresponds to the named part, Aristotle feel s that it is inappropriate to extend that name to it. In these cases the demarcation has not been set by common usage. Without a definite contrast pair, the definition of one member may vary. While this flux in definition is quite marked in the cases of analogues, it is endemic to Aristotle's whole method,

which does not provide full definitions from the outset, but uses partial definitions in an often ad hoc manner.

69 Analogy in Aristotle's Biology 3. Analogues and the More and Less

Having considered the arguments of the relativists we must now turn to the functionalists, and show that analogy involves not only identity of function, but also material and structural similarities. 28 Most commentators have recognized that analogues exhibit material similarities that may be characterized by the more and the less, and this is the source of the problem of analogy. It hardly needs lengthy proof and a few examples will suffice: bone and cartilage, though they are analogues, share the same nature and are related by the more and the less, bone being earthier and harder than cartilage (PA [1.9 655a23-34). Feathers, hair, and scale all arise from the moist material under the skin (GA V.3 783b2-8). Talons and hooves are made of the same basic horny material (PA [1.9 655b2-4). Blood and its analogue have a close material relation: 'The watery part of the blood is serum «xwp), either owing to its not being yet concocted, or owing to its having become corrupted' (PA [1.4 651a1718). Blood is a further concoction of ichor together with fibre, which is added or formed in the concoction, and this fibre aids coagulation in the blood (HA [[[.19 521a17-18; 520b25-26). The blood of the very young is ichor-like (521a32-33). Ichor is at once materially similar to blood and the analogue of blood. As Aristotle says, even among animals in different genera there are common affections (EOT' yap fmQ, 7ra8'r] /cOLVa Kal. TOVTOtSPA 1.4 644al4-16).29 . 4. Analogues and Position

While the material similarities are notorious, the importance of position, the arrangement of a constituent part within a whole, in determining analogues has been underrated. 30 But the importance of. position is not

28 In the following review I have nOt included uses of a1.'Ti or any other looser expression where one part is substituted for another that performs the same function. To do so would immediately prejudice the results in favour of a purely functional interpretation of analogy. I do not assume that Aristotle explicitly used avaAOYov on every appropriate occasion, any more than he explicitly calls every genos YfllOr and so on, but any even-handed study must start from his actual use of the tenn . 29 Among other examples that indicate the material similarity of analogues, we find DA 11.11 423aI2-15: 'For no living body could be constructed o f air or water; it must be something solid. Consequently it must be composed of earth along with these, which is just what flesh and its ana/oglle tend to be.' 30 Richard Owen (1804-92) first drew the distinction between homology (structures differing in function and appearance but deriving from the same part in the 'archetype')

70 Aristotle's Theory of the Uniry of Science surprising, when we consider that the organization of the HA and the PA is largely based on the position of parts within animals. Analogous organs in generically different animals cannot, of course, have identi cal positions,

since the position is always relative to the particular kind, but their positions can correspond. While viviparous quadrupeds have hair, oviparous

quadrupeds have the analogue horny scales: these scales correspond in position (o!,owv XWp'f) with the scales of fishes (PA IV.U 691a16).31 Still, neither similarity of function nor similarity of position is individually a sufficient condition of analogy. For a function may be discharged by a variety of different parts without those parts being called analogous. And though parts may occupy the same relative position, they are not necessarily analogues. Humans have hands (X"P«), and polydactylous animals have paws closely analogous to hands (jJ.a.)"'TTa ava.,\oyov HA [1.1 497bl8-20). For they use their paws for some of the same functions as hands, such as grasping things and defending themselves (PA IV.10 687b28-688a2). Aristotle draws a contrast between them and hooved animals, which explicitly do not have such analogues (PA IV.10 688a2-4). They have forelegs (7rpou$,a) instead of arms (avTl TWV /3paX'ovwv HA II.l 497b18-19). So, even though the forelegs occupy the same relative position, since they do not perform the same function as hands, they cannot be analogues. Conversely, though hooved animals use their back legs for defence (PA IV.lO 688a2), these are not called analogous, because, even though they perform some of the same functions as hands, they are not in the same

relative position. Again, though elephants have a trunk (jJ.VKT~p) instead of a hand, it is never called analogous (HA II.l 497b26-27), in spite of the fact that the elephant uses it as a hand (PA 11.16 658b35-36). Likewise, mouths and teeth are used for defence, but are not called analogous to . hands (PA III.1 661b3-6). By contrast nail (iivvt) and hoof (67r'\~) are analogous (HA I.l486b20). Both are organs of defence (PA 11.9 655b4-5), but this is not sufficient and analogy (structures performing similar functions, but not necessarily derived from the modification of one and the same part in the 'plan' or 'archetype' according to which the 'two animals compared were supposed to be constructed). Aristotle does .not make a distinction between homology and analogy. His examples, however, are usually obvious cases of homology rather than analogy, although they do not involve the notion of archetype. LeBlond mistakenly claims that Aristotle did draw this distinction (1973, 221). Nor is Aristotle concerned with visible fonns of ideal prototypes (contra Thompson 1929, 55; d. Lennox 1980, 327-9). 31 Cf. wings and fins at fA 18 714b3-7.

71 Analogy in Aristotle's Biology to make them analogues for it is clear that they occupy similar relative 1

positions and are made of similar material (655b4-15). Even among internal organs, analogues share relative position in ad~ dition to having similar material constituents . The most frequently men-

tioned are the heart, blood, blood vessel, and flesh and their analogues. Together they form the most basic nutritive and sensitive system of an animal. Heart and its analogue are the principle of nutrition, movement, and sensation; flesh and its analogue are the medium of touch. Blood and its analogue are food for flesh and its analogue, and must be contained in a blood vessel or its analogue. Among these analogues shared function is not the only consideration. The /lUTtS in cephalopods is clearly the analogue of the heart because it occupies the same position (PA IV.5 681b28-30 furl TO aVO,AOrOV Tff KapOiq. TOVTO TO jJ.0PLOV, 017AOL (; T07TOS' (O~TOS' yap f(rnV 0 aUTOS)). 2 The position of the P:UTtS' is not incidental to its

on o·

function: the heart and its analogue occupy the central position of the

body, because they are the sources of control (PA IV.5 681b33-34). Again, the fact that the fluid in the /lUTtS is sweet and has undergone concoction shows that it is the analogue of blood. 33 Likewise, it is necessary that blood and its analogue should be contained in a vessel (PA III.5 667b18- 20). At HA 1.4 489a19-22 Aristotle mentions various similarities between blood (aT/la) and its analogue, ichor (ixwp).34 They are both found throughout the body, and they exhibit various material similarities. But ichor, when present in blooded animals, does not serve the same function as blood. It is only as parts of systems that parts can be analogous. The brain is the only clear case of an inference to the existence of an

analogous organ on the basis of principle without any perceptible evidence of position or material. All animals have sense perception, and since no activity can be continuous, sense perception must occasionally rest, and

this state is called sleep. Although Aristotle cannot say with certainty that all animals sleep, he accounts for those in which sleep is observed, namely all the blooded animals, cephalopods, and insects, and says that if his argument from sensation is persuasive (7HeaVOS'), it will persuade 32 That position plays an important role in analogy was recognized and briefly commented on by Lones (1912, 211): 'It cannot be decided to what extent, if any, Aristotle was thinking of the plan of structure of the parts, when he compared them [by analogy], but it is clear that he was rderring chiefly to their functi ons, positions, and mere external resemblances.' Cf. also Leblond 1945, 41-2. 33 For sweetness of the blood, HA III.19 520bl8-19. 34 Elsewhere he mentions the counterpart of blood without calling it ichor (e.g ., 645b8-10, 648a4-5, 650a34-35). At PA IVA 678a8-9 blood's analogue is said to be without name.

72 Aristotle's Theory of the Unity of Science us that testacea sleep as well, though their sleep is not evident (Somn. 1 454bl4-23). Moreover, he explicitly makes the assumption that the causes of sleep are the same or analogous in blooded and bloodless animals, and are the same in blooded animals as in man (Somn. 2 455b32-33: inroil:rI7TT€ov €ivat TO. aina TOU 1Tci8ovs. ~ ravro'ry TO. Q.vaAoyov TOtS B' €Vai}lOLf!: a.7f'fP TOtS av8pw7ToLS). Nevertheless, he never mentions any features of the analogous parts, except to say that since the bloodless animals lack blood, they have little heat, and so presumably require smaller brain analogues. Aristotle seems more certain in the PA that bloodless animals have an analogue of the brain (PA Il.7 653a10--12). But apart from the octopus he mentions no case of a brain analogue (652b23-25). It is clear that if Aristotle did not see the brains of bloodless animals, then they could hardly be generically related, that is, related by difference of degree. Nevertheless we can assume that, since sleep is caused by the rising vapours of food to the brain, brain analogues will have to be situated in the upper region of rhe body. Thus, while analogues frequently exhibit obvious perceprual similarities, in this case they are assumed on the basis of a principle. Although Aristotle does not discuss how bloodless animals sleep, it is clear from his assumption of a brain analogue that he supposed that the mechanism and position would be much the same as in blooded animals. There are examples of more remote analogies. An eggshell is called an analogue of a womb (GA III.2 753b35-754a5), but even this is not a purely functional analogy. The embryo must be in contact with the mother, and in the case of the egg the mother is in the womb, namely the yolk in the egg. But in spite of the inversion the analogy is partly based on the similarity of structure, since the womb and its analogue, the shell, enclose and protect the embryo. Even the roots of plants, which are the analogue of the mouth, are in the same relative position Uuv. 1468a9-12), since plants are simply upside down (PA IV.IO 686b31-687a1) . The notion of shared relative position is so basic to analogy that Aristotle is willing to view plants as inverted animals to achieve the parallel.

5. Analogy of Function So it is clear that analogues are based on more than shared function. But even the function that analogues share cannot be identical, for there are analogies of functions as well as of parts. Alrhough the passage is neither clear nor consistent, Aristotle at least recognizes that activities (7TpatHS') may be analogically, generically, or specifically identical (PA 1.5 645b20-28):

73 Analogy in Aristotle's Biology We have, then, first to describe the common activities, and those which belong to a genus or to a species. By 'common' I mean those which belong to all animals; by 'to a genus,' those of animals whose differences from one another we see to be matters of degree - Bird is a genus. Man is a species, and 50 is everything not differentiated into subordinate groups. In the first case the common attributes may be called analogous, in the second generic, in the third specific.

If we can assume that Aristotle is talking about activities throughout this passage, then the 'common activities' in the first line is to be glossed by 'analogically,' as he explains in the last sentence. It is strange that he explains commonality in terms of whole animals rather than their activities, but perhaps we can suppose that he has in mind generic bird activities and specific human activities. Elsewhere Aristotle considers the pOSSibility that plants perform an action analogous to sleep (GA V.1 779a2-4). Although he thinks this is a far-fetched analogy, he does not say that functions cannot have analogues. Other passages make the same point more clearly. Along with the activities, the ways of life (f3iOL) and habits (~e~) are said to admit of the same kinds of identity as the parts (HA VII (VIII).l 588a25-31). But little actual use is made of the scheme. Most of the habits seem simply to be shared more and less among various animals. This is because the analysis by activities and habits tends to ignore the instrumental parts, and so the correspondence between the parts on the one hand and the activities and habits on the other becomes less clear, especially with the emotions. The exception is intelligence, which man has primarily and the other animals have analogically. Aristotle draws correspondences between intelligence and material conditions. Art (T'XV~), wisdom (rro<j>ia), and understanding (UVV€ULS-) are peculiar to man, but other animals have analogues. In general, colder and thinner blood is conducive to sensation and intelligence, and the same applies to the analogue of blood in bloodless animals. So bees are intelligent (<j>POVL!'OL) because of the coldness and thinness of their blood analogue (PA 11.2 648a4-8). While it is easy to see how the function of walking is determined by the particular material constitution of the leg, it is much less easy to see how psychological functions like thought and the emotions could have analogues, and for this reason Aristotle rightly leaves this part of his scheme undeveloped. Nevertheless, analogues of function limit the degree to which parts that perform these functions can be the same, and make clear that Aristotle did not intend the functions to serve as higher genera under which the analogues could be species. If functions can be analogues, they cannot be abstracted from the instrument that performs them. Walking,

74 Aristotle's Theory of the Unity of Science for instance, is a function that only legs can perform, and only wings can fly. Since the function of parts cannot be considered separately from those parts, function cannot provide the genus-creating unity that the orthodox account (or Pellegrin) suggests.

6. Genus as Matter Like the functionalist account we just considered the genus-as-matter approach tries to establish a clear demarcation between generic and analogical identity, but it rejects as arbitrary or ad hoc the more and less criterion. Instead it finds an empirical solution in certain facts about embryological development. Aristotle does, in fact, provide some tantalizing hints that embryos develop towards greater articulation and specification from a more common and generic form . But according to the genus-as-matter interpretation there is some point in their development when all embryos of a genus will have a common form that later becomes differentiated into the various specific forms. This common form is the matter for further differentiation, and will be different for each genus. Thus birds are generated from bird matter, fish from fish matter, and so on. If this were true, then generic boundaries could be determined by a thorough study of the embryos. There are two variations on this account, corresponding to two rather different views of division. The first treats the differentiations on the model of Metaphysics Z.12 and successive divisions, for instance, footed, clovenfooted. On this model embryos become successively differentiated from a common genus, and the history of this development can establish those common attributes that are truly generic from those that are analogicaL 35 The second account begins from the system of differentiation laid out in PA 1.2-4. 36 Starting from a group of generic characteristics that all embryos of a genus have in common, each species takes on its specific differences. This account would seem to be more consistent with the basic approach of the biological works. Both accounts, however, face the problem that there is no clear evidence in the GA that Aristotle seriously tried to establish or

A.c. Lloyd (1962) argues for a physical process of differentiation from the genus that he identifies with matter to the ultimate species, identified with fonn. M. Grene (1974) has pointed out difficulties that Lloyd and those who identify matter and genus face. Though there are clearly passages where they are identified (Met. 6..28 1024b6-9; Z.12 1038a3-9; H.6 1045al4-25; 1.8 1058a21-26), it is not dear that matter must mean material substrate. While these kinds of genus may be related by analogy, they are not the same (Grene 1974, 65). 36 Once championed by Lennox: 1987h, 358. Since that time he has repudiated this view, hut it is important to consider it for the lessons it teaches about analogy.

35

75 Analogy in Aristotle's Biology justify his demarcations through an appeal to the facts of embryological development. While Aristotle does discuss the order of development in individual cases, there is no mention of fish matter or bird matter becoming specified, and instead he confines himself to the order in which different parts of an organism develop. He makes use of the basic principle that parts which make other parts (i.e., the heart) must be the first to be formed; parts that are the purpose of the animal (i.e., organs of sensation) are formed second, and finally those parts that are instrumental to the end (e.g., legs, viscera) are formed last (GA II.6 742a18-b17). He addresses his remarks here at a very high level of generality, and he believes that this basic order is a common feature of all animals. He clearly cannot have intended the order of development as a practicable empirical criterion, since he express ly says he has observed the formation of the heart only in blooded animals Uuv. 3 468b28-30), and nowhere does he consider specific differentiations from a generic type. The only suggestive evidence within the biological works is the passage at GA II.6 743b18- 25: The upper half of the body, then, is first marked out in the order of development; as time goes on the lower also reaches its full size in the sanguinea. All the parts are first marked out in their outlines (a7To.vTa. Of TatS 7Tfptypacpa'is OtOpiC€To.t 7TPOT€POV) and acquire later on their colour and softness or hardness, exactly as if nature were a painter producing a work of art, for painters, too, first sketch in the animal with lines and only after that put in the colours.

Though this passage offers some superficial support for the position, the genus that is differentiated here is animal, not one of the greatest genera. Yet it was essential for the argument that it be the matter of the greatest genera that is differentiated, if the matter is to be that which distinguishes the genera. In fact, all of the parts whose development Aristotle describes in this chapter are parts common to all animals, and not generic parts or attributes at all. ROT translates a:rravTa as referring to all the parts, but this passage as a whole is found in a discussion about the formation of homoiomerous parts, and Aristotle is describing the changes that occur in the nutriment to form these parts. It is far more likely then that Q.7TavTa refers to these homoiomerous parts, and this is corroborated by the differences these parts later take on: differences of hardness and colour are associated with flesh, skin, nails, and so on. 37 And homoiomerous parts,

37 Cf. GA Its 741bll-lS, which clearly says as much.

76 Aristotle's Theory of the Unity of Science as we have observed "above,. have only a very loose correspondence to the greatest genera of whole animals. The strongest argument against the genus-as-matter view is that it would entail that all parts of two different genera could only be analogically identical, which seems unlikely in view of the evidence adduced above. When the matter of each genus is what separates the genera from one another and all the parts of each genus are generated out of this matter, analogy can be the only level of identity among parts of animals of different genera. To look to embryological development to solve the problem of generic identity is to ignore more obvious evidence close at hand. The genera of animals are distinguished by their external form. The fact that some animals are internally and externally viviparous, others oviparous or laxviparoll5 simply corroborates most of the other internal and external differences. Not only is the embryological approach implausible, it is contrary to Aristotle's stated method (PA I.1 640a10-19), which begins by taking the phenomena, then goes on to consider how each animal comes to be formed. 38 From such material and efficient causes we can explain and demonstrate the phenomena, but it would be a mistake to suppose that we can use embryological research to establish or justify the demarcations. 39 Although Aristotle did not exploit the physical application of the genus-as-matter approach, the logical formulation, in which, for example, hooked beak is a differentiation of the generic beak, turns out to be very important, since it provides the basis of an order of explanation that distinguishes analogical from generic similarities. Differentiations of a part must be treated together, and different parts must be treated separately. The logical formulation distinguishes these patterns on the basis of the adult form rather than embryological development, and ultimately what

38 A similar point is made by Preus 1983, 344. Preus treats the 'genotypiC' (roughly the account through embryological development) and the 'phenotypic' (common-sense divisions of genera) to be rival methods of classifying animals, rather than two parts of an explanation of phenomena. 39 Compare what Balme (1961, 208) says about the dualiZing animals: 'They are not dismissed as exceptions that prove the rule, nor are they assigned to both sides of a division .. . [T]hey compel a more precise definition of the division ... Their proper grouping is rarely decided, and they seem to be brought into the discussions, not in order to be classified, but in order to bring out sharper distinctions in the differentiae concerned, or more precise statements of the ways in which the differentiae can be combined.' Aristotle's method allows for increased accuracy and finer distinctions, but even in a thoroughly empirical study such as biology, common-sense distinctions must remain more or less intact.

77 Analogy in Aristotle's Biology qualifies as a variation or an entirely different part is a matter of definition

and first principle. The physical and logical formulations of the genus-as-matter interpretation correspond to two different notions of potentiality. Aristotle in the GA traces the development of embryos from menstrual fluid (KaTaI':'Ivia) to the articulated organism. This development involves a transformation of matter and potentiality through the addition of form: Karal''lvia is the matter and potentiality for the formation of homoiomerous parts. The matter and potentiality in this case is a substrate for transformation, and as such is quite different from the kind of genus that is determined by the more and the less. For in the latter case there is no transformation, only a specification of a more general form. This general form is a potentiality, but it is not a potentiality to be transformed as KaTa/J:ryvia is transformed into flesh or skin: a long or short wing is still actually a wing, whereas KaTafJ.1Jvia transformed into flesh is no longer actually KUTuIlTfvia.

A Solution Aristotle, then, recognizes analogy as a legitimate and distinct level of generality based on perceptible similarities as well as functions. The weakness of the functionalist, the relativist, and the genus-as-matter interpretations is their failure to provide a convincing theoretical framework that accommodates these facts. Analogy was not always a part of Aristotle's system of identity and difference. Neither the Categories nor the Topics makes use of it. 40 But in the biological works, as we have seen, it is clearly ·introduced in contrast to the relationship between genus and species. However inadequate the more and less is as a criterion of generic identity, the very fact that Aristotle invokes it shows that he intends the species-genus and the genus-analogy relationships to be different. The relationship between genus and analogy is not intended to be a recapitulation of the relationship between genus and species, and the efforts to make it so, especially to view analogy as a functional genus, silence Aristotle on a point he seems urgent to make. A simple observation about the species-genus-analogy hierarchy may serve as a starting point towards providing a reason for this difference. The species-genus-analogy system (let us call this the SGA system) is a narrow 40 If these works are early and represent a pre.hylomorphic stage of Aristotle's thought, there is good reason, as we shall see below, for the absence of analogy in them.

78 Aristotle's Theory of the Unity of Science and limited system'! Although species, genus, and analogy represent different levels of generality, the hierarchy cannot be expanded upward or downward. We do not find extended divisions of successive genus and species terms as we do with dichotomy. The system of multiple generic differentiae discussed in PA I has done away with that. As a result we find the following sort of SGA string: analogy genus species

wing: bird: :fin: fish wing long wing

The system is limited to three and only three steps, and there is nothing more specific than long wing or more general than the analogy, wing:bird: :fin:fish. It is also a narrow system in the sense that the genus term appears at all three levels of generality. These genus terms are particular denominated parts: wing, blood, hoof, and so on. They form the pivot or centre of the system, and of these there are determinations of 7Tae~fJ.aTa (species) and correspondences (analogues). The parts, which are the cornerstone of the system, are those picked out by common language. What Aristotle says concerning whole animals (PA 1.3 643b10-13) applies equally to the parts: We must attempt to recognize the natural groups, following the indications afforded

by the instincts of mankind, which led them for instance to form the class of Birds and the class of Fishes, each of which groups combines a multitude of differentiae, and is not defined by a single one as in dichotomy.

The common names pick out the appropriate groups, and although birds and fish share some common features, these groups should be separated and variations on the basic type should be taken together (PA 1.4 644a12-23). Importantly, the various great genera of animals are not in turn species of some higher genus like animal, nor are they distinguished among themselves by contraty differentiae of more and less. Instead, birds are defined by the generic differentiae 'having wings: 'having beaks: and so on. The sum of these differentiae provides an autonomous characterization of the genus defined in its own terms rather than by its difference from other genera. Each genus, then, is other than, and not different from, the other genera. The situation is exactly similar with the parts. Aristotle 41 Balme 1962, 88-9, makes this observation in support of his claim that the eidos' and genos are not used in the biological works as they are in the logical works.

79 Analogy in Aristotle's Biology consistently uses common names and maintains the common distinctions

between them. Each part constitutes a genus and is defined by its generic differentiae. Each is autonomous and other than, rather than different from, all others. Since difference operates only within the genus, it follows that one generic part cannot differ from another by more and less. Conversely, a part may differ by more and less only within the determinate limits of the genus. For a wing can be a long wing or a short wing, but it cannot be modified so as to cease to be a wing. The requirement that a part must remain what it is in spite of its modification is reflected in the way Aristotle describes the more and less in the passage from HA 1.1:

they are contraries of affections «vavnw
some flesh is soft, some hard, some things have the bill long, others have it short. Soft, hard, long, short are differentiae of the genus, and yet they are hardly constitutive of the genus. For the 'what-is-it' of flesh or bill is not its hardness or shortness, but its function and so on. Certainly many of the variations are essential features of species of the genus, especially

when they are confirmed by causes (e.g., birds of prey have hooked beaks, because they are rapinous), but at the generic level the variations do not affect the essence of the genus· 3 42 Cf. also for the same idea HA 1.6 491a19 SI.a.r;f>if)E' TWV .7Ta.8-qp.6..WU (vo.unoTl]n. Bonitz's Index cites Met. A.4 985b1D-13: 'And as those who make the underlying substance one generate all other things by its modifications, supposing the rare and the dense to be the sources of the modifications, in the same way these philosophers say the differences in the elements are the causes of all the other qualities' (Ka.6o.'7I'EP oi EV 71'OWVVTES' ~u inroKHllill1Jv oWiw T(~.\Aa TOtS' 71'0.8(o'lV aUrijS' yt'VVWul, TO 1Ul1l0V Kal TO '7I'1JKlIOll D.pXo.<; n8ill€VO~ TWV '7I'a91tJuiTwv). The rare and the dense are not themselves '7I'u8lj,uara, but are the principles or sources of the 1Tu8lj,uura. The 1Ta8~,uara are the great variety of phenomenal qualities that are generat~d from a limited group of apxui.. Most important is the contrast between the U1TOK€tlliv'J] OV(1'LU and the '7I'u8lj,uum. It is the substance and not the 7TO.8lj,uam that is essential and answers to the 'what-is-it.' Peck is surely wrong in identifying these as secondary sex-characteristics (1965, 5 n.(b)). Further evidence for this view of 1Ta8lj,uara comes from Phys. V.2 226a26-29, where modification (d..\Aoiw(nS') is defined as change in respect of quality and as 'alteration in respect of affection.' As Kirwan points out, when Aristotle says at Met. 6. 211022b15- 18 that the '7I'0.80S' (and as Bonitz points out [Index, 554a56-b23], Aristotle's use of 71'&.80S' and 71'a.91t,ua is promiscuous) is a quality in accordance with which a thing is capable of undergOing alteration, he implies that there are qualities in accordance with which a thing is not capable of undergoing alteration, namely essential differentiae (Kirwan 1993, 171). 43 Aristotle mentions 7Ta8lj,uara at the beginning of GA V like blue and dark colour of eyes, high and deep pitch of the voice, colour of feathers and hair, that is, differences

80 Aristotle's Theory of the Unity of Science The SGA system is one of the great organizational hierarchies in the biological works. It is a system of identity and difference dependent upon the genus term, and each genus is autonomous and incommensurable with every other genus. But just because there are no relations of difference between one genus and another does not mean that there are no relations at all between genera. For all these genera are organized in the other great hierarchy, the hierarchy of composition, the whole-parts (WP) system. Aristotle describes this at the beginning of HA 1.1 (486a5-14) and PA Il.1 (646a13-24), and it is clear that it informs the conception and presentation of the biological works. Whole animals, like birds and fish, are constituted from complex parts, like wing, fin, stomach, hand, kidney, and so on. In tum these are made of homoiomerous or simple parts, feather, scale, skin, horn, flesh, bone, etc., which are shaped from stuffs often of the same name, horn, blood vessel, bone, ichor, etc., and these finally arise from the powers or 3vvaJ.'Ets, hot, cold, sticky, brittle, wet, dry, etc.: Whole animals Complex parts

Birds wing

Simple parts

feather

Simple stuffs

horn

Powers

hot

cold

Fish fin

Testacea stomach

scale

flesh

flesh

bone

sticky

brittle

Crustacea

hand tooth

kidney skin

blood wet

dry

To some extent this is an organizational hierarchy of matter and form. Each

item consists of matter from a lower level and is formally detennined by its contribution to a higher level. Nevertheless, it does not distinguish and separate the formal and material components of each part; each level is simply a more highly organized hylomorphic compound. Primarily it is a hierarchical system of biological subjects. Each of the terms provides subjects for biological predicates or serves as a predicate for some other term on the table. At various places in the biological works Aristotle talks about the attributes of blood, kidneys, wings, and birds. These are the entities whose existence must be hypothesized and whose -essence must be defined 4 ' As such, they serve as the first principles of this part of biological science, and this is why they are introduced first in both the HA and the that do not make for differences in species. These 'Iralhjp.am are not species-creatin& because they are not backed by teleological causes (Lennox 1980) . They are 71"a87/p.ara not only with respect to the genus, hut also with respect to the species. 44 These are the hypotheses and definitions discussed in APo 1.2 72a14-24.

81 Analogy in Aristotle's Biology PA. If Aristotle does not expressly posit their existence or provide their definitions, that is not unusual, for as he says at APo 1.10 76b16-19: Nothing, however, prevents some sciences from overlooking some of these things [statement of principles}, - e.g. from not supposing that its genus is, if it is evident that it is (for it is not equally clear that number is and that hot and cold is).

Each of these parts has per se predicates that belong to it qua itself, and each is found in the demonstrations characteristic of the PA. Each of the levels of the table provides definable subjects, and none can be reduced to another: wholes cannot be eliminatively reduced to their component parts.

Moreover, it is dear that Aristotle intended to map the SGA system onto the WP system. He explicitly describes this mapping in HA 1.1 (486al4487a10), where he first discusses the SGA levels of complex parts, then the SGA levels of simple parts: we find species, genus, and analogy at the middle levels of the whole-parts system, the complex and simple parts. We do not find analogy at the level of whole animals for reasons already considered, and we do not find analogues at the level of powers for reasons that will be important below. Since the WP system is a system of composition, not difference, each part is not different from, but other than, all others. They are certainly related to one another, but not by sameness and difference. They are beyond difference, and as such provide grounds for the application of analogy. At the same time, the WP system displays the correspondences typical of analogy. For as we saw, analogy depends on relative position and similarity

of material as well as function, and these are displayed by the WP levels above and below a part. So a feather is a certain simple part of the whole animal bird, just as a scale is of a fish, and they correspond in their relative position in their complex whole. Likewise, they have a similar material origin in horny stuff and moisture, which appear at a lower WP level. The WP system displays the parts of animals as a table of interrelated subjects, and it is the task of the PA to explain these parts and their properties. It is dear from the first lines of HA 1.1 and PA 11.1 that we start from the material composition of the animals, saying first what those parts are, and then why they are the way they are and why animals have them. We start from the common conception, what is familiar to us, the sensible and particular, and work towards the formal. intelligible, and universal. These parts are the subject of our inquiry, and they are, of course, not randomly chosen. They all belong to the same broad type, organic physically isola table components of animals. They would certainly all be found in the same category of existence. But there are good reasons

82 Aristotle's Theory of the Unity of Science why they do not form a genus of the 'programmatic' variety. That system of phenomenal identity and difference would fail to capture their most important essential nature, namely their compositional relationships. If we were to gather generic parts into higher genera based on function we

would immediately upset the compositional WP hierarchy. For lung and gill, for example, do not have identical compositional relations. In the presentation of the HA and PA, Aristotle gives precedence to composition over function. The WP system, organized on the basis of

composition rather than difference, provides the theoretical ground for analogy. The SGA system, as we have seen, is a system of difference, but like the WP system, it is based on material and phenomenal features, as the relationship between species and genus makes clear. As such the SGA system makes a good yoke-mate for the WP system: together they provide an interlocking hierarchical organization of the material nature of animals. But biological nature can be studied from perspectives other than material parts. At a later stage in the investigation, when Aristotle comes to the MA, the PN, and the DA, he chooses new subjects that are more formal, more universal, and less familiar to us, the soul activities, nutrition, sensation, thought, and locomotion 4 S In the DA, for example, matter is considered only to the extent that it is a potentiality for these activities. We see

here a different set of subjects, and as a result a different set of analogies, primarily among the sense organs and their operation.46 We cannot, as

the relativists would have us do, casually form a new genus from the analogues on the basis of the common function those analogues perform. For to do so would be to change the subject of discourse and the qua-level of the science. In the HA and PA the parts are the subjects and each has a definition in accordance with its name. Functions are important, of course, especially in the FA , but they are not subjects, they are middle terms.

Aristotle's method involves a fairly strict division of labour between matter and form." Considering that HA and PA deal with material parts,

45 The investigation begins with what is more familiar to us and moves towards what is more familiar without qualification . The order of the treatises as I have laid them out here does not, therefore, reflect a logical priority. Indeed, Aristotle makes clear (Met . Z.10 1035bl4-22) that the parts of the soul of the animal are prior to the composite and that parts of the body (with the exception of the heart [or brain}) are posterior. This same passage, however, clearly distinguishes the parts of the body from the parts of the soul, and so wa rrants their being treated as different subjects. 46 For example, there is the analogy, sharp I fl at: hearing:: sharp I blunt : touch at DA 11.8 420b1-4; we find the analogy between taste and smell and their sensibilia at II.9 421016-20. 47 See Peck 1983, 9-10, for one interpretation.

83 Analogy in Aristotle's Biology there is little surprise that their species are distinguished by material 'lfa8"Jlam and that analogues should be materially and structurally based. We can also understand why Aristotle studiously avoids any functional description of analogy: analogues are merely proportionally related beyond a difference of degree. There is also no surprise that functions that are treated universally in the VA are discussed as analogous in the PA. For :within the qua-system of commensurate universals that lies at the foundation of demonstration in the PA, the cause must be coextensive with the subject and the attribute. And 'things the same by analogy have their middles the same by analogy' (APo 11.17 99a15-16). Since functions provide the middle terms in the PA, there will be analogues of functions as well.

A Challenging Case Let us return to the case of bone and its analogues, which has been widely cited as an instance of hopeless confusion in Aristotle's use of analogy and

genus just because of the close similarities they exhibit. As we shall see, this case illustrates some of the factors Aristotle had in mind in calling parts analogous: the dependence on definition in accordance with the name and the tendency to choose as analogues parts that are similar in material and relative position.

As we might expect, Aristotle does not always give the same account of what the analogues are. In the APo (11.14 98a20-23) he says that bone (OOTOVV), fish-spine (aKav8a), and pounce (cn)1TWV in cephalopods) are analogous. [n his main treatment of bone in the PA they are bone (OO"TOVV), fish-spine (aKav8a) in some fishes, and cartilage (xovopo<) in other fishes (11.8 653b35-36), and their purpose is the preservation of the soft parts. Later, when dealing with the internal parts of bloodless animals (IV.5 679a21-23), he says that the pounce (cn)mov) is cartilaginous (xovOpWOE<)48 Thus, the representative genera of animals are (1) man and viviparous quadrupeds, (2) oviparous fishes, and (3) either selachia or some cephalopods. Moreover, the correspondence between analogue and greatest genus is not strict. Birds have weak bonesi in small serpents the bones are spinous (aKav8woT/<); in big serpents they are bony; selachia are cartilaginousspined (xovopaKav8a PA 11.9 655a17-28). The flesh support of these animals forms a 'series of graduated changes' (Peck; 1TapaA""TT" KaT" JlLKpOV) as 48 The tn/7Ha are especially earthy, indicated by the earthy ink and the presence in them of the tn/7J'tOU (PA IV.S 679alS-21).

84 Aristotle's Theory of the Unity of Science we move from viviparous quadrupeds through birds, oviparous quadrupeds, fishes, and cephalopods. Moreover, there are variations in the hardness of bones among viviparous quadrupeds and among serpents (PA 11.9

655a12-14; a20-23). Again, the materials are very similar. Bone and cartilage have the

same nature (~ 4>vO'« ~ aVT~) and differ by more and less and for this reason neither continues to grow when cut off (PA 11.9 655a32-34). These analogues also share relative position: they are clearly contrasted with the exoskeletons of crustacea and testacea, which though they discharge the same function are not called analogues, because their relative positions are

different (PA 11.8 653b35-654a19). For all these reasons these analogues are as close as any Aristotle offers and could conceivably be treated as a genus. But at the same time, there are reasons why they are not. Though they share many attributes, they are parts bearing different names, and each has its own definition. At APo 11 .14 (98a20-23) Aristotle says that one may excerpt commonalities according to analogy: ffor you cannot get

one identical thing which pounce and spine and bone should be called.' There is no common term that can be applied to all three kinds of flesh support, But the lack of a common name is merely a sign of the lack of a genuinely common nature. One reason for denying that these parts differ by more and less is the fact that there are sharp discontinuities in the 'series of graduated changes' from small cartilaginous animals to large bony animals. Aristotle clearly does not think that the kinds of flesh support are determined solely as a function of the size of the animal they are found in. Dolphins, for example, which are no larger than many selachia and oviparous fishes, have bone rather than fish-spine (PA 11.9 655a16- 17). Moreover, as corresponding parts of different systems, bone, fish-spine, and cartilage have a claim to autonomous genera. One of the major external

differences between selachia and oviparous fish, and one that marks them off as different genera, is the presence or absence of gill coverings. While fish have them, seIachia do not, since the gill coverings require fish-spine

for their formation, and the selachia have a skeleton invariably made of cartilage-spine (nl oE O'€AO.Xry 71'avTa xovopaKavGa PA IV.13 696b2-6). The difference in material has other effects in their 71'pat
those of selachia are sluggish, since they have neither fish-spine nor sinew (696b6-8). So the case can be made that these flesh supports should be analogous, since they correspond to other major differences as well. Though selachia and oviparous fish share a great number of external parts, Aristotle clearly

85 Analogy in Aristotle's Biology distinguishes them not only by their skeletons but also by their modes of reproduction, skin covering, and gills. This, however, concedes the argument to Pellegrin, that cartilaginous and spiny animals are analogous as soon as we select those groups as genera.

But perhaps a more convincing solution to this difficulty lies in the WP system: simple part

affection power

/

bone

~

harder

softer

hard

/ harder

cartilage

I

~ softer

soft

As Aristotle's description makes clear, the powers are paired in contrary

qualities (PA ILl 646b20-22): 'one part will be soft, another hard, another fluid, another solid,' and so on. As such, in their very nature they are relative and on a scale of more and less. But the simple parts, like bone and cartilage, have different powers, and inasmuch as the powers contribute to the 'what-is-it' of a part, they are essential features of that

part. Aristotle's description in PA 11.1 treats the participation of the power in the generic part as essential. So bone will be essentially (absolutely) hard, blood essentially (absolutely) fluid. But, in addition, each part may differ by contrarieties of affections (n;'v 7Tae'lllaTwV EVaVTLW(Tm). Like the powers, these are contraries, but they are not essentiaL A part may vary more and less in respect of these affections while still maintaining its essential power, which is its nature as that part. Now it often happens that

a part may have the same quality both essentially and non-essentially. There is, for example, an absolute hardness of bone that is necessary for bone to maintain its essential nature and a different hardness that, while

not being essential to bone, makes lions' bone especially hard. While the power is absolute, the affection differs by more and less within the genus. The confusion for bone and cartilage arises because the power, which is necessary and absolute for the simple part and its nature, may be considered

by itself separately from any part 4 ' When it is so considered it is simply a contrary quality admitting of more and less (some parts are hard, some soft, some wet, some dry). For this reason, the statement

bone is harder than cartilage may be taken as ambiguous between 49 Cf. Mary Louise Gill 1997, 154-7, who makes similar observations about flesh based on different levels of organization.

86 Aristotle's Theory of the Unity of Science (1) bone qua bone is a harder form of the same essential nature as cartilage qua cartilage and

(2) bone qua having the power hard is harder than cartilage qua having the power soft. According to Aristotle, (1) is false, (2) is true. By keeping in mind that the various compositional levels of the WP system are causally related but not reducible to one another, we can see why parts may be analogues while exhibiting material similarities to one another.

·Analogy and Abstraction The SGA system of difference based on common names for parts and whole animals is combined with the WP system of composition. Variations within each part are important and revelatory of nature, but differences

based on affections among the parts (e.g., the liver is softer than the heart) do not reveal much of scientific significance. Rather it is the compositional

relations and finally the causal relations among the parts that explain most about their nature. For this reason it seemed most profitable to Aristotle to

limit the study of difference to the generic part, then continue with other forms of relation among the parts. Analogy has a liminal position in this dual system. It is placed within the SGA system of difference, but it is logically dependent on the WP system in a way that neither species nor genus is. The compositional system is not necessary in order to identify the genera and species of parts, but it is necessary in order to identify analogies, since analogies are determined by material and positional factors, and these

are determined within the WP system. This liminal position between the two systems is mirrored by analogy's dual nature. Analogues fall into different genera, because each analogue has its own per se predicates (that is, the predicates contain the term of the analogue in their definition) and these are treated qua that genus. This makes each analogue an autonomous subject, and explains (or at least makes manifest) that they do not fall into a single genus. But there are also reasons why analogues are gathered together as analogues of each other. They have something in common, of which the WP table provides intimations. As I noted above, the WP table is to some extent a table of form and matter, but each component is itself a hylomorphic compound. The table has arranged the parts in such a way as to make the causal relationships among them graspable without explicitly stating them. The lower levels of the table provide part of the material cause for the higher levels. The higher levels point towards the final and formal cause, since position within a whole is an important ' clue to function. The WP table,

87 Analogy in Aristotle's Biology then, is not explicitly causal, but points towards cause. Analogies belong in the WP system for this very reason: their similarities are pointed towards,

but not made explicit. Functions within this system are fully embedded in the parts. Analogues, while not haVing any term in common, point towards a common term. There are two sets of related terms, a proper set, per se and qua related to the special substrates, as snub and bandy are related to nose and leg, and a common set, no longer qua related to the substrates. The two sets are related because the common set is per se predicated of its own particular manifestations (as curved is contained in the definition of snup

and bandy). The common set, then, is abstracted from the proper. Analogy arises in this context, when terms specifically embedded in certain genera are per se re lated to other terms that are more general and therefore at a different and more abstract qua leveL So, for example, wing belongs to bird qua bird; and fin belongs to fish qua fish. Wing and fin have their own peculiar per se and qua relations. The sciences that study these features

are the science of wing and the science of fin, or morely properly the science of bird qua winged and the science of fish qua finned. But wing and fin have per se features in common. They are both instrumental parts for locomotion that have joints and are related to the anterior pair of

the points of motion. These features extend beyond either of the particular genera, and although they may be useful in proofs concerning the particular genera, attributes cannot be proved of the particular genera at

the qua-level that corresponds to these general features. If we want to consider rather than just use the general causes and attributes, we must select a more abstract and general genus, for instance, animals qua jointed or animals qua progressing. Otherwise, to cross between the general and specific genera is to commit metabasis. It is just within the tension between the per se and the qua requirements that analogy operates. Analogues are of different and autonomous genera in virtue of the qua requirement, but are treated together in virtue of their common per se relation. As we move from lower to higher subject-genus we are not moving up a genus-specie.s chain. It is clear from the series wing, joint, heart, desire that the more abstract entity is not the genus of the less abstract. A joint is not what a wing and fin are, and even less is a heart what a joint is. But each more abstract term is in one way or another a cause for the more concrete tenn , and each is per se, but not qua, related to the subject before

it in the series. Each, therefore, forms a different but related subject, partly abstracted from its predecessor. Analogues exist in this no man's land between the level of lower and strictly autonomous genera and a higher common genus. This no man's

3 Analogy and Demonstration

While the relationship between the SGA and the WP systems seems to account for the phenomenal demarcation of analogy from other forms of identity, the place of analogy in demonstration is more difficult to account for. There are clear indications in the Posterior Analytics that analogy plays a distinctive role in demonstration, but just what that role is, and whether

and how it is worked out in the biological writings is far from clear. Part of the difficulty lies in the fact that analogy was not a central interest to Aristotle when composing the APo. In fact, of the three passages in which analogy in the appropriate sense is discussed, all seem to have the status and importance of footnotes to major discussions. Moreover, the passages do

not all point in the same direction. Some suggest that analogy is manifested in a distinctive form of demonstration, others seem to present analogues as specific instances to which general principles and causes are applied. The same difficulty, too, arises in Aristotle's analogical demonstrations in

the biological works. We often find distinctively analogical demonstrations, but more frequently general explanations seem to be applied universally to several analogues.

As we saw, the underlying genera of the PA are whole animals and their parts, each with its own definition in accordance with its name. We

can now fill in some details from the Analytics 1 APo 1.4-10 discusses demonstration in terms of the most stringent conditions, demonstrative

syllogisms in Barbara, where all the terms are related per se and qua the subject. Proofs that fall short d this are incidental. Now the predicates of animals and their parts apply at various levels of generality. Some 1 For more elaborate attempts to organize single.genu s biological proofs on the APo model see Gotthelf 1997 and Dete11997.

90 Aristotle's Theory of the Unity of Science predicates belong to a part qua that part, or to a species qua that species, while other predicates will belong qua something more common. If we use a specific part as a subject of demonstration, then attributes and middles must belong qua the part, that is, they must be in the same genus as the part (1.7 75blO-ll). Predicates that belong commonly must have a common subject, and belong qua something common. These common subjects will be different from the specific subjects and will form different genera, subjects of different sciences. If we try to prove something of one subject through the per se predicates of a different subject, we will commit metabasis. An example of a final-causal syllogism will help us to explicate some of these relations: wing IPO flier flier IPO bird therefore, wing IPO bird We learn that being a flier is in the oVlIia of a bird, and therefore it will appear in the account of its essence (PA IV.12 693bl3-l4). The relationship between having a wing and being a flier is one of hypothetical necessity: if something is to fly, it must have wings. We may express this hypothetical necessity through definitional inclusion in the following way: wing is predicated of flier because in the definition of wing we find the term flier (or a paronym thereof), since a wing is by definition an instrumental part for flying. In the conclusion that birds have wings, wing will be a per se accident of bird. The proof will have proceeded within the genus. The proof concerning fish, fin, and swimming will be exactly parallel but in a different genus, and clearly we must not use terms proper to birds in a proof concerning fish. Analogous parts, though they share common features, do not form a common subject. Each constitutes its own separate genus. The predicates that apply to it must apply at its qua-level and must be adapted to that genus. Any common features that analogues share cannot be treated as strictly common. So, if the subject is bird, then wing and flying will be predicated of it universally, but if the term locomotion is used of the subject bird, that term must be adapted as 'locomotion for a bird,' that is, 'flying,' since bird is not the appropriate subject for the general predicate, locomotion. Terms predicated of each analogue must be predicated commensurately with the analogues. For if a Single general term is unambiguously predicated of two subjects, then, at least insofar as that predicate is concerned, the subjects are instances of a genus rather than analogues. Indeed in such cases the general term cannot be predicated of

91 Analogy and Demonstration

the instance qua what it is, but only through an application argument. Analogy arises, then, within the strictest conditions for demonstrations laid out in the core of Aristotle's demonstrative theory.

Analogy in APo: Passages and Discussion Since the APo is primarily interested in demonstration within a single subject-genus, and analogy is an exception to or special form of demonstration, it is treated rather briefly in that text. In fact there are only three passages that make direct reference to analogy: Of the things they use in the demonstrative sciences, some are proper to each science and others common - but common by analogy (KOWa Of Kar' avaAoyia.u), since things are useful (XP";UlJ.LOV) in so far as they bear on the genus under the science. Proper: e.g. that a line is such and such, and straight so and so; common: e.g. that if equals are taken from equals, the remainders are equal. But each of these is sufficient (LKavov) in so far as it bears on the genus; for it will produce the same result, even if it is ' not assumed as holding of everything, but only for the case of magnitudes - or, for the arithmetician, for numbers. (1.10 76a37-76b2) Again, another way [to grasp problems] is excerpting in virtue of analogy (Kanl avaAOYOV EKAtyUV); for you cannot get one identical thing which pounce and spine and bone should be called; but there will be things that follow them too, as though there were some single nature of this sort. (11.14 98a20-23)

TO

And things which are the same by analogy will have their middle terms the same by analogy (KaT'
From the first and second passages we learn that analogy affects both axioms and special subject-genera; the third shows us that if major terms of a demonstrative syllogism are analogous, the middle must also be analogous. Since analogies can only obtain between different genera, all the terms of one demonstration will be in a different genus from the analogous demonstration. But these passages also point in two different directions, the first of which is towards a trivializing of analogy. The first passage explains that certain principles are common, but common by analogy, rather than common absolutely. But in this case there seems to be no reason intrinsic to the principles themselves that they should be analogous, since they seem to admit of a completely general formulation. Rather, what seems to be at issue is the range of application of the common principles. Though the

92 Aristotle's Theory of the Unity of Science principles, like the 'equals' axiom, extend beyond numbers, when we treat

this restricted subject-genus, we require that the principle hold good only for number. Does Aristotle mean by this that in applying the common principle we should retain its general formulation (if equals are taken ... ), and simply use it in the special subject-genus, or that we should adapt it to the specific subject matter (if equal numbers are taken from equal numbers, equal numbers remain)? By describing the commonality as 'by analogy' Aristotle indicates that he prefers the latter alternative: when the common principle is used, it must be specifically adapted, not merely applied. Nevertheless, the equals axiom seems to be quite intelligible in its general formulation, and its adaptation to the specific subject-genus seems to be a trivial matter of substitution of terms. It is true that Aristotle held to the common opinion that arithmetic and geometry were separate

genera and studied quite different objects, but the common principle will be analogical only because the genera in which it is used are different and not because the principle itself is ambiguous. If this is so, then the cause of the analogy of the principles in this case is the subject-genera to which they are adapted, and the common prinCiple, even if it admits of a general account, is given analogical formulations only because the subjects to which it attaches are analogues. This is surprising, since what we have learned about analogy so far

would lead us to expect that analogical identity would be reflected in a distinctive pattern of demonstration. At least this seems to be the import

of the third passage from 11.17. The fact that the middles of analogues are analogues implies that the causes of analogous phenomena are themselves analogous. But again Aristotle is not clear in his expression, and this statement can be interpreted in at least two ways: that the middle terms are analogous in their own right, that is, though they are not identical

with one another, they hold identical relations within their corresponding demonstrations. On this interpretation the fact that the middles are analogous will explain why the major terms are analogous. Alternatively, the middles may be analogous merely because they apply to subjects that are themselves analogous, and because the rules of demonstration require them to be adapted to their genus. In this case it is the analogous subjects

that explain why the middles are analogous. This interpretative dilemma clearly corresponds to that between the relativist and orthodox views discussed in the last chapter. The relativist interpretation claims that demonstrations and tenns in demonstrations are analogous just because their subject-genera are treated as different genera.

This thesis is the demonstrative correlate of the relativist analogy theoty of Pellegrin and Balme. On this view, attributes are analogously the same

93 Analogy and Demonstration when they are predicated in different genera. If we take this as a sufficient condition of analogy, there will be every reason to suppose that generic

attributes can be analogously adapted to species. This is precisely Balme's and Pellegrin's contention. But, if there is one thing that Aristotle makes clear it is that generic features are not adapted to species by analogy (e.g., the 2R theorem is not adapted analogously to the three kinds of triangle). The second passage provides little clarification for our problems. Superficially only the lack of a name to apply commonly to pounce, fish-spine, and bone seems to prevent their forming a genus. But the mere lack of a name is no bar to establishing a generic nature, and

if there is a nature it

can be named at least in principle. Malakostraka (HA 1.6 490b10-12) form a genus, but they do not have a single name (avwvvl'a ivi ovol'an). The problem with bone and its analogues is not the lack of a common name to apply to a common nature. Aristotle simply does not think that these objects form a single genus, and that is the reason why they do not have

a common name. And yet, as he says here, there are items that follow

bone, pounce, and spine as if they were a single nature, and this suggests that for some purposes analogues may be treated as species of a genus. So, again, it is not clear whether these common items are generically common or common only by analogy. The third passage is found in Aristotle's discussion of whether the same thing may have different explanations, and it deserves to be quoted more extensively (II.1? 99al- 16): Is it possible for there not to be the same explanation of the same thing for every case, but a different one? or not? Perhaps if it has been demonstrated in itself and not in virtue of a sign or accidentally it is not possible (for the middle term is the account of the extreme), but if it has not been demonstrated in this way, it is possible? One can inquire accidentally both about what it is explanatory of and about what it is explanatory for - but these do not seem to be problems. Otherwise, the middle term will have a similar character - if they are homonymous, the middle will be homonymous; if they are in a genus, it will have a similar character. E.g. why do proportionals alternate? For the explanation in the cases of lines and of numbers is different - and the same: as lines it is different, as having such and such an increase it is the same. And so in all cases. The explanation of a colour's being similar to a colour and a figure to a figure is different in the different cases. For what is similar is homonymous in these cases; for here it is presumably having proportionate sides and equal angles, but in the case of colours it is that perception of them is single, or something else of that sort.

94 Aristotle's Theory of the Unity of Science And things which are the same by analogy will have their middle term the same by analogy too.

In a lax sense of 'same' and 'different' it is possible to explain the same thing in different ways, but, in fact, in two explanatory demonstrations with the same explanandum (major term), the explanandum is a unity only to the extent that the explanation (middle term) is. When the major is ambiguous, the middle too is ambiguous, and where the major is gener-

ically the same, the middle is generically the same. The examples Aristotle provides are not intended to correspond precisely with these degrees of identity, but they clarify his general point.' The alternation of proportionals among lines and numbers are given different explanations when

treated as different genera. The alternation of proportionals among these genera will be analogous, and the explanations will be analogous, as we saw above. But when the genus, magnitude, is abstracted, the alternation of proportionals will be generic and the explanation generic. Fully ambiguous terms, like similarity among similar figures and among similar colours,

will have two unrelated explanations. Aristotle goes on in this chapter to discuss the relationships between

the terms of a demonstrative syllogism, outlining the schema for application arguments (99a16-37), and cases where a single major term belongs for different reasons to different subjects (99a37-b7). These latter cases have strong affinities to analogical explanation, and the example Aristotle offers may provide some insight into the demonstrative structure of anal-

ogy (99b4-7): It is possible for there to be several explanations of the same thing, but not for things of the same species - e.g. the explanation of longevity for quadrupeds is their not having bile, but for birds their being dry or something else.

The fact that this example is based on the genera of the biological works suggests that it might be relevant to our problem, although it does not deal with any of the standard analogues we have seen. Aristotle does not make explicitly clear which, if any, of the three candidates for multiple causes the longevity case corresponds to, but the context indicates that it is not an application of a generic feature to an instance, nor does longevity

seem to be radically homonymous in the way that similarity is (TO Ol'owv) when applied to similar triangles and similar colours. After all longevity

2 Contra, Ross 1949, 668.

95 Analogy and Demonstration in both birds and quadrupeds is judged by the same criterion (they live for several decades), whereas similarity in figures and colours is judged by quite different criteria. Analogy, therefore, seems to be the most likely candidate.' The explanation for longevity is different in the case of quadrupeds and birds. Now in the second book of the APo Aristotle regularly identifies the definition of a major (or minor) term with the middle, that is, the cause. If this doctrine may be applied in such cases as these, the definition of longevity will be different for birds and quadrupeds, since the cause will be different in each case. That is, longevity has a different significance in the two genera' We can fill in the details of longevity from elsewhere: life is dependent on vital heat Uuv. 6 470a19-20; Resp. 17 478b32-33), which can be exhausted or extinguished Uuv. 5 469b21-22). And it can be extinguished by excessive moisture (d. Resp. 20 479b19-26) or by bUe. Bile is a useless residue, the opposite of nutriment, which fuels the vital heat. Bile, therefore, causes impurity in the blood and contributes to shortness

of life (PA IV.2 677a25-35).' Dryness and bilelessness both contribute, therefore, to the preservation of vital heat. The subjects of our demonstrations here are birds and viviparous quadrupeds. The demonstrations are analogical, not merely because birds and viviparous quadrupeds belong to different genera, but because dtyness and bilelessness are different. That is, the cause of longevity is not merely stipulated as different because the subject-genera are different. The causes just are different and they discharge a corresponding function within their genera. To be sure, longevity is an item that follows these two different subjects. This folloWing term has a common nominal definition (say, longevity is the capacity for long life in each case) that offers a common account and reveals some fact about the object that is more familiar to us, but that requires further explanation. But in spite of this common account,

3 McKirahan 1992, 171-2, treats longevity, but does not comment (except hriefly in n. 39) on its connection with analogy. 4 This is the conclusion that Goldin 1996, 147, comes to from an examination of the relationship between the nominal definition (the major) and the causal explanation. He denies, however, that Aristotle 'envisages the possibility of this sort of homonymy' in which one nominal definition might have two causal definitions (147n13). 5 Cf. PA 11.2 648b2-8: 'There ought, then, to be some clear understanding as to the sense in which natural substances are to be termed hot or cold, dry or moist. For it appears manifest that these are properties on which even life and death are largely dependent, and that they are moreover the causes of sleep and waking, of maturity and old age, of health and disease.' Even among vivipara dryness may contribute to long life; d. EN VIl.3 1147a5-6: dry food is the most healthy.

96 Aristotle's Theory of the Uniry of Science longevity remains ambiguous because it has different causes. The nominal definition provides the fact, and the causal definitions, bilelessness and dryness, provide the cause 6 The common fact is an effect of differing causes. 7 The subjects, bird and quadruped, are conceived of as different in

virtue of their being bileless or dry and it is from these different causes that we can infer the common effect, their capacity for long life. It is, however, in virtue of the familiar fact of their longevity that birds' dryness and quadrupeds' bile less ness are gathered together as analogues, since this is a conclusion that follows from both of them S And yet that is hardly the end of the story, for it is clear that we need not settle for' capacity for long life' as a common definition of longevity. Instead, 'preservative of vital heat' seems to provide a common cause for

longevity in birds and viviparous quadrupeds, and this can serve as the common middle and the causal definition of longeviry. We would now have an unambiguous (generic) middle explaining an unambiguous (generic) major. What, then, would be wrong with accepting the general explanation of longeviry, that which preserves vital heat, and applying it directly to the specific instances? The reason has to do with the asymmetry of causal explanation. We can construct the following explanatory syllogism for it:

1) longevity IPO preservative of vital heat 2a) preservative of vital heat IPO bilelessness

2b) preservative of vital heat IPO dryness

3a) bilelessness IPO

3b) dryness IPO birds

viviparous quadrupeds therefore,

4a) longevity IPO viviparous quadrupeds

4b) longevity IPO birds

6 There has been a considerable amount of attention given to the issue of nominal definition: Bolton 1976; Demos and Devereux 1988; Goldin 1996. 7 Similarly in PA 1.4, in his defence of the common division of animal groups, Aristotle says that water animals and feathered animals, though their correspondence is only by analogy, share some 7ralhj . 8 In Long., Aristotle actually does discuss the causes of absolute longevity. He explains why generally larger animals are longer-lived than smaller animals, viz., they contain more moisture and this moisture is hotter and less liable to freeze or congeaL Bilelessness is not mentioned in Long. as a cause of longevity, nor is dryness a cause in animals (though it is in plants 16. 467a6-8}) . The scenario Aristotle lays out in Long. does not involve the same examples as in the APo.

97 Analogy and Demonstration We can see that in contrast to the single-genus proofs for triangles having 2R, there is here an additional premiss (2a and 2b) providing a distinct reason in each case. It is ultimately not in virtue of one cause that longevity is predicated of birds and viviparous quadrupeds. There are two sets of middle terms: preservative of vital heat is the same in both cases, but bilelessness is different from dryness. According to the following chapter, APo 1l.l8, when there is more than one middle term between major and minor (e.g., preservative of vital heat and bile lessness/ dryness), the proper explanation is the middle term that is closest to the minor. The scheme of explanation is asymmetricaL because we cannot invert preservation of vital heat and bilelessness in the order of explanation. Bilelessness explains preservation of vital heat in quadrupeds, not the other way around. This principle is stated immediately after the II.17 example of longevity, and is clearlyintended to block an attempt to find a universal explanation for the analogous term. The reason we choose the middle closest to the subject is clear: the more specific middle explains the more general but not vice versa. Thus, if we were to choose the middle nearest the major, the analogy (or homonymy) could easily escape our

notice. There are some important similarities and differences between the longevity case as I have interpreted it and Aristotle's treatment of analogy in the biological works. In both cases, common features are attributed to different genera for different reasons, thus making these features analogous. We also find a similar distinction between general and specific cause, where the latter is appropriately adapted to the subject-genus, and the former is not. In all the important formal respects longevity is a case of analogical explanation. But there are also some significant differences that point to the variety of forms and degrees of abstraction in which analogy can be found. In the case of longevity, the common feature is the major term or the fact, while the middle terms or causes are distinct. This is not always the case in the biological practice. Frequently, to all appearances the causes for which features belong to analogues are common. On other occasions the entire demonstration has analogous terms throughout, the common terms being explicitly nowhere in sight. Moreover, in the PA, which is devoted primarily (though by no means exclusively) to explaining biological phenomena through the final cause, this cause tends, as we shall see, to be more common and universal than the phenomena it explains. In the case of longevity, by contrast, the causes, being material and efficient, cons titute different explanations for a common explanandum. And indeed it is generally the case that the relationship of common and specific terms

98 Aristotle's Theory of the Unity of Science are oppositely arranged in demonstrations that involve final. from those that involve efficient/material causes. So the variation apparent throughout Aristotle's brief discussion of analogy in the APo is mirrored in his practice in the biological works. Aristotle tends to identify the form with the function as common and universal, and the material conditions with plurality and specificity" In demonstrations that relate form and matter (i.e., causal demonstrations invoking the final and material cause) there will often be a tension between the formal terms, which are more general, and the material tenns, which aTe more specific. In such cases it is not clear whether the COIDman terms are analogous in a merely relative sense or whether they are naturally or really analogous. Aristotle's answer within the highly constrained criteria of demonstration is that common terms when predicated in different genera will always be common by analogy unless an application argument is used. As we saw with the case of alternating proportion, it is possible for a predicate to be treated in both ways: alternating proportion is proved of lines and number by separate but anal-· agaus demonstrations, but alternating proportion also can be proved of general magnitude and then applied to the species, line and number, by application argument. This answer is made more plausible through the observation that definitions are first principles of demonstrations and do not admit of proof or justification. As a result, when we adapt a term for a demonstration, that adaptation becomes a part of the definition of the term and a first principle. The question, then, whether the adapted term is 'naturally' analogous (the orthodox position) or analogous merely because it has been formally adapted to different subject matters (the relativist position) makes little sense. Since the adaptation is part of the definition, the adaptation is as much a part of the essence of the term as any other part, and so there is no further need to argue for the term's being analogous. In this way Aristotle's theory of demonstrative understanding, which concerns the relations between terms and between prem isses, imposes constraints on the meanings and significance of terms. The formal language of qua and per se captures some of the common insight that terms mean different things in different contexts, and when we say something about some subject, what we say applies only to that subject and no further. The use of a term, for Aristotle, is to a large extent its meaning. 9 It is important to distinguish the material cause in the sense of the components that make up the developed form from the materials that undergo change so as Ilew materials. It is the former that are identified as plural and specific.

to

become

' 99 Analogy and Demonstration Analogy in the Biology As in the APo, so also in the biological works there is good evidence that Aristotle often used a distinctive form of demonstration when treating analogues. But, as in the APo, here too there is no one single pattern. Instead, we can discern three basic forms, in which the importance of analogy is displayed to a greater or lesser degree: L Analogous attributes proved of analogous parts by parallel demonstrations. 2. Systematic variations on analogous parts that are covariant with a common feature proved by parallel demonstrations, 3, Apparently common attributes proved commonly by a general cause and applied to analogues, '

The progression from the first to the third is a progression from greatest to least importance of analogy in demonstration, and from the orthodox to the relativist conception of analogy, As a result of this variety of form, the interpretative difficulties we faced in the APo presentation are manifested again in the biological works: (a) While there are cases in which analogy clearly has a profound influence on the proof structure, there are other cases in which the traits being discussed appear to be absolutely common. In the latter cases the introduction of analogues seems to be irrelevant to the proof at hand. (b) Not all the terms of a demonstration are explicitly analogous, Indeed there are usually common terms involved, and the analogues are often treated together under some common designation, as, for example, blood and its analogue are often discussed together as nutriment (TPOCP~), in spite of the fact that this is a functional designation, (c) Analogues are not introduced on all appropriate occasions, Often the lesser analogue (the unnamed one) is not mentioned or is dropped midway through a discussion, (d) In spite of what Aristotle says at APo IL14 (98a20-23), analogues are not always treated together for every purpose. Sometimes their common aspects are treated together and their peculiar traits separately. So, for example, heart and its analogue (when nameless) are treated together, but the analogue, when named (}.tVH,), is treated separately, One observation at the outset strongly suggests that analogy has an effect on demonstration. Aristotle often says that certain parts and

100 Aristotle's Theory of the Unity of Science functions are in the essence of an animal. Gotthelf has assembled a list of such essential parts and functions and it includes such principles as being blooded (PA IV.5 678a31-34), having a claw (PA IV.8 684a33-35), or having a lung (PA 1ll.6 669b8-12).1O Other principles mention functions, like being a flier (PA IV.12 693b4-13), a swimmer (PA IV.13 695b17-19), or a thinker (PA IV.lO 686a25-28). All of these, whether functions or parts, are mentioned elsewhere as having analogues. Now, since they are

irreducibly part of the essence of an animal, they are starting points of explanation and mark first principles in demonstration. Since they form

part of the definition of the animal groups, they are predicated of the animal subjects per se and universally. It is not the more general terms that are part of their definitions. The general term 'having nutriment,'

for example, is not part of the definition of blooded animals, but rather 'having blood.' For this reason we should expect to find separate rather than common demonstrations concerning and involving analogues.

In the first form of analogical explanation, Aristotle explicitly follows the prescription of APo 11.17, that analogous attributes have their middles the same by analogy. So, for example, at PA 1ll.5 668a4-7 Aristotle gives the reason why the blood vessels are distributed all over the body: [T]he reason for the vessels being distributed throughout the entire body is that in the vessels, or in parts analogous to them, is contained the blood, or the fluid which in bloodless animals takes the place of blood, and that this is the material from which the whole body (CTw!'aTo,) is made. (modified ROT)

We may safely assume, in view of the second use of 'vessels,' that the

first use is lax, and properly should be 'blood vessels or their analogue.' In this passage we find two entirely analogous demonstrations appearing

in parallel. The analogous major terms - blood vessels being distributed all over the body, and blood vessel-analogues being distributed all over the body - are predicated of blooded and bloodless animals respectively in virtue of the channelling of blood and its analogue. Major, middle, 10 Gotthelf 1987, 190-1. Without providing the details, his list is the follOwing: sensation is in the definition of animal; lung is present in the OWI.a. of lunged animals; blood is in the logos defining the oixT{a of blooded animals; having many origins (of movement and sensation) is present in the oixrla of insects; the reason lobsters have claws is that they are of the kind that has claws; one kind of octopus has only one row of suckers because of the length and slimness of its nature; thinking and reasoning is in the nature or owla of man; being a flier is in the oUrT{a of bird; being a swimmer is in the logos of the ourria of fish; being disproportionate in length relative to the rest of the bodily nature is pan of the ourria and essence of snakes.

101 Analogy and Demonstration and minor are all analogous. ll Again, later in the same section Aristotle explains why veins appear during emaciation (668a23--28): since blood and its analogue are potentially the body (which is flesh and its analogue), the former may actually become the latter and disappear until starvation makes them reappear. Elsewhere we find a more telegraphic form of parallel explanation (PA II.12 657al8-23): In birds, on the other hand, there are only the auditory passages. This is because their skin is hard and because they have feathers instead of hairs, so that they have not got the proper material for the formation of ears. Exactly the same is the case with such oviparous quadrupeds as are clad with scaly plates, and the same explanation applies to them (0 yap a.UTOS ap}J.O(JH Kat E7r' EKEtVWV "-OYOII).

ap/J.o(€w is often used where corresponding or analogous arguments are implied 12 It is clear in view of APo II.17 that" atJT'" Myo, must mean the same by analogy, but the fact that Aristotle does not express himself accurately is an indication of how lax he can be in practice. In the second group of demonstrations not only do we find analogues between parts, but also among the 'more and less' variations. These variations are the same by analogy because they are covariant with some common feature. In this group common explanatory terms are frequently used. So, for example, the demarcation between lungs and gills is clear, both from their shape and from the kinds of animals that possess them. They are mentioned as analogous in a programmatic passage (PA 1.5 645b6). While lung is treated among the internal parts of blooded animals (PA III.6), the gill is considered an external part of fish (PA IV.13). The functions of the organs are also called analogous (HA VII [VIII].2 589b18- 19): as air passes in and out of the lung, so water passes in and out of the gill (Resp. 21 480a23-b20). We can provide a common formulation that covers both cases: the fact that all blooded animals are hot accounts for the need for respiration, but neither this formulation nor any variation upon it can account for the materially and formally specified organs.

11 Strictly speaking, this passage seems to involve a double demonstration: proving first that blood is transported allover the body, and then using that as a premiss to show that blood vessels are distributed all over the body. The first conclusion will hypothetically necessitate the second conclusion. Double demonstrations are common in the biology, but no provision is made for them in the APo. There is a great deal about packing, but APo recognizes only purely transitive fonns of inference. 12 E.g., Phys. IV.1 209.9; IV.8 214b22-23; Pol. IV.11288b12; d. Pol. III.1 1275033-34.

102 Aristotle's Theory of the Unity of Science They must each be referred to their own proper function: only the fact that one group breathes air and the other respires water explains the presence of each organ: two different, but parallel final causes explain the analogous parts. For this reason merely respiring is not a sufficient explanation, and having a lung must be in the o1)(ria of those animals that have them (PA Il1.6 669b8-12). Variations on these organs likewise can be explained in parallel ways, and we can show that common properties follow upon this grouping of analogues. Since viviparous quadrupeds are especially hot, they have bloody and large lungs, and since ovipara are cooler, their lungs are small and spongy (PA III.6 669a24-32). By analogy fish that are hotter have more numerous gills, while cooler fishes have fewer (PA IV.13 696b16-20). Thus, we find attributes common by analogy shared by both of the analogues. On the one hand, lung and gill meet the common need to cool the animals, but they also display variations according to an ana logous principle: the hotter the animal, the larger the lung or the greater the number of gills. The two analogues are treated as different subjects, but they vary in analogous ways according to the same principle. In this case analogies exist both at a general and a specific level. So not only do we find correspondences in the explanatory structure between the analogous parts, the animals to which they belong, and their causes, but we also find correspondences among the variations.

Again, throughout the HA, PA, and GA, Aristotle discusses various kinds of body covering: hair, feathers, scaly plates, and fish scales. Some of these analogues are more closely related than others. Some attributes are analogously common to them all, others just to some. At HA 1.l486b21-22 Aristotle says that what the feather is in a bird, the scale is in a fish, and it is clear that they are not related by difference of degree. At a general level, they share a function, external covering for the animal, but they also share certain material and structural similarities . They form a covering over the skin, made of many discrete identical parts of similar basic material lodged in the skin. To this extent hair among viviparous quadrupeds is also analogous. The hair is said to protect from the heat and cold (PA Il.14 658a6-7). Treating oviparous quadrupeds separately, Aristotle says that they are covered with horny scales for the same reason. Crocodiles and tortoises have especially hard and bony horny scales (PA IV.ll 691a17-19). Aristotle tentatively says that the shell acts as a lid for the heat (PA 11 .8 654a5-9)." 13 Note that this is also a function of exoskeletons and shells, which are, of course, nowhere called analogues of hair and feathers.

103 Analogy and Demonstration Some animals have more or less hair, longer and shorter hair, just as other animals have more or fewer feathers or scales, and so on. These variations on the generic type are explained by the varying amounts of moisture and earthy deposits from which they all are formed. Especially interesting is a passage at GA V.3 782al4-20: Men go bald on the front of the head, but turn grey first on the temples;. no

one goes bald on these or on the back of the head. Some such affections occur in a corresponding manner also in animals which have not hair but something analogous to it, as the feathers of birds and scales in the class of fish.

Balding, whether of hair or its analogues, occurs because, as the animal grows older, it becomes drier, the skin becomes harder and thicker, the heat fails, and the moisture, which is the material cause of the hair, fails as well (GA V.3 783b2-8). There is no suggestion in these examples that the moisture itself has analogous manifestations. One kind of moisture, it seems, plays the same role in all the demonstrations, and the definition of moisture is not explicitly adapted to fit each demonstration. 14 At PA II.2 648a2-7, Aristotle describes the differences in blood: thick and thin, dear and muddy, cold and warm. There is also the difference between those animals that have blood, and those that have instead some other such part «TEPOV TL }lOpWV TawilTav): The thicker and the hotter blood is, the more conducive is it to strength, while in proportion to its thinness and its coldness is its suitability for sensation and intelligence. A like distinction exists also in the fluid which is analogous to blood. (T~V aVT~v 0' EXEt otacpopav Kat TO ava'\oyov {nrapxov 7rPOS TO aip.a.) This explains how it is that bees and other similar creatures are of a more intelligent nature than many sanguineous animals.

We see here that intelligence is predicated of animals in virtue of the middle terms, cold blood / cold blood-analogue. The intelligence which bees have is in some ways similar to man's, but it too is analogous. In this case it is nat perfectly dear whether the major term (intelligence) is generically or analogically common. The result may be two entirely analogical demonstrations or two partially common demonstrations. 14 Likewise, differences in hair and its analogues correspond to differences in gender. At HA IV.11 538b8-9 Ariswtle remarks that the female is more delicate in hair ~nd where there is no hair she is less strongly furnished in some analogous substance. Here again we observe analogous parts covariant with common features.

104 Aristotle's Theory of the Unity of Science Finally, we find analogies of the senses of hearing and touch, which also involve variations of more and less. These analogies do not involve demonstration, but they illustrate the general point that analogies are often systematic, involving not just the general case, but also variations upon it. They are also peculiar in another respect. They concern sense perception, which is an activity of the soul, rather than a part of the body. This represents a higher level of scientific generalization, but here too there are analogies. The terms sharp (at.,) and flat (j3a.pv) are applied metaphorically to sound from the realm of touch, where they mean respectively what moves the sense much in a short time, and what moves the sense little in a long time ... There seems to be an analogy (auQ.Xoyov) between what is sharp or flat to hearing and what is sharp or blunt to touch; what is sharp as it were (oLov) stabs (KEVTf'i), while what is blunt as it were (orov) pushes (Weft), the one producing its effect in a short, the other in a long time, so that the one is quick, the other slow. (modified ROT; DA II.S 420a3D--b4)

Although there is no explicit demonstration here, it is clear that there is an explanation of what makes sounds sharp or flat. The explanation is parallel in the case of hearing and touch, and there is even a general explanation of a sort available: what moves the sense in a long or short time is sharp or flat/ dull. Notice that in spite of the general explanation Aristotle avoids using language in one genus that properly belongs to another genus. For this reason he uses the expressions oiov KEVT€~ and orov weft. Likewise, . it seems that there is an analogy between the senses of smell and taste, and that the species of tastes (7(1 EWl1 TWV XlJ,uwv) run parallel to those of smells ... As flavours may be divided into sweet and bitter, so with smells. In some things the flavour and the smell have the analogous (civa.\.oyov; not as ROT, the same) quality, e.g. sweet smell and sweet taste, and their opposites. Similarly a smell may be pungent, astringent, acid, or succulent. But, as we said, because smells are much less easy to discriminate than flavours, the names of these varieties are applied to smells in virtue of similarity. (DA II.9 421a17-bl)

Again, the same features are apparent, including explicit mention of the fr~l1 of tastes corresponding to those of smell. No causal explanations are at work in this case, but we may safely assume that Aristotle would feel obliged to give a common account of these variations. We do see some explanations at work in the following passage (Sens. 5 443b3-12):

105 Analogy and Demonstration It is clearly conceivable that the moist, whether in air (for air, too, is esser:ttially moist) or in water, should imbibe the influence of, and have effects wrought in it by, the sapid dryness. Moreover, if the dry produces in moist media and air, an effect as of something washed out in them, it is manifest that odours must be something analogous to savours. Indeed, this analogy is, in some instances, a fact; for odours as well as savours are spoken of as pungent, sweet, harsh, astringent, rich; and one might regard fetid smells as analogous to bitter tastes; which explains why the fonner are as unpleasant to breathe as the latter are to drink.

All the explanations canvassed above invoke different kinds of cause (final, material, and efficient). In each of these cases some common formulation can be provided, and each group of analogues can conceivably be denominated by some functional description, for instance, blood-cooler, external surface residue, that which has intelligence, sensation. Clearly, then, some common account can be substituted even in these cases, and variations on this new common item can be accounted for by variations in some other common feature, more or less heat, more or less moist residue, longer or shorter time. But to provide a common account would be to abstract beyond the appropriate subject matter of the sciences, for in each case Aristotle is talking about the specific part or function. The third and final form of demonstration, in which the major and even middle terms are apparently treated as common and in which there are no systematic variations, is the most frequent. It is a common practice for Aristotle to provide a general argument that ends with a mention of the analogues to which the argument applies. At PA 11.1 647a24-33, for example, Aristotle says [A]s the sensory faculty, the motor faculty, and the nutritive faculty are all lodged in one and the same part of the body (EV TaVTC{J j.L0pl.'fl TOV (J'wj.LaTos) it is necessary that the part which is the primary seat of these principles shall on the one hand, in its character of general sensory recipient, be one of the simple parts; and on the other hand shall, in its motor and active character, be one of the heterogeneous parts. For this reason (Ot07T€p) it is the heart which in sanguineous animals constitutes this central part, and in bloodless animals it is the analogue. For it is divided into homoiomeries like each of the rest of the viscera, and yet it is anhomoiomerous on account of its shape. (modified ROT)

Aristotle provides a general argument concerning the common seat of sensation and movement. At the beginning of the argument the parts have not been given their proper names, and only subsequently are analogues

106 Aristotle's Theory of the Unity of Science identified. They are treated as a single nature throughout. The last two sentences of th e passage seem to constitute an application argument: since both the heart and its analogue have a homoiomerous and anhomoiomerous nature, they qualify as the seat of these faculties 1s This pattern of explanation is also found very frequently in the GA. We see Aristotle discussing and explaining various common traits of the principle (apx~), then stating that this principle is the heart or the analogue of the heart. So, for example, 11.1 735al6-26: Hence it is that only one part comes into being first and not all of them together. But that must first come into being which has a principle of increase (for this nutritive power exists in all alike, whether animals or plants, and this is the same as the power that enables an animal or plant to generate another like itself, that being the function of them all if naturally perfect). And this is necessary for the reason that whenever a living thing is produced it must grow. It is produced, then, by something else of the same name, as e.g. man is produced by man, but it is increased by means of itself. There is, then, something which increases it. If this is a single part, this must come into being first. Therefore if the heart is first made in some animals, and what is analogous to the heart in the others which have no heart, it is from this or its analogue that the first principle of movement would arise.

Here the general argument extends not only beyond the analogues themselves, but even beyond animal to encompass everything capable of nutrition. Again, the general argument seems to be applied to the heart and its analogue as to species. These examples of demonstration seem to belie the claim that a COIDman genus and a common explanation cannot be given for analogues. For Aristotle seems to be perfectly capable of articulating the cause at a general level and applying it directly to the analogues. These cases, then, support the relativist interpretation whereby analogues can with no modification be gathered into a genus. How are we to account for this wide variation in practice, where sometimes, as we see, purely general arguments seem to be applied to analogues as if to species, sometimes general features seem to be adapted to genera

15 So also at PA 11.1 647al4-21 we are told the reason for the existence of flesh and its analogue, but in general terms; sensation takes place in the simple parts, but tou ch takes place in the least simple of the parts. This part must be more complex, because this sense deals with more than one sensible. Only after providing this general explanation does Aristotle say that the sense organ of these, the flesh and it s analogue, is the most corporeal of the sense organs.

107 Analogy and Demonstration to a greater or lesser extent, and sometimes again demonstrations are fully analogo.us? One is tempted to fall back on the common and correct claim that the biological works are not syllogized in the formal way that would be necessary in order to reveal the intricacy of analogical demonstration. Formalization would involve the tedious and unnecessary process of stating explicitly all the per se and qua relationships. The mention of analogues in contexts where demonstrations are not fully formalized may represent a sort of promissory note, an indication of the mode of proof to be pursued if one wishes to formalize. No doubt, this view explains the variation in practice to some extent. Aristotle throughout the biological works prefers to use a non-technical and non-formal language, and the logical apparatus of the APo to the extent that it is present remains largely implicit. But our difficulties are not solved by this means alone. The other, more important reason is that any given item must enter into causal relationships with several other items at various levels of generality.16 This fact is made clear by the organization of the WP system. The lower levels on the table provide the matter and are the material cause for the higher levels. But the matter often has a different extension from that for which it is the matter. Horny material, for example, provides the stuff for a variety of different organs, fingernails, talons, and horns. Horny material, that is, extends further than anyone of the homoiomerous parts for which it is the materia1. 17 This situation occurs not just among the components of the WP system, but also in the process of generation, as the following passage makes clear (GA 1.19 726bl- S): We have previously stated that the final nutriment is the blood in the sanguinea and the analogous fluid in the other animals. Since the semen is also a residue of the nutriment, and that in its final stage, it follows that it will be either blood or that which is analogous to blood, or something formed from these.

Though in many demonstrations semen will be related to other terms that have the same level of generality as itself, this is not the case here with its material cause. Now, it would not be difficult to analyse this 16 This problem is discussed by Goldin 1996, 148- 51, who solves it by claiming that Aristotle is not consistent in his injunction against metabasis, and that he frequently invokes principles from other sciences. Goldin assimilates such cases [0 the use of mathematical middles in optical demonstrations . 17 PA II.9 655b2-4; cf. ILl 646b3O-34, where some of the viscera are made of a common homoiomerous material, differentiated presumably just by their shapes. So also Met. H.4 1044a25-31, where a single matter may have. two forms and two different matters may have the same form.

108 Aristotle' s Theory of the Unity of Science case in accordance with the model of longevity and assume two different but parallel causal processes of concoction whereby blood and its analogue are transformed into semen. Semen will then have one general cause and two analogous causes. As a concoction of nutriment it has one cause, but as a transformation of blood and a transformation of blood's analogue it will have two, and semen in this case will be ambiguous 1 8 But even if we can provide an adequate analogical analysis for these cases, and claim that for the sake of brevity Aristotle chose not to do so himself, we are merely evading a more pervasive problem. We have seen that analogues have their origin in the phenomenal analysis of the WP and SGA systems. There each part was hypothesized as existent and fitted into a compositional network. Generically different parts with similar material and compositional constitutions were deemed analogous. The analogues were hypothesized as generically different, but were called analogous because they fit into corresponding positions in the WP table . There was as yet no consideration of cause or demonstration. But it is precisely these correspondences and similarities that must either be explained or serve as explanations in demonstrations, and it is precisely these that, when they arise, are treated as common. We noticed the underdeveloped state of analogies of function in the PA. Though Aristotle recognizes them in theory and occasionally uses them in practice, he tends to treat functions as common. In fact, this tendency is a manifestation of a widespread feature of Aristotle's general methodology, which starts with the material, the speCific, and the familiar and moves to investigate the common cause (d. KOLV~ aiTia MA 1 698a4). Analogy appears especially clearly at a precausal stage of investigation. But once causes are brought to bear on the subjects, the common begins to prevail, both in the material cause, which often extends more widely than the specific explanandum, and in the final cause, which is expressed as a general function. We have already seen in Aristotle' s study of animal movement the transition from the material, the specific, and familiar fact to the formal, generic, and abstract cause. The various aspects of animal movement (e.g., wings, joints, hearts, desire) are best treated at different qua-levels, because they have different extensions. And yet these qua-levels cannot be entirely

18 Again, at GA 11 .3 737a36-b4, All bodies are held together by the glutinous; this quality, as the embryo develops and increases in size, is acquired by the sinewy substance, which holds togeth er the parts of animals, being actual sinew in some and its analogue in others.' Sinew and its analogue are both glutinous, a material feature necessitated by their common function. As such they share a power, and therefore differ by the more and the less in a weak sense. And yet they remain analogues. I

109 Analogy and Demonstration causally isolated from one another, the latter being causes for the former. Likewise, we see in APo II.19 that in some cases the search for the cause and the search for the universal is one and the same: the search for the immediate connections of demonstration is the search for the universal. By allowing specific subject matters to be subsumed under more general and abstract subject matters, the assimilation of the cause and the universal

produces that scientific unification through hierarchy which is so characteristically Aristotelian. But at the same time it creates a tension with the rules of demonstration, which require that the cause be treated at the same qua-level as the fact. The tendency to introduce the universal cause is especially strong when

the analogy on the phenomenal level is not matched by a terminology of cause at the same level. This is especially prevalent with nameless ana-

logues. So underdeveloped is Aristotle's vocabulary that often an analogous part is nameless; so much more likely is it, then, that the function of that part,

which already tends in Aristotle's conception towards the universal,

will have no special name. It is not surp~ising, then, that the vast majority of cases involving demonstrative analogy of the third kind involve parts with nameless analogues. Analogies arise in a demonstrative context when the subjects we are treating are generically different. According to the rules of the APo, the

terms of the demonstrations must be adapted to the subject-genus. The terms of analogous demonstrations, though they are adapted to their genus, can be abstracted and generalized, but in so doing, the terms no longer remain the same, and the subject matter changes and a different science

emerges. In cases where Aristotle does not follow this strict model, the tendency to generalize the cause is usually matched by the unavailability in the common language of specific causal terms. The language of facts is more specific than the language of causes.

Analogy and the Scala Naturae There is another form of explanation operative in the biological works that is often confused with analogy. At the widest level, spanning the whole range of animal kinds, Aristotle has established sweeping continuities, which constitute what is traditionally known as the scala naturae. The scala admits two different theoretical interpretations. It may either be considered

solely as a scale of difference with no normative implications, like that of cartilage and bone, or it may also involve value, one end of the scale being

better than the other. It is clear from what we have said that various parts of animals have different extensions, and some attributes, for example,

110 Aristotle's Theory of the Unity of Science mouth, extend to all animals and vary by differences of degree. Mouths are different because they serve different functions, and not because one mouth is better than another mouth. In the same way, all animals have vital heat, but some have more and others less. Furthermore, the scale of heat may correspond to or be covariant with other attributes, like the modes of reproduction and so on. Such scales, since they connect all the genera of animals together, have threatened to erase generic distinctions

by representing animal kinds as a smear of variation rather than as discrete groups. Dualizers (f7raJloTEpi("oVTES), like dolphins, are doubly challenging in this regard: because they stand between two great groups, they are difficult to place in either one of the groups, but because they can equally be placed in either, they make the great groups themselves indistinct and indefinite. These scales when treated non-normatively present the same problem as we faced with bone and cartilage. Because the essential features of the two parts differ by more and less, it is difficult to place an exact line of demarcation between them and distinguish them exactly. But the scala may also be a normative system, in which one end of the scale is positively valorized, and all other points fall short of it for various reasons. As a result, two objects on a scale are not just different, one is better than the other, and we explain features of one kind of animal in terms of its proximity to a different, but normative, kind. Indeed, the challenge of the scala arises not so much within the first interpretation, but rather when it is conceived as a hierarchical tool of explanation, in which animals and their parts are explained as deficiencies from one primary type, usually man. For on this view the usual injunction against metabasis breaks down, and principles proper to one genus are used in the exp lanation of a

different genus. Indeed Pellegrin has asserted that analo~l has the purpose of joining together animals in an intelligible hierarchy: [I]n the Hi story of Animals (8.1.588a25), Aristotle explains that psychological faculties differ between man and various other animals either by the more and the less or analogically. And this example helps us to understand the truly fundamental function of the analogical relationship in biology. It does not serve so much to set apart natural families of living things as to relate one group of animals to another by some point of reference, and ultimately to relate all living things to one unique being, taken as a model of intelligibility, man ... Thus, in a sense, all the 'anatomical' parts of the Hi story of Animals. really do not constitute, 19 1986a, 90--2. He cites Leblond's attempt to tie analogy to taxonomy by supposing that analogy allows comparison of parallel and independent genera, and as such is a kind of comparative morphology within a taxonomy (LeBlond 1945, 41-2).

111 Analogy and Demonstration despite what some have mistakenly said, a comparative anatomy, but are rather an anthropocentric anatomy and ethology, and that thanks to the employment, explicit or not, of analogy ... Animals are, as it were, sketches of the human animal Aristotle declares that, in relation to man, they are like dwarves, that is, badly proportioned and badly constructed men.

Pellegrin's argument here is an extension of his claim that there is no natural distinction between genus and analogy, and that analogues are interchangeable with genera. Here the more and less, analogues, and hierarchy all aim at one grand purpose. But, in fact, series arguments, which are the basis of the scala naturae, presuppose a norm with respect to the shared attributes in that scale, and that norm provides an explanatory principle?O Analogical arguments/ _by contrast, make no such presupposition. Because they maintain their generic autonomy foremost, analogues do not as such show any tendency to priority and posteriority. Although there is indisputable evidence in general for a scala naturae, it does not threaten to obliterate generic distinctions that are the basis of analogy. Any attempt to construct a purely scalar arrangement of the parts and their attributes would result in an overly simple scheme of explanation incapable of accounting for the phenomena. 21 Although the non-normative interpretation of the scala has been discussed elsewhere,22 it is useful to clear up some confusions in what has become a standard interpretation. The classic passage at the beginning of HA VIII suggests in the Revised Oxford Translation that Aristotle thought it difficult to make distinctions between genera: Nature proceeds little by little from things lifeless to animal life in such a way that it is impossible to determine the exact line of demarcation, nor on which side thereof an intermediate form should lie.23 Thus, next after lifeless things comes the plant, and of plants one will differ from another as to its amount of apparent vitality; and, in a word, the whole genus of plants, whilst it is devoid of life as compared with an animal, is endowed with life as compared with other corporeal entities. Indeed, as we just remarked, there is observed in plants a continuous scale of ascent towards the animal. So, in the sea, there are certain objects concerning

20 See Preus 1983 for this and other normative aspects of Aristotle's biological definitions. 21 See Lovejoy's judicious comments on Aristotle's use of scalar arguments, 1964, 55-9; also Coles 1997. 22 These issues have been effectively discussed by Granger 1985. 23 OVTW l)' EK TWV a'/tvxwv Et~ TO. (0a IJ.ETaj3atvn KaTo. IJ.tl
112 Aristotle's Theory of the Unity of Science which one would be at a loss (588b4-13)

to

determine whether they be animal or vegetable.

This passage does not claim that demarcations are impossible to determine. In the first sentence the subordinate clause is constructed with WfJT€ and

the infinitive of natural result, and as such does not affirm that it is impossible to determine the exact line of demarcation, but only that it is something that would naturally escape our notice 24 Obviously Aristotle does not think that it has escaped his notice. Indeed, comparison of other passages with WaTE plus Auv8civftv clearly shows that what escapes notice nevertheless unequivocally exists." It is also seldom observed that this passage is situated in the midst of Aristotle's introduction to the psychological traits of animals, and that throughout he is remarking not on the difficulty of distinguishing the external forms of the various genera of plants and animals, but of locating demarcations in psychological capaci ties.

It is difficult to tell, for example, whether certain animals sleep or have sensation. This passage, then, cannot be used to suggest that Aristotle thought his generic distinctions based on parts could be reduced to scales of more and less. In spite of their own peculiar ambiguities, the physical forms of the genera are clearer than the differences in functional capacities, which can be associated with wider variety of externa l form.

We see the same kind of issue at stake in the other oft-cited passage, PA IV.5 681a9-15: The ascidians differ but slightly from plants, and yet have more of an animal nature than the sponges, which are plants and nothing more. For nature passes from lifeless objects to animals in such unbroken sequence, interposing between them beings which live and yet are not animals, that scarcely any difference seems to exist betWeen two neighbouring groups owing to their dose proximity?6

Again we see the same tentative natural-purpose clause with a verb which distinguishes appearance from reality, and which states that the distinction, though obscure, nevertheless exists. 27 Again, Aristotle seems to be

24 Smyth 1956, 507-10. 25 Cf. HA 11.15 506a15; 11.17 508a16; and GA III.5 756032. 26 ~ yap cptxn<; }J.fTo.fjo.tllft O"VllfXWS ebra TWII iJ.vroxWII fis ni Wa lie" TWII (WVTWII }J.fll OUK OllrwlI lif (4xuIl. oUTwr W(1Tf OOKfiu 1Ta.I-'7TlllI JUlKpOV lilllcpipnu 8o.Tf.pOV 8anpoll Tee a-VllfyytJS aAAJjAOlS. 27 Cf. also a small selection of many passages: GA 1.2 716b5-9; 717a4-6; HA 510a21-23; 527b22- 24; 533,28-30: 540bl-3.

113 Analogy and Demonstration perfectly able to distinguish ascidians from sponges, and presumably these two groups from algae and the various kinds of terrestrial plants. That is, while the demarcation between animal and plant is difficult to observe, the sub-groups are clear enough, and they do not blend into one another. The reason, again, is that the demarcation between animal and plant is not so

much structural and based on parts as it is psychological and functional. Sensation and movement are considered to be essential features of animals,

and yet some animals are sessile. Sponges, when pulled off from their attachments die just like plants (681aI5- 17). Sponges and sea cucumbers have no sensation (681aI9-20). Ascidians are sessile like plants, but they are fleshy like animals and therefore probably are capable of sensation of a kind (681a25-28). The loci classici do not support the interpretation that the scala is so continuous as to erase the distinctions between genera. 28 In fact, dualizers, far from destroying the distinctions between groups, are a strategy employed to preserve the essential natures of the genera. The problem of dualizers occurs not because there are no generic differences,

but precisely because there are and those differences are set by the system of internally defined multiple differentiae. Only in a system of dichotomous division could we ensure that there are no dualizers. There is also clearly a normative component to the scala naturae. 29 One passage, for example (PA IV.I0 686a24-687a2), places man first among the animals because of his upright posture. Man stands erect because he is god-

like, and so must think and be wise. This hypothetically necessitates his being not earthy, since earthiness impedes thought. Man has the natural and normative posture (what we might call the default posture that occurs

if nothing prevents), and increased earthiness causes an animal to tend downward and so require four legs for support: Dwarf-like again is the race of the birds and fishes; and so in fact, as already has been said, is every animal that has blood ... The explanation, as already stated, is that in many their psychical principle is corporeal and impeded in its motions. Let now a further decrease occur in the elevating heat, and further increase in the earthy matter, and the animals become smaller in bulk, and their feet more numerous, until at a later stage they become footless and extend full length on the ground. (PA IV.l0 686b20-31)

28 Herein I concur with Granger 1985 . 29 Lennox 1985, 313-15, has argued briefly that the normativity of Aristotle's biology is overrated. Coles 1997 has collected the data and argued more fully and persuasively than anyone that Aristotle had in mind a single and coherent scala. He, however, did not directly address the possible conflict with analogical explanation.

114 Aristotle's Theory of the Unity of Science Other blooded animals are like dwarves having their upper parts larger than their lower; this presses them down, makes them quadrupeds (or worse) and incapable of thought. Such an argument has important implications for generic unity. For it can prove that viviparous quadrupeds are quadrupeds

without invoking the principle that quadrupeds have four legs; instead it uses man as a principle and demonstrates quadrupediry as a conclusion. For one of the premisses must state that quadrupeds are dwarf humans, and as such quadrupeds will be related per se to humans. This is either a clear case of Jlfj(J./3acns or it genuinely erases generic distinctions. Scalar arguments of this sort depend upon the highest member of the scale to provide a principle for all the members. But it is evident by the fact that Aristotle introduces many more specific principles to explain groups of narrower extension that he did not consider the broad scalar attributes fully explanatory. The subsequent changes from humans through quadrupeds and testacea to plants cannot all. be explained on the principle of increasing weight and dwarfishness. In fact, no single set of principles starting from man can explain the variery of animals and their parts, and Aristotle clearly does not suppose that they all can be completely explained as deficient humans. The normative status of the human is also undercut by the fact that this passage explicitly states that thinking is in man's logos. For this implies that thinking is a specific element in the definition of man, and as such is not present in the logos of other animals. The series argument, by_contrast,

suggests that 'human' will be a per se predicate of other animals inasmuch as they are deficient humans. That is, if they were not impeded by their earthy nature and defiCiency of heat they would be humans as well. But the denial of thinking as a part of their essence indicates that they are not principally to be defined as deformed (7I'E7I''1pwjJ.Eva), in spite of the fact that certain resemblances in their nature suggest

as much. In fact, Aristotle.

makes it just as easy to view man as a deviation from quadrupeds through the addition of his thinking faculry. His intellect makes him capable of using hands (PA IV.I0 687a8-23), and if he is to have hands, he must go on two legs, and so must be upright, and be less earthy than quadrupeds. On this view quadrupeds are causally primary and man is explained on the basis of them. It is unclear which order of explanation Aristotle thought correct. Ultimately the explanatory factors are so numerous and so complex that any attempt to create a single scala can only capture a few closely related genera of animals, and explain their attributes only in the roughest way. The posture scala would seem to treat birds as closer to man than quadrupeds, and yet the reproduction scala treats them as further removed.

Although Aristotle clearly thought that vital heat was the common element

US Analogy and Demonstration in these various scala, the accompanying attributes are not consistently covariant. As a result, each genus must still be treated independently. Aristotle does not introduce analogy in the biological context in order to facilitate and ground scalar arguments, but in order to complement their deficiencies. The need for analogues as stafting points cannot be eliminated by the occasional presence of arguments of scale or more and less. Without denying that analogues exhibit structural and material similarities and that sometimes these are scalar, they cannot fully explain the variation and distribution we find. Some aspects of apart's nature can be explained by scalar arguments, but other aspects are sui generis, and can be explained only within the genus.

4 The Structure of Focality

'Focal meaning' is a term that was coined by G.E.L. Owen to translate the phrase Trpo) €V A.eyOjlEVOV,1 !t is used in several Aristotelian contexts, and provides an explanation for why a word is applied to a variety of objects that are neither specifically or generically identical nor completely unrelated: [E]ssence will belong, just as the 'what' does, primarily and in the simple sense to substance, and in a secondary way to the other categories also, - not essence simply, but the essence of a quality or of a quantity. For it must be either homonymously that we say these are, or by making qualifications and abstractions (7J'po(J"nBivras Kal. dcpaLpovvTas) (in the way in which that which is not known may be said to be known), - the truth being that we use the word neither homonymously nor in the same sense, but just as we apply the word 'medical' when there is a reference to one and the same thing, not meaning one and the same thing, nor yet speaking homonymously; for a patient and an operation and an instrument are called medical neither homonymously nor in virtue of one thing, but with reference to one thing. (Met. 2 .4 l030a29-b3)

1 Earlier discussions of focality have tended to concentrate on issues of meaning, including G.E.L. Owen's (1960, 184), who called it 'focal meaning: Leszl, who has also treated thes~ issues extensively, presented them largely in terms of synonymy, homonymy, and meaning, and, unable to see how 'being' could apply to non·substance within this framework, supposed that it applied metaphOrically from its application to substance. See Hamlyn 19n-s for a critique of Leszl. For a new study in tenns of homonymy see Shields 1999. The debate is now emerging from the confusions of linguistic philosophy, and some attempts have been made to place focality and issues of meaning within the framework of demonstrative science, e.g., Ferejohn 1980 and Bolton 1995. For other attempts to remove Aristotle from the grip of conceptual analysis, see Irwin 1981 and 1982.

117 The Structure of Focality There must, then, be three kinds of friendship, not all being so named for one thing or as species of one genus, nor yet having the same name quite by mere accident. For all the senses are related to one which is the primary, just as is the case with the word 'medic~l'; for we speak of a medical soul, body, instrument, or act, but properly the name belongs to that primarily so called. The primary is that of which the definition is contained in the definition of all (Bonitz's 7rU(Tt for MSS r,J.llV); -e.g. a medical instrument is one that a medical man would use, but the definition of the contained is not implied in that of 'medical man.' (EE VII.2 1236a15- 22) So, too, there are many senses in which a thing is said to be, but all refer to one. starting-point; some things are said to be because they are substances, others because they are affections of substance, others because they are a process towards substance, or destructions or privations or qualities of substance, or productive or generative of substance or of things which are relative to substance, or negations of some of these things or of substance itself. It is for this reason that we say even of non-being that it is non-being. As, then, there is one science which deals with all healthy things, the same applies in the other cases also. For not only in the case of things which have one common notion does the investigation belong to one science, but also in the case of things which are related to one common nature. (Met. r.2 1003b5-14)

We can draw a number of preliminary and tentative conclusions from these passages: 1. In a certain sense focally related items share a name, for instance, medical skill and medical instrument; substantial being and qualitative being. However, focally derivative objects also have their own proper names (scalpel, quality, etc. ), and the common focal term is predicated of them in addition to this name. Properly speaking, then, they do not share a name, but have the same term predicated of them. 2. There is a focus or primary term whose definition or whose name is present in the definitions of the derivative terms, for example, medical instrument is by definition a tool useful for the medical man.' We get

2 For the substitution of a name for a formula in focality, see Ferejohn 1980, 118-19. Also, Met. Z.5 1030b23- 26: 'And such attributes [per se attributes1 are those in which is involved either the formula or the name of the subject of the particular attribute, and which cannot be explained without this; e.g. white can be explained apart from man, but not female apart from animal: On the replacement of the name for the definition, see Owen 1965, 262, who cites D1 21a29-32, APr 49b3-5; and Top. 101b39-102a1, 130,39, 142b2-4, 147b13-14, 149a1-3.

118 Aristotle's Theory of the Unity of Science definitions of primary items from definitions of secondary items and vice versa by addition (7rpo0"8«m) and abstraction (acf>aipEO"L<). 3. There is a group of relationships that qualify as focaL In addition to the examples listed in the third passage, others mentioned in the context of health and medical are preserves x, produces x, symptom of x, capable of x, possesses x, is naturally adapted to x, and is a function of x. 3 This is a very broad group and not restricted to the categories of Being. I will first take up the issue of eligible relationships and argue that these represent the variety of ways in which items in a normal science can be related to one another, and that as a result there is no structural difference between focal and normal science" I shall then return to the first two conclusions in the form of objections to this view. We shall find that the reason 7rPO~ EV AEyOj.l€Va share a name is because the terms are related by natural causal connections. It is these causal connections, rather than the commonality of name, that are fundamental and allow us to analyse focality in terms of demonstrations. On this basis we shall be able to distinguish between demonstrations of linguistic fact, which show why objects are called by the same term, and demonstrations of cause, which manifest the causal relations among the objects. We shall then be in a position to consider whether the focus term is identical with the minor term and the subject of demonstration. For it is reasonable to suppose that the focus term is what the science is about. A closer investigation, however, will force us to refine some of our ideas about the role of the minor term as the determinant of the subject-genus, and will lead us to expand our conception of the subject-genus in an important new way. We shall find that, though the focus is in a certain sense the subject-matter of the science, the derivative terms also form semi-abstractable and dependent subject matters. We have seen in chapter 1 that a normal science is constructed by selecting a subject-genus and developing demonstrations from its per se and universal' predicates. We also noticed that there is a relationship between the subject-genus and the divisionary genus, according to which a divisionary genus is divided into species, and both the divisionary genus

3 For EPYOV as function (i.e., final cause) see Met . Z.10 1035b16-18, where the soul is equated with the EPYOV; also 2.11 1036b30-32 and 0.8 1050a21-23. 4 Bolton (1995, 427) independently came to the same conclusion, noting that the per se relations of focal science are the same as those of demonstrative science according to the APo. His interest is not in categorial focality, however, but rather - if I may characterize it in my own tenns - with the core science of substance discussed in the later chapters of 2.

119 The Structure of Focality and its species may then form subject-genera for demonstrations. This relationship implies that a single subject-genus will be composed of a single kind of object. For example, when beaks are divided into straight beaks and hooked beaks, and hooked beaks are treated as a subject-genus, hooked beaks are all the same kind of thing. Confusion, however, arises when we try to treat as a subject-genus objects that do not form a single kind of thing, and that are not species derived from a division of a single genus, for example, hooked beak and being predatory. This confusion becomes especially acute when these objects are all described by the same term, and so appear to be species of a common divisionary genus and treatable as instances of the same kind of thing. Now, such confusion does not usually occur among objects that share the same name by accident. The attempt to treat capes (the article of clothing and the geographical feature) as a single subject-genus is too obvious a mistake to cause trouble. Serious difficulties, however, arise among homonyms that are related to one another essentially, but not as species of a genus. Medical instruments (scalpels) and medical people (doctors) are not species of the same divisionary genus, but they can be considered to belong in the same subject-genus, since there is an essential relationship between them. In fact, between every focal term and its derivatives there is a per se relation. Not only is the definitional inclusion criterion a guarantor for the essential relationship between the terms, Aristotle's list of focal relations also recalls the array of relations typical of normal demonstrations. Processes towards a focus and things productive of a focus, things naturally adapted to or functions of a focus are all explanatory causes of a focus, and so are descriptive of the immediate per se connections of demonstrative premisses. Symptoms are attributes of a focus and are descriptive of per se accidents or conclusions of demonstrations. Indeed, with the exception of the accidental predications (affections, qualities, etc., to be dealt with in the next chapter), all the focal relationships mentioned by Aristotle correspond to the causal explanations in normal sciences, and are described in the same way as the relationships between terms in normal demonstrative sciences. In fact, Aristotle himself draws the parallel between focal and nonnal demonstrative science in the Met. r.2 passage, where he explains the structure of the science of Being through a comparison to the structure of medicine. No one would dispute the fact that medicine is a science of the normal sort, and by showing that the science of Being has a structure corresponding to this science, Aristotle can argue that the science of Being is of the same basic kind. Just as the terms of medical science are not all drawn from the same divisionary genus, so it is also with the science of Being. It is only because medicine is uncontroversially a normal science

120 Aristotle's Theory of the Unity of Science that Aristotle can assimilate the science of Being to it, and argue that Being forms a subject-genus. Yet there are a number of important objections to the view that the focal relation is the same as the per se relation characteristic of normal

demonstrative science. At the most obvious level, focally related items share a name, whereas this is not explicitly the case among the terms of a normal science. And even if we are willing to dismiss that objection as a relatively trivial issue and concentrate instead on the logical and definitional relations, we still face problems with the criterion of definitional inclusion. Let us take these questions up in turn. It is important to be clear what focal homonymy consists in. Since

scalpel, patient, and so on are different names and refer to different things, there is clearly no homonymy among them. Likewise, there is no homonymy between quality, quantity, and substance. Homonymy arises only when a common term, medical or Being, is predicated of them, but each in a different sense. This way of viewing the matter gives the appearance of a one-over-many structure, and this is why Aristotle says that in some sense the focal term is predicated univocally (we' EV r.2 1003bl4-15):

medical is predicated of patient scalpel operation doctor in virtue of the relation of undergoing instrument means having The issue of homonymy, then, which results in an apparently universal

predication, is the problem to be solved, and when Aristotle solves it by invoking definitional inclusion, he effectively dismisses the issue of names.

For if names and the definitions of these names signify the same thing, then we can replace all the names with definitions and thereby eliminate the homonymy. For example, it does not change the structure of the science

of health if we just talk about food, climate, exercise, and disease, without explicitly saying that they are all healthy. The fact that they are all healthy things results from their being related to the primary item, not from their common name. That is, their focality does not arise from their being called

healthy climate, healthy exercise, or any other name, but from the fact

that their definitions contain 'health' in them. s Focal homonymy causes

difficulties only if we fail to make the distinction between the primary and

5 So also Bolton 1995, 428.

121 The Structure of Focality derivative terms. If we suppose that there is no difference between them, if we suppose 'health' is predicated of bodies in the same way it is predicated of climates, we make the typical Platonic mistake. To take a biological example, bone is focally related to flesh, since bone is defined as 'support of flesh.' Flesh is contained in the definition of bone, because flesh is a final cause for bone in animals that have it. We might say, then, that flesh is the primary fleshy thing, and bone is called fleshy, not because it has the attributes that flesh has, but in virtue of its relationship to flesh. But, of course, Aristotle never calls bone fleshy, because focality is not a strategy for creating homonymy, but for resolving homonymy by appealing to the per se connections characteristic of normal science; and the talk about a common predicate need only be made explicit when the homonymy is in current usage. Since it is obvious in what way flesh is related to bone, and we do not call bone fleshy, there is no need to make explicit the definitional inclusion latent in these terms. It is only in especially abstract cases, like Being, where the nature of the object is so difficult to determine, that such confusions arise. The fact that normal demonstrations in the natural sciences do not regularly make their focality manifest is irrelevant to the fact that these sciences are focal sciences and are focal sciences precisely because they are based on the causal connections of normal science. The per se relation gives us important information about the nature of focality. For focality is an application of the per se relations of ordinary science to solve a problem that arises from the confusion between the two senses of genus. Objects that because of their common name seem to be, but are not, members of a common divisionary genus, may fall within the same subject-genus. Since these objects are not specifically or generically identical, the only remaining way to include them in a single science is by relation. At the same time, focality and especially the examples of health and medicine provide important clues about the structure of ordinary science and the interpretation of the per se relation in that context. The definitional inclusion criterion suggests that whenever some item is used in a science, it must have the definition of the focal item in it. Because of this strict criterion for focal inclusion in a science, focality provides an answer to a question we faced in the last chapter, namely, whether common terms mean different things when used in different sciences. To judge by the focal relationship, the answer is yes, since the relation of the item to the subject matter must be specified in the definition of the derivative item. So, for example, in medicine the knife is medical and contains medicine in its definition, but in cookery the knife is culinary and contains cookery in its definition.

122 Aristotle's Theory of the Unity of Science

Focality and Per Se Predication I would like now to address in more detail the question whether focality is amenable to an analysis in terms of per se predicates and demon~ stration. There are good reasons why it should be. First, Aristotle announces at the beginning of Met. r that there is a science of Being qua Being and the attributes that belong to it per se (ov y, OV Kat Ta TOVTI!' lJ7rapX{'VTa
It is clear that focality involves predication. Healthy is predicated of drug, and in general healthy is said or predicated in relation to one thing, body, which is the primary healthy thing (TO UY
is healthy, because health is present in the definition of drug. Health is predicated of drug, because drug is by definition a material that brings about health. The fact that we now have a predication and a reason for asserting the predication leads us to make a first attempt to place these terms in a demonstration in such a way that the definition of the minor term serves as the middle term:

healthy IPQ material that brings about health material that brings about health IPQ drug heal th y IPQ drug There are a number of peculiar features in this demonstration. First, the conclusion itself appears to be an immediate per se fact. As we already

noted, the focal predication seems to be a per se (1) predication, and as such is immediate. This supposition is corroborated by the fact that health appears both in the major and the middle terms. And the repetition of the term suggests that there are one too many premisses here. If the conclusion is an atomic fact, then the deduction cannot be a demonstration. Second,

123 The Structure of Focality the demonstration seems to explain a linguistic fact, namely, why it is that

we call drugs healthy, rather than the natural causal relationship between drug and health. In order to show the linguistic fact of focality (i.e., that we call drug healthy), the derivative term (i.e., drug) will appear as the minor, the focus term (i.e., healthy) will appear as the major, and the definition of the minor as the middle. These two features suggest that this is not a proper demonstration, and for this reason it is a poor candidate on which

to base the structure of a focal science. We can instead formulate genuine demonstrations that make use of the focally related terms and that reflect the natural causal relationships of normal scientific demonstrations. Whereas the improper demonstration

that proves the linguistic fact consistently places the focal term in the major position, the demonstrations of natural connections are much more flexible,

and in fact place it in any of the three positions. Using as a model the causal demonstrations discussed in APo II.ll and the rather loose way in which Aristotle connects terms there, we can arrange the focally connected terms in a variety of ways:

healthy IPO material restoring the uniform state of the body material restoring the uniform state of the body IPO drug healthy IPO drug By substituting 'health' in the middle term with a definition of health, 'uniform state of the body,' we provide an explanation, not of the linguistic

fact anymore, but of the natural fact. Now, the explanation given here is the formal cause, and indeed, this sort of substitution will in every case change a demonstration of the focal linguistic fact into a demonstration through the formal cause. Obviously, too, in this case, the arrangement of the terms and the premisses will remain the same as in the linguistic demonstration. But when we provide other causes, we must often rearrange

or change the terms of the demonstration: taking drugs IPO restoring health restoring health IPO patient taking drugs IPO patient In this case the focus is contained in the middle term and provides the final cause. Middle and major can also be interchanged, thus changing the final into an efficient explanation. The focus will appear as the major, as in the linguistic explanations, but here the explanation is not of the term, but of

the fact:

124 Aristotle's Theory of the Unity of Science restoring health IPO taking drugs taking drugs IPO patient restoring health IPO patient Examples in which health occupies the minor position are rare, because health is a state of the body, and is generally predicated of man or patient. Moreover, objects that are predicated of health (e.g., good, desirable, useful, pleasant, harmony) seem to be poor candidates for focality, since we do not usually call any of these things healthy. The reason for this is that all these predicates are generic and extend more widely than the focus subject. But at least one seems amenable to this scheme: pleasant IPO having a uniform state of the body having a uniform state of the body IPO health pleasant IPO health So the arrangement of the terms in demonstrations of natural facts is different from and more flexible than demonstrations of linguistic (focal) facts' More important, according to this scheme the focally related terms can be arranged into demonstrations, and so actually pass muster as a science. It seems, then, that focally related terms must be arranged in this normal manner if there is to be a focal science. Moreover, as we saw, th e linguistic demonstrations are dependent on the natural causal connections, 6 When we manipulate the focal tenn$ to produce scientific (rather than linguistic) demonstrations, we change the nature of the per se connections among the terms. Now, Aristot.le leaves us in no doubt as to whether the causal definition passes muster as an immediate and ne<essary connection, for it is the staple of the demonstrations in APo II. But he does not discuss it in APo I.4, except if we interpret the fourth per se relation as causal (as e.g., Ferejohn 1991, 118-19, does). Nevertheless, the predicational arrangement in the major premiss is different from any of the per se relations, and bears comment. For to predicate something of the phrase that states its definition (e.g., man is predicated of two-footed animal) is covered by none of the per 5e relations, but it dearly forms an admissible demonstrative premiss. There are important results that come out of this observation. There must be more per 5e connections than those in Aristotle's list in APo I.4 and they must include such causal connections. These causal per 51'! connections aTe also definitionally related, but in a different way: a name is predicated of its own causal definition per Sl'! . It is the reverse of per se (I) predication in which a definitional element is predicated of a name; here a name is predicated of a definitional element. The causal per se connection is also different from the per se (1) con nection in that the causal per se connection must meet the coextension criterion. Whereas a genus term (which extends Wider) can be predicated per Sf (I) of a subject, this is not possible for causal per se connections, since causal explanations must operate at commensurate levels of universality.

125 The Structure of Focality and without these there would be no grounds for the focal relationship. Focal science, then, to the extent that it is science, depends upon the natural causal connections of nonnal science. The demonstration of the linguistic fact is only an apparent demonstration. Because the focal relationship is (usually) an immediate per se relationship, the syllogisms that show this are not strictly demonstrations. There are two principal problems in identifying focal and normal demonstrative science that have to do with the per se criterion. The first is that focality forces us to provide a single unified subject for a science, which all related terms must contain in their definitions. This is a demanding requirement, and one that we have already considered. While it is certainly true that in a normal science all the tenns are connected to one another through a series of per se relations, it seems impossible for them all to be connected directly to one single term through per se relations. After all, th~ conclusion of a demonstration states a connection that is not contained in the definition of its subject, and for this reason we might suppose that the major term is not focally related to the minor. As we saw in chapter 1, Aristotle recognized the conclusion as a per se connection, but not one that required immediate definitional inclusion. But if focally related terms are to appear in demonstrations, the conclusion must also have an immediate definitional connection. This, however, would destroy the nature of demonstration. There are two solutions for this problem. First, it may be that, after all, the definitional inclusion at work in focality is not the same as the per se connection, but instead may be something looser, like a relevance criterion that marks the derivative item as broadly related to the central subject of the science. This is an interesting possibility, since it would make the unity of a subject-genus dependent on something other than per se connections. Alternatively, immediate definitional inclusion may not be essential to the focal relationship. Instead, two terms may be focally related even if one is only the per se accident of the other. That is, the focal relationship may be transitive. There are two considerations which suggest that this latter possibility is the more likely. First, Aristotle does not draw the distinction between the two kinds of connection postulated in the first solution. He recognizes only per se connections made explicitly in definitions. Second, he clearly explicates the focal relationship in terms of per se connections, and these connections may be used to prove remoter connections. The possibility that focality is a transitive relationship is strongly suggested by some examples in r.2: things that are 'productive or generative of substance or of things which are relative to substance, or negations of some of these or of substance itself' are said to be (I003b8-10). To take an extreme case,

126 Aristotle's Theory of the Unity of Science it seems quite likely that even that which is productive of a negation of a quality of a substance will be said to be and so be included in the science of Being. Since these linguistic facts must be backed by natural causes, the transitivity of the linguistic facts will be matched by transitivity of the per se relations. For one term to be focally related to another does not, then, entail immediate definitional inclusion.

There is a second problem in interpreting the focal science as a normal demonstrative science, a problem that will lead us to a reconsideration of the nature of the subject-genus. We might expect the focus term to serve invariably as the ultimate subject of predication in the minor position. After all, a science studies a genus and its per se attributes, and APo I.7

75a42- b2 implies that the genus is that of which the attributes are proved, and this can only be the minor term . And yet it is clear that among the focally related terms the focus will frequently, and in the specific case of health most often, not be found in the minor or subject position. Not only will the focus not be the subject, but there will be a variety of different subjects and therefore a variety of different sciences. For if we accept the claim that the identity of a science is determined

by the minor term, then

either there will be many sciences where there should only be one (in the demonstrations given above, a science of patient, of health, of drug, etc.), or all these demonstrations must ultimately be attached to some basic subject, which will be the true genus of the science. An obvious candidate for such a genus is patient or man qua healthy. The latter is especially appealing, because it points to the two-fold answer to the question. The subject-genus is determined by the qua expression, but the subject of predication is what appears before the qua expression? This is Aristotle's practice in the PA. The ultimate subjects of predication are the animals, which have parts and attributes, but in each demonstration they are treated qua having some part or other, and this is the genus. So, for example, having lungs is the cause of having necks in animals that have necks (IlI.3 664a12-36). The subject of predication is animal, but not animal universally. In this passage Aristotle is talking about necks, so the subject-genus and minor term of demonstration is animals qua having necks:

having having having having

a a a a

neck IPO having a larynx larynx IPO having a lung lung IPO animals qua necked neck IPO animals qua necked

7 There is some evidence to suggest that the subject lenn must be a substance. APo 1.22 83,2-17; Met. Z.9 1034.30-32. Cf. Lewis 1991, 57.

127 The Structure of Focality Likewise in his discussion of cause as substance in Met. HA, Aristotle mentions two cases in which an attribute belongs to a substance, but not straightforwardly in virtue of that subject. When we seek the cause for things, we must beware what we are seeking the cause of: Nor does matter belong to those things which exist by nature but are not substances; their substratum is the substance. E.g. what is the cause of an eclipse? What is its matter? There is none; the moon is that which suffers eclipse ... In the case of sleep it is not clear what it is that proximately has this affection. Surely the animal, it will be said. Yes, but the animal in virtue of what, i.e. what is the proximate subject? The heart or some other part. Next, by what is it produced? Next, what is the affection - that of the proximate subject, not of the whole animal? Shall we say that it is immobility of such and such a kind? Yes, but to what process in the proximate subject is this due? (1044b8-20)

The subject of predication in the case of eclipse is moon, a substance. And since asking what an eclipse is is the same as asking why darkne~s is predicated of the full moon (Z.17), the subject of predication is a substance, moon, but not moon without qualification, since the eclipse occurs only when the moon is full. Similarly sleep is an affection of animals, and animal is the subject of which it is predicated, but it is in virtue of some part of the essence of animal that sleep belongs to it, namely, the heart. To return to the case of health, under this interpretation we would modify the minor term so that it is not the focus, but is itself a derivative term, that is, not health, but that ·which has health as such, for ultimately we need as a subject a recipient of the state of health. With that in place it may be possible to discuss the entire science of health as both a focal science and one with the subject of health as such as the subject of the science, for the minor term is considered only insofar as it is the recipient of the focus term. In the first two demonstrations we provided above, we can easily substitute 'patient' for 'that which has health as such.' In the single case we considered in which the subject was health, we can again easily reformulate it so that pleasure is predicated of the healthy subject as such. In sum, the focal science can be interpreted as normal science, the focal term being the genus of the science, and its substrate, if it has one, being the subject of predication or minor term of the demonstrations. 8 8 This also distinguishes focality from paronymy to which it is often likened. For the paronymy relationship exists between a substantive noun and its corresponding adjective, e.g., courage and courageous (tivopda and avep€tos-). Paronymy makes no commitments regarding the categorial status of the paronyms: the word from which

-------------------------

128 Aristotle's Theory of the Unity of Science The final and most important challenge to the view that focal science is logically identical with normal science argues that I have simply misinterpreted Aristotle's basic intentions. Aristotle, the objection contends, did not think of the focally derivative terms as the per se accidents and causes of the focally primary term, and did not intend to force them into a demonstrative mould. Instead he was concerned to show how various subject-genera each with its own causes and per se attributes might he considered as parts of a single science. My solution may solve the problem of unity but at the price of destroying the architecture of focal science that Aristotle wanted to account for. The 'normal science' solution simply does away with the derivative terms as subject-genera, and makes them instead into causes and attributes in demonstrations concerning the focal subject-genus. This challenge is important because the answer to it opens up a new and wider conception of subject-genus and clarifies the connections between focality on the one side and analogy and semi-abstraction on the other. Focality is the meeting-point of two conceptions of subject-genus. The narrow subject-genus, now very familiar, is proper to the realm of demonstration. It is the subject of the demonstration, and attributes and causes are predicated of it. Since these attributes and causes do not belong in the same divisionary genus as their subject-genus, they are included in the subject-genus by focality . This focal inclusion of other terms is uncontroversial, and indeed a necessary condition for demonstrative proof as we saw in chapter l. But there is a wider sense of subject-genus, beyond that of both the minor term of a demonstration and the whole demonstration together. Many of the terms that are used in a demonstration, and that are therefore bound to the specific subject-genus per se and universally, may be abstracted to some degree from that subject-genus and treated as subject-genera in their own right. In many cases, and in all cases of natural substances, perfect conceptual abstraction will be impossible. The semi-abstracts maintain their per se - though not their universal- connections to the genus from which they are abstracted. When there is a variety of terms that are abstracted in this manner and treated as semi-autonomous subject-genera, they may be drawn back together in virtue of their remaining per se relations into a single focal science. This view of focal science does not attempt to fit the paronym is derived need not be a substance, though it must be a noun. By contrast, the focus must be that of which attributes may be predicated, even if the subject need not be a substa nce as such. The subject of health does not have to be man, but only that subject which admits of health.

129 The Structure of Focality focally related terms into a single demonstrative syllogism; it is rather a means for organizing semi-autonomous subject-genera.

There is no doubt that this is a great organizing principle of Aristotelian science. In Aristotle's lists of the focal relations we can virtually read off the treatises of his biological works: the affections of animals are the subject of the HA, generations of animals are the subject of the GA, the preservation and destruction of animals are the subject of Juv., instruments of animals are the subject of the PA and lA, the various activities of animals are the

subject of the MA, PN, and DA . Since the focal term is animal, we might look for a subject-genus of animal apart from all the derivative sciences. Of course, it does not exist separately,9 Animal is always the ultimate subject of predication, but it is always qualified by some qua expression. This system of organization is not peculiar to the biological or even to the theoretical works. The ethics too manifests all the traits of a wide focal science. It studies. eudaimonia, which is defined as activity in accordance

with virtue. Accordingly, EN III and IV discuss the various species of virtue, courage, liberality, and so on. They also study the things focally related to virtue, the negations of virtue, vice, and later those things, like friendship, that contribute to virtue. So once again, focal science turns out to be normal science, though this wider view describes new aspects of scientific organization. The wide and the narrow view of focal science are hardly exclusive, indeed they form a two-stage organization related through the nexus of semi-abstraction. A term that is a focal member of a narrow genus may be semi-abstracted from that narrow genus to become a subject-genus of a new science. But since it has been only semi-abstracted, this new subject-genus remains

focally related within the wider focal science. An important corollary of this connection between wide and narrow focal science is that the subject of predication of the narrow science is the

same as the focus of the wide science. In the zoological works it is always animal. In the narrow science the subject of predication is animal without qualification, while the several biological treatises themselves are focused on animal qua this or that feature .

The Limits of Focality in the Biological Works Before turning to the metaphysical focalities, I want to discuss an aspect of biological focality in the demonstrative mode. Focality is a means of 9 Aristotle suggests that it can exist, but that it is too cumbersome to treat animal s in that way (PA 1.1 639alS- 29).

130 Aristotle's Theory of the Unity of Science treating generically different terms as belonging to the same genus. How far outside the divisionary genus can one go, and still remain within the

subject-genus? Can or does Aristotle use the techniques of focality to develop a logic of interdisciplinarity? Just as scalpels are part of the medical science through focalization, so we might expect nests to be included in the study of birds (because they are the shelter for birds), or even antelope to be included in the study of lions (because they are the prey of lions). In fact, Aristotle generally remains within quite narrow limits in the biological

sciences. His procedure may be contrasted with evolutionary theory, which finds sources of explanation both in the internal nature of the animal and in the external environment. The genetic code proposes and the environment disposes; the environment poses a problem that the genetic code must solve on pain of extinction. Evolutionary biologists explain features of animals as adaptations to the environment, and so make the environment (e.g.,

niches) a source of explanation for the animal. The study of ecology, the way species are affected by one another and by inorganic factors, is a natural development of this mode of explanation. Aristotle for the most part avoids explanatory factors that come from outside of the animal, and when avoidance is impossible, he redescrihes them so as to make them internal to the animal's nature itself. So, for example, the environment is

described as a way of life or {3ios internal to the animal. Marsh birds are well adapted to marshes, not because the marsh environment has exerted evolutionary pressures, but because it is the internal nature of

marsh birds to live in marshes, and if they are to do so, they must have such and such features. This is consistent with Aristotle's general system

of explanation in the PA, which provides the causes of parts of animals from within the essential functions and activities each animal perfonns.

The reason why Aristotle chooses this method is fairly clear: his method privileges unity of definition, while the evolutionary account makes a large

part of the cause and therefore the essence of an animal external" to the animal. Obvious difficulties arise if we make antelope focally related to lions because they are prey for lions. For in the definition of the antelope would be found the fact that they are essentially food for lions. The problem here is not that this would represent a constraint on natural teleology, but rather that those constraints would come from the outside rather than, as Aristotle invariably presents them, from within, either as material limitations or as limitations imposed by the need to fulfil other functions. Aristotle does, however, discuss some cases where environment, living and non-living, plays a role. The terrestrial and marine environments

provide sources of explanation, but they have been focalized and are

131 The Structure of Focality represented as land animals and water animals.lO These definitory facts of their {3io, explain the different kinds of limbs and modes of respiration. Habitat may also have a more specific influence: the hot and dry environment of Libya seems to grow large animals (PA II.9 655aS-1O). Man has the hairiest head because hair shelters the head from excessive cold and heat (PA II.14 65Sb2- 7). Among the living environmental factors, some animals are related to other animals

by the f3{or; of being- carnivorous. Bones

of carnivores, for example, are hard because they have to fight for their food (PA II.9 655a12-17). We also find adaptations designed for defence or preservation (aAK~ and O'wT'/Pia). But only rarely (as with eyebrows and eyelashes, PA II.l5 65Sbl4-15) does Aristotle state explicitly what external threat these parts provide defence against. Now, Aristotle does not provide a hypothetical deduction for the existence of parts instrumental for defence, but if he had, his clear inclination would be towards explaining them as hypothetically necessitated by the life of the animal, rather than as means to avoid being injured by something external. This tendency towards exploiting internal principles of explanation has some effects on his selection of facts for which he provides explanations. In explaining why some animals lack certain modes of defence, he never cites lack of external threats but only notes that the animal's own nature prevents such defence from being useful. The major source of external causation, however, is in the explanations for sensation. For the organ of sensation is potentially what the sensible object is actually, and the nature of the sense organ must correspond to the nature of the sensible and the medium for the sensible. Since the actual is prior in knowledge to the potential (Met. 0.S), external sensible objects will have a causal role in animals l l So since the organ of touch deals with more than one kind of sense-object, it must have several oppositions in it, even though it is a uniform part (PA II.l 647al4-19). Likewise, the ears are placed on man halfway around the head because they have to hear sounds from all directions (PA 11.10 656b26-29). Environment also clearly plays a role in the explanation of why fish have fluid eyes (PA 11.13 65Sa3- 10): 10 Cf. Top . VI.6 144b31-145al: 'See, too, if he has rendered being in something as the differentia of a thing's substance, for it seems that locality cannot differentiate between one substance and another. Hence, too, people condemn those who divide animals by means of the terms terrestrial and aquatic, on the ground that terrestrial and aquatic indicate locality. Or possibly in this case the censure is undeserved; for aquatic does not mean "in" anything; nor does it denote locality, but a certain quality; for even if the thing is on the dry land, still it is aquatic - and likewise a land animal, even though it is in the water, will still be a land animal and not aquatic.' 11 See Cleary 1988, 57.

132 Aristotle's Theory of the Unity of Science For animals that move much about have to use their vision at considerable distances. For land animals, the air is transparent enough. But the water in which fishes live is a hindrance to sharp sight, though it has this advantage over the air, that it does not contain so many objects to knock against the eyes. For this reason, nature, which makes nothing in vain, has given no eyelids to fishes while to counterbalance the opacity of the water they have eyes of fluid consistency. (modified ROT)

Sense perception is not only an external cause; it is also the ultimate final cause of animals, and all other parts and functions are in one way or another instrumental towards this end. In fact, all the major soul faculties and their objects (nutrition, sensation, and intellection) provide explanatory grounds outside of the animal in the wider world, and in all three cases . Aristotle provides this connection with a theoretical basis in potentiality and actuality. So the material in the environment that animals ingest is given a functional description as a potentiality and is consistently called food (TpO~) (e.g., PA II.3 650a2-8). Only rarely does Aristotle describe food in independent per se terms. For example, in his discussion of beaks, the kind of food each bird eats provides an explanation for the shape of its beak. Crooked-taloned birds have hooked beaks because they feed on flesh; their beaks are useful for them to master their prey and for the exertion of force. Conversely, some birds have finely constructed beaks, because they pick up seeds and minute insects. Swimming birds have broad beaks because they dig for roots, and sometimes they have a sharp point at the end of the beak by means of which they may easily deal with herbaceous foods (III.l 662a33-b16). There is one notorious case of environmentalism (PA IY.13 696b2431): [In] the dolphin and the Solachia, [the mouth] is placed on the under surface [of the body]; so that these fishes turn on the back in order to take their food. The purpose of nature in this was appar~ntly not merely to provide a means of salvation for other animals, by allowing them opportunity of escape . . . but also to prevent these fishes from giving way too much to their gluttonous ravening after food.

If we are to follow the strict criteria of APo, 'preserving other animals from them' must be per se related to dolphins and selachia and therefore part of their definitions. It is probably for this reason that Aristotle provides an alternative internal explanation for their mode of eating, which he seems to consider more likely, namely avoiding the dangers inherent in the natural gluttony of sharks.

133 The Structure of Focality The extent to which Aristotle has restricted his use of external explanations is dear through a brief comparison with some of the explanations Plato provides in the Timaeus. Throughout the description of the structure and composition of man, we find theological and moral principles invoked: the head would have survived much longer if it were fleshy, but it would have been less sensitive, and since it is better to live a short but good life, rather than a long but inferior one, the gods ordained the former (75b-c). The final cause of the liver is said to be the means for receiving prophetic dreams (71d-72b). All other animals are food for humans (77a-c). Even geometry provides principles: weaker triangles from which food is made are overcome by the triangles of the body, which break them down for use (81c--
12 See Cleary 1995, 71f£., for a discussion of Aristotle's critique of Plato's use of mathematical principles in physics.

5 Metaphysical Focality

Our study of the definitional inclusion criterion and Aristotle's examples of health and medicine have led us to interpret focal science as structurally identical with normal science. We must now apply this interpretation to the science of Being and consider whether metaphysics fits the model of normal science. The importance of medicine and health as examples of sciences has been largely ignored or denied. Most commentators have been content to focus on the issue of homonymy and its logical form without considering the scientific implications of the examples' Owen, however, related focality to the issue of the autonomy of sciences and argued that focality provided Aristotle with the means to unify the science of Being, and thereby to establish a qualified return to Platonic universalism.' Ferejohn has extended this observation and attempted to provide a sketch of what the focal science of Being would look like.' He confined his remarks to Met. r .2 and even within that chapter dealt only with the relation between substance and the non-substantial categories. But he made the important advance of treating the science of Being as a demonstrative science. He interpreted the science of substance as a superordinate science over the subordinate sciences of non-substances. The theorems to be proved in the subordinate sciences were proofs of the existence of some of the objects in those sciences. On the grounds that science A is superordinate to science B if some of

1 E.g., Owens 1978, 119; Ross 1924, i, 256. Kirwan 1993, 81, comments only on the inadequacy of the illustrations to vindicate the possibility of metaphysics. Burnyeat et a1. 1979, 25-8, do not mention these cases at all. Ferejohn 1980 and Bolton 1995 are notable exceptions. 2 Owen 1960, 1965. See Shields 1999, 225-36, for a criticism of Owen's position. 3 Ferejohn 1980.

135 Metaphysical Focality the principles of science B are proved within science A, Ferejohn argued that the existence of quality can be proved from the principles proper to the science of quality. One of the principles of the science of quality is the statement that translates 'quality exists' into 'quality is predicated of substance.' But that translation principle contains 'quality is predicated of substance,' and Ferejohn claimed that if this statement is provable at all, it must be provable in a science whose genus is composed of substances, that is, in the superordinate science. 4 Ferejohn made only modest claims for this attempt to relate focal Being to the theory of science. He did not try to extend the interpretation to cover the other focal relations mentioned even in r.2, nor did he deal with the discussion of categorial focality that arises in the early chapters of Z. But apart from the fact that Ferejohn did not provide a comprehensive theory, there are reasons for rejecting his suggestion that we should interpret the relation of substance and non-substance as a superordinate-subordinate relationship. Although there are some hints in the text that point in this direction, Aristotle makes no mention of the paradigm case of superordinate and subordinate sciences, geometry and optics, in connection with the focality of BeingS And yet we would expect him to call upon this example rather than develop the new, or at least seldom used, example of medicine which makes no pretense of illustrating the superordinate-subordinate relationship at all. There are philosophical objections as well. A superordinate science is capable of being formulated in complete abstraction from the genus of the subordinate science. Geometry qua geometry has no per se relations to optical rays. If it had, it would not be a superordinate and different science. If the science of substance qua substance were superordinate, then we would expect it to have no per se connections with the non-substance. But in fact this is not so. One of the essential functions of substance is to be a substrate, that of which other things are predicated but which is itself not predicated of anything else. In virtue of this nature, substance is per se related to predications of non-substance. Ferejohn admits this fact freely, indeed, it is necessaty for his argument that' quality is predicated of substance' be proved within the science of substance. But it is impossible for a superordinate science to have such per se relations with the subordinate science, and for this reason the superordinate-subordinate model must fail. 4 Ibid., 126. 5 Aristotle says that the focus is called a principle, and the other things are said on account of it (l003b5-6; lOO3b16-17); he also says that these parts of the science of Being may be arranged like universal and special mathematics (1004a6-9) .

136 Aristotle's Theory of the Unity of Science Yet Ferejohn has pointed the way towards interesting possibilities, since Aristotle himself extends the promise that the science of Being will be a demonstrative science.' In this chapter I want to explore a group of related issues concerning the science of Being. This exploration is not intended to be a systematic exposition of Aristotle's doctrine, because in many respects

Aristotle allows us only the most tentative and sketchy conclusions. This is nowhere more true than at our starting point, Aristotle's avowed reasons for denying a genus of Being. In fact, I shall conclude rather reluctantly that the reasons for his denial are relevant to the focal solution he proposes only in the most general way. I shall then go on to consider focality in the context of the categories of Being, and finally broaden the discussion by considering the rather neglected focal relation between the One and Being. On all these issues the difficult and ambiguous texts require both c.a ution and speculation.

The Genus of Being The reason that focal analysis has to be applied to Being is that Being does not form a genus. Under the conventional understanding, therefore, it cannot form a single subject-matter for a single science. Although Aristotle repeatedly stresses that Being cannot form a genus, he usually treats this as an assumption, and argues the thesis only in one brief passage in the aporetic book B of the Metaphysics.' It would stand to reason

that this argument should shed light on the focal science of Being that Aristotle introduces. However, the context of the passage iS ,an argument

against the Platonists, who hold that the highest genus is the highest principle. Since Aristotle merely needs to refute the Platonists, he need not introduce a full-blown theory concerning the categories. Nevertheless, the

6 Met. B.2 997a25-33: 'Further, does our investigation deal with substances alone or also with their attributes? I mean for instance, if the solid is a substance and so are lines and planes, is it the business of the same science to know these and to know the attributes of each of these classes (the attributes which the mathematical sciences prove), or of a different science 7 If of the same, the science of substance also must be a demonstrative science; but it is thought that there is no demonstration of the essence of things. And if of another, what will be the science that investigates the attributes of substance?' 7 There is a brief recapimlation of this argument at K.1 1059b31-34. For Being being said in many ways: DA I.5 410a13, Met. E.2 1026a33, Z.l 1028a10, Z.4 l030bll, H.2 1042b25, 8.10 1051a34, 1.2 1054a14. Being falls immediately into genera: r.2 1004a5, 1\.4 1070bl-2. For a recent treatment of this argument see Shields 1999, 247--60, who argues against its relevance to the categories. His book was published too late for me to take proper account of his argument.

137 Metaphysical Focality argument is important since it supports a position that Aristotle clearly held and without which there would be no need for a solution of any kind at all. Aristotle argues that there is no genus of Being because a genus term cannot be predicated of the differentia taken by itself apart from the species: But it is not possible that either unity or being should be a genus of things; for the differentiae of any genus must each of them both have being and be one, but it is not possible for the genus to be predicated of the differentiae taken apart from the species (any more than for the species of the genus to be predicated of the proper differentiae of the genus) (B.3 998b22-26)

The argument consists of two premisses: no genus can be predicated of its differentiae, and Being must be predicable of all differentiae. of course, from these premisses Aristotle is only permitted to conclude that Being as a genus is not predicated of its differentiae. But since Being is such a predicate that it must be a generic term and express the essence of whatever it is predicated of, Being can only be predicated as a genus. For details of the reasons why a genus cannot be predicated of its differentiae, we must turn to Topics VI.6 144a31-b3: 8 Again see if the genus is predicated of the differentiae; for it seems that the genus is predicated, not of the differentia, but of the objects of which the differentia is predicated. Animal (e.g.) is predicated of man and ox and other terrestrial animals, not of the differentia itself, which we predicate of the species. (a) For if animal is to be predicated of each of its differentiae, then many animals will be predicated of the species (Eioovs"); for the differentiae are predicated of the species. (b) Moreover, the differentiae will be all either species or individuals, if they are animals; for every animal is either a species or an individual.

In spite of the specific example Aristotle has chosen, this argument seems to be of general application, and there does not appear to be anything preventing our applying it to Being. We may best begin with Aristotle's 8 Ross 1924, i, 235, cites this passage as an explanation of the Metaphysics passage, and provides the following interpretation: '(a) If Igenus were predicated of the differentia], the genus would be predicated of the species many times over, since it would be predicated of each of the successive differentiae which constitute the species. (b) If "animal" is predicable of each of its differentiae, each of them will be either a species or an individual, since "an animal" always means one or the other.' There is no reason to suppose with Ross that Aristotle has successive differentiae in mind. As in 2.12, the iteration of the predicate is not impossible, just redundant.

138 Aristotle's Theory of the Unity of Science second objection (b), which is clearer and more cogent. Like the Metaphysics passage this argument depends on the presupposition that a genus term by its very nature as a genus term can be predicated only of species, and whatever a genus is predicated of must for that reason be a species. The

clause 'if they are animals' (Er7fEp (0a 144b2), implies that the genus must be predicated as the what-is-it (TL fUTL) of the differentiae, and so if animal is the genus term predicated of the differentiae, then the differentiae must be species (or individuals) of animal. Since biped is obviously not a species of animal, the genus cannot be predicated of differentiae. This argument prompts us to think of the genus as a pile of objects to be divided up. If this pile is to be divided by differentiae, the differentiae cannot be members of the pile, since the differentiae function quite differently from a species of the genus. And so if we place the differentiae in the genus, we would have to include both the items in the pile and the criteria used to distinguish one sub-pile from another. The first objection is less obvious and less cogent, but it probably involves the issue of babbling ("OO'\EOX"")' a dialectical misdemeanour (SE 3 165b12- 17) perpetrated when someone repeats himself (usually implicitly) a number of times. Strictly speaking, babbling occurs in the context of relative terms (SE 13 173bl-11) and so is not properly applicable to this situation. Notwithstanding, Aristotle probably has in mind a less vicious form of babbling, in which the same information is given twice, once explicitly through the genus of the species and once again implicitly through the genus of the differentia. If there are multiple differentiae for one species the genus will be given many times. 9 Now, Aristotle claims that both the differentia and the logos of the differentia are predicable of the species (Cat. 5 3a22-28). If that logos contains a genus term, then the genus of the differentia will also be predicable of the species. So man, who is a biped animal, may have two genera predicated of him, animal and legged, if legged is the genus of biped. Aristotle requires this conclusion in order for the babbling charge to hold. And yet this same conclusion opens up the possibility of a genus being predicated of a species, but not as a genus of the species (legged is not the genus of man), and this seems to

9 So Ross 1924, if 235. Alexander objects that these arguments are tOO dialectical (206.12-13) and provides a couple of counter-examples. First, if all differentiae are qualities (7Tot6v), then the differentiae of quality will be qualities, and so in the category of quality, the genus will in fact be predicated of the differentiae. Second, even if the immediate genus is not predicated of the differentia of a substance as, for example, biped taken by itself is not animal, yet at a higher level biped is ollsill . Alexander's two objections arise out of the unclear categorial status of the differentia.

139 Metaphysical Focality undermine Aristotle's argument against the genus of Being. For if we are not saying the same univocal thing twice, then we cannot be babbling. Even

apart from this difficulty, babbling is at worst a venial sin, one that anyone talking about the physical realm is bound to commit. The definitions of snub nose and all natural substances also entail babbling (Met. 2.5), but this does not immediately exclude their being defined. They may still be defined with a qualification. We face further problems when we apply the general argument of the Topics to the specific case of Being. According to Aristotle's objection (a), if we admit a genus of Being, we are forced to babble, since all definitions will take the form, 'x is a Being differentiated by y whiCh is a Being.' According to objection (b), a species is a Being with a differentia, which is itself a Being. This species, then, would be many Beings, whereas in fact it is just one. Again, the predication of the genus is to be taken in the strictest sense: the genus is always predicated of species and when predicated always creates species. Under this interpretation, a species like

man will not just be many Beings (which hardly seems problematic if we understand animal and biped as two Beings), but he will be many species. Since a man is essentially his differentiae, if his differentiae are species of his genus, he will be several species of the same genus, and the unity of man will clearly be lost. This strict interpretation of the genus predication reveals further presuppositions of the argument. It is not possible for one object to be two species, and the what-is-it question must have a unique answer for every well-formed object. This presupposition becomes clear when the correct genus is predicated of the differentia, for though the object will have two different genus terms predicated of it, if its differentia is part of the what-is-it of the species, it will not belong to two genera, since the genus of the differentia is not the genus of the species (e.g., man is legged, but legged is not his genus). By contrast, when we attempt to predicate the genus univocally of its differentiae, the differentiae become species of the genus in the same sense as the species (e.g., man) themselves. Aristotle also presupposes that if the genus is predicated of a differentia, then that genus cannot create species that will stand alongside (i.e., be cogeneric with) the species of which the differentia is predicated. This is tantamount to saying that the genus and the differentia play different roles in definition and classification. If we try to predicate a term like Being of both the species and the differentia, then we are assuming that, if Being is univocal, it is being predicated in the same way, whereas in fact it is not. To be a genus, then, implies among other things that its species are of the same logical and predicational type.

140 Aristotle's Theory of the Unity of Science

If we insist on a unified genus of Being, Aristotle argues, the individual and species will become many and lose their unity. We must therefore sacrifice unity at the highest level of generality in order to achieve unity at the lower levels. Genus and differentia will be different kinds of Being, but the species will be a single thing, a unity of genus and differentia and not two species. Given Aristotle's prejudice towards the species and the individual, this is a reasonable response. Uniry at the lower level is maintained by distinguishing different kinds of predication. Plato, by championing the unity of the genus in the theory of the Forms, did not allow for the unity of the species or individual, and as a result a thing becomes many by participation. All the forms exist equally and have a common nature to the extent that they are forms, and each species falls under many kinds. Aristotle alludes to the Platonic origin of this problem in a different context, Metaphysics H.6 1045al4-17: What then is it that makes man one; and why is he one and not many, e.g., animal and biped, especially if there are, as some say, animal itself and biped itself> (modified ROT)

There are a number of ways of interpreting the claim that Being is not a genus. Drawing on the class model, we may suppose that the differentia, since it is Being, will be a member of the pile of Beings; but since it is a differentia, it must be the criterion by which the piles are divided. If a differentia is a criterion, it cannot be a member, and so cannot have Being. Conversely, if it is a member, we shall need a new criterion by which to divide the pile. Nothing on this view prevents all existing things from forming a pile, but this pile cannot be divided and therefore cannot be a genus. It must remain one pile, indeterminate and indeterminable, an inchoate unintelligible AIL Not only can it not be divided, but nothing positive can be said of it at alL Certainly no predicate can be applied to it, since that predicate is Being, and therefore must be applied to all Beings and itself. Since the predicate is a Being, we must still find something predicable of all Beings, and so we must look for a further predicate, and so on to infinity, In this way the genus of Being falls victim' to a third-man argument. Again, Aristotle assumes as a premiss of his argument that all differentiae are Beings and, as such, have Being predicated of them. 1O As a result,

10 B.3 998b23-24; at Top. JV.6 128a26-29 they are nOta.

l41 Metaphysical Focality Being cannot be predicated of them as a genus. But as 1.2 l 053b20- 21 says, Being is the most universal of predicates, and so Aristotle seems to be canvassing the possibility that even if Being is not predicated as a genus, still it is a univocal universal predicate. But none of the other predicables definition, property, or accident - seems to be a possibility. In saying that differentiae are, what else are we saying than that Being is their genus /" Since Being is predicated of all Beings, but is neither a single genus nor any other predicate, it follows that Being must predicated as more than one genus: the Signification of Being must be different for the species and its differentia. Being, therefore, is not a general predicate. Even if Aristotle had something like this interpretation in mind, it nevertheless fails as a problem that the categories solve. His argument merely requires that differentiae and species not be in the same sense, as the pile analogy makes clear. It does not require the ten ca tegories as a solution. In fa ct, it does not require any of the canonical ca tegories at all. How does he intend to bridge the gap / He does not explicitly provide an argument, but he may. have had something like the following in mind. There is no genus of Being, that is, of everything. But let us accept that there are some genera, if only, say, low-level genera, like animal, that are divisible into species. Animals, then, form a genus in the heap of Being. Now we ask whether there is anything that prevents animal from being a member of a higher genus, living things. If nothing prevents, we may proceed to form a higher genus and continue the procedure up to the highest level possible, that of the categories. At this point we are prevented from going further. The categories are genera, but they are not species of 11 According to Loux 1973, while Aristotle's argument that there is no genus of Being is valid, it does not entail that Being is equivocal. He is not satisfied with Aristode's indirect method of es tablishing that there is no genus of Being, and accordingly he provides his own argument, which is predicated on his understanding of genus. For Loux a genus is an answer to the what-is-it question. And for there to be such an answer, 'there must be competing, incorrect answers,' that is, other genera (230). A genus, therefore, must have a place in a classification system. Loux then goes on to argue that 'one can make sense of the claim that T-words [transcendental tenns like being and one] are ambiguous on ly if he grants implicitly that the claim is false' (236). For the categories are, according to Loux, a classification of things that are, and to speak of 'things that are' is to assume an unambiguous sense of the term. Loux's understanding of genus is mistaken. In fact, his description applies not to a genus, but to a speci es, which is what it is by being differentiated from another species. A genus is determined internally, without reference to differences from other thi ngs, as we have already seen in the biological works. See Loux's retraction (1991, 27n29). For another view of the argument see Wein 1983.

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142 Aristotle's Theory of the Unity of Science any further genus. 12 The determination that Being is ambiguous along the lines of the categories is the result of a closing in on these highest genera from two sides. The first argument establishes that Being is not a genus, but rather a heap, and then since there are genera, there must be highest genera, and these must constitute the ultimate groups or parts of the heap. But as Alexar:tder observes, the introduction of the categories creates

more problems than it solves B If all differentiae are ?TOt", as Aristotle claims at Topics IV.6 128a26-29, then the genus of a quality will be predicated of its differentia. And even if we defend Aristotle on the grounds that he distinguishes ?TOt" as differentiae (a 'sort of' or determination of a genus) from categorial quality, then 'we must still answer the question about the categorial status of the differentia. 14 If it is not to be placed in any category at all, then there will be no reason to worry that the genus will be predicated of the differentia and there will be no argument against a genus comprising the rest of categorial Being.

Since this is the only argument Aristotle provides for his claim that Being does not form a genus, it is important to ask how it is related to the solution Aristotle apparently developed for it, focality . The argument against the genus of Being involves a fundmental distinction between genus and differentia, and the categories seem at best secondary in this scheme. If we assume that genus and differentia are the principal kinds of Being, then we should expect these to enter into the focal relationship. On this interpretation genus would be ·the primary and differentia the derivative Being, containing in itself the focal term, genus. This is a plausible interpretation of the relationship, since differentia is arguably a per se (2) predicate of genus. There is a focal solution that corresponds to this problem, precisely that which solves the aporia quoted above in the passage from H.6 1045al4-17. The genus animal is potentially man, and the differentia biped is man in actualiry. They form a single thing just because they are focally and per se related to one another, as we shall see more clearly in chapter 6. Genus and differentia, then, cannot be in the same genus of Being, but they can be studied by the same focal science of 12 So Met . 6.28 l 024b9-16: 'Those things are said to be other in kind (TeP )'fllH) whose ultimate substratum is different, and which are not analysed the one into the other nor both into the same thing ... and things which belong to different categories of being; for some of the things that are said to be signify essence, others a quality, others the . other categories we have before distinguished; these also are not analysed either into one another or into some one thing:

13 In Metaphysica, 206.13-22. 14 Cf. Met. Ll.14, which distinguishes the senses of 7TOWV (differentiae from the ·attributes of natural bodies); K.12 l068b18-20.

143 Metaphysical Focality Being. All the same, this is not a solution that applies to the categories. Substance is primary, and categorial Being, not differentia, is derivative. In fact, since differentia is part of substance, it too will be primary, not

derivative. 15 So clearly the problem of Being in Metaphysics B is not a problem solved by the form of categorial focality we find in Z. Now, one might point to Met. H.2 and its assimilation of the differentiae and Beings in non-substantial categories. If differentiae of substance are predicated in all the non-substantial categories, then the argument may point the direction towards the genera of the categories. However, nothing prevents OUf substituting accident into the argument in place of differentia and arriving at the same conclusion. If the genus of man is predicated of his accidents, in the same man Being will be predicated many times. over

and there will be many Beings. But accidents clearly are, and therefore Being must be of a different kind in the case of accident and what the accident is predicated of. This version of the argument seems as valid as the differentia form, and moreover, it will come closer to generating the canonical categories. At least it fits the description of the categories we

find

at Topics I.9. For there the ti esti corresponds to genus, and the other

categories are in the first instance non-ti esti predications, that is, accidents.

So the accident version of the argument rather than the differentia version is more suitable to the generation of the categories. It also avoids some of Alexander's criticisms, since a thing and its accident are not in the

same category. Aristotle did not make use of this version presumably because the context of the B passage is an argument against the Platonists,

and he does not require the theory of the categories for his immediate purposes. Nevertheless, the argument of B.3 suggests that Aristotle's basic objection to a genus of Bein& whether that objection is described in terms of differentia and genus or in some other way, consists in his observation that

different Beings have different logical functions, and that discourse itself depends on the difference in these functions. To treat all things as species of a genus will destroy discourse as surely as the sophists destroy discourse by replacing all essence with accident. If this is the fundamental insight, it is one that focality can address. For focality is precisely intended to provide within a single study a treatment of items that are functionally related to one another without being species of a genus. It is ideally situated to deal with the problem of the unity of genus and differentia just because its objects are relatives rather than congeners. 15 On this interpretation we shall face the problem that once again the same genus wlll be predicated of both species and differentia; Top. VI.6 143a29-32; Met. Z.12 1038aI8- 21.

144 Aristotle's Theory of the Unity of Science

Categorial Focality in Metaphysics Z Whatever the deficiencies of Aristotle's arguments against the genus of Being, it is clear that he held that position, conceived of the problem primarily in terms of categories, and sought to solve it by means of focality. I shall argue that Aristotle lays out a focal science of Being that matches the pattern described in the previous chapter. This science consists of two closely related parts, corresponding to the focus term, namely substance, and the derivative terms, namely the non-substantial categories, One, potentiality, and so on. As we have seen, this conception corresponds to the

model of health and ordinary science generally. The core science studies substance and its functions, being a substrate and essence. But just as health does not exist without a body or an animal without activities, so substance does not exist without non-substance. Indeed, the most characteristic feature of substance, its being a substrate, requires that it be a substrate for something. As such, substance in its designation as substrate cannot be completely abstracted from that of which it is the substrate. In this way the core notion of substrate points to the more expansive science of Being, a science that includes non-substance. In addition to being substrate, substance is also essence, and in a similar manner substantial essence will necessarily imply non-substantial essence. For example, in the study of nose (which is a substance or part of a substance) we must consider snub (presumably, a quality), and in the study of animal, we must consider male and female (an affection). Again, this view is in accordance with the model of health: we can hardly have grasped much of the essence of the focus health, if we do not know that it is the body that has health, or much of medicine, if we do not know that it aims at the medical goal health 1 6 I aim to show, then, that by taking seriously Aristotle's models of focality we can construct a coherent interpretation of categorial focality and maintain that in its broad outlines metaphysics is a normal science. But first a couple of preliminary issues and observations. The claim that the focus implies the derivative or network terms seems to be in direct contradiction with the statement that the focus does not contain the derivative objects in its definition (EE VII.2 1236a21- 22). But, simple reflection on the cases involved shows that the situation cannot be so straightforward. Some of the focally derivative items, as we have already 16 It is clear that the two examples of focality, medicine and health, are themselves focally related, presumably with health as the core, since medicine contains health in its definition, but not vice versa. This fact serves as a further indication that derivative tenns can form semi-abstract subject matters on their own. Cf. EE VII.15 1249b9-13.

145 Metaphysical Focality noted, must be present in the definition of the focus. So, for example, the goal (,pyov r.2 l003b3) of medicine is essential to the art of medicine, if anything is. Others, while not specifically mentioned in the definition of the focus, must be implied in some way. For example, intelligent and dextrous people are medically talented «VCPUE, 7fPO, aVT~v l003b2-3). But though being talented is not present in the definition of the medical art, talent is certainly implied through necessary connections: an art necessarily has practitioners, who necessarily are more or less talented. In this way a derivative term need not be related to a core term by direct definitional inclusion in order to be implied in the network. Likewise, substance in its role as substrate does not contain in its definition quality, quantity, and so on, but rather it implies a predicate being predicated of it, and that predicate necessarily must be either a quality or a quantity and so on. This may seem rather pat, but in fact, definitional inclusion is often made to fit demonstrative convenience. Indeed, the focal criterion often means little more than that the focus is the subject of the science and the derivative terms are useful and adapted to it. For this reason, one science's focus is another science's derivative, as Aristotle's own examples make clear. So, for example, the art of medicine is the focus for operation, patient, and knife, because the art is contained in their definitions. But the art of medicine can also be called healthy, and serve as a derivative term in the genus of health. Moreover, the connections among terms can become multilateral without ever being confused. We may call medicine human for two quite different reasons and include it in two quite different sciences. Since health is a state of the human body, it can be called human and be included in the genus of the substance man. For this reason, medicine, too, can be human, in virtue of the transitivity of focal relations through health. But in addition, medicine, since it is a cognitive state of the human soul, can be called rational, and so be focally dependent on human in a different way. For all the versatility of these focal relationships, there is never any reason to confuse them, and it is always clear why medicine, insofar as it heals our bodies, should be treated by a different science from that which considers it as a cognitive state ·of the soul. The focal science of categorial Being is constructed on an ambiguity in the treatment of the non-substantial items, which arises as a result of their being considered both strictly as predicates of substance as well as in their own right. From the first perspective, they serve solely as non-essential, sometimes accidental, predicates of substance (e.g., man is white); but as per se Beings they themselves are treated as subjects of further predication, and this predication is essential (e.g., white is the measure of colour). These two perspectives give rise respectively to the core science of Being (substance)

146 Aristotle's Theory of the Unity of Science and the extended science that includes the other categories. This ambiguity makes it necessary to consider the nature of the categories, especially the non-substantial categories. Unfortunately, Aristotle's statements on this issue are almost perversely obscure. In various contexts and with confusing examples he conceives of the non-substantial items as accidents of substances, as per se predicates of substances, and as objects that have essences predicated of them. 17 Nevertheless, there is clear evidence, even before the Metaphysics, that the non-substantial categories are treated both as accidents and as per se Beings. 18 Topics 1.9 provides the clearest account of how the two views are related and provides much of the framework for the focal science of Being that emerges in the Metaphysics: Next then we must distinguish between the categories of predication in which the four above-mentioned [predicables] are found. These are ten in number: What a thing is (ri €OTt), Quantity, Quality, Relation, Place, Time, Position, State, Activity, Passivity. For the accident and genus and property and definition of anything will 17 A less serious difficulty concerns what is being focalized in metaphysics. Are categorial items, like quality, being made focally dependent on substance, or are more specific genera within each non-substance category, like snub and odd, made focally dependent on specific genera of substance? Aristotle's statements and examples point towards both the categorial and the generic interpretation of metaphysical focality. But inasmuch as Aristotle is outlining a science of Being qua Being, his concern cannot be with the genera that constitute the subject matters of the special sciences. When the science of Being is focused narrowly on substance, the non-substances are predicated of substance and no distinction is made as to whether they are per se or accidental; they are not part of the what-is-it of the subject under consideration (substance) and, therefore, their essence is irrelevant. They are merely properties or accidents of substance. However, these same Beings can be semi-abstracted and treated as per SI! subjects. As such they have essences (in a qualified way). This distinction holds whether we consider substance and quality, etc., as categories or whether we consider particular kinds of substance and quality, like nose and snub. 18 In the Cafegories the non-substantial categories are often treated as subjects with essences in their own right. Chapters 5-8 form an incomplete study of the nature of each category, starting with substance. We learn the basic sub-classes of each category (for quantity [chap. 6], e.g., that some are continuous, other discrete), and their properties (e.g., quantity does not admit of opposites or more and less; that they are equal or unequal). In this incomplete survey the categories are considered not as predicates of substance but as subjects, i.e., they are the kinds of things that exist, rather than the way substance is qualified, quantified, etc. At the same time, the essence of non-substance seems to be rather limited. For example, among the non-substantial categories there is no mention of species, genus, or differentia in the appropriate senses. The genus-species relationship in the Categories seems restricted to substance (Frede and Patzig 1988, 66).

147 Metaphysical Focality always be in one of these predications; for all the propositions found through these signify either what something is or its quality or quantity or some one of the other types of predicate. It is clear, too, from them (€~ avrwv) that the man who signifies what something is signifies sometimes a substance, sometimes a quality, sometimes some one of the other types of predicate. For when a man is set before him and he says that what is set there is a man or an animal, he states what it is and signifies a substance; but when a white colour is set before him and he says that what is set there is white or is a colour, he states what it is and signifies a quality. Likewise, also, if a magnitude of a cubit be set before him and he says that what is set there is a cubit or a magnitude, he will be describing what it is and signifying a quantity. Likewise, also, in the other cases; for each of these kinds of predicate, if either it be asserted of itself, or its genus be asserted of it, signifies what something is; if, on the other hand, one kind of predicate is asserted of another kind, it does not signify what something is, but a quantity or a quality or one of the other kinds of predicate. (Topics 1.9 l03b2Q.-39; modified ROT)

In this passage Aristotle first enumerates the categories, commenting briefly on their relation to the four predicables (definition, property, genus, and accident) and their place in propositions before drawing a further conclusion from them (ft aiiTwv). In the first step of this argument, Aristotle thinks of the T{ €(J'n predication primarily as substance and the non-T{ fun predications as accidents (necessary or not). Once this scheme is laid down (it aUTwv), Ti fO"TL can secondarily apply to the other categories as well. 19 This two-step procedure shows how the same non-substantial predicate can be treated both as an accidental predicate of substance and as a subject admitting of essential predication. It suggests that though one step comes before the other, non-substance can be treated in both ways, and that they need not be confused. One item may be predicated as quality only or as what-is-it and quality, depending on whether it is property or accident on the one hand or a genus or definition on the other. It is an important consequence of this scheme that when a quality is predicated as a quality alone, it may be predicated either as a property or as an accident, and the categorial scheme does not distinguish between the two forms of predication. 2o

19 Though the categories play only a very minor role in the Topics, Aristotle is very generous in providing definitions of non-substances and treats them as uncontroversial. It is clear that his treatment of non-substance as essential is not confined to I.9. 20 See Frede 1987a and Malcolm 1981 for promising attempts to provide an essentialist reading for Topics 1.9. I do not, of course, follow Frede in his contention that substance is not a category in the Topics.

148 Aristotle's Theory of the Unity of Science

Metaphysics Z provides a more searching investigation of the relationship between the categories and the centrality of substance in that relationship. Focality among the categories of Being is featured in three early chapters (1, 4, and 5), and in each chapter non-substantial Being is per se. 21 Aristotle discusses the problem of categorial Being before he ever comes to a definite conclusion regarding the nature of substance itself, and so it is clear that the question of the focality of categorial Being can be satisfactorily addressed without entering into a discussion of form and matter. Z.l, as we shall see, considers Being as per se (3), a self-subsistent subject of predication in its own right. Aristotle asks to what extent non-substances have this 'sort of per se Being. Both Z.4 and 5 consider Being as essence, which is predicated as a per se (1) predicate, that is, what can be predicated essentially of something. Substance has essence primarily and -the non-substance categories have it by an addition (7Tpo(J'8w'''). Z.5 also takes up per se (2) Being, in which categorial Being is treated as belonging to its primary recipient. Z.l begins with a recapitulation of the ambiguity of Being: There are several senses in which a thing may be said to be, as we pointed out previously in our book on the various senses of words; for in one sense it means what a thing is or a 'this' (Ti fern Kal T(}OE TL), and in another sense it means that a thing is of a certain quality or quantity or has some such predicate asserted of it. While 'being' has all these senses, obviously that which is primarily is the 'what,' (r{ EUTL) which indicates the substance of the thing. (Met. Z.1 l028a10-15)

21 Mctaphysics 11.7 also seems to provide a per se analysis of the non-substantial categories. It enumerates and describes four of the major senses of av, accidental, per sc, true I false, actual! potential: Those things are said in their own right (per se) to be that are indicated by the figures of predication; for the senses of 'being' are just as many as these figures. Since some predicates (rwv KanrYOpOVjJ.EVWV) indicate what the subject is, others its quality, others quantity, others relation, others activity or passivity, others its place, others its time, 'being' has a meaning answering to each of these. For there is no difference between 'the man is recovering' and 'the man recovers', nor between 'the man is walking' or 'cutting' and 'the man walks' or 'cuts'; and Similarly in all other cases. (11.71017a22-30) But there are many features that suggest the predicational approach. The emphasis in the passage is on predication, as indicated by the partitive genitive (rwv KarllyopoVjJ.EVWV), which introduces the enumeration of the kinds of predication. Furthermore, the examples cited at the end of the passage, man recovers, man walks, man cuts, all seem to be accidental rather than pcr se predicates. See Ross 1924, i, 307-8. Met. B.2 996b14-22 makes th"e same distinction that the Topics makes.

149 Metaphysical Focality This passage commences with an allusion to t..7, and because Aristotle had joined the issue of categorial Being with per se Being in t..7, it is reasonable to suppose that the discussion in Z.l will likewise be centred on per se categorial Being.

We notice that the first category has changed, and in place of the simple what-is-it (rt €a-n) that we saw in the Topics we find rL tOIL Kat n. This does not, however, prevent the what-is-it from being applied to nonsubstances later in the chapter (1028bl-2) and again at Z.4 (1030a17-23). It merely implies, as in the Topics, that the what-is-it is applied first and foremost to substance. The this (ToIiE Tt) is the subject of predications, and it itself is not predicated of anything else. Because of the identification of the what-is-it with the this, subjecthood and essence belong primarily to substance. Now, there has never been a doubt that substance serves as subject, but the question becomes whether non-substances can also serve as subjects. This question is addressed in a passage starting Z.11028a20:

roo€

And 50 one might raise the question whether 'to walk' and 'to be healthy' and 'to sit' signify in each case something that is, and similarly in any other case of this sort; for none of them is either self-subsistent (Kat)' aim)) or capable of being separated from substance, but rather, if anything, it is that which walks or is seated or is healthy that is an existent thing. Now these are seen to be more real because there is something definite which underlies them; and this is the substance or individual, which is implied in such a predicate; for 'good' or 'sitting' are not used without this. Clearly then it is in virtue of this category that each of the others is. Therefore that which is primarily and is simply (not is something) must be substance. (1028a20-31)

The distinction in this aporia between that which walks (TO /3alii(ov) and to walk (f3a/ii(ELv) lies in the fact that the latter is not per se (3) (i.e., self-subsistent) or capable of being separated from substance. By contrast, there is something underlying that which walks, and therefore it involves something self-subsistent. It is clear, then, that the sense of per se used in this passage does not refer to a per se predicate, but rather to per se Being, and it is described by the same example of walking that we find at APo 1.4.22 It is Aristotle's point in Z.l that although 'that which walks' is not a per se Being, it is more like one than 'to walk' is. While such a Being 22 'What is not said of some other underlying subject - as what is walking is something different walking (and white), while a substance, and whatever signifies some "this" (T(~bE n) is just what it is without being something else. ' (73b6-8).

150 Aristotle's Theory of the Unity of Science is explicitly called accidental in APo (73b9-10) and Z.5 (1030b20- 21), it is granted in Z .I, rather paradoxically, a dependent per se status. By contrast, 'to walk' has no per se (3) Being, because it does not have a substrate. Since per se (3) Being is the Being of the individual subject (TO KaB' EKarrTOV, 1028a27), non-substantial Being of the 'to walk' kind seems to have per se (3) Being least of all, since it is a subject least of all. That which walks' at least implies in itself a subject of the appropriate kind, and identifies such a subject, even if accidentally. In Z.1 Aristotle recognizes the possibility that entities like 'that which walks' may have a qualified per se (3) Being. The innovation in this chapter lies in the introduction of focality and the language of causal and definitional priority of substance over the other categories to describe how this is possible:23 And all other things are said to be because they are, some of them, quantities of that which is in this primary sense, others qualities of it, others affections of it, and others some other determination of it. (1028a18- 20) And in formula also {substance} is primary; for in the formula of each term the formula of its substance must he present. (1028a3S- 36)24

Derivative Beings are said to be in a very qualified and attenuated sense. Only because the subject is implied in predications of the kind 'that which walks,' do such things have per se existence. Since the non-substance contributes nothing per se in itself, substance in such compounds is the only Being in this sense. It is only because such tags as 'that which walks' pick out individual substantial subjects that 'that which walks' qualifies as per se (3) Being. In this case focality provides a redescription of the natural and ontological dependence of non-substance on substance. 25 In fact, Aristotle draws this conclusion at 1028a29-30 when he says that it is

23 It has long been noted that the paronymy relationship of Cat. 1 1a12-1S is a precursor to the focal relationship. It differs from focality, however, in that.it makes the non-substantial category the focus, rather than the substance (the grammatical contains grammar in its definition). Moreover, paronymy, for all its similarity with focality, simply is not invoked as a means of scientific unification . See Owen 1960 and Patzig 1961. 24 Cf. the recapitulation at 0.1 1045b27-32: 'We have treated of that which is primarily and to which all the other categories of being are referred - i.e., of substance. For it is in virtue of the formula of substance that the others are said to be - quantity and quality and the like; for all will be found to contain the formula of substance.' 25 So Ferejohn 1980, 122-3 .

151 Metaphysical Focality on account of substance that each of the non-substances is. He clearly does not mean to say that the non-substances make no contribution in any way to the compound, but only that they do not contribute to its per se (3) Being, its subjecthood, and without subjecthood there is no Being at all. What precisely is the focal connection between predicate and subject? How is substance implied in the definition of its predicate in these cases? This question is of the first importance because the answer tells us how Aristotle intends the science of categorial Being to form a unity. It is clear from the examples that that which walks implies substance as a category, and does not imply something specifically adapted to the predicate, like legged animals. Aristotle makes no use of examples like the snub to suggest that the subject must be per se related to the predicate in a speCifically adapted way. More importantly, accidents no less than essential features and properties require a subject. 26 The non-substantial categories, as we saw, frequently pick out accidents predicated of a subject, and their chief function is to identify features that are not the what-is-it of the subject. 27 Since being a subject is the roo£ n function of substance, and the T()OE n is an individual subject, the focus term is not conceived of as an essence. The upshot is that, even though substance must be included in non-substance in order for non-substance to be a subject, the essence of some specific substance need not be included. For example, the essence of nose need not be included in snub in order for 'the snub' to be a subject. Likewise, for 'that which walks' to be a subject is for walking to be predicated even accidentally of a substance in its subject function. More than any of the others in Z, this form of dependence seems to be a recapitulation of the natural priority of the Categories, and in fact Aristotle uses some of the same tags. 28 In Z.4 Aristotle turns from the self-subsistent to a discussion of substance as essence (ro rl ryv ELVat). Here too the notion of essence involves what is per se. However, the sense of per se is not that of per se (3) Being, but what is predicated per se (5 A'YETat 1029b14). It is clear,

Kae' auro

26 The fact that the subject is 70 Ka8' (KarrrOV (1028a27) does not have any Significant effect on the nature of the definitional inclusion. Both the categorial and the generic relationship can be expressed individually (white is predicated of this/these individual substance[s]; white is predicated of this/these individual surfacers]) or universally (white is predicated of substance; white is predicated of surface). . 27 It may be objected that Aristotle's fonnulations 'the healthy,' 'the sitting' do not invoke accidental relations. However, they are part of an aporia that explicitly (ota 1028a20) grows out of the categorial distinction that dearly treats non-substantial items as accidents. 28 For example, that 'good' or 'Sitting' are not said without substance (1028a28-29); d. Cat. 5 2a34--b5.

152 Aristotle's Theory of the Unity of Science or at least assumed for the time being, that essence belongs primarily to substance. In Z.4 Aristotle considers whether essence can be extended to the same sort of entities that were treated in Z.l, compounds of substance and accident. The central problem of this chapter concerns white man, an obviously accidental compound, and Aristotle explicitly asks whether there is a logos of the essence of such compounds (1029b22-27). The mention of the accidental at 1030a14 further indicates that accidents are the subject of this chapter. However, the focal solution beginning 1030a17, if it is a solution, makes no mention of white man, and instead argues that there is some way in which non-substances, like the qualified (TO ?TOL6v) can be defined. The difference between the two formulations can be exaggerated, however, and I think that white man and the white can be treated as much the same for the purposes of extending essence to non-substantial categories. 29 In spite of the fact that the chapter concludes with a statement that the problem has been resolved and that accidental compounds, like white man, have definitions, but in a different way from that which is white, the difference between the two is clear and not very significant. For in both cases the essence will have to embrace an accidental compound that includes substance. The difference between the two is that, in the case of the white, the substance will remain unspecified, whereas in the case of white man, the essence of man will be included in the definition of the compound. 1029b22 introduces the major problem of the chapter, whether there is an account of the essence of compounds of substances and non-substances (O'VVeETa), like white man, which Aristotle then denominates 'mantle,:30 But after all, 'definition,' like 'what a thing is,' has several meanings; 'what a thing is' in one sense means substance and a 'this,' in another one or other of the predicates, quantity, quality, and the like. For as 'is' is predicable of all things, not however in the same sense, but of one sort of thing primarily and of others in a secondary way, so too the 'what' belongs simply to substance, but in a limited sense to the other categories. For even of a quality we might ask what it is, so that a quality also is a 'what: - not simply, however, but just as, in the case of that which is not, some say, in the abstract, that that which is not is - not is simply, but is non -existent. So too with a quality. (Met. Z.4 1030a17-27)

29 So Frede and Patzig 1988, 64-5. 30 There does not seem to be any necessity to rename this object, but Aristotle does so perhaps to indicate that many of our words, including mantle itself in its normal designation, denote accidental compounds just like white man, and that if white man does not admit of definition, many other objects that are commonly named also will not.

153 Metaphysical Focality Alluding to Top. 1.9 and Met. Z.l 1028bl-2, Aristotle says that the nonsubstantial categories also admit of the what-is-it. But within this passage he does not explain how they do, nor does he invoke definitional inclusion, except in the cryptic remark about the non-existent. For the dear use of focality we must look to the immediately following passage: [EJssence will belong. just as the 'what' does, primarily and in the simple sense to substance, and in a secondary way to the other categories also, - not essence simply, but the"essence of a quality or of a quantity. For it must be either homonymously that we say these are, or by making qualifications and abstractions (TrpOunf3EvTos Kat acpa.~pofjvTas) (in the way in which that which is not known may be said to be known), - the truth being that we use the word neither homonymously nor in the same sense, but just as we apply the word 'medical' when there is a reference to one and the same thing. not meaning one and the same thing, nor yet speaking homonymously; for a patient and an operation and an instrument are called medical neither homonymously nor in virtue of one thing. but with reference to one thing.

(Met. Z .4 l030a29-b3)

Essence can be extended to white man and the white in much the same way. White man and the white will have essences because in their definitions will be found respectively man (or its definition) and substance (or its definition). The inclusion of non-substance in the science of essence is based on the same inclusion of substance in a quality and quantity as we saw in Z.l. Such inclusions extend to accidental relationships and are not restricted to per se relationships such as that between female and animal or snub and nose. It is because a quality, whether it is an accident or not, must be predicated of a substance, that its definition and essence will contain substance. Aristotle seems also to express the focal relation in terms of addition and abstraction, and it is probable that he had in mind the same logical operations we have discussed in the first chapter. For in both cases what is abstracted is part of the essential nature of some more concrete entity. Now, it is easy to see how we can get -rrpo,; fV definitions by addition: we simply add the definition of the primary entiry in the proper logical relation to the other elements of the derivative's definition. But it is more difficult to see how abstraction works, and there has been some dispute. 31 In view 31 Ross 1924, ii, 171, reports Ps.-Alexander's view, hut disagrees and offers 'If we say that they [non- substances} are OUTa we add a qualificati on to, and deduct from the full meaning of, Oll.' (Owens 1978, 350, agrees.) Bumyeat et al. (1979, 27-9) considered this question twice. They are unhappy with Ross's suggestion because it means that different types of things are being added and subtracted. If linguistic items are subtracted, then

154 Aristotle's Theory of the Unity of Scie"ce of the similarity with DC III.1 299a13-17, which says that mathematicals are said it aa
by abstraction from the derivative terms we arrive at

the primary term. If we start from the primary term, we obviously need no addition to arrive at its definition, but if we start from the definitions of compounds we must abstract the essence of substance from them, just as 'known' can be abstracted from 'not-known.' The abstraction and addition in this context proceeds in the opposite ontological direction from the abstraction we observed in the mathematical context in chapter 1, but the underlying logic of definitional inclusion is the same. Mathematics abstracts quantity from sensible substance, and treats it in its per se nature. The mixed sciences add quantity to sensible substance and treat the composite nature. Conversely, the science of substance abstracts the

essential nature of substance from the accidental compound and treats it separately to the extent that it can, though unlike mathematics it cannot be treated as if it were wholly separate. The science of compounds adds substance to accident and treats the compound essence.

Z.4 continues the work of Z.l, then, by investigating the essence of accidental compounds. The Z.l investigation began with the subject function of substance, admitted non-substances as accidents, and consideTed how these accidental non-substances might be subjects. 2.4, in turn, studies the essence function of substance and considers how these same accidental non-substances might have essences.

In Z.5 Aristotle considers a fundamentally different kind of case from those in Z.l and 4. Here focaliry is based on per 5e (2) predications. These cases are introduced in the context of the problem that arises if one denies that there are definitions by addition (iK 7rPOU8'UEW5). One kind of definition by addition is that of coupled terms, like snub nose.32 Aristotle explicitly distinguishes these per 5e predications from accidental we have (a) Ps.·Alexander's suggestion, or (b) given 'Socrates is a man,' one subtracts 'a man: In the next session, someone suggested that addition·subtraction was different from '"par EV. Frede and Panig 1988, 70, note the problems with Ross's interpretation, and claim that quality existing only as quality of substance represents addition, and the not·known being known only as such, i.e., the not· known, represents a subtraction. 32 Frede and Patzig 1988, 77-8, argue that the snub and similar cases are introduced to bolster the plausibility of the argument of Z.4 that accidents include substances in thei r definitions. Similarly Scaltsas 1994, 176, assimilates the case of white man and white surface as both accidental predications. I argue instead that white surface is identical in form to snub nose (as Z.4 1029b16-18 makes clear).

155 Metaphysical Focality predications like white being predicated of Callias or man with a description (1030b18-24) that matches the one at APo 1.4. He further distinguishes the two kinds of predication by stating (1030b25-26) that white can be made clear without man, whereas snub cannot be made clear without nose. However, Aristotle seems to assimilate these per se (2) cases to catego-

rial predications in a claim at 1031al-3 that there is definition of substance only, 'for if the other categories are definable (El yap Kat TWV aA.A.WV KaTT/yopLWV), it must be by an addition, e.g. the odd, for it cannot be defined apart from number.' He does not explain just how such predicates will be definable, if indeed they are definable, though he does remark that they will be defined in the same sort of way as other predicated non-substances (1031a7-11). Snub and odd are clearly considered to be in categories different from substances, but it is equally clear that they are related to their subjects in quite a different way from the way white is related to man, which was the case examined in Z.l and 4. For these contain specific kinds of substrates in their definitions: snub contains nose, odd contains number. The focality here depends on the essence function of substance rather than the subject function. The significance of these kinds of predicates lies in the different manner in which they and the predicates of Z.1 and 4 are focalized. We have traced through the Topics and Metaphysics what amount to two subject matters involved in the science of categorial Being. These manifest different per se and accidental relations. The first and central subject matter is substance. Concerning substance Aristotle's basic distinction is between the what-is-it

and the other predications. The non-substantial items may be predicated either as property or as accident, and there is no distinction drawn between these two modes. Because at this stage they are not answers to the what-is-it question and because they are predicates, not subjects, the non-substantial items are not part of the core science of Being except by negative inclusion. That is, just as the not-known can be said to be known,

so non-substance is Being because it does not fulfil the functions of Being. 33 33 In order for there to be a science, its terms must be essentially related. "For this reason, the science of Being too must treat essence, and cannOt treat accidental cases. This is why Aristotle rejects a science of accident in E.2. But accidents may be included in the science of Being through the rule of negative inclusion, which Aristotle describes as the inclusion of that which is not, because it is not. Accident is included in the science of Being, because science concerns that which is per se related, and accident is not per se related, it is the opposite of being per se related. Accident is whatever occurs neither always nor for the most part (1026b27-33). For this reason he speaks approvingly of Plato's identification of non.being with the accidental (E.2 l026bl4-21). This method allows for the inclusion of accident as such, and gains further support from the text at

156 Aristotle's Theory of the Unity of Science It provides the limits of the study of Being, and helps us make sense of the distinction between subject and non-subject, essence and non-essence.

But non-substantial items can also be treated in another way. They may be treated in their per se nature both as subjects and as essences.

Aristotle's thoughts on this issue are far from clear, and many factors are involved that are not altogether consonant. Z.1 suggests how non-substances may have subjecthood. This form of subjecthood is open to accidental as well as necessary attributes. Accidents are included now in the wider focal science, not merely by negative inclusion, but in virtue of the fact that their accounts include substance as subject. Essence too is extended from substance to non-substance, but this extension takes two forms. Z.4 treats the essence that corresponds precisely to non-substantial subjecthood, a form of essence that can cover accidents. And within this

rype of essence there appear to be two further sub-types, the fully specified accidental compound, like white man, and the unspecified accidental compound, the white. Such compounds have essences because the essence of substance or the essence of a specific substance is included in their

definitions. The second main form of non-substantial essence is the special concern

of Z.5. Snub is predicated of nose, male and female are predicated of animaL These predications are not and cannot be accidentaL By contrast, white is an accident of man, and there are no focal relations between white qua white and man qua man. Not only are the predications of the snub type not accidental, the per se relations are more varied and

do not adhere strictly to the substance/non-substance relations of the categorial level. A non-substantial item does not have to be immediately predicated of a substance. Although it is true that nose and animal are substances or parts of substances, other substrates that Aristotle mentions

are not substantial. So, odd is predicated per se of number, but number is not substance (Z.5 1031a2-5). White is predicated per se of surface, but surface is not substance. Now this peculiarity is problematic, because

Aristotle does connect the odd-number predication closely with the categorial predication. It is supposed to serve as an example that there is

definition only of substance, and that of the rest of the categories there is definition only by addition. In fact, this difficulty is only apparent. Such items will still have essence and belong in the science of Being in virtue of a mediated focal relationship to substance. Odd, for example, 2 .4 l030a23-27. This interpretation could account unproblematically for the example of white man, a genuine accidental compound with no per se connections between white and man. It is considered by the science as that which is not a per se thing.

157 Metaphysical Focality is predicated per se of number, which in turn is predicated per se of substance. 34 Aristotle recognizes such mediated relationships in r.2, where he includes in the science of Being things that are destructions and priva-

tions and qualities both of substance and 'of things which are relative to substance' (1003b8-9). Nevertheless, the fact remains that the logic of odd and snub is different from that of accidents, and their importance for the science of Being is

indisputable. For the definition and existence of such objects form the first principles of demonstrative sciences (APo 1.10), and metaphysics in some way provides these first principles (r.l). If Aristotle cannot account for the Being of such entities, then his theory of science is in grave peril.

For such predications are the bulwark of the special sciences. We need, therefore, some account of the essence of objects that are not substances and whose Being is not merely to be accidentally predicated of substance (as white man or the white is). In fact, the very model of focal science itself, health, is in danger of lacking an essence for exactly this reason, Health is a state of a living body, not a substance itself, and yet Aristotle t~eats it as the focus of its genus, upon which other objects are dependent. In order for it to do its work as the subject of a science, its Being and essence cannot be merely an accident of some substance, since accident is not the subject of any science. It is for this reason that the coupled terms are so important. For whereas the Being of accidents and its corresponding science is questionable at best, the Being of necessary attributes (per 5e (2)) dearly comes under the purview of the science of Being (for this science studies Being qua Being and its per se attributes 1003a21- 22), and if Being means in the first instance substance, such per se (2) attributes of substance are also a part of the science. The focal science of Being, then, consists of two parts. The first is the core study of substance. The science of Being is the science of substance (Z.l 1028b2-4), because substance is the focal term to which all other terms of the science are related. Of substance in general, some things can be said and perhaps even proved, for instance, that it is species form or individual form; that some substance is enmattered, and therefore is sensible; that because substance is a subject, it has attributes, both necessary and accidental. These and similar propositions and proofs constitute the core science of substance. 35 In addition, the derivative items may themselves act as parts of a more diffuse focal science and may be treated in different sections of that science. 34 So Loux 1991, 84. 35 See Bolton 1995 for an attempt to flesh out some aspectS of this core science.

158 Aristotle's Theory of the Unity of Science Quality qua quality can be semi-abstracted and studied as a per se entity." As such it is similar or dissimilar to other qualities; it has potentiality, actuality, unity, plurality, substrate, and so on. It is in virtue of this semi-abstraction that all the generic qualities and non-substantial items, like snub, odd, and health can serve as subjects with essences in their own right. Aristotle alludes to this in a passage concerning the nature of mathematicals at M.3 1078a5-8: Many properties attach to things in virtue of their own nature as possessed of some such property; e.g. there are attributes peculiar to the animal qua female or qua male, yet there is no female nor male separate from animals.

Aristotle here exaggerates the conceptual separability of female and male, but it is clear nevertheless that he recognizes some way in which male and female can be provided with a qualified essence, and be a subject of study in their own right. It is important also to note that though female cannot be separated from animal, it is not coextensive with animal or any kind of animal. As a result there are properties that can only be treated as belonging to female and not as belonging to animal in general. The clear implication is that subjects within the wider focal science will have extensions different from that of the core science, and yet this will not compromise the unity of the science.

Demonstration in the Science of Being We can now hazard some suggestions as to the demonstrative structure of the science of categorial Being. But first some caveats. There is little evidence of a richly developed demonstrative science here. 37 Though demonstrations are common in the PA, they are very· rare in the M etaphysics, in spite of the fact that in his discussion of the aporiai Aristotle seems to consider the science of substance demonstrative. 38 The obvious 36 At APo H.l3 96a34-37 and 96b5--6 Aristotle extends the tenn ovrrla to the definition of triad (which is dearly not a substance). 37 The degree to which metaphysics is amenable to demonstrative analysis continues to be debated . See Bolton's (1994) arguments against Code concerning demonstrative metaphysics in r and Bolton 1995 for a different view on Z. 38 B.2 997a25-32: if the .science of substance concerned both substance and its per se accidents, then the science will be demonstrative, since the per se accidents will be proved from the essence and definitions of substance. Bolton (1995) discusses this passage in his model of metaphysics as a demonstrative science. He argues that Met. Z is laid out according to the canons of APo II, and in a manner familiar from PA. i.e.,

159 Metaphysical Focality reason for this difference is that metaphysics is the science of principles (A.1 982al-3), and to this extent the focal science of categorial Being will not be similar to any ordinary demonstrative science. For the special sciences make no study of the what-is-it. Rather they make it clear by perception or assumption, and they prove the properties from their assumptions (Met. E.1 1025b7-13). Even so, special sciences do not have to be richly demonstrative in order to be scientific. After all, the Physics, like the Metaphysics, clarifies and discusses principles, but provides little in the way of demonstration. The principles that the Physics proVides are scientific, because they are based on necessary connections. So, the per se relations characteristic of focal sciences are the same per se relations characteristic of ordinary science, even if those relations are not strung together into long chains of deductions. All the same, there seems to be some scope for demonstration in the science of categorial Being. There is at least one demonstration in Z.l which proves that non-substances have per se (3) Being, but confusion arises when we try to prOVide a specific formulation of it: 'Clearly then it is in virtue of this category [substance] that each of the others is.' Substance is said to be a cause of Being (3<" TaVT1/V 1028a29-30), and as such we expect it to appear as the middle term of a demonstration. At the same time it is the subject-genus of the science of Being, and as such we would expect to find it as the minor (subject) term of demonstration. How, then, are we to construct the demonstration? Confusion is especially acute in this case, because Aristotle makes use of three levels of discourse, and each level has its own distinct predication relations. The natural discourse occurs when we predicate non-substance of substance, for example, man is white, whiteness is predicated of man. This form of predication expresses the natural subject function of ·substance and the predicate function of non-substance. Second, there is a focal discourse according to which substance is predicated per se (1) of non-substance, because substance is present in the definition of non-substance, for instance, the white is man. Although this predication relation is reversed from the natural predication, it is dependent on the natural predication. That is, it is only because of the natural relation between substance and non-substance that the focal predication holds. Finally there is what might be called universal predication, according to which Being or existence is providing causal definitions for facts that are more familiar to us and that are found in the Cat. (458). According to this view, the various candidates for substance, substrate, genus, universal and essence are causes of the familiar fact (e.g., self-subSistence), of substance, rather than substance themselves.

160 Aristotle's Theory of the Unity of Science predicated of both substance and non-substance. This form of predication is to all appearances universaL but in fact it is based on the focal predication,

and ultimately on the natural predication. The distinction between focal and universal discourse is mentioned by Aristotle at 2.4 1030a27-32 and 1030b3-4. In these passages he discusses various ways of talking about the essences of substance and non-substance and draws the distinction between a dialectical mode of expression (AOYLKW, 1030a25), which states how one should speak about them (7TW, /l" AiYEL" a27) and how things really are (7TW, EXEL a28).39 The dialectical or universal mode of expression predicates Being of quality and even of non- Being without considering the grounds on which the predication is made. Aristotle says that it does not matter which mode of expression we wish to use; it does not matter, that is, whether we treat the Beings as homonymous, or as a single universal type, or focally, just so long as we keep the facts straight. It is important to keep this distinction in mind in order to avoid the confusion that arises on account of the fact that the terms involved in focal predications are themselves natural predications.

We may begin solving the problem of constructing the demonstration

by turning again to the demonstration concerning the model of medicine and health: medicine (medical) IPa instrument of medicine instrument of medicine IPa scalpel medicine (medical) IPa scalpel This demonstration expresses the argument that scalpel is called medical because it is an instrument of medicine. The common focal term, 'medical,' does not in itself explain why the various medical things are treated by the same science; rather 'instrument of' and similar relational terms explain the application of the focal term to the derivative items. For this reas'on, when we consider our demonstration in the science of Being, the proposal Being IPa substance substance IPa quality Being IPa quality hardly seems satisfactory. Although substance is clearly in the middle position as befits its role as cause of the Being of non-substance, nevertheless

39 Following the interpretation of Frede and Patzig 1988, 68.

161 Metaphysical Focality substance alone by itself does not express the relation in virtue of which quality is called Being. Instead, we might reorganize the terms starting with:

substance (Being) IPO ? ? IPO quality This more closely follows the medical example by placing the focal term in the major position, but it is unclear what relation can explain why quality should be treated by the same science as substance. Accordingly we must alter the example: substance (Being) IPO quality predication quality predication IPO red substance (Being) IPO red Or more universally: substance (Being) IPO quality predication quality predication IPO a quality item substance (Being) IPO a quality item A quality item is called Being because it is predicated as quality of a substance. We make use here of the distinction Frede has clarified, that between the predicate and the predication, that is, between the item predicated and the mode or relation in which it is predicated. 40 The predication relation (e.g., predicated as a quality of) must always be in the middle position, and the item that is predicated must be in the minor position. This scheme reveals that the cause of Being is not just substance, but the predication relation to substance. It is clear that the modes of predication provide the explanation for the existence of the items predicated. Under this interpretation we must distinguish the subject of ontological predication (substance) and the subject of demonstrative predication (the non-substantial item of which existence is predicated). It is precisely this ontological dependence characteristic of nonsubstantial categorial Being that proVides the most powerful challenge that metaphysics does not follow the pattern of the science of medicine or health. Ontological dependence is not an issue in the case of medicine.

40 Frede 1987a.

162 Aristotle's Theory of the Unity of Science Scalpel is not predicated of medicine in the same way that quality is predicated of substance. It is certainly true that if medicine did not exist at

all, neither would scalpels exist, but a scalpel is at least physically separable from the state of the doctor's soul (the medical art). This is not true of quality and substance. In fact, it is clear that the ontological priority of substance over quality, quantity, and so on, is the very basis of the categorial focality. For if qualiry were not dependent on substance for its existence, then there would be no reason to suppose that substance is

included in the definition of quality. For since a quality can be predicated as an accident, there is no other reason than ontological dependence to include

substance in the definition of the accident. If this is the case, then categorial metaphysics, contrary to what Aristotle avers, is focal in a different way from medicine. It is focal for ontological (dependency of existence) reasons. This means that its subject matter is special and importantly different from that of medicine or health. There are a number of answers to this challenge at a couple of levels. First, even if the challenge is cogent, nevertheless the ontological basis of focality applies only to the categorial form of Being, and not generally throughout all the areas of metaphysics. Processes towards Being, mentioned in r.2, for example, are not predicated of substances in the same way as qualities arc, and therefore arc not focally related to substance on

the basis of ontological priority. For this reason, the ontological predication involved in categorial Being cannot be the grounds for focalizing the whole science of Being, since the same ontological conditions do not obtain in the other parts of this science. Nothing, then, prevents most of the science of Being from following the pattern of medicine. Moreover, there are reasons to suppose that the challenge itself does not hit the mark. While the ontological dependency certainly grounds and provides the cause for the definitional inclusion, ontological dependency is not identical with the focal relationship. The distinction we drew above between natural, focal, and universal forms of predication makes this clear. The demonstration,

per se (3) Being IPO what is predicated in the category of quality of a per se (3) Being what is predicated in the category of quality of a per se (3) Being IPO qualified thing per se (3) Being IPO qualified thing manifests and distinguishes all three levels of discourse. The conclusion of the demonstration displays a connection that applies universally (Ku8' EV)

163 Metaphysical Focality to all non-substances, and as such it is couched in the universal discourse. The terms in the premisses of the argument are bound to one another

by per se connections, which display the focal relationship between the qualified thing and substance. In the minor premiss 'what is predicated in the category of quality ofa per se (3) Being' is a definition or partial definition of 'qualified thing.' And in the major premiss the relationship between ' per se (3) Being' and 'what is predicated in the category of quality of a per se (3) Being' is a per se (1) predication. It is this first premiss that expresses the focal relationship. Finally, natural predication is exhibited in the terms themselves. The natural fact that substance is not

predicated of anything else is manifested in its being a per se (3) Being. The natural fact that quality is predicated of substance is manifested in its being what is predicated in the category of quality of a per se (3) Being. Thus this one demonstration, which proves that non-substances are

subjects, involves all three forms of predication and displays the dependency relationship, according to which the universal conclusion is proved from focalizing premisses constructed out of terms that express the natural relations. If these predication relations are distinguished, there is no reason to

suppose that the science of categorial Being is extraordinary. Although the natural relations have to do with ontological dependence and predication, these relations are just as amenable to being expressed in focal terms as any

other per se relationship. In fact, they are mentioned in r.2 alongside other quite different focal relationships. Along with privations of substance and things that generate substance, we find qualities and affections of substance

(lO03b6- 1O). The ontological dependence of non-substance on substance is just one of the many focal relations. And just like all focal relations, it can be expressed in terms of per se predication. It is strictly irrelevant to focality that the item being focalized is itself a predication relation. Thus, though the natural priority of substance over quality is the basis of the definition of quality and the inclusion of substance in that definition, it is the per se relations that ground the focality of categorial metaphysics. Metaphysics is indeed unusual in that most sciences do not take predication relations as such for their subject matter, but there is no reason to suppose that the focal structure invoked in metaphysics is in any significant way

different from the focality we find in a normal science like the science of medicine. . In fact, the normalcy of the science can be seen when we alter the focal demonstration so that the conclusion no longer expresses the universal fact

that quality is a per se (3) Being, but rather expresses the natural fact that quality is predicated of substance:

164 Aristotle's Theory of the Unity of Science a quality item IPO quality predication of substance quality predication of substance IPO substance quality item IPO substance A quality item is predicated of substance because substance is of such a nature that it admits a predication in the category of quality. Here the conclusion reflects the natural order of predication, and the middle term expresses something of the nature of substance. Such demonstrations are parallel to the natural demonstrations concerning health that we saw in the last chapter: pleasant IPO having a uniform state of the body having a uniform state of the body IPO health pleasant IPO health Again categorial metaphysics is unique in taking as its subject matter predication relations, but its logical form is common. To the extent that the content of categorial metaphysics is demonstrable, we may expect it to take this form. Demonstrations concerning essence can be formulated in the same way as those concerning subjecthood. 'Essence' is a universal predicate that belongs to all non-substance categorials in virtue of the middle term, 'logos containing substance in it': essence IPq logos of quality containing essence of substance in it logos of quality containing essence of substance in it IPO quality essence IPO quality

The universal conclusion (essence IPO quality) is proved through premisses focally related (,essence' is a per se (1) predicate of 'logos of quality containing essence of substance in it') and consisting of terms that express the natural relationship between the essence of quality and the essence of substance (quality logos containing substance). The especial ground for confusion in dealing with the focality of essence is that the natural and the focal relationship are expressed by exactly the same per se relations. At the natural level, the essence of quality implies that it will have a natural relation to a substance, and this is precisely captured by the definitional inclusion criterion characteristic of focality.41 It is for this reason that 41 For a similar distinction between essence used as a predicate and the natural predication that backs it up, see APo 11.4 91bl-7.

165. Metaphysical Focaliry non-substance is included in the science of Being, not just because it is related to substance, but also because it stands alongside substance as a

subsidiary subject. For snub naturally contains nose in its definition, and this makes it part of the science of nose; but at the same time, the essence of nose contained in the definition of snub provides snub with its claim to essence and per se Being. The Wider Focal Science of Being Categorial focality is only one part of the science of Being. Focality shows its unifying power, not only by joining substance and non-substantial categories, but also by joining a host of other items. First, the science of Being treats substance and its essential attributes: We must inquire ... whether OUf investigation is concerned only with substances or also with the essential attributes of substances. Further, with regard to the same and other and like and unlike and contrariety, and with regard to prior and posterior and all other such terms, about which the dialecticians try to inquire . (Met. B .1

995b18-24) Aristotle then goes on to include qualiry as well as the things that belong to quality per se. This will naturally include substance (since substance is per se related to quality) but also other things, for example, 'it is in virtue of qualities only that things are called similar and dissimilar' (Cat. 8 11a15).42 In focal terms, the statement 'qualified things are similar' forms part of the science of Being, because similar is per se (2) predicated of a qualified thing, and qualified thing, of course, is per se related to substance inasmuch as it implies substance as its subject. Thus, this statement in the science (still

not adapted to a specific demonstration) is about the attributes of quality, but at the same time maintains the dependence on substance necessary for

unified focal science. In this way the science of Being is articulated and ramified. r .2 presents an outline of the elements and architecture of the science of Being. In general Aristotle's task is to show that a number of different subjects fall under the same science. Focaliry is one, but only one, of the means used to accomplish this task. The two great parts of the science,

TO DV and TO iv, for example, are joined in a different manner. Their 42 Cf. also Met. B .1 995b26-27, where Aristotle considers the possibility that the science should treat not only the what~is-it of the accidents, but also whether each has a Single opposite:

166 Aristotle's Theory of the Unity of Science connection is more intimate though less clear than focality: they are of one nature (cpvem), though they are not made clear by one "oyo< (1003b22-25). Minimally, they are coextensive, but they also imply one another, and imply one another necessarily, since Aristotle says that the substance of each thing is one not by accident (ov KaT" uv!'-(3,(3'1KO< b32-33). For this reason they belong in the same science. If we can describe them in focal terms at all, they must be 'bifocally' related. Aristotle, in any case, does not use the focal technique to unify them . Their being of one nature is sufficient to warrant their inclusion in the same science.

There is in addition a third technique of inclusion, the rule according to which the same science treats opposites. Again, Aristotle invokes this

rule without any mention of focality, although, since one of the pair of opposites is explainable by the presence or absence of the other (Met. Z.7 1032b2-5; Phys. 1.7 191a6-7), and presence or absence is a focal relation (Met. r.2 lO03b8), the rule of opposites can be subsumed under focality. These, then, are the three techniques Aristotle uses to unify the science of metaphysics. Other information is provided in Met. i, but from r .2 alone we can construct an already quite elaborate scheme, as illustrated in the accompanying figure. Within r the science of One is represented as a large part of the science of Being. I wish to discuss it in some detail, because the connection between

Being and One is not entirely clear and has been largely ignored. [ shall argue that the most promising candidate for the connection between Being and One is the notion of measure, which is the Single nature (cpvu«) that receives different logoi according to whether it is treated as Being or as One. It is the difference in these logoi that accounts for the structural differences in the two parts of the science. Aristotle's claim that One is said in as many ways as Being leads us to expect that the ambiguity of One will be isomorphic with Being and will be overcome by the same focal strategy.43 He encourages this expectation in r.2.44 He argues that One is studied by the same science as Being (1003b33-36), and that One and Being are the same and have a single nature (1003b22-25) and follow one another (i.e., are coextensive), though they do not have the same logos's Aristotle even goes so far as to say that

43 2.4 1030b8-12; 2,16 1040b16; 1.2 1053b22-24; r.2 1003b33-34. 44 [n a passage that Jaeger in his ocr (following Alexander) thinks breaks the argument and is out of place (lOO3b22-1004a2). I tend to agree, though it certainly belongs somewhere nearby, since it discusses what the subject matter of metaphysics is. 45 For how they can have the same nature but not the same logos, see 1.1 1052b1-19; d. teeth and bone in GA 11.6 745b2-9.

167 Metaphysica! Focality denial (not Being)

I qualifications

engenderings productions

affections of

road to

~

/

' - , , - - - - - - - _ substance _ _ _ _ _ _ _--'

I ! ,-------------__ on< ______________-, Being (species of)

similar

same

equal

[p rivation / denial}

I dissimilar

other

unequal

~

many _ _ _ _ _ _ _ _+_ difference _

A

making

opposition

having - - - - - - - '

Science of Being qua Being according to r.2 lOO3b5-1004a31

we may suppose that the logoi are similar, since the phrases 'one man and 'man being' and 'man' do not refer to anything different from one another. His argument is intended to show that the species of One are as many as the species of Being (l003b33-34), and that the reason why Being forms its species applies to the One with analogous results. We are led to expect, then, that the articulations of the science of Being (categoria! Being, potentiality, etc.) will be mirrored in the science of One. Moreover, if One is ambiguous in the same way as Being is,

168 Aristotle's Theory of the Unity of Science we would expect the resolution of the ambiguity to occur in the same way, with a focus on substantial unity. In fact, Aristotle does consider the possibility that substantial unity is the primary kind of unity (<:'.6 1016bl-3; 1.1 1052a31-34). He also presents forms of unity corresponding to the categories, identifying the species of One as Same, Similar, and 50 on (1003b35-36). But this is neither the only nor the most important analysis of One. Moreover, it is difficult to see why Similar, a form of unity in the category of quality, should contain in its definition Same. For this reason too it is difficult to provide a focal account for this categorial form of One. Again, Aristotle's discussions of One and Being in <:'.6 and 7, though they are clearly written as a pair, do not establish a correspondence between meanings of the two terms. The chapters contain the same basic division between the accidental and the per se use and these clearly correspond to one another, but Aristotle also provides some meanings that have no clear correspondence. Whereas ~.7 analyses the per se uses of Being in terms of the categories, we find no corresponding analysis in <:'.6. Again, while Being can mean truth, there is no corresponding serise for One. Conversely, One is analysed as measure and as that which is continuous, and for neither of these is there a corresponding sense of Being. We cannot, therefore, draw the straightforward correspondence between the senses of One and the senses of Being, and this fact in turn makes it more difficult to establish the basis for the unified science of One and Being. The difficulties are further increased by the fact that the One itself suffers from an especially troublesome ambiguity. On the one hand, in r.2 Aristotle identifies the species of One as Same, Similar, and so on (1003b35-36). He clearly has in mind here a relational sense of unity. To be One in this sense is to belong to one group in virtue of some shared feature. So, two substances are the same if they share a single form. We shall call this the 'relational' sense of One 46 On the other, there is a non-relational, 'internal' sense of One according to which a thing constitutes a unity in itself and is not merely a heap. So, for example, 46 Kirwan (1993, 134, on 6. .6) quotes Popper's distinction between type 1 questions regarding unity ('what are the conditions under which x and y make up one thing, or under which the combination of x and y is Singular and not plura!?') and type 2 ('what are the conditions under which x and yare one and the same thing, and not different things?'). There seems to be a correspondence between this distinction and that between my internal unity and relational unity. Kirwan (wrongly, 1 think) places Aristotle's discussion of accidental unity with type 1. Kirwan is aware of the possibility of confusion, and defends his claim by citing b23 that artistic and Coriscus are one 'because one coincides in the other. '

169 Metaphysical Focality that which has one form, like the shoe assembled from its parts is one (1'>.6). Likewise, that which is continuous (O"vv'X~,) is one in this sense, because it is one thing, not twO. 47 Aristotle holds out a fleeting promise that both senses of One may be unified with the science of Being in a way that mirrors the dependence of non-substantial categories on substance. But in the end he leaves both schemes undeveloped and takes up instead the notion of measure. It is the internal sense of unity that promises the closest connection between One and the categories of Being. Aristotle argued in Z that a definition can apply to a substance and cannot apply properly to anything with an addition. The addition clearly takes away from the definability of the object and also from its unity. Substance is prior in definition, because it can be defined without reference to anything else. Items in other categories cannot be independently defined. Unity and substance, therefore, coincide in essence and definability. For this reason he says that the cause of the unity of substance is the first unity (1.11052a33-34). At H.6 essence 'is by its nature essentially a kind of unity, as it is essentially a kind of being a this, a quality or a quantity ... This is why none of these has any reason outside itself for being one, nor for being a kind of being' (1045a36-b5). The connection between One and Being through the unified essence extends the promise that One will be explicated along categoriallines, just as Being was in Z, and in one short passage Aristotle does seem to relate One to the categories: Now most things are called one because they do or have or suffer or are related to something else that is one, but the things that are primarily called one are those whose substance is one, - and one either in continuity or in form or in formula; for we count as more than one either things that are not continuous, or those whose form is not one, or those whose formula is not one. (.6. .6 l016b6-11)48

At first glance this appears to be a reference to the focality of One: there will be a Single primary substantial Unity to which all the derivative non47 There are differences between the presentations in 6.6 and 1.1. 6.6 is primarily concerned with the relational sense: of the seven uses I count, four are relational. By cOntrast, in 1.1 all uses besides measure are internal. Aristotle starts by leaving per accidens uses out of account, and for this reason his interest in relational similarity may retreat to the background. 48 Cf. 1.4: 'the other contraries must be called so with reference to these, some because they possess these, others because they produce or lend to produce them, others because they are acquisitions or losses of these or other contraries' (1055a35-38). The same kind of focal arrangement for One is mentioned at r.2 1004a28-31.

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170 Aristotle's Theory of the Unity of Science substantial Unities (activity, state, passivity) are related. 4Y But to interpret this as a focality focused on substance would be a mistake. For while we find definitional inclusion, there is no primary focal One to which all the derivative Ones are related. It seems rather to be a recipe for accidental unities. If a thing is one if it does one thing, then for example a baker is one thing because he doe; one thing, namely, baking. The odd feature of this relationship, then, is that it reverses the usual priority in the realm of Being: according to this passage an accidental compound is called one in virtue of the accident that is predicated of a substance: the accidental unity of the man performing the baking activity is a unity in virtue of the baking activity, rather than in virtue of the unity of the substance, man. As such it is reminiscent of the paronymy relationship of Cat. 1, which also names an accidental compound. 50 If this is what the passage intends, then One and Being are not focalized in a parallel manner, since the unity of accidental compounds is dependent on the unity of the accidental addition. Nevertheless, we can see how this order of priority would be useful in the special sciences, which depend on the ability to abstract a unified accidental feature of substance and treat it as essence, while letting the substance fall into the scientific background. Even if this passage makes accident prior to substance, that does not imply that the orthodox priority of substance over accident in unity does not also apply. In fact, t..6 (on One) and 7 (on Being) treat the accidental forms in a similar manner, and it is clear in this context that the accidental unity is a unity because accidents inhere in one thing, the substance. Substance is the cause of the unity of the compound. In the end, there does not seem to be a contradiction between the view that the substance is the cause of unity and the view that the accident is the cause of unity. In fact, the distinction between them seems

. 49 The predominant interpretation of the passage, however, which stems from Alexander and is accepted by Ross (1924, i, 303-4) and Kirwan (1993, 138) views the One here as relational: honey is one with honey because it affects things similarly, musician is one with musician (having), the heated with the heated (suffering) . This interpretation is, however, almost certainly wrong. Kirwan finds the passage intrusive and strange, bur, in fact, the immediate context (starting 1016b1) shifts from the relational to the definitional sense of unity. That passage argues that those things, of which the thought of the essence 'is one, are one. If man qua man does not admit of division, it is one. Substances most of all are one in this way. Whatever does not admit of division in this sense is one. It is at this point that Aristotle adds his focal qualification: most things are called one because they do things that are one, etc. The immediate context gives no indication that Aristotle is considering relational unity. 50 Cf. Lewis 1991, 88-90.

171 Metaphysical Focality to correspond to the two parts of the science of Being in Z, the narrow science of substance in which non-substance is viewed strictly as something predicated of substance, and the wider science in which non-substance is treated as per se Being. It is interesting and important for the unity of

metaphysics that these two ways of treating One correspond to ways of treating Being. But for all its interesting consequences, Aristotle leaves this

strategy undeveloped. There is also some evidence of categorial focality in the context of

the second, relational, form of unity. r.2 lists as kinds of One, the Same, Similar, and such like (1003b35-36), which suggests that he has catogorial species or forms (cLOry) in mind. The Same means oneness in substance, Similar means oneness in quality, and so on. However, there is no attempt to arrange these relational predicates in focal order, and rightly so, since Similar does not seem definitionally dependent on Same. Moreover, when Aristotle elaborates the ambiguity of these terms in 1.3, he does not observe the strict categorial correspondences. So the Same is used to denote what is

numerically the same, what is the same both in form and number, and what is the same in the definition of the primary essence. For the latter Aristotle

provides the example, equal straight lines are the same, and so makes clear that 'same' does not refer solely to substances. Likewise, Similar is not restricted to quality: 'Things are similar if, not being absolutely the same, nor without difference in their concrete substance, they are the same in

form, e.g., the larger square is similar to the smaller' (modified ROT; 1054b3-6). It is clear, then, that relational unity is not focally organized in a way parallel to categorial Being. We have considered two possibilities of focal ordering within the field of One, the first concerning internal unity, the second concerning relational unity. In both cases we see that Aristotle does not develop these schemes

fully or consistently. This result leads us to approach the question from a different angle and to consider whether the study of relational unity has anything to do with the study of internal unity, or whether they are independent of one another. The answer to this question in turn will lead us to a more satisfactory answer to the problem concerning the relation of

One and Being. What is the connection between relational and internal unity? Two

heaps of objects may be identical either numerically or in description without either heap forming an internally coherent unity. Heaps have no essential unity, and yet two heaps can be identical with one another. So it seems clear that internal unity is not a necessary condition for relational

unity (and it hardly need be said that relational unity is not a necessary condition for internal unity).

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172 Aristotle's Theory of the Unity of Science Aristotle intends to unify the science of One through the primary designation of One, measure, in such a way that measure will be a focus for both internal and relational unity. Measure provides the criterion of sameness. One thing, whether quantity or quality or substance, is the same as another thing with respect to measure. At the same time, measure

provides internal unity: to be one is to be the first measure of a kind (genus) (1.1 1052bl8-20). This measure is indivisible and one (1052b31-32) . It is true that measures are often arbitrary, as in the case of measures of weight and so on, which occur in the genus of continuous quantity, but in the category of substance, where the object measured is not continuous quantity, measure will be based on the essences of substances. The view that the reconciliation of the forms of One is to be found in measure is

confirmed by Aristotle in 1.1 where he distinguishes the things said to be One from the essence (T{ ~v etVaL) of One, and says that measure is the essence of One. If measure is the essence of One, all uses of One should be explicable with reference to it. So although internal and relational unity are not mutually explicable, measure will, nevertheless, be the focus of both kinds of One. This is one possible strategy for unifying the science of One, according to which measure provides the focus for both relational and internal unity. But there is also a more direct way of establishing the connection, and at the same time establishing a connection with Being. Essence is the common term. It takes little effort to show that essence is fundamental to measure. Outside of continuous magnitude, the unit will be determined by some essence or quasi-essence, depending on the category of the genus

measured. Nor is it difficult to establish that internal unity is dependent on essence, since it is precisely essence that is the cause of unity of an object. T~e distinction between essence and accident is just the distinction between internal unity and internal plurality. A substance together with an accident is not a unity, at least not in the same privileged way as a

substance alone is. Difficulties by all means arise if we demand a metaphysical structure identical to that of Being, one that sets substance in the preeminent position. For measure is found primarily in the category of quantity. Nevertheless, to the extent that there is an internal unity to measure, that unity will be based on essence. It is somewhat more complicated to establish the nature of the connection between essence and relational identity. As we noted, there seems to be no reason to suppose that identity depends on essence. One man may be identical with another man, one heap with another, and the degree of internal coherence of the objects being compared is irrelevant to the issue

of identity. And yet it is clear that all identity is identity in some respect;

173 Metaphysical Focality so two objects are identical in number or in form. Similarly, two objects may be accidentally the same, as the white and the musical are, if they are both this man. Two objects may be identical, of course, in one respect, for instance, in form, without being numerically or accidentally identical. As a result, the notion of identity is incomplete without further specification, and that specification must make the distinction between essence and accident. In order to identify two objects, there must be identity conditions. Even if the objects being compared are heaps, we must know the essence of a heap, to the extent that a heap has an essence. Even a heap has unity of position, and this will be its essence to the extent that it has one. Now, relational unity is posterior to internal unity. Internal unity is of various degrees, that of the heap, of the accidental compound, of the substance. We need to detennine the degree of internal unity we are interested in before we can make an evaluation of relational unity. In order to determine whether two objects are identical in essence, we must know what essence is in general and what their particular essences are, and this is tantamount to knowing their internal unity. Though Aristotle does not provide this analysis of unity, the unification of the science of One is clearly one of his goals. This interpretation provides a unification scheme consistent with Aristotelian doctrine, and is constructed out of the major components of his focal theory of One and Being. More important for Aristotle than the focalization of the ambiguities of One is the relation between One and the other objects included in the same science, the many, same, different, and the other, opposite, and privation. The One in its primary designation is measure, and it is explicated in terms of genus: 'but [to be One] is especially to be the first measure of a kind, and above all of quantity' (1.1 1052b18-19). Thus measure and One have per se relations with genus, and continuing in this way Aristotle increases the scope of the science. The measure is of importance in knowledge, because it is the principle of number, and number is that by which we know quantity. The measure also is one and indivisible, and necessarily indivisible, and so again indivisibility joins the list of terms of the science. Now, opposites are included in the same science, not only because of the old sophistic rule, but also because that rule can be subsumed under the focal scheme. For opposites are relative, and relatives by their definitions are defined in terms of one another, and are therefore focally related. The opposite of One is Many, and so Many too is included in the science of the One.51 51 This is not the only way of connecting One and Plurality. Without a lot of fanfare, Aristotle introduces plurality in 1.3: 'that which is divided or divisible is called a plurality.' In this case the order of priority is reversed: 'the one gets its meaning and

174 Aristotle's Theory of the Unity of Science Of course, the interesting feature of the passage above is the claim that measure is found first and foremost in the category of quantiry, rather than in substance. This is peculiar, and shows the extent to which Aristotle was unconcerned to maintain isomorphy between Being and One. It may be argued that the whole discussion in I is less dependent on r than I have supposed, but r clearly mentions as focally related precisely the subjects that Aristotle discusses in J. The significance of the One lies in the fact that the internal organization of the terms of this part of metaphysics does not follow the organization of the terms concerning Being. Just as

non-substantial categories can be semi-abstracted and treated as per se Beings with their own per se attributes, so too One has a nature of its own, however logically dependent that nature is on Being. Measure, for all its connections with essence, means something different from essence and operates differently from Being. Focality, as a flexible strategy of generic unification, can both explain the unity of a subject matter and provide for an articulated study of the disti~ct elements within that subject matter.

explanation from its contrary .. so that in formula, plurality is prior to the indivisible: It is clear that the divisible must be de6nitionally prior to the indivisible, so that if this is what we mean by One, then it will be posterior to plurality. The oddity of this reversal of priority is increased by Aristotle's statement that 'plurality and {he divisible is more perceptible than the indivisible' (l.3 1054a26-29). This is obviously unusual for Aristotle. Perception ·cannot ground definition this way, and it is impossible that plurality should be prior to one, for in order for there to be plurality, there must be a measure, and the measure is the unity. So the measure must be prior to the plurality measured. Moreover measure, the principle of number, is that by which quantity is known: plurality cannot be prior to one. This difficulty points to the problems involved in establishing the appropriate priority relations. If we define the One as the indivisible we may not be defining it in terms more intelligible without qualification, and if we define in this way, as Aristotle makes dear in Topics V1.4, we cannot show the essence of the definiendum (141b15-18). Such a definition is intended only to lead a less scientific mind to some understanding of the subject.

in

6

Mixed Uses of Analogy and Focality

Because the categories constitute the irreducible genera of Being, and everything that exists is predicated in one of these categories, it is reasonable to suppose that relational similarities among them will best be expressed by analogy. However, as we saw in the biological context, analogies are resolved into identities by choosing a new common subject, which, though not their genus, is nevertheless pe"r se related to them. Among the categories, by contrast, there is no common Being that is not already a Being in one of the categories, and so analogies at this level cannot be resolved into a more abstract identity. For this reason analogy in metaphysical contexts has sometimes been viewed as significantly different. 1 For since no absolute identity can be found, analogy is the only form of commonality available. I want to argue, however, that this difference between categorial analogy and analogy in the special sciences has been exaggerated. We often find that these metaphysical analogies, like potentiality and good, are not in fact based on the categories, but rather on lower and abstractable genera. But more importantly, we invariably find that they are based on a commonality, not of course on the absolute generic commonality of the biological analogies, but on some kind of natural or focal relationship among the subject-genera. Whereas wings and fins share common principles of locomotion, potentialities are found in categories, like substance and quality that are focally and naturally related. In no instance, however, is analogy a fundamental and independent form of similarity; there is always some relationship besides analogy that exists between the· subject-genera. Now, this issue has had a controversial history. G.E.L. Owen, because of his

1 Hesse 1965.

176 Aristotle's Theory of the Unity of Science developmental view, conceived of focaliry and analogy largely as competing principles of organization, and though he recognized that the development of focality did not eliminate the usefulness of analogy, he saw them as alternative solutions to the same problem.' So, for example, he (rightly) observed that Aristotle does not mention focality in his discussion of the principles in the supposedly early Met. A, and omits analogy from r in favour of focality. From this observation (and others) he concluded that the analogical presentation of A was an inadequate unification of the science of Being and was superseded by r's focality. Though Owen's view has been influential and provocative, it has not become the received opinion. Most scholars, whatever their views on the general question of philosophical development, agree that many groups of objects are amenable to both analogical and focal analysis. j. Owens may be taken as the vox consensus in pronouncing that 'the two types though clearly distinct are not mutually exclusive.,3 On this view A does not aim at unifying the subject-genera of the science of Being, as r does, but at drawing to our attention the differences and identities among the principles of various kinds of Being. Different problems, even if they involve some of the same objects, will naturally require different solutions. The arguments in favour of this consensus are compelling, but a stron-

ger claim should also be made. Whether or not focality was explicitly articulated at a later stage of Aristotle's development, in its logical nature it is prior to analogy in two ways.4 At a general level it is a logical precondition for all analogy, and as a result one might say that analogy is a focal derivative of focality. For in order for there to be analogy, there must be different genera, each one constituted out of elements per se related to its core subject in the focal manner. So, while focality can exist independently of analogy, analogy cannot exist independently of focality. Since th~ focal connection is identical with the normal per se connection, this focal precondition has generally escaped notice, in spite of the fact that it is common to all analogies. It is most apparent in the case of potentialities: they are analogously the same, but each is homonymous 2 1960,193 and n. 39. 3 1978, 125; so also Berti 1971; Rist 1989, 276; Menn 1992; Code 1996; for recent contributions on the question of development see Wians 1996. 4 Cf. M. ~ D. Philippe 1969, 46-7: 'These various ways of considering unity in diversity [analogy and focality] do not necessarily exclude one another; on the contrary, they can complete one another, yet remain distinct, each having its own proper character.' However, Philippe holds that analogy has precedence over focality: 'unity according to analogy is surely ultimate, since it is achieved within the greatest variety and reduces this diversity to a certain unity.'

177 Mixed Uses of Analogy and Focality with its corresponding actuality (e.g., the potentially and the actually hot) and includes its actuality in its definition.

There is, in addition, a special use of focality that, together with the natural priority relation, provides the framework for some metaphysical analogies. As we have seen, analogues must share some abstractable and

essential feature. Among metaphysical analogues, however, there is no absolutely common feature to be abstracted, because the analogues are found in several or all of the categories of Being. Nevertheless, analogues, if they are to avoid the metaphorical and unscientific quality Aristotle criticized in Plato, must be bound by some essential connections, even if a common abstractable is not available. For otherwise the analogies will be accidental. Among the metaphysical analogies the necessary connection is

provided by natural or focal priority. Sometimes the categories of Being provide this framework, but more often they do not. Two cases reveal the interaction of analogy and focality especially clearly, potentiality and the good. The discussion of potentiality is dominated by analogy, but throughout focality (or natural priority) provides the framework for the analogues in more or less explicitly developed ways. Good, by contrast, is dominated by focality, and since focality is logically prior to analogy, analogy's role becomes ultimately inconsequential.

Matler and Potentiality In three separate passages (Met. A.4-S, Phys. 1.7, Met. 0.6) Aristotle discusses two pairs of principles: actuality and potentiality, and form and matter. There are good superficial reasons for considering these passages and pairs together. The passages are among the few in which Aristotle discusses the most general principles in terms of analogy and, because he often elides the two pairs, he is clearly talking about closely related elements and principles. A close examination of the contexts of the passages, however, reveals a multiplicity of purpose. Let us first consider why Aristotle treats these principles as analogous, and then ask how their underlying subject-genera are related to one another. Aristotle has two basic reasons for treating the principles as analogous, corresponding to the relativist (formalist) and realist (orthodox) view of biological analogy, which we saw in chapter 2. According to the relativist account, prevalent in Met. 1\.4-5, potentiality and the other principles are analogous, because they are principles of sciences, and as such are bound to their subject-genera. The various potentialities and other principles will be analogous at any level of generality we choose to examine: the potentialities associated with light and sound are analogous, and likewise the

178 Aristotle's Theory of the Unity of Science potentialities of substance and quantity (A.S 1071a26). On this interpretation potentialiry and the other principles are analogous solely because of their use and function in various subject-genera, and there is nothing peculiar about their natures themselves that makes them capable of only analogical identity. As we shall see, the subject-genera themselves are connected by natural priority. The second, realist view, found in Phys. 1.7 and Met. 0.6, applies specifically to potentiality or matter and looks to the kinds of potentialities or matters in each case: potentialities are analogous because they are different kinds of potentiality. The potentialities function differently in each case: one is associated with change and another with activity, or one is associated with artefacts and another with substance. They are different conceptions of what it is to be potentiality. These different conceptions are related by focality and the logic of abstraction and addition. Specifically, Aristotle leads us from a more familiar to a less familiar conception of potentiality by a process of induction (E7TaywY'i). This induction is not a path to a universal definition of potentiality, but rather a movement between different but logically related conceptions. The strongest evidence for the relativist interpretation of analogy and its underlying scheme of natural priority is found in A.4-S. Because Aristotle is concerned here not only with matter, but also with the other causes, principles, and elements of things, including form, privation, and the moving cause, it is clear that the multiplicity of subject-genera is the reason for the analogy. The principles are analogical because they are used in different genera: These things then have the same elements and principles, but different things have different elements; and if we put the matter thus, all things have not the same elements, but analogically (Tee avaAoyov) they have; Le. one might say that there are three principles - the form, the privation, and the matter. But each of these is different for each class [my italics; YEvos-I, e.g. in colour they are white, black and surface. Again, there is light, darkness, and air; and out of these are produced day and night. (A.4 l070b16-21)

Aristotle explicitly connects analogy with the fact that the principles are found in different genera; and this difference in the genera certainly provides the reason why they can be treated as only analogically identical. It is also dear that analogy holds equally among the categories and among the more specific genera. The passage above cites specific genera, but the question concerning the identity of principles is first taken up in -the context

179 Mixed Uses of Analogy and Focality of the categories (1070a33-b10), and the analogical solution that immediately follows seems to be directed to that question. Moreover, categories are explicitly mentioned and included among more specific genera in the context of analogy later in A.S (1071a26). The fact that Aristotle treats special genera and categories as equivalent for the purposes of analogy shows that the justification for the analogical identity of the principles does not reside in the nature of the things that are called principles, but rather in their function as principles of different genera. For while arguments might be produced to show that the kinds of things that are potentialities in substance and in quality should be analogous, it is very difficult subsequently to extend this argument to specific genera. For if the substantial and qualitative potentialities are analogous to one another, then we have assumed that the substantial potentiality forms a genus and that the qualitative potentiality likewise forms a genus. We cannot then argue that the potentialities among the various genera of substances are analogous. If we do, we

have clearly already supposed that all the analogies are purely formal. And if analogy applies to potentiality for this reason, it applies equally to all the other principles merely because they are principles of several genera. In corroboration of the relativist interpretation is the fact that Aristotle

is explicitly discussing the principles of things, and talk about the principles of things is distinct from talk about things in their own right. We can, for example, talk about earth, its nature and transformations, in which case earth is the subject-genus and receives predications. But once we caU earth a potentiality, we treat it as relative to something else, say wood. Earth now explains something about wood, namely its material nature. s This distinction between subject and principle is made clear in a different context at Met. 1.1 (10S2b7-16): This [that there is sometimes a difference between what a thing is called and the essence of the thing so denominated] is also true of 'element' or 'cause', if one had both to specify the things of which it is predicable and to give the definition of the word. For in a sense fire is an element (and doubtless 'the indefinite' or something else of the sort is by its own nature the element), but in a sense it is noti for it is not the same thing to be fire and to be an element, but while as a particular thing with a nature of its own fire is an element, the name 'element' means that it has this attribute, that there is something which is made of it as a primary constituent. And so with 'cause' and 'one' and all such terms.

5 See

eill 1997 for similar observations in the context of Mete. IV.l2.

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180 Aristotle's Theory of the Unity of Science Aristotle makes this claim of all terms that describe relative functions rather than things. Fire has a nature in its own right, but relative to some other subject it performs a certain function. To say that fire is an element

is to include this relative function in its definition. All causes and elements as such will be definitionally related to that of which they are the causes and principles. This very distinction provides a reason why matter and potentiality especially should be considered analogous: matter is said to be that which is potentially form or privation directly and per se (1fpwrov Ka8' aim) A.4 1070b12-13). This fact about matter and potentiality clearly impressed Aristotle, since he mentions it on several occasions. 6 Potentiality or matter is not like any other term that happens to be useful in a specific genus; rather in its own nature it is adapted to that of which it is the potentiality. Unlike earth, which can be both a per se thing and a principle, for something to be a potentiality, it must be defined in terms relative to its actuality, and as a result it cannot even be logically abstracted from what it is the potentiality for without ceasing to be a potentiality. This seems to be less the case with a principle like form or actuality, because form and actuality are not what they are relative to something else. There is no difference between being something and actually being something, and this is certainly why Aristotle pays more attention to the analogy of potentiality than to the analogy of actuality. This interpretation is attractive, but there are some reasons to suppose

that it is not an adequate basis for the analogy of potentiality. When we say that two things are analogically the same, we say, among other things, that they do not have a wholly common definition. And yet Phys. 1.9 (192a31-32), for instance, provides the following general account of matter:

by matter I mean the primary substratum of each thing (€KaO"Tce), from which it comes to be, and which persists in the result non-accidentally. (modified ROT) There is no mention here of specific actualities of which matter is the

potentiality. The definition seems perfectly general and unadapted to any specific subject matter? Potentiality can, it seems, be treated as a genus. 6 In reference to privation Phys. 1.8 191b15-16; Met. Z.3 1029a20-26; DA 11.1 412a7-8. 7 Cook 1989, 117-18, argues that we understand through analogy not what the underlying nature is in general, but rather what it is in particular cases, but she suggests that Aristotle can nevertheless give a general account of it.

181 Mixed Uses of Analogy and Focality This 'general' definition, however, exhibits a characteristic that we see in several other definitions,' an ambiguous term, 'of each thing,' which makes dear that the account must be adapted to each use. This same kind of formulation is used for friendship (NE VIII.2 1156a3-5) and motion (phys. III.1 200b32-201a1), both being genera that contain a latent plurality. It is clear that Aristotle does not consider the plurality to be trivial: I

To be friends, then, they must be mutually recognized as bearing goodwill and wishing well to each other for one of the aforesaid reasons [pleasure, utility, virtue; my italics].

There is no such thing as motion over and above the things. It is always with respect to substance or to quantity or to quality or to place that what changes, changes. But it is impossible, as we assert, to find anything common to these which is neither 'this' nor quantity nor quality nor any of the other predicates. Hence neither will motion and change have reference to something over and above the things mentioned; for there is nothing over and above them .

The matter or underlying nature (il'7rOKHJ.tEY7) <1>-0,,«), just like friendship and change, cannot be defined without adapting it to some specific application, and there is no formulation that is abstracted from any of these specific kinds.' All the same, we can grant that a potentiality cannot be a potentiality without being a potentiality for some specific thing, and still claim that that very fact, namely that potentiality is a relative term, is common to potentialities in general and might be included in the account in order to render a legitimate general definition. This feature of potentiality, after all, arises from the fact that it is a relative term (TWY 7rpo< n Phys. IL2 194b9), and yet Aristotle does not suggest in the Categories that relatives are any less amendable to general definition than any other non-substance term (Cat. 7 6a36-37): 'we call relatives all such things as are said to be just what they are, of or than other things, or in some other way in relation to something else.' It is, however, precisely because potentiality is a relative that a common definition is impossible. For at Topics VL8 146a36-b1, Aristotle recommends that 'if the term is relative, either in itself or in respect of its genus, see whether the definition fails to mention that to which the term,

8 For a similar point see Owen 1978-9, 283; and Kung 1986, 11.

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182 Aristotle's Theory of the Unity of Science either in itself or in respect of it s genus, is relative: 9 The specification of the relata is an essential part of the definition of the relative. While these considerations reveal a plurality in potentiality, they do not explain why that plurality cannot be included in a definition . A final answer may be provided by noting that a potential something is a Being, and its Being and essence is to be potentially some Being. Since Being is not a genus, potentiality, since it necessarily is defined relative to some actual Being, will be predicated in all the categories. The analogy of potentiality arises from the fact that definitions in the proper sense can only be provided for existent Beings. To be susceptible of real definition (and not merely a nominal definition), something must be a Being, primarily a substance, secondarily some non-substance. A potential Being can be defined, and a general definition can be given to the extent that its relative can be generalized and still remain a Being, that is, to the level of the categories. By contrast, potentiality abstracted from anything that is a Being is not a Being and cannot be defined. While it is possible to provide a general account of the meaning of the word 'potentiality,' this cannot be the definition of any existent thing. This interpretation would explain the relativity of analogy and the various levels of analogy we find in A .4-S, categories and particular genera. For at whatever level of generality the Being is determined, at that level will the analogy be found. Granted that analogy in A is of the relative sort, we must now ask how the genera and categories in which the principles operate here are connected to one another. Though the principles may be analogously related, it is an important fact that, properly speaking, the categories of Being themselves can never be analogously related IO Quality cannot be analogous to substance, since an analogy requires at least four terms. Only something related to quality, like a principle of quality, can be analogous to something related to substance. Met. H .2 comes the closest to claiming the analogy of Being, but even here it is clear that what is analogous is the cause of ·(" ' ) .In eac h case. 11 t hB e emg atnov TOVA €LVat 9 At Top. V .B 13Bb23-26 Aristotle sa ys that simple iden tity of relation is revealed by analogy: 'The rule based on things that are in a like relation differs from the rule based on attributes that belong in a like degree, because the fanne r point is secured by analogy, not from reflection on the belonging of any attribute, while the latter is judged by a comparison based on the fact that an attribu te belongs: 10 In spi te of Owen 1960, 193n38: 'beings are the same by analogy because as one use of "being" is to substance so another is to quantity, etc.' 11 H.2 1043a2-7: 'It is dear then from th!!se facts that if its subs tance is the cause of each thing's being, we must seek in these differentiae the cause of the being of each of these things. Now none of these differentiae is substance, even when coupled with matter,

183 Mixed Uses of Analogy and Focality We are accustomed from biological analogy to find some abstractable or semi-abstractable commonality that provides the necessary connections be-

tween the analogues. The commonality extends further than each analogue, but not further than the group of analogues. This commonality prevents the analogues from being incidentally or metaphorically connected; it prevents the introduction of inappropriate analogies, like sail:boat::wing:bird, into biological science. Minimally, the analogies must occur at the same level of generality, categories with categories, genera with genera, and in

selected contrast sets, and minimally the relata must be essentially of such a nature as to admit of that relation. Where are we to look for a similar commonality among the analogues of potentiality? One obvious answer is that since thes e analogies are pur-

sued at the highest level of generality, there is no danger of metaphorical analogy, since there is nothing outside of the genera in which the analogies occur that could ·be irrelevant and non-scientific. There is nothing that

could be a metaphorical analogy to potentiality in the way a sail could be a metaphorical analogy of a biological wing or a fin. Such an answer makes the defensible assumption that the categories of Being are exhaustive

of reality (APa 1.22 83b13-l?). But because we may be comparing one irrelevant heap with another, we should look to other, more rigorous, means by which the various genera are related. In A, the obvious candidate

is natural priority. Aristotle opens chapter 4 by asking whether the causes and principles are the same for all things, and begins with the answer that there are a couple of ways of looking at the issue: The causes and the principles of different things are in a sense different, but in a sense,

if

one speaks universally and analogically, they are the same for all. (1\.4

1070.31- 33) The expression 'universally and analogically' (Ka86Aov ... Kat KaT' dvaAo~

yiav) is initially surprising, but as Aristotle goes on, he makes clear what kinds of sameness and difference he has in mind. 12 In a way the causes

of substance are the causes of all things because if they are destroyed, the other things are destroyed (A.5 1071a34-35). This expression of natural

yet in each there is something analogous to substance; and as in substances that which is predicated of the matter is the actuality itself, in all other definitions also it is what most resembles full actuality.' 12 There is no reason to suppose that the Kat is not epexegetic. For another use of Ka8dholJ that does not mean 'univocal universal,' see Phys. 1.1 184a23-25. Cf. r.2 l003bl4--15, where focally related Beings are said to be Ka8' fV.

-.-

--

--

---------------~~~~

184 Aristotle's Theory of the Unity of Science priority establishes the causes of substance as universal principles. Aristotle makes clear that this is not a contradictory but merely an alternative and

perhaps complementary way of looking at the question (1071a29-35). If the members of non-substance categories like light and colour are viewed as subjects in their own right, they must have their own principles, but in another sense substance is the principle of everything, because it is

naturally primary. Aristotle nowhere says that the analogies hold because some other relation holds. Nevertheless we have seen reasons why analogues should be fixed in a framework avoidance of metaphor and, what is essentially the same thing, the need for the parts of a science to be bound by per 5e relations. Of the connection between the analogy of principles and the underlying connections among their subject-genera, Aristotle has little to say. His comments opening A..5 are the clearest: Some things can exist apart and some cannot, and it is the fanner that are substances. And therefore all things have the same causes, because, without substance, affections and movements do not exist. Further, these causes will probably be soul and body, or reason and desire and body.

Aristotle is hardly clear in his expression, and he could be implying several things: 1. Substance is the cause of all, because it is the cause of itself and the cause of non-substances. 2. The causes of substance are the causes of all, because they are the causes of substance, and they provide the substrate for non-substance. 3. The causes of substance are the causes of alL because the causes of substance are identical with the causes of non-substance (i.e., potentiality for substance is potentiality for quality, etc.). The third interpretation is attractive inasmuch as it provides the greatest unity among the principles, but it is also the least likely since Aristotle holds that the causes are different for different things (though analogously the same). It is clear that the causes of substance are limited in their explanatory power, just as the oblique course of the sun is a limited moving cause (1071a15- 17): they do not explain all the essential features of the Beings. The first interpretation is recommended by the fact that Aristotle at the beginning of A.5 draws the distinction between what is separable and what is not. This distinction seems to be important in explaining why substance

185 Mixed Uses of Analogy and Focality functions as a general cause. But separability is a feature of substance, not of its causes, least of all matter and privation.

The statement at the end of A.5 that 'the causes of substances are the causes of all things, in this sense when they are destroyed all things are destroyed' (modified ROT; 1071a34-35) supports the second interpretation. Indeed, in 0.7 Aristotle presents a way of understanding the causes of substance, at least matter and form, as the causes of all other things. Aristotle says there that man, both body and soul, is the substrate for his affections, the affections being the white and the musical (1049a29-30).13 It is clear that musical is an affection of the soul and white is an affection of the body. If we understand the issue in this way, then the causes of substance, both matter and form, serve as subs trates, potentialities, and existential preconditions for non-substance. 14

Although this natural priority does not proVide as tight a form of unity as foca lity and definitional inclusion, it does provide a sufficient framework

for treating the principles as an analogical unity. The non-substantial genera are dependent on substance for their existence, and they are dependent in a specific way, not as I am dependent on the sun, but because they are inseparable (0,) xwp'O'T
sical is an affection of the soul, and white is an affection of the body (1049a29-30). One of the causes of substances, then, is identical with one of the causes of non-substance: the principles of substance serve as the substrate and potentialities for non-substance. Moreover, the other causes of non-substances also are caused by substance, because these causes can

only be predicates of substance, as for example white, which is a principle of colour, is a predicate of body. At a categorial level and at a generic level, non-substance is dependent on substance. Without going too far beyond the apparatus of A, we can say that the causes of substance furnish the substrate for non-substances, and to that extent there is an essential 13 Cf. Z.3 1029a23-24, where the other categories are predicated of substance and substance is predicated of matter. 14 In Z.l Aristotle provides a focal reinterpretation of this precondition, but in A we find no mention of definitional indusion. And yet, the difference between the two concepts in this context can be exaggerated. After all, Aristotle is talking here about the causes of things, and causes provide what he considers to be scientific explanations, and scientific explanations must have a per se relation with that of which they are the explanation . Natural priority here necessarily involves a per se (2) relation: non-substance belongs to substance, because substance is included in the definition of non-substance.

_.

-

--

186 Aristotle's Theory of the Unity of Science commonality among non-substances. This commonality is the basis upon which the various categories and genera can also be treated analogously. At the same time, in substances as well as non-substances there are proper principles that discharge the function of form, privation and moving cause. The passage at Phys. 1.7 191a7-12, though it manifests superficial similarities to A, does not invoke the genus argument, and so leads us away from the relativist towards the realist account. 15 We find that here and at Met. 0.6 Aristotle treats as analogous different senses of what it is to be potentiality: The underlying nature (V7TO/cELJlEV1J CPl)(Tts) can be known (E7HOTl1T?j) by analogy. For as the bronze is to the statue, the wood to the bed, or the matter and the formless before receiving form to anything which has form, so is the underlying nature to substance, i.e. the 'this' or existent.

The motivation for introducing analogy here is different from A, in spite of the fact that the principles of sensible bodies are at issue in both passages. In order to discover what this motivation is, we may most profitably start with

the grouping of examples: on the one hand, statue, bed, and other things that have form are contrasted with bronze, wood, and the unformed before it gets form (7Tpiv !l.a{3.lv T~V !-,opcp~v); on the other side of the analogy, the underlying nature is contrasted with substance (overia) and the particular thing (T66. n) and the being (TO ov). The grouping within the analogy suggests that the first three pairs illustrate some common relation. If so, Aristotle is not interested in shOWing the analogy of potentiality across all genera as he was in A. Instead he is pointing to two sets of differences in the very notion of potentiality. First, craft production (though a!-'opcpov is certainly ambiguous in this respect), in which there is, a pre-existing substrate, is contrasted with substances (like animals) in which there is no pre-existing substrate, but only a coexisting one. Second, there is a

15 Charlton (1970, 78-9) mentions the two standard interpretations: a traditional interpretation has connected this passage closely with Met. Z.3 and claimed that Aristotle is trying to arrive at a conception of prime matter. On this view the analogy involves a series of inductive steps whereby properties are stripped away until prime matter is reached. Alternatively, 'underlying thing' is a generic name for the relationship that exists between the members of the proportion (the position Charlton accepts). There is a further interpretation, by which the heuristic analogy induces not to a concept of prime matter, but to the matter underlying substance. Accordingly Aristotle is trying to grasp the nature of substantial change, having dealt with the general principles of change earlier in 1.7 (Witt 1989, 67). See also Hesse 1965 and Cook 1989, for further references.

187 Mixed Uses of Analogy and Focality contrast between coming-to-be and being. The wider context of Physics J, however, makes the coming-to-be/persistent Being interpretation somewhat out of place. As Aristotle says just after this passage, there had been a move among his predecessors from positing just the opposites as principles towards including a third principle, the underlying thing. Our passage is introduced as part of the proposal that these three principles may be considered in a way as two in number: the underlying thing can be considered numerically identical with one of the contraries, privation. This identification will serve as the key to the paradox of change, which earlier philosophers had engendered (1.8), a solution already alluded to in 1.7 190b17-27 16 By reducing the contraries to presence and absence in a substrate, and insisting that the substrate changes in a way per se related to itself (e.g., it is the patient, not the man, that is healed), there comes to be a logical unity, which had not been present before, between the substrate and the element changed. As Aristotle says, this solution can also be expressed in the two-term contrast between actuality and potentialiry (191b27-29). Rather than just the contraries being related (a situation in which change is still difficult to explain), the substrate and form will now be per se related. It is this context that motivates our analogy. Aristotle needs to show how the two different conceptions of the principles (their being two or three in number) are related. The generalizing description 'as the matter and the formless before receiving form to anything which has form ' represents the three-principle view, involVing the matter (,)1..1]),17 privation (ap.opq,ov. 7rP'V 1..a{3fLv T~V p.opq,ryv ), and the form (TOW 'XDVTWV p.opq,ryv), while the last pair, 'so the underlying nature is to substance, i. e. the this or existent,' represents the two-principle view, which Aristotle is moving towards as a solution to the problem of change. The examples of the three-principle view come from the realm of artefacts, because artefacts have an ambiguous

status between the three- and the two-principle view. With res pect to their names they behave like substances (wood:bed::f1esh:man), but their categoriallogic is closer to that of an accidental compound, since the q,UG... of bed is not bed, but wood, and bed is an accidental arrangement of wood. According to the logic, therefore, artefacts follow the three-principle structure: wood is what exists before it takes on the form; it is formles s, then it takes on a form. The analogy, then, is not primarily about a comparison between artefact and natural substance, since it is clear that the general formulation in the first half of the analogy is applicable to cases other than artefacts (e.g., substance-accident relations). Nevertheless, artefacts setve 16 50 Charlton 1970, 80; see Waterlow 1982, 14nll. 17 Keeping the reading of the M5S against Diels ~nd Ross 1936, 494.

188 Aristotle's Theory of the Unity of Science both as a paradigm case of the three-principle view and as a station along the way towards understanding the two-principle structure, which is best adapted to natural substances. Why, then, on this interpretation is the analogy necessary? It is note-

worthy that Aristotle does not explicitly state that a general definition of the underlying thing is impossible. Although induction is not explicitly mentioned, the fact that the underlying nature is known (E7ftaT'IT~) by analogy recommends the inductive view, and this in turn may suggest that we are supposed to arrive at a universal account. Moreover, there is a clear movement of discovery in the chapter as Aristotle approaches a solution

to the paradox of change using the pre-existing philosophical material at his disposal and setting the pieces in a new arrangement. But the inductive context of analogy does not entail the move to a universal account. Quite the opposite. Aristotle rarely uses analogy in an inductive context, and

does so in fact only in this passage, 0.6, H.2 (1042a4-5) (all passages concerning principles), and in the discussion about excerpting problems in APo 11.14 (98a20--23). In all these passages Aristotle carefully distinguishes

between what belongs universally and what belongs according to analogy. It is clear, then, that universal connections are treated differently from analogical connections, and that even in an inductive context the standard considerations of analogy are still relevant.

The fact that Aristotle is working with different views of potentiality, based on three and two principles, recommends a realist view of analogy.

The three-principle view, especially in the realm of artefacts, makes a clear distinction between matter, privation, and form, just because the matter can exist separately from the form. Indeed, that which is the matter for the form has itself a per se existence, as wood and bronze do, and only

incidentally does it lack or have the specific form. By contrast, in the two-principle view the matter exists only insofar as it is related to the form,

and its being is to have that form potentially. Aristotle makes this clear when he says that the potentiality-actuality distinction is an alternative

solution (1.8 191b27-29). As a result, the principles have different per 5e relations in each case, and therefore belong in different genera. At the same time, the constituent genera of the analogy are not in-

cidentally related. Artefacts provide more than merely metaphorical understanding of the underlying principle in substances. The three-principle genus is related to the two-prinCiple genus in virtue of the fact that only in the latter is the matter directly and per se related to its form. That is, a per se relation is added to the three-principle genus in order to generate

the two-principle genus. Equally, a principle, privation, is subtracted. That is to say, a relation of subtraction and addition, similar to that in Met. Z.4,

189 Mixed Uses of Analogy and Focality binds together the two genera between which the analogy arises. For the notion of capacity for a form is added to the notion of persistent substrate

of change. At the same time, the addition entails the subtraction of the principle of privation conceived independently from the substrate. The fact that they are related by addition and subtraction ensures that the principles will be of different genera, but it also ensures that they will be per sc related. And this in turn provides a reason why the two genera should be treated together and why we may legitimately move in the process of understanding from one to the other. Although this structure is only implicit in the Phys., Aristotle develops it further and more explicitly, though with different emphases, in Met. 0.6 18 The discussion of potentiality in

e

is most interesting for our purpose

because of the explicit interaction between focality and analogy in a realist account. Aristotle distinguishes two kinds of livval'm. The first kind, which he treats in 0.1; 2 and 5, is concerned with change (Kivry
per se Being in its own right. We noticed that, when this happened, the per se relations of non-substance did not remain entirely consonant with those of the first step. For instance, when non-substances, like white or odd, are treated as per se beings, they do not dir,ectly contain substance generally or any specific substance in their definitions. And even if ultimately, through several focal connections, white and odd are per se related to substance, nevertheless this connection is expressed differently from the connection of accident to substance. White, treated as an accident, has different per

se relations (it contains raj substance directly in its definition) from white treated as a per se Being. In a similar way the ovvci,u.€t), when considered

18 Cook (1989, 118) denies the parallel between 8 .6 and Phys. 1.7: 'The 191a7- 12 analogy and the 86 analogy do not have the same sort of structure. In 86, Aristotle uses generalization from examples to understarid what sort of "thing" actuality is. We understand this through understanding the role that actuality plays in the actuality-potentiality pairing. At 191a7- 12, we come to know through an analogy what the underlying nature is in particular cases of substantial coming-to-be.'

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190 Aristotle's Theory of the Unity of Science· m the context of change, have a different significance from the OWal'''' when considered in the context of persistence. Just as non-substance can be treated as per se Being only if the focal relationship between accident and substance is broken, so here too the OVVa.,uH~ of persistence can only emerge, if the focal connection characteristic of change is dissolved. Aristotle begins his discussion of DVVal't< with a focal scheme in the context of change. In 8.1 he takes up the sense of 'active capacity,' and defines DVVal't< as a 'principle of change in another or in itself qua other' (1046a10--11). This sense he designates as primary, and explicitly builds a focal scheme of derivative tenns around it. One of the derivatives is the passive capacity, the principle of being affected in change by something else (im' a""au) or by itself qua other (1046a11-13). Owen proposes for the focally derivative formulation 'source in patient of change effected by another or (by itself) qua other, viz. by a source of change (something which is/has dunamis [in the primary senseD,19 When we come to 0.6 Aristotle reiterates the important methodological claim he made in 0.1, saying that he will introduce EV
19 Burnyeat 1984, 47. For a full focal transcription of related terms see 46-8. Scrupulousness in definitional inclusion can be overdone, since it is dear from the present passage that Aristotle is casual: 'the accounts of the prior SVllcillt:t~ are somehow present in the accounts of these SVVcillt:t~' (Wo"TE Kat (I) TOt~ TOWWV A6)'ot~ (vv7rcipX0txTl 7TWS 01 TWI) 7TPOTEPWI) SVllall(WV Myot 1046a17-19). Aristotle may have wanted the definitional inclusion to be casually expressed for reasons that pick up on problems discussed in chapter 4. It is difficult to see why the active capacity is primary and the passive secondary, if, as Owen has claimed, the inr' aAAov phrase is the basis for the focality. For JUSt as the passive capacity clearly implies the active capacity (that implication is noted explicitly at 1046al4-15, inr' apxfis p.ETaJ3A1]nKfj~) , so that which is capable of changing something for the same reason surely implies something that is capable of being changed. Since Aristotle clearly intended the inT' aMov expression to be the basis of the focality, it is impossible on the basis of definitional inclusion alone to assign focal primacy to one or other of the pairs. For otherwise we quickly face the problems of recursive definitional inclusion to which Aristotle was so sensitive: active capacity could be defined as 'principle of change in another or in itself qua other (i.e., in something that has a principle of change by another or by itself qlta other [i.e., by something that has a principle of change in another or in itself qua other ... 1).' Cf. snub nose nose . . . Within the framework of change some kind of mutual or bifocal relationship seems to be inevitable. Burnyeat et a1. 1984, 11-13, on H.3 1043a29-b4 discuss the ambiguity of 'man' and the problem of the focal meaning, and suggest two readings (soul is primary; man [as composite] is primary). They are reasonably perplexed as to which of the twO senses of 'man' is primary. This example reveals the disturbing fleXibility in the notion of definitional priority.

191 Mixed Uses of Analogy and Focality is not the only one. We may come to know this new form of 3VvaJ.L'S by analogy: Actuality means the existence of the thin& not in the way which we express by 'potentially'; we say that potentially, for instance, a statue of Hermes is in the block of wood and the half-line is in the whole, because it might be separated out, and even the man who is not studying we call a man of science, if he is capable of studying. Otherwise, actually. OUf meaning can be seen in the particular cases (E7Tt TC;JV /CaB' g/CQOTa) by induction (i.'rraywyfi), and we must not seek a definition of everything (7TQVTOS' opov) but be content to grasp the analogy, - that as that which is building is to that which is capable of building, so is the waking to the sleeping, and that which is seeing to that which has its eyes shut but has sight, and that which is shaped out of matter to the matter, and that which has been wrought to the unwrought. Let actuality be defined by one member of this antithesis, and the potential by the other. But all things are not said in the same sense to exist actually, but only by analogy - as A is in B or to S, C is in D or to 0; for some are as movement to potentiality, and others as substance to some sort of matter.

(1048a30- b9) We note some immediate similarities with the Physics passage: induction is explicitly mentioned (E7TaywY'i); the statement that the potential is known as different from the form or actualiry (fOT' a~ EV€py"a TO V7Tapx"v TO 7TpdYJ.La J.L~ OVTWS wrnrEp A€yoJ.L'" BvvaJ.L" 1048a30-32; J.Lia J.LEV ouv iipX~ aVTl1. ouX ovrw jJ.ia ova-a Ou~€ ovrws- OV WS TO r6~£ n 191a12-13) . In addition, it is clear that Aristotle is engaged in a process of discovery, since he begins from the more familiar senses of Suva/.us- and moves to the less familiar and technical senses; moreover, he is investigating the familiar sense for the purpose of arriving at the technical sense (B,o ('1ToilVTfS Kat 7TEpt TOVTWV a,~A80J.LEV 1048a30). This process is linked with induction and analogy in the passage above (1048a35-37). Nevertheless, even in the context of induction the rigours of per se connections apply. The language of definition and the distinction between universal and particular are present (opos, TWV Kae' EKaOTa, 7TavTos). In this passage the use of analogy is an explicit indication that no universal definition of BVvaJ.Lts can be attained. The scheme introduced in the first chapter of 0 in its simplest form had consisted in the focal relationship, active BVvaJ.L'..-passive BVvaJ.L's, According to this scheme the application of the first element to the second produces change. It is reasonable to suppose that when EV€PYELa is introduced it will be paired with each BVvaJ.L'S, and that by this pairing a new sense of BvvaJ.L's will emerge. Aristotle does not make explicitly clear how

192 Aristotle's Theory of the Unity of Science he intends the introduction of EVEpYfLa, but he seems to have the following scheme in mind:

active ~UVa.J..LL~ (building art)

I

passive Bvva/-LLS

(buildable material)

I

active fvepYELa

passive fvepy€ta

(building activity)

(a building being built / having been built)

The examples provided here are still suitable for and adapted to bVVa}LLS in the context of change, and as a result the conception of the scheme has not

moved significantly beyond 0.1. But a new sense of OVVa}LLS emerges when the focal relation bet~een active and passive 5vva,u.Ls is set aside, and the significance of the OVVci,uHS' are no longer seen in relation to one another, but each in a new relation with its corresponding form of Evipyf.w. This

new relationship is described at 0.8 1049b12- 17 in terms of definitional inclusion, and so has the logical form of focality, even though the items do not share a name: EvePYHa is prior in definition to ovvap.ts. By setting aside the primary focal relation between active and passive OVVajlLS, Aristotle is at the same time setting aside the EV aAA1p-{nr' aAAov relations characteristic

of change that bound them in the first scheme 20 Change is now no longer being considered as an essential feature of ovva}u~, and is abstracted from the definitions of the terms. The new scheme contains the same terms as

the original (but now expanded) scheme, but those terms are understood in a new set of per se relations, and therefore take on a new significanceY The

senses of ovva}LL< and EVEpYHa are now apprehended by analogy, since the focal arrangement based on change (EV aAA'f'-inr' aAAov) that kept active and passive capacity linked has been set aside, and the BVVG.}LEL< are being treated in relation to their actualities.

The chief difficulty in understanding the import of the analogy has been interpreting the examples provided. The clearest (though still hardly lucid) contrast is provided at the end of the quoted passage: EVEPYHa is not the same in all cases but is analogical; as

KiV17GU

is to ovvaJlt~, so ovuLa is to

some vA'I (1048b6-9). This in some ways seems to recapitulate the Physics analogy. The· first pair seems to imply change, the second pair persistence.

It has been often pointed out that the distinction between the OVVa}LLS of 0.1- 5, ovva}L'~ for change, and the ovva}LL< of 0.6, ovva}LL< in stable 20 Charles 1994, 97, discusses the significance of this distinction between the two schemes. 2] This seems to be Frede's (1994) basic point, though he seems to extend the focal sense from the first scheme to the second (190 and passim).

193 Mixed Uses of Analogy and Focality being, seems to fit the purpose of the Metaphysics insofar as it aims at an

understanding of being qua being and not qua moving and changing. 22 But the examples provided at 1048a37- b4 do not fit this pattern well: waking/ sleeping and seeing/having eyes shut do not suit either side of the analogy. I follow Gill, therefore, in interpreting all the examples as belonging to the conception that has been abstracted from change: building, waking, and seeing are active €V€PY€laL that correspond to the active owaf"«' ability to build, sleeping, and being able to see but having one's eyes shut. No doubt the activity of building usually implies change, but strictly within the pair as Aristotle has provided it - building and the ability to build - there is no change in another thing or even in oneself as other. 23 It is merely the actualization of the internal learned capacity. The last two examples of ivipYHa, that which has been separated from the matter (a7ToK'Kp(f'ivov) and that which has been worked up (o:TrHpyaap.€vov), co.rrespond to the passive QvvafJ.EL>, matter and what is not worked up. As Gill points out, the fact that perfect participles are used in both cases suggests that the persistent state, not change, is at issue .24 On this interpretation, then, active ovvaj.w; is a capacity for an activity, passive ovvaf'« a potentiality for a form. The KtV'1CT«-ovvaf'« pair (1048b8) must accordingly be interpreted as ivipYHa- OVVaf'«.25

What is the relationship between the original focality and the analogy that arises between the

OVVcljJ.H)

in the context of persistence? When

actuality is added to the original focal scheme, nothing prevents the expanded scheme from being applicable to change. In fact, the example of building provides a complete range of terms to fill up a scheme associated with change. In this case, the original focality and the original range and 22 Gill 1989, 172ft and 214ff. distinguishes the first scheme concerning change from the second scheme concerning persistence; d. Ide 1992, 3-4 and Burnyeat et al. 1984, 48, who advert to the use of SVVaI-'LS' and fVfpYHa in H.6. 23 Gill 1989, 21Snll cites DA II.S 417b8-9 for building as pure activity. 24 Gill 1989, 215. But how are we to interpret the first set of examples? The first two representing MVUI-'LS' are the Hermes in the wood and the half in the whole. They are potentially, because they could be taken out of what they are in (d. the almost identical example at Phys. 1.7 190b7-8 in the context of coming*to.be). The third is the knower who is not actively studying/ contemplating. The first two, then, seem to imply change, and the third does not. I suggest that since at this point Aristotle has not yet introduced analogy or the induction, we should not be too concerned about finding consistency in this set of examples. Their purpose here is merely to give an outline of the distinction between actuality and potentiality, and to introduce actuality as a kind of Being not like potentiality. Aristotle then goes on (in accordance with his stated purpose) to distinguish the senses and draw the analogy. 2S See Gill 1989, 217 and Ross 1924, ii, 251.

194 Aristotle's Theory of the Unity of Science significance of 5vva,."tr; remain in place, and the focality is based on the EV aA.ACf-inr' Q.AAOV relation. But in order to extend the sense of ovva}lt'l beyond change, the EV aAAcp-tm' al\i\ov relation must be set aside, and an

analogy rather than a focality will take its place. The focality will cease to exist, because the necessary relations concerning change no longer hold universally. It is dear that the first pair at least (e.g., active thinking, seeing, etc.), when it is considered complete in itself, extends beyond sources of change in another and encompasses activities that do not result in any

products or any changes in other objects. The relationship between the two conceptions of bVva!"t< (change and persistence) is similar to what we saw in Z between non-substance considered as an accident of substance and non-substance considered as per se Being. For in order to arrive at the per se conception of non-substance, we had to break the accidental relationship between white and man and set white into a new per se relationship with surface. The function of white is quite different in the two relations. In a similar manner, the relationship

between the active and the passive

owa!"". is broken in order that each

may enter into a new per se relationship with their respective EVEpy€ta; and the function of ovva!"L> is quite different in these two relations. Aristotle, then, makes two very different uses of analogy in the context

of potentiality and matter. One is a relativist use appropriate for the study of principles, the other a realist view intended to lead us to a new conception

of matter and potentiality. In all cases, however, we find a relationship of natural priority or focality connecting the genera of the analogies, which either allows us to treat the principles as a single group or allows us to

move from one conception of the principles to another by addition or abstraction.

The Good The good has traditionally been treated alongside other transcategorial terms, like Being, One, and potentiality, in discussions of analogy and focality. 26 It seems especially promising for our purposes, because Aris-

totle's discussion of the good in EN 1.6 1096b26-29 contains the only passage in the corpus that mentions analogy and foeality immediately together. OUf discussion begins again with Owen: since the EE lacks a

passage parallel to EN's discussion of analogy and focality, Owen argued for the ea rly dating of the EE. He supposed that Aristotle had not yet

26 E.g., Alexander on Met.

r. ,242.5-6.

.--~-

'"'-

195 Mixed Uses of Analogy and Focality thought to use focality in the context of transcategorials, and so had not yet developed the focal solution that is fully revealed in Met. r.2. But Owen was misled by EN 1.6 1096a23-29 (where good is said to be predicated in all the categories) into supposing that the 1.6 1096b26- 29 passage was relevant to the categories, and his misreading seems to persist in some recent accounts." Interpretation of the passages is further bedevilled by the fact that the context throughout is a critique of the Platonic idea of the Good. Aristotle adduces arguments in both the EE 1.8 and EN 1.6 only to the extent that they are useful for his critical task, and where he does make positive comments (1096b26-29) he explicitly recognizes that they are strictly speaking out of place (1096b30-31). In response to Owen's claims concerning the EE, Berti has argued I think successfully - that Aristotle implicitly recognizes the basis of a focal arrangement in the EE. This arrangement consists in the means-ends relationship, and it fulfils both of the formal criteria of focality. Both means and ends are called 'good,' and the definition of the end is contained in the definition of the means.28 Robinson, while agreeing with Berti about the EE, urged that a focality based solely on ends and means would result in a single ultimate good, which the EN with its multiplicity of per se ends denies (1096b16-25).29 In this state, more or less, the controversy has rested. There is, however, more to be said about the scope for focality and analogy among the goods and the role of categories in these arrangements. Both the EE and the EN offer further evidence for a focal arrangement among means and ends, and this becomes apparent in light of the intimate relationship between focality and demonstration. For a passage at EE 1.8 1218b16-24 expressly discusses the final good as T
--

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196 Aristotle's Theory of the Unity of Science A series of means and ends, which are connected in hypothetically neces-

sary premisses (civaYK'11218bI9), can be displayed in a syllogism. The ends are causes (bI6, 18) and principles (24), and as such take the middle position. The per se relations, which underlie focal relations, are clearly present and at issue here. The use of the relative is a further indication of the focal arrangement (avciYK17 rODE Eiva~ TO crV}J.cpEpOV npos aVT7JV). We see the familiar distinction between the natural and the focal demonstration. The natural final-cause syllogism

"'po,

exercise IPO health health IPO man exercise IPQ man does not contain the term 'good,' though it is implicit through our understanding of the relations between the terms. The good can be made more evident through a linguistic, focal demonstration,

healthy IPO conducive to health conducive to health IPO exercise healthy IPO exercise, in which 'conducive to' implies the relationship of means to ends. By substituting 'conducive to' and 'exercise' for other terms we can fill out the terms of the science of health. Finally, if we substitute 'health' and 'exercise' for the general 'good,' we shall have the desired focal demonstration: good IPO conducive to the final good conducive to the final good IPO means (specifically exercise) good IPO means (specifically exercise) It is easy, then, to see how ends and means

fit into the wider focal science.

The derivative good, means, has a different significance and different properties from a good in some other derivative sense, for example, evil, which,

ov

by the I'~ rule of focal inclusion, can also be called 'good.' Means, though they qualify as focally derivative because they are homonymous with the focus and imply the focus in their definition, are also peculiar in that they

actually share some properties with the focus. For the final good and the derivative good are both objects of desire and both are pursued. This is obViously one of the reasons that Plato was led to the idea of the Good, and it is preCisely this fact that allows goods to be treated analogically as

197 Mixed Uses of Analogy and Focality well as focally. It is an arrangement closely akin to cumulative series, as

we shall see in the next chapter. In the EN as well, Aristotle maintains the focality of ends and means (1.6 1096b8-14), and although he does not use the 7TPO< iiv expression in this context (perhaps because he is arguing in this section that the means are not related 7TPO< iiv but 7TPO< 7ToMa) the language of focality is unmistakable. The means are described as 'those which tend to produce (7TOL'lnKa) or preserve (q,vAaKnKa) these [ends] somehow or to prevent their contraries' and they 'are called so [good] by reference to these (BLD. ravra Aiy«reaL) and in a different sense.' These are the standard formulae of Met. r.2 30 But the EN also moves beyond ends-means focality . The further development comes at 1096bl4-26, where Aristotle calls on us to set aside the means and consider whether the ends themselves are goods in accordance with a single form (KaTD. /liav 1biav). He claims that the definitions of honour, prudence, and pleasure are different and distinct qua goods (iiTEpOL Ka, BLaq,ipoVTE> 01 A6yOL ralJTy/ Vayaea). Since they are not related as ends and means and do not share a common definition qua goods, we are forced to consider whether they are chance homonyms (1096b26-31) : But then in what way are things called good? They do not seem to be like the things that only chance to have the same name. Are goods one, then, by being derived from one good or by all contributing to one good or are they rather one by analogy? (a.hA' ct.pa.)'f TCp clq,' EVo) fivQt 17 7rpo) Ell a7rQVTQ UVVTfAE1v 17 p.O.AAOV Kar' civaAoyiav;) Certainly as sight is in the body, so is reason in the soul, and so on in other cases. But perhaps these subjects had better be dismissed for the present; for perfect precision about them would be more appropriate to another branch of

philosophy. Since Aristotle does not provide a solution to this question here, we

should not immediately take the disjunction, ~, to imply that only one or another of the techniques of unification is correct, nor even that thet; are exclusive.31 Certainly to look for three distinct techniques is hopeless. 2 The first two disjuncts are to be treated as a unit, T~ acp' €vO~ ElvaL r, 7TPO~ €V a:rravTa CTVVTEhELV. Granted, the diction, as Fortenbaugh has pointed out, 30 Met . r .2 1003a35-36: CPVNiTHIV, 7fOl£lV; 1003b17: ~l ' 0 AEYOVTal . 31 Berti 1971, 170, claims that the goods can he both analogically and focally related. So also Menn 1992, 551n11. 32 Ross 1914, 291, distinguishes acp' EVOS as the efficient cause, 7fPOS fV as the final cause. This is not an Aristotelian usage.

,

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198 Aristotle's Theory of the Unity of Science does not correspond to the technical expression for focality,33 and there are hints towards a means-ends interpretation:

(T1)VTEA£tV

is chosen in part

because of the root TfA-; and it is connected with usefulness at GA 1.18 725a5. Nevertheless, a passage at PA IlL5 667b21-26, though in a quite different context, contains similar diction and suggests that

"'pos fV

act>' €VOs and

represent two ways of looking at the same phenomenon. 34 And a more relevant use for CTVVTfAE'V is found at SE 1 165a35-37. Concerning sophistical arguments, Aristotle says that he will discuss how many kinds there are, the number of their elements and parts, and the other things that contribute to this art (7T€pl. TWV aAAwv TWV CTVVTEAOVVTCOV ELS T1JV T€xvrJV TavT~v).35 He provides some indication of what he thinks the CTVVTfAOVVTa are at the beginning of SE 34: the appropriate order of questions, how to solve arguments and solecisms, and so on, both of which go beyond a mere enumeration and description of the parts and elements. This passage is the

closest parallel to the EN, since it deals with the logical organization of an investigation. 36 As the order of questions contributes, but is not neces-

sarily an element, so the per se goods contribute to a single good without necessarily being elements of that good. The traditional interpretation that reads this phrase as a reference to focality, then, is not likely to be far off the mark. 37 . If this is correct, can Aristotle provide a focal arrangement for these per se goods 138 He lists four: intelligence, sight, certain pleasures, and honours (1096b17-18), to which we might add virtue generally (from 1097b2; Aristotle already provides p6V~CT"). Unfortunately, Aristotle provides no example of what he has in mind and expressly dismisses the question as too exact for his study. Moreover, in the remainder of book I he leaves aside the relations among these per se goods, because he has already asserted that they are also desired for the sake of something else, and it is this 33 Fortenbaugh 1966, 188-9. 34 'The reason why these two vessels [the aorta and the great vessel] coalesce into one source and from one source ((is' ",ia.I1 apxi]v a-vVT£A.t"tv leal cina ,tuas) is that the sensory soul is in aU animals actually one, so that the part in which it primarily abides must also be one' (modified ROT). 35 TWV ci.v..wv TWV cTVlITEAovlITWV means 'the other things, I mean the ones contributory': the parridple 'is emphatically attributive. 36 This tells against Fortenbaugh's generic interpretation, since Eta77 TWV Ao)'wv (165a34) are dearly distinguished from the contributory factors . 37 E.g., Owens 1978, 116-17. 38 Fortenbaugh has tried to show that the phrase clef {vat Eivcu 11 1TpOt iv Q'l'T(U)TCl O'lWTEAEiv does not refer to focality, but to generic affiliation through means and ends. This is, of course, impossible since Aristotle has already set this possibility aside at 1096bl4-16

and b24-25.

199 Mixed Uses of Analogy and Focality something else that he pursues in 1.7 through the methodology of the means-ends scheme. This obviously does not preclude other relationships alluded to in the 7rPO, EV ITVVTfAElv phrase, for how can we exclude some other relationship to €VOaLMOvia if we do not yet know what EvoaLMovla is? What that relationship might be, we are left to speculate, and yet, our understanding of focality provides a clear direction for the search. We should look beyond the confines of EN I to the later books, and seek Aristotle's final word on the focal relationship in the host of per se relationships that bind together the central terms of his ethical theory. Each of the per se goods is not just a means to EVOaLj.wv{a in some vague sense, but also enters into a very precise relationship with EVaaLJ1-0vla and with the terms in which Ev~a'Jlovia is defined. 39 A brief survey of these reveals that their relationship to EvoaLfLov{a is not the same in all cases. f:voaLjlOv{a, the human good, is the activity of the soul in accordance with virtue, and if the virtues are severaL then in accordance with the best and the most complete of them (1098al6-17). Virtue, then, is obviously a central part of the theory, because it is per se (1) related to happiness. It is a state of the soul concerned with choice, lying in the mean relative to us, this being determined by reason and in the way in which the man of practical wisdom would determine it (11.6 1l06b36-1107a2). Virtue is good because it is the activity in accordance with this state that is good. Accordingly, q,povryIT" too is part of the theory, because it is a virtue, indeed in many ways it is the most complete virtue. For C/>POVTfa"LS is not only a virtue (whose activity constitutes the human good), but it is the virtue that determines the mean states that constitute the other virtues (whose activities in turn constitute the human good). It is therefore both a species of virtue, and related to ethical virtu~. Honour turns out to have a plurality of roles in Evoa'Jlovia. Ev~a'Jlovia itself is honoured (1102al; 1178b31-32). But honour is also that with which the state of pride is concerned. In this sense it is not a good at ali, but rather it is how we act and react relative to it that is a good; and honours and dishonours are the object with respect to which the proud man is as he should be (that is, has the human good) (IV.3 1123b20). Pleasure has the most interesting relationship to EVOaLfJ.OVta. In a general way, all ethical virtue is concerned with pleasure and pain (7rEPL ~~ovas yap KaL Alma, 'ITn ~ ~elK~ apET~ 11.2 1l04bS-9; d. X.l), since virtue concerns action and reaction, and pleasure and pain attend every action and reaction. But pleasure enters the theory through another relation, and thereby has a different significance: pleasure

39 See Tuozzo 1995 for some similar conclusions, though from a different perspective.

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200 Aristotle's Theory of the Unity of Science completes the (best) activity not as the inherent state does, but as an end that supervenes (X.4 1174b31- 33). We do not have to determine the exact nature of this form of pleasure to see that it has a different significance from the more general form. Finally, of sight Aristotle has little relevant to say in the ethical treatises, but the outlines may be filled in from the first chapter of the Metaphysics. In general, then, the per se goods may be said to contribute to a single end through a variety of focal relationships without being means to that end. Although Aristotle left us to speculate about the focal relationship, he does provide an example of the analogy of the goods: as sight is in the body, so reason is in the soul. Sight is the good for the body, in that the body generally (the instrumental parts) is to be explained with reference to it. Though sight may also contribute to the welfare of the body, we enjoy sight most of all for its own sake, since it is the purest (EN X.51175b36-1176a1). The genera, body and soul, are obviously related as matter and form. Sight and reason will be the goods of the two parts of the substance. Moreover, we have here a continuous analogy (A:B::B:C), since sight is an activity of the soul, and soul is for the sake of reason. This analogy is obViously complete as it stands, and it is difficult to see how pleasure or honour can be fit into the scheme. For this reason the analogy should only be taken exempli gratia. A much more promising field for analogy is found among the crafts. After all, tradesmen need only know the good of their own craft (1097a3- 8), and the good of each activity and craft is different (a16-18). But Aristotle also makes clear that the analogy is not sufficient in itself, or at least that it must be framed by some further form of commonality. For all the crafts derive their ends from the political craft, connected by ends-means focality. Similarly among the per se goods, a simple analogy without some framework would result in incommensurability of ends, and

would be no guide for a rational life. We might think back to exchange value, which though it was analogically distributed among the various trade goods, nevertheless was made somehow commensurable by being treated in terms of need through money. If we want to avoid complete incommensurability among the per se goods within the analogical scheme, we could try to commensurate between them in some way, seeking so much honour and expending so much intelligence for it, trading as it were among the ends 50 as to achieve a certain balance in life. This is, of course, not Aristotle's solution. Focal unity is the ultimate unity among the goods. The mention of voils as a per se good and the fact that analogy is found among terms associated with the categories has encouraged the assimilation of this passage with the passage at 1096a23- 29, which also discusses the ambiguity of the term good. In the context of refuting the Platonic idea

201 Mixed Uses of Analogy and Focality of the Good, Aristotle asserts that the good is not one thing, because it is said in as many ways as Being. Essentially the same argument is found in the EN and EE with only minor modifications: [S]ince good is said in as many ways as being is said (for it is said40 both in the category of substance, as God and reason, and in quality, e.g. the virtues, and in quantity, e.g. that which is moderate, and in relation, e.g. the useful, and in time, e.g. the right opportunity, and in place, e.g. the right locality and the like), dearly the good cannot he something universally present in all cases and single; for then it would not have been predicated in all the categories hut in only one. (EN 1.6 1096.23-29) [T]he good has many senses, as numerous as those of being. For being, as we have divided it in other works, signifies now what a thing is, now quality, now quantity, now time, and again some of it consists in being changed and in changing; and the good is found in each of these modes, in substance as mind and God, in quality as justice, in quantity as moderation, in time as opportunity, and concerning change that which teaches and that which is being taught. As then being is not one in all that we have just mentioned, so neither is good, nor is there one science regarding Being or the Good. (modified ROT; EE 1.8 1217b25-34)

The key to the correct interpretation of these passages comes from Topics 1.15 107a3-17: terms, like AfVKOV, when they are applied to subjects, like body and sound, have different significance, and indeed refer to predicates in different categories· 1 For a body to be AfVKOV is for that body to be

40 A slight alteration from the Oxford translation, which reads 'since things are said to he good in as many ways as they are said to be {for things are called good both in the category .. .' The Oxford translation inclines towards the correct interpretation, hut without indication from the Greek. 41 lowe this interpretation to Ackrill 1978, who noticed the significance of the Topics passage: 'Look also at the classes of the predicates signified by the tenn, and see if they are the same in all cases. For if they are not the same, then clearly the term is homonymous; e.g. good in the case of food is what is productive of pleasure, and in the case of medicine what is productive of health, whereas as applied to the soul it is to be of a certain quality, e.g. temperate or courageous or just; and likewise also, as applied to a man. Sometimes it signifies what happens at a certain time, e.g. what happens at the right time; for what happens at the right time is called good. Often it signifies what is of a certain quantity, e.g. as applied to the proper amount; for the proper amount too is called good. So then good is homonymous. In the same way also hUlK"" as applied to a body, signifies a color, but in regard to a sound it denotes what is easy to hear.' Notice that this tapas does not consider the possibility of ambiguity between the good in the area of food and good in the area of medicine {a shock for a

202 Aristotle's Theory of the Unity of Science somehow qualified; for a sound to be A.evKov is for that sound to cause

some effect. Since the Topics treats the cases of good and II.€VKOV as parallel, the term good, when predicated of various objects, will likewise fall into different categories. For a man to be good is for that man to be virtuous,

to have virtue predicated of him (Le., to be somehow qualified). Similarly, for the weather to be good is for it to be neither too hot nor too cold, to be moderate (i.e., somehow quantified). For a delivery to be good is for it to arrive before 5:00 pm, at the right time (i.e., sometime). This interpretation fits the examples provided by both the EE and the EN versions. For it is clear that the examples are essentially goods in their

category, but it is equally clear that the predicate, that which teaches, is not the only good in the category of change. Virtue, moderation, and so on

are predicates that signify 'good' for various things, and these predicates fall under different categories. Within some categories, doubtless, 'good' has several significations, for others it has not only just one signification

but one object of which it is predicated. 42 In view of the proximity of the EN passage to the passage later in the same chapter that proposes a logical organization among per se goods,

it has been suggested that good in our present passages is amenable to being expressed as an analogical or a focal unity·3 It is true that there is no explicit mention of analogy in these passages, and, in fact, it would probably be inappropriate in the context of Aristotle's critique of the platonic doctrine of the unity of the good, but the claim that the good is said in as many ways as Being encourages an analogical view along the same lines as potentiality.44 However, analogy among the goods at a

categorial level, while possible, is not especially useful for Aristotle, and for this reason he makes no mention of it.

The examples of the Topics passage do provide some superfiCial encouragement for an analogical arrangement of the good along categoriallines: as

food is good because it is productive, so man is good because he is qualified (TO 7TOlo'V e1'vat). But a brief examination of these examples reveals that the reader of the Gorgias), since the first is 1TOU7TlKOV of pleasure, the second 1I"OUITUCOV of health. Since both goods are 1J'Otl1TIICOV, no ambiguity can be detected· by this topos. The ambiguity of the good is treated solely on a categorial level. For a different view see

Shields 1999, 202-4. 42 For the problem of god and mind, see Ackrill1978, 23, and more recently, Menn 1992. 43 So Owen 1960, 193n38, and to some extent Menn 1992, 550-1 and n. 11 . Broadie has li nked the passages for the purposes of focality (1991, 28-9). 44 As Rist points out (1989, 276), we should not expect to see Aristotle saving the Platonist position by introdUCing focality in the midst of an anti-Platonist polemic.

203 Mixed Uses of Analogy and Focality . category of the subject and the category of the predicate do not have to be the same. Only in the case of substance, where self-predication is the only logical possibility, are the subject and predicate necessarily of the same category: for god to be good is for god to be reason (ie., a substance). Since the categories of the goods do not consistently correspond to the categories of the subjects of the goods, it is clear that the Topics examples cannot provide a model for the analogy of the good along categorial lines. If we look, not at the predicate-subject relation, but instead at the relationship between the good predicated and the category in which it is predicated, we find a more promising candidate, virtue:quality::god:suhstance,

and so on. In this analogy, the goods are clearly not the goods for a category, in the sense that Aristotle develops his analogies of the good elsewhere. While in some sense substance is for the sake of god, clearly quality is not for the sake of virtue. If these goods were the goods for their categories, then all and only the members of the category would be instrumentally good for the good of that category. Vice would then be an instrumental good for virtue. Moreover, as we saw, the goods by no means have to be in the same category as that of which they are goods, so there is no reason to suppose that the good for a quality will be a virtue. Again, if the good for a category falls into several categories, then there can hardly be one good that is the good for that category. This seems to happen in many cases: the good of an express delivery (a 7TO"'V) is a 7TOT<, but the good of a dry-cleaning (a 7TO"'V) is a 7To
45 So Gomez-Lobo 1989.

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204 Aristotle's Theory of the Unity of Science so on are the terms given in each category to the things that are aimed at or chosen. This is not, however, a very interesting or revealing analogy,

because it is the 'for the sake of' relation that does the real explanatory work. This may be one of the reasons why the good is not treated extensively in the Metaphysics (with the exception of god, whose essence is to be good), and with that exception does not belong in a study of being qua being: good is an accident and is best understood in the context of action and in the analogical and focal arrangements that relate one good

to another rather than to Being. Their categorial status, which is the basis of the science of Being qua Being, is largely irrelevant 4 ' In thi~ respect the good is significantly different from potentiality, for which the categorial analogy is genuinely significant. For potentiality discharges its function as potentiality in the category for which it is the potentiality. Good does not. Potential substance does not exist in several categories, but if in any category, in substance. 47 The categorial status of

non-substantial potentialities is arguably twofold. For non-substance the substrate is always the same, substance (Z.3 1029a23-24). Of course, the substrate is actually a substance, but it is potentially the non-substance it may become (in a different sense of is, of course). So air is actually air, but potentially transparent (so as to be light). However, since the privation is in the same category as the form, and since the substrate is considered

only insofar as it is relevant to the form (Phys. 1.8 191b4-10), Aristotle makes the matter essentially adapted to take on that form. Inasmuch as the matter is potentially, say, transparent, it is potentially qualified and so is in the category of quality. If a categorial analogy of the good is an unpromising arrangement, Aristotle extends even less of an invitation to interpret the categorial goods

focally, in spite of the attractive suggestion that god as substantial good can be viewed as the focus 4s It is true that god is the ultimate final cause and end (DA 11.4 41Sa23-b7), the goal towards which all things strive, and that for the sake of which they do whatsoever their natures render possible. At the end of EE (VII.IS 1249a21-b2S) god and the ruling principle in us are likened to health and medicine respectively: it is with an eye to

46 Shields 1999, chap. 8, comes to a slmilar conclusion from a very different argument. 47 As 6.7 says, per SI! being is said in the categorial ways (1017a22-27; d. 2.3 1029a20-23), so potentiality, since it is not a per se being, may be thought not to be in a category. But A.4-5 presents matter as associated with categories, and matter is one sense of Ol/sin (e.g., Z.10 1035a2; H .2 1043a19-21), and so would seem to be categorially detennined. 48 As Berti rightly points out (1971, 166), Aristotle's positive thesis about the organization of the goods does not depend on the doctrine of the categories.

205 Mixed Uses of Analogy and Focality god that the ruling principle directs the part of us that takes commands. And just as there is a focal relationship between health and medicine, it is not unreasonable to posit a focal relationship between god and the ruling principle: the ruling principle is called good, because it aims at attaining, to the extent possible, the primary good (god). And since the ruling principle defines virtue and virtue defines EvbaL!,ovia and the human good, in the definition of the human good will ultimately be found, by one or more steps of focal inclusion, the term god, or its definition, and since its definition is

to be the good substance, substance, too, will be included in the definition of the human good. Mutatis mutandis, the same situation applies to the good of all other things. We can and should accept this form of focal inclusion as important for Aristotle's ethical theory, since he argues that god is a determinative cause in the human good, and as such must be included in

the theory. That inclusion, however, does not depend on substance and its relations

to the other categories of Being. The fact that good falls into all the categories is not relevant to Aristotle's theory of the good, alid he only alludes to it in these passages because he is criticizing the Platonic idea of the Good. The dependence of the good does not follow the dependence of Being. For virtue (as good quality) includes in its definition a substance, not god, but man, or whatever substance of which it is the quality. And the case is similar with all the other non-substantial categories. Moreover, the proposed focality is peculiar in that the non-substantial goods are dependent on god rather than on substance generally, as is the case with the focality of categorial Being. Since there is no substantial good except god, non-substantial goods must be directly dependent on god for their goodness. This is clearly not the way that Aristotle chose to develop the focal relations among the goods in his ethical theory. Aristotle made the important and anti-Platonic discovery that, though it is a transcategorial,

good does not follow Being per se. As such the categorial organization of good does not reveal the nature and function of the term, and in fact disrupts the fundamental relation of means and ends. To pursue the good through categorial Being and essence is to resign oneself to a second sailing and to ignore the winds blOwing towards the o~

fV€Ka.

Analogy and focality, then, are not merely compatible means of providing necessary scientific relations among terms; rather, they bear a fixed and determinate relation to one another. In the cases we have studied, analogy is posterior to focality (or some similar logical arrangement such

as natural priority or subtraction/ addition). Potentiality is dominated by the analogical structure, but is framed by focality. Because it is a relative term, its primary affiliation is to the genus in which it functions;

206 Aristotle's Theory of the Unity of Science but if potentiality is to form a single subject, and if we are to pass in understanding from one form of potentiality to another, there must be some per se relations between them or their subject-genera. The good, by contrast, is dominated by focaliry, and as a result of the prioriry of focality over analogy, largely dispenses with analogy. The concept of good is best adapted to the unification provided by focality.

7 Cumulation

Finally, we turn to a fusion of analogy and focality, an Aristotelian technique I shall distinguish by the term 'cumulation.' According to this technique objects from the same categoty form a series of priority and posteriority, each member of which potentially contains in its definition the antecedent term. We have already seen similar techniques in the scala naturae and the ends-means relationship among the goods. It is due to this similarity that cumulation is sometimes supposed to be a focal relationship, but I hope to show that this is not accurate 1 In spite of the fact that focality and 'cumulation share the definitional inclusion criterion and manifest an order of priority and posteriority, they have very different logical properties and involve different kinds of objects. Whereas focally derivative objects have a single subject to which they are causally related, each cumulative object is first and foremost a subject in its own right, though it may also exhibit certain causal relations with other objects in the series. It is not the purpose of cumulation to form one genus. In contrast to focal objects, Aristotle takes pains to show why cumulative objects cannot form a single genus. Although these objects are the same basic type of thing at a certain level of generality, they show less coherence with one another than do focally related objects. The difference between cumulative objects and other serial objects, like the scala naturae and the goods, is more subtle. The latter series might be called series of perfection, because the first members are the perfect instances, and the subsequent members are qualifications and diminutions 1 E.g., Owen 1960, 187, who notes that there are differences between foeality and cumulation without discussing them. Shields 1999 most recently con£lates them as 'core-dependent homonymies.'

208 Aristotle's Theory of the Unity of Science of the first. In such series the focal aspect predominates, and as a result the genus is strong. Means are good, for example, because of their rela-

tionship to the end, and they are intelligible as goods only in virtue of that relationship. By contrast, in cumulative series, where the members

are not primarily viewed in causal relationship with each other, the genus is weaker: the sensitive soul is a soul in its own right and not because it requires the nutritive souL Because perfective series are best understood as a variation on focality, my main attention will be on cumulative series. Two cases are of especial interest to us, souls and friendships. Aristotle's treatment of souls is a paradigm case of cumulation and allows us to determine the pattern. The discussion of friendship provides variations on the theme and allows us to compare a focal arrangement (in the EE) with a hybrid account that contains elements of cumulation and elements

of similarity (in the EN). We shall, however, return at the end to a series, which Aristotle seems to understand as perfective, but which may be more amenable to a cumulative interpretation, the series that locates theology

in the science of Being qua Being.

Souls In turning to Aristotle's treatment of the soul in the de Anima we are completing the task of chapter 3 by considering the affiliations among the functions of animals at the most abstract level (KaT' aKpif3ELav 402a2). For this treatise deals with the highest functions of animals, nutrition, sensation, locomotion, and intellect, and these constitute the final causes

of all of the instrumental parts. These highest functions are, however, not independent of one another. In an intricate analysis Aristotle considers in turn whether they are universally (KaB' fV), or analogically, or cumula-

tively related. Aristotle's analysis in DA 11.1-3 of the kinds of souls and their relationships to one another is framed as an answer to three problems that he has introduced in 1.1. As he solves these problems he calls upon the universal (
There follows a second closely related problem: if the soul does have parts, should we study it as a whole or should we study these parts, their per se accidents, their functions and objects, and, if we should, to what extent (402b9-403a2)? Finally, are all the parts of the soul enmattered «vvAa) or are some separable from matter, and for those that are inseparable should

209 Cumulation we define them in terms of their final cause or in terms of their material conditions (403a3-b19)? Each of these problems presents a contrast between abstract and concrete approaches to the subject. While we must look for the most general legitimate explanation, if we focus too narrowly on abstractions, we run a risk of committing one of three related errors corresponding to each of these three problems: defining a genus where there is none, providing a definition that explains nothing about how living things live, and asserting that the entire soul is separable from the body. Aristotle devotes DA II.1-3 to solving these three problems in a preliminary way. As he solves each problem, he moves in turn towards a fuller account of soul. Since voil, does not easily fit into the organizational format he is constructing, he leaves it conspicuously on the side. 2 He takes the problems in reverse order, declaring that the faculties of the soul are for the most part not separable from the body. The reason he gives constitutes the first' definition' of the soul: the soul is the first actuality of a natural organic body potentially having life (Il.1 412b4-9). Since the soul is the actuality of a body, it is as inseparable from the body as the impression of a signet ring is from the wax that bears it. Without completely solving this problem (Il.1 413a8-9), he moves on to the second aporia, which is the subject of the second chapter and half of the third (to 414b19). The quick answer is that we simply cannot study the whole soul, since soul is said in many ways. We must distinguish the faculties, since each is a sufficient condition for calling a thing living (413a22-23). Later at II.3 414b6-14 (and again at II.4 415al4-23) Aristotle impliCitly accepts the need to consider the objects of the senses as well as the individual faculties, and so answers both parts of the second problem. Again he promises further investigation (414b14). In the last half of II.3 he takes up the first problem, and concludes that we must consider the individual kinds of souls, since there is no single kind (414b32- 33). The tendency in all three solutions is to drive the investigation away from the general account towards the particular, and away from the separate soul towards the composite. The three solutions are set in a discussion that moves from the most common and familiar account of the soul to the most sophisticated and explanatory. Each of the three successive accounts of the soul explains and grounds the preceding account, and is contained in the next. They are respectively universal, analogical, and cumulative. Let us consider them in more detail. 2 IU 413,8-9; IL2 413,31-32; 413b24--27; II.3 414b16-19; 415,11-12. Cf. Me'. E.1 1025b34--1026,6.

210 Aristotle's Theory of the Unity of Science 1. The Analogical Account The first, universaL account presents the soul as the first actuality of a

natural organic body potentially having life (11.1 412b4-5). Before introducing his second account of the soul at 11.2, Aristotle says that this first account is more evident to us (tK cpaV€PWTEpWV) rather than more familiar in account (KllTa TOV AOyov yvwP'/,-WT€pov), and that it plays the role of the conclusion of a demonstration rather than the middle, as a definition should (413a11-20). The first definition is too general to deduce all the per se accidents of the soul from it. Though it tells us something about souls, it does not tell us what soul is, since soul is not a Single general thing. In the Topics (V1.10 148a25-26) Aristotle had already cast this problem in terms of homonymy: ' [IJf the definition applies in a like manner to the whole range of the homonym, it does not define any of the objects described by the term. ,3 Life is homonymous, he goes on to say, and there is no single

definition that holds good for both animals and plants. Dionysius' account of life, which Aristotle quotes in the Topics passage as 'movement of a creature sustained by nutriment, congenitally present in it,' is common to

plants and animals, but is not the definition of either because (W'I names particular kinds of life, not an abstracted and general concept of life 4 In 3 There is no mention here of ordered series, or what kind of homonyms we are dealing with, and Aristotle does not suggest that some kind of homonyms can be gathered together under one definition. Owen (1960, 187) notes the Topics position as a stage along the path to the final position in the DA. Comparing the use of 'focal meaning' in metaphysics and psychology, he remarks, '[Alt the same time there are large differences in the two uses of focal meaninSt and we are not concerned with the psychology.' A more thorough study of the DA forrilUlation could well have altered some of his conclusions, especially his depreciation of the role of analogy (192-3): he denies that analogy engages in studying 'a particular connexion between the definitions of a polychrestic word ... [I]t is merely to arrange certain tenns in a (supposedly) self-evident scheme of proportion.' 4 We find a similar test for homonymy in APo II .13 (97b7-15): We should look at what are similar and undifferentiated, and seek, first, what they all have that is the same; next, we should do this again for other things which are of the same genus as the first set and of the same species as one another but of a different species from those. And when we have grasped what all these have that is the same, and similarly fo r the others, then we muSt again inquire if what we have grasped have anything that is the same - until we come to a single account; for this will be the definition of the obje<:t. And if we come not to one but to twO or more accounts, it is dear that what we are seeking is not a single thing but several. Aristotle cites as an example high-mindedness (p.eyall.0o/uxia.) and advises us' to look at individual cases - Achilles, Ajax, Socrates. There is nOt just one thing in virtue

211 Cumulation the DA Aristotle elaborates this argument by introducing the language of demonstration as a way of explaining the homonymy of the objects. At II.2 he sets aside the common 'definition,' and turns to the species of soul. We can deduce from the definitions of the species both their specific per se accidents and the general account, which is posterior (414a17-28). This is not to say that Aristotle considers the conclusion of the first chapter false, but its status is down-graded from that of a first principle to a theorem of psychology. He can prove the first' definition' by means of the second using the same scheme as we used for longevity; first actuality of a certain body IPQ that in virtue of which things live (414a12-19) that in virtue of which things live IPO nutrition, sensation, intellect (413a22-25; bl-2) nutrition, sensation, intellect IPQ soul (413bl1-13) first actuality of a certain body IPQ soul (414a27-28) From the conclusion we can further deduce that the soul is not separable from the body, since inseparability from the body is predicated of the first actuality of a certain body. Since soul is homonymous in the sense that many values can be substituted for it, the conclusion must be proved for each of the homonyms S Although Aristotle's argument is not so neatly laid out as this, it is clear that he reaches this conclusion at the end of 11.2. When Aristotle claims that living (TO 07v) is homonymous (413a22), he is not denying that plant and animal life have something in common. What he denies is that the definition in accordance with the name is the same in each case. When we answer the question 'What is it for this plant to be alive?', we say that it absorbs nutriment and grows. When we answer

of which they are called high-minded, but two, unwillingness to brook insult and indifference to misfortune. If there is some attribute common to both, say self-respect, it is secondary and explained by the two kinds of states of the soul. The fact that unwillingness to brook insult is manifested in different actions, withdrawing from the fight (Achilles), committing suicide (Ajax), and making· war (Alcibiades), does not mean the 'unwillingness to brook insult' itself is homonymous. These actions are not kinds of high-mindedness, but rather the results of high-mindedness. Unwillingness to brook insult is not part of the concept of committing suicide, even though it may be a result of it in particular cases. Such cases are contrasted with animal, which, at least in the Categories, is predicated of man and ox in virtue of the same account of substance. S Bolton (1978) has proposed that the definitions of the soul in Il.1 (he counts four) are indeed proved by the definition of Il.2, but they are proved generically.

212 Aristotle's Theory of the Unity of Science the question for animals, we say 'It moves and has sense perception.' If we give the most general account that will cover all the cases, it will make no mention of any faculties in virtue of which we sayan animal is alive. Since we say something is alive in virtue of its thinkin~ perception, nutrition, growth, and so on, we say that so long as there is one of these faculties present, a thing is alive (413a22-25). There is not a single set of necessary and sufficient conditions for life; there are many sufficient conditions or causes. For a plant to be alive, it must have nutrition. For an animal to be alive, it must have sensation, and what it is for animal to be and to be alive are the same thing. But as we saw in APo Jl.l7, there cannot be two different causes of things that are the same in species; so where there are two causes, the things caused must be different, and so the actuality of the body potentially having life in it will be different in each case. There are several other reasons why Aristotle should adopt the analogical strategy in the case of the souls. As a result of the analogy, inseparability cannot be proved universally for all the kinds of souls, but only specifically for each kind. This fact is of advantage when Aristotle comes to deal with voi), 6 For the fact that there is no general proof for inseparabiliry makes it easier to accept the possibility that there may be an instance of soul that is not the actuality of some body. If we admit a case of separabiliry .- and Aristotle must prepare for it, even if he does not immediately deal with it - the universal/definition' of soul is incorrect. If vovs is a faculty of soul and is separable, it cannot fall under the common definition provided, and must be related to soul, or be soul, in some other way. The analogical account of soul provides a solution both to the separation problem and the second, parts / whole problem. Moreover, the fact that the general account is couched in terms of actuality and potentiality without a specification of a particular actuality and potentiality should remind us of the warnings Aristotle issues regarding the analogy of principles in Metaphysics A. Moreover, as we have seen, definitions as well as terms can be ambiguous (e.g., the definition of 'quick' in Phys. VII.4), and the general account of soul contains an ambiguous term, 'life.' Thus, the actualities and potentialities mentioned

6 Bolton 1978 deals more extensively with this feature. I think he is generally right in saying that there is no fundamental contradiction between the hylomorphic view of the soul in the VA and the unembodied soul of the unmoved mover. Aristotle is almost completely consistent in his resolve to deal with soul only among 8v'T/TCt. I disagree with Bolton, however, that there is a generic definition of soul. Like Hicks, he assimilates the serial problem to the nonnal dependency of the genus on the species. More recently, G. Matthews (1992, 190-1) has also tried to discover a generic definition of life.

213 Cumulation are of different sorts of things, and this is sufficient to eliminate the general account as a universal definition.

Finally, the analogical strategy also suits the basic Greek conceptions of the soul. It is among humans primarily and, through theories of transmigration of sout among other animals too, that the traditional Greek notion of tvx~ is most at home? For Greeks it is an extension of the term to apply it to plants. Aristotle complains that previous thinkers had confined their discussions to human soul (1.1 402b3-5), but in fact they were doing nothing more than following common conceptions. But the common conceptions are also the source of the homonymy. Since "'VX~ is a term that applies first and best to humans and to what human beings are, Aristotle and the Greeks in general find it more natural than we do to say that man lives by virtue of his intellectual soul. It would be for Aristotle an abuse of the term to say that human "'vX~ is a "'VX~ in virtue of its vegetative functions. Moreover, the higher faculties are in some way the purpose of the lower faculties, and thus are the most important part of the

definition of higher living things. When Aristotle extends "'vX~ to other animals and plants, they must be alive in virtue of some other faculty than intellect. For all these reasons, the analogical strategy seems more suitable than the universal. But the analogical account does not do full justice to the phenomena. Whereas among the biological analogues there was some common essential feature to which all the analogues were related, but that was not their genus, Aristotle has not yet provided any common feature among the souls, which would serve as the framework for drawing analogies.' It is clear that it cannot be a common function, since the souls are themselves functions and are fundamentally different from one another. What, then, prevents the homonymy among the souls from being chance homonymy or the analogy between them from being pure metaphor? Aristotle has two answers. First, from the definition of each subject separately we can deduce at least one shared property that only those subjects have. But that shared property, to be an actuality of a natural organic body, is defined in terms of the matter rather than the form, and so hardly provides an adequate connection among the souls themselves. The second and more compelling answer is that the souls are related among themselves by a variety of per se 7 For some of the limited evidence on animal and especially plant souls, see Bremmer 1983, 125£f. 8 Hamlyn (1968, 94), who rightly subscribes to the 'empty' theory of the general definition, suggests that the general definition will be uninformative because it will leave out the crucial fact that the species are serially ordered.

214 Aristotle's Theory of the Unity of Science relations, which have the effect of gathering together the several subjects of study. The souls fonn a group because of their serial order and their definitional inclusion relations. This does not make them a Ka8' EV genus,

but it does legitimate their being treated under the same study. 2. The Cumulative Account The second half of DA 11.3 answers the first aporia, concluding that there is no genus soul, and explaining how instead the souls are related to one another. Here Aristotle considers the serial nature of the faculties and its

implications: the faculties of the soul are cumulatively organized. While it is true that any faculty of the soul is a sufficient condition for life, in fact, only the vegetative soul can be found apart from the other faculties. This fact complicates but does not nullify the analogical relationship between the faculties. It shows that the causes, which have been so far treated only as analogical, are related in some more intimate way. Aristotle explains the implications of the serial order of the soul faculties in a difficult and controversial passage: It is now evident that a single definition might be given of soul in the same sense as one might be given of figure. For, as in that case there is no figure apart from triangle and those that follow in order, so here there is no soul apart from the forms of soul just enumerated. There might be a common definition given for the figures which will fit them all, but it will not be the peculiar definition of any figure. So here in the case of the aforementioned souls. Hence it is absurd in this and similar cases to look for a common definition which will not express the peculiar nature of anything that is and will not apply to the appropriate indivisible species, while at the same time omitting to look for an account which will. The cases of figure and soul are exactly parallel; for in both the case of figures and living beings the predecessor is potentially contained in each successive term, e.g. the triangle in the square, the nutritive in the sensory power. Hence we must ask in each case, What is its soul, i.e. What is the soul of plant, man, beast? (modified ROT; 11.3 414b19- 33)

The two basic features of cumulation are clear from this passage. First, souls and figures form series by adding some factor to a prior member in order to form a posterior member. Second, the addition does not alter

the category or basic type of the object, that is, the addition of a triangle to a triangle creates another figure, and the addition of sensitive faculties to nutritive faculties creates another kind of soul. This is in contrast to

focality, where the addition of 'operation of' to 'doctor' creates an object

215 Cumulation of a different category from that of the focus term, 'doctor.' Yet in spite of the explicit comparison between figures and souls, there are several ways in which the likeness is inept. Since this passage is the locus classicus for cumulation, it is important to examine in detail how the example of figures

is inappropriate for Aristotle's purpose. I shall subsequently argue that a different example concerning types of citizenship found in the Politics is more apposite. There are some important differences between figures and souls.

Whereas the figures form a potentially infinite series, the souls form a finite series; and whereas the figures are generated by the same addition at each step, the generation of the souls requires a different addition. 9 For thi s reason sensitive and intellectual soul cannot be ana lysed into vegetative soul, as if three digestive systems connected together could make a mind.

Furthermore, if this passage is taken as a denial of a genus of figure, then Aristotle ·is not entirely consistent with himself. For at Met. 6.28 (1024a36-b3) he says that plane is the genus of plane figures and that each figure is a plane of such and such a kind (€"i"dlov TOLOVOi) . There are also difficulties in understanding the nature of the series itself. Though Aristotle says that the predecessor in the series is potentially contained in each successive term (aEt yap EV T'i' Ecpefr,!> irmipX€L l>vvaf-L€L TO "ponpov), he does not explain what he means by potential containment. In view of the fact that he is looking for a definition, it is reasonable to suppose that the containment is logical, if nothing else besides. However, it is clear from the term l>vVaf-LEL that this containmen t is not explicit definitional containment. This is also clear from the examples: th e square is not defined in terms of triangle, though it necessarily contains two triangles in it; the sensory power is not defined by nutrition, though it presupposes nutrition. Natural priority also seems to be at issue, at leas t in

these examples. The prior member can exist independently of the posterior, but the posterior cannot exist without the prior (415al - 11). In the context of psychological faculties this natural priority can also be described as hypothetical necessity: if an animal is to have sensation, it must have the nutritive faculty to sustain it (d. PA I.l 640a34-35). Nutrition, therefore, is not present in the essence of sensation, but is necess itated by it. In the geometri cal context, the triangle is naturally prior, since if there were no

triangle, quadrilateral could not exist. Most important for our purposes is determining the role of th e general

accou nt of the series, for Aristotle says, ' [T]here might be a common

9 Cf. Met. 1.2 l054a3-4, where the triangle is the uni t measure of rectilinear figures.

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216 Aristotle's Theory of the Unity of Science definition given for the figures which will fit them all, but it will not be the peculiar definition of any figure.' Concerning this difficulty there are two interpretations. First, by drawing on parallel passages at EE 1.8 1218al-9, EN 1.6 1096a17-23, and Met. B.3 999a6-14,'0 one can argue that it is impossible for objects arranged in a series to form a genus. Aristotle provides a dialectical and ultimately unsatisfying argument for this position. Although these passages use series of mathematical objects, including figures, and so support the contention that Aristotle intended to deny a genus of soul in our passage, they are all polemic arguments against the Platonists, and rely on premisses granted by them to refute their own position. For this reason the denial of a genus over a series need never have been an Aristotelian doctrine. This interpretation, however, has become orthodoxy, and whether or not it has been viewed as a valid argument, most scholars agree that Aristotle intended to apply it to his series of souls. It will be necessary, in consequence, to spend some time in its refutation and to argue that although it is valid for a Platonic context and a Platonic understanding of genus, Aristotle could not have used the argument in his own voice. The second interpretation of the difficulty begins by comparing a different form of the series argument found at Pol. III.1 1275a34-b5 concerning forms of citizenship, and argues that Aristotle did not intend to reject a genus of souls on purely logical, but rather on pragmatic, grounds. That is, when objects are arranged in a series, their genus contains so little of causal significance as to be negligible. This second interpretation seems to be better adapted to the DA passage, and relies on peculiarly Aristotelian doctrines of demonstration and explanation. The first, dialectical interpretation receives its clearest expression in the context of the refutation of the platonic idea of the Good in EE 1.8: [I]n things having an earlier and a later, there is no common element beyond, and, further, separable (xwPW"Tov) from, them, for then there would be something prior to the first; for the common and separable element would be prior, because with its destruction the first would be destroyed as well; e.g. if the double is the first of the multiples, then the universal multiple cannot be separable, for it would be prior to the double ll ... if the common element turns out to be the Idea, as it would be if one made the common element separable.

10 The Metaphysics argument intends to do away with separate genera altogether, showing that they are secondary in every case, and not just among series of prior and posterior. 11 There seems to be a lacuna here in the text. See Woods 1992, 72.

217 Cumulation

EN 1.6 1096a17-23 assures us that this argument had a Platonic origin, and was used to deny Forms over Form numbers and over any other series in which there was prior and posterior. Aristotle turns the argument against the Platonists by showing that trans-categorials like the good, among which substance is prior, cannot have a genus. Even in its Platonic contex~ the motivation for the argument is not undisputed. There are those who hold, contrary to Aristotle's express statement, that the argument is directed specifically and solely against Forms of Form number. Their position can be outlined as follows. Plato identified three kinds of numbers, sensible, mathematical, and Form numbers. The mathematical numbers (we can ignore sensible numbers) are combinable with one another and subject to all manner of ordinary mathematical operations . They are eternal and without matter, but there is a multitude of each kind so that, for example, two can be combined with another two so as to make four. Of Form number, by contrast, there is only one of each kind, Oneness, Twoness, and so on. These numbers, being Forms, cannot change or undergo operations. They cannot be divided so .as to become other numbers, for in that case they would admit of becoming and not-being. Unlike mathematical numbers, Form numbers exhibit an order of priority and posteriority, since their unchanging Oneness, Twoness, etc. make them well suited to staying in their appointed order. Cook Wilson, the champion of this view, asserted that there is no Form of Form numbers because Form numbers are aa1;M{3A:TlTO~, incomparable with one another, and therefore uncombinable; and because the numbers are incombinable, they form series of prior and posterior over which there is no Form or genus. This uncombinability stems from their being Forms, since no Forms can be combined with one another. 'They are entirely outside one another, in the sense that none is part of another. Thus they form a series of different terms, which have a definite order.'l2 This interpretation does go some way towards explaining why they are uncombinable: if the Two and the Three were combinable so as to make up the Five, then the Three will be part of the Five. But it does not explain why their uncombinability entails their forming a series of priority and posteriority. After all, in order to be related as prior and posterior, Form numbers must be related to one another, even if they are not part of one another. Making them uncombinable and incomparable is precisely to take away the grounds upon which they may be compared as prior and posterior. The Two cannot be prior to the Three in generation, since Form

12 Cook Wilson 1904, 253; d. Cherniss 1944, 513- 14.

218 Aristotle's Theory of the Unity of Science

numbers are not generated; nor can it be prior ontologically, since one Form does not depend on another for its existence; nor logically, since in the realm of the Forms logical priority is identical to ontological priority. What makes the Two prior to the Three, if not the fact that the Three is One more than the Two? Form numbers must either be combinable or they cannot form a series. Contrary to Cook Wilson, then, the uncombinability of the Form numbers, far from providing a sound reason for priority and posteriority, destroys any possibility of there being a series among thernY Not only is the Form number interpretation of the argument suspect on its own grounds, but Aristotle also states that Platonists considered the argument valid in all series of prior and poste rior, and not just among Form numbers.14 Michael Woods, while adduCing reasons why such an argument could not be held by Platonists at all, suggests a different approach to the Platonic argument, one that neither relies on the uncombinability of Form numbers to ensure their serial order, nor restricts the series argument solely to Form number. In the main issue he is correct. Woods's interpretation relies on seriality to show that there can be no genus, and as such has the virtue of being consistent with Aristotle's claims about the argument. He points out that the Form of the Form numbers will be prior to the Form numbers, and because of the self-predication of the Forms, the Form of Form numbers will also share in the essential features of Form numbers. But he argues that the Form of Form number will be prior in a different sense from that in which the first member is prior to the second: '[TJhere seems no good reason why a holder of the theory of Forms should retain the premiss that the number two is, without qualification, the first number. It may be the first number in the number series, but there seems 13 For variations on the Cook Wilson thesis, see Burnyeat 1987, who claims that incomparability is the Aristotelian incomparability of the constituent units of each Form number. 14 Cherniss charged that Aristotle misunderstood Plato's argument in a way that affects his own prior-posterior arguments. He argued that the Platonist argument was intended only for application among Form numbers, that the priority and posteriority here is numerical order and not ontological priority and posteriority (1944, 522); that Aristotle's criticisms, which imply that the Platonists did not distinguish between the twO senses of priority (first in the sense of ideal and first in the sense of first term of a series), is belied by the fact that the Platonic 'first one' and 'first twO' etc. (mentioned Met . 1081b8-10) did not imply a series of ones and twos, etc. (520). Cherniss contends that when Aristotle extends the prior-posterior argument beyond mathematicals by generalizing the argument and making it hold good in every case of ontological priority (to which, citing Met. 1019a11- 12, Cherniss claims Aristotle reduced all other forms of priority), the argument that had been inappropriate against the Platonists suffices for his purposes to show that there cannot be a genus of things arranged in a series.

219 Cumulation no reason why a holder of the theory of Forms should continue to hold that it is the first number in every sense, if he holds that each Form is prior to its particulars and is itself a possessor of the character it represents. The

Form of number will itself be a number, and in an appropriate sense prior to any member of the number series. /1S Contrary to Woods's assertion, however, there is no reason to suppose that the Platonists did not accept

the full implications of their own argument, and admit that the Form of Form number will become the first member in the number series. For the power of self-predication entails the Form's inclusion in the series, and

therefore makes the Platonic argument valid for (Aristotle's interpretation of) Platonic metaphysics: since it is an essential characteristic of the Form numbers to be members of the series of Form numbers, the Form of Form number must also share this characteristic, that is, it must be in the series of Form numbers, and since it is also prior to all Form numbers, it will be prior to the first in the series. If we emend Woods's interpretation in

this way, the argument does what Aristotle says it is meant to do. For he says that the Platonists denied Forms over series of prior and posterior things generally, and not only over Form numbers. This argument holds good in all cases where members of series are essentially serial, and for the Platonists that will occur wherever Forms are serially ordered. It also

shows how being a series prevents there being a genus of it, and does not rely on the obscure argument from uncombinability. Problems arise, however, when we suppose that Aristotle accepts the argument as his own and applies it to the soul series. To create an Aris~ totelian metaphysical framework for the argument we need only change the meaning of XWPLrrTOV from 'separable' to 'logically or conceptually distinct.'16 The denial of the genus is established by two sub-arguments. First, it is a fact about series that the first element is a member of the series, a subject alongside all the others, for all that it may also be the principle of the series. If it were to serve as the genus of the series, the members of the series, including the first member, would become its species. The identical thing, the first member, would have to be both a species and its own genus; and this is impossible, since a species is distinct from its genus. This argument is sufficient to eliminate the first member of the series as a candidate for genus. Second, it is necessary to argue that there is nothing

15 Woods 1992, 71. 16 Bonitz's Index (1961, 86Oal1-21) identifies a use of XWpKHV meaning 'ratione et notione distinguere: used principally for the function that the differentia discharges: Tau WlOV T17~ oixrias £.occlOTO'U '\o)'ou Ta,~ 7f€pl E.ocaOTou oua:ia,~ lllacpopatr XWpi(HU dWOalJ.(U (Top. 1.18 l08b6). According to this use XWptOTOU means 'distinct.'

220 Aristotle's Theory of the Unity of Science common to and distinct from all members of the series including the first. Such a thing would be an element in the logos of all the members of the series. Aristotle's argument at a very dialectical level might be that such an element would be prior to the first member (TOi) 7rPWTOV 7rpOTEpOV), and nothing can be prior to the first. This argument is based on the implausible assumption, as Woods points out, that priority is univocal and that the first member of the series cannot be preceded in some other way; for we can

grant that a genus will be prior without admitting that it must be the first member of the series. For this reason, Aristotle might make the stronger claim that the prospective genus must become the first member in the series displacing the previously first member. He describes this prospective genus as common, distinct, and naturally prior. But the prior members of the series are also described as common, distinct, and naturally prior to the posterior members

(d. t..ll1019a3ff.). By describing the genus in such a way that it has all the same logical characteristics as a prior member, Aristotle might argue that the genus will become the new first member of the series. And if this occurs, then the genus is identical with one of the species, and this is impossible. Such an interpretation provides a fine description for a Platonic genus, but does some violence to Aristotle's notion of genus and consequently faces serious difficulties in explaining why this argument would apply to the souls 17 The Platonic genus is naturally prior to the first member of the series, is common and separable, and this will make it into the new first member of a Platonic series. 18 But this does not fit Aristotelian doctrine. For if the common element were an Aristotelian genus, the difference between it and the original first member would have to be the specific differentia of the original first member, and since we are supposing that all.the members of our new series have the same logical relationship to one another, the genus-species relationship, which holds between the new first member and the original first member, will hold between all the subsequent members of the series. The result will be that the series is merely an extended genus-species string. 19 Since the series will form a string, each successive species will be differentiated by the differentia of the preceding differentia, in the manner of Met. 2.12's footed, cloven-footed model. But Aristotle's argument never explicitly assumed that series create genus-species strings, and a consideration of the applications of the argument amply shows that 17 Chemiss 1944, 513ff. 18 For these characteristics of a Platonic genus, see Met . B.3 999a16-23 . 19 This position is defended by A.c. Lloyd (1962) .

221 Cumulation the assumption is absurd: a quadrilateral is not a species of triangle nor a sensitive soul a species of nutritive SQu1. 20 Posterior members are not 7TOta of prior members . On logical grounds also it is impossible: there cannot be only one species of a genus, but this is what this argument entails. 21 The EE argument against the genus of series, then, seems to be better adapted to Platonic than to Aristotelian logic and metaphysics. So far, then, the dialectical interpretation of the DA passage provides only unAristotelian reasons for denying a genus over a series. There is, however, an alternative interpretation. There are two contexts in which Aristotle uses the prior / posterior argument in his own voice, our DA passage and in the Politics, and in neither passage do we find the dialectical formulation for the rejection of genera of ordered series. Instead, other, pragmatic reasons are offered. At Pol. III.1 1275a34-b2 Aristotle discusses the definition of the citizen: But we must not forget that things of which the underlying things (imoIH:i,uwa) differ in kind (njJ Ei'OH), one of them being first, another second, another third, have, when regarded in this relation (Y TOtaVra), nothing, or hardly anything, worth mentioning in common. Now we see that governments differ in kind, and that some of them are prior and that others are posterior; those which are faulty or perverted are necessarily posterior to those which are perfect. (modified ROT)

The passage itself seems clear as far as it goes. Unlike the previously considered passages, Aristotle does not deny that there may be some commonality among the citizenships, only that this commonality is negligible . This is quite a different objection from arguing on dialectical grounds that per impossibile the genus will become the first member of the series. The passage suggests that, when the objects are arranged in a series TOLaiha) , the first member is contained in all the others, and therefore by treating it, one not only treats something that is explanatory, but also everything that is common to the series. Accordingly, he leaves open the possibility that there may be some arrangement other than a series in which there is significant generic commonality. This is borne out in Aristotle'·s discussion of the citizen. The definition of the first citizen is provided immediately prior to this passage, a definition that he says is most adapted to all those who are called citizens (}.ta)u(1T' Ecpapp.oCTa~ OPLCTP.O~ E7T1. 7T(iUTa~ TOV~ A€yOP.€UOV~ 7TOAtTar; 1275a33- 34):

en

au

20 Cf. Me t. A.9 992a18- 19 for a similar series; ' [TJhe broad is not a genus which includes the deep, for then the solid would have been a species of plane.' 21 So Top . 1.5 102a31· b3 .

222 Aristotle's Theory of the Unity of Science the citizen is one who shares in the indefinite offices (deliberation and judicial administration) of the state (1275a30-33). For the real power of the state resides in these offices, which have no fixed tenure. As it turns out, however, some bona fide citizens do not

fit this definition. For he

says (1275b5-6) that the definition is best adapted to the citizen of the democracy, which is only one of the perfect constitutions (aristocracy and

kingship being the others). In Sparta and Carthage, by contrast, it is only the holders of the definite offices who are admitted to deliberative and judicial offices, and therefore they are not indefinite officers. That is, they hold executive offices for determinate lengths of time, and they judge and deliberate ex officio. Aristotle is unwilling to emend the definition so as to make any office-holder a citizen, because he thinks that the citizen is the one who has the power in the state, and the power is exercised

through deliberative and judicial function, and not, say, through being an overseer (a Spartan ephor). For this reason, Aristotle treats the Spartan citizen as a perversion of the perfect citizen. Accordingly, he provides a

second definition, 'whoever has the power (itovCTia) to have a share in deliberation and judicial administration' (1275b18-19)." This definition potentially contains perfect citizenship insofar as it covers perfect citizenship, but it does not define it in the strict sense that the first definition does. The difference between the two definitions seems to consist in this: the democratic citizen, who holds the indefinite offices, is a citizen most

of all, since he has a penn anent hold on these offices and exercises them throughout his life. The Spartan citizen, who holds definite offices, has limited opportunity to be a citizen; and limited in two ways: limited in time

because of the definite tenure of the office, and limited in extent, since the deliberative and judicial job is split up among the various definite offices. The second definition is more generaL in the sense that it will include the democratic as well as the oligarchic citizen, but it is also defective because

in the addition of the itovCTia clause is contained the notion that the ex officio potential for citizenship activity is sufficient to qualify as a citizen. In those respects in which the second kind of citizen is similar to the first, it is similar because it is related to the first, that is, it is a perversion

of the first. The first member, then, will appear in explanations concerning the second, but not vice versa. In the investigation of the citizen we should

22 Irwin 1990, 82, has sensibly argued that the first definition is not annulled by the second, but that they are serially ordered. He provides a different reason for the order: the first definition is first because it accounts for the fact thaI in order for the citizen to be good, he must rule as well as be ruled, and this is not ensured by the Spartan or Ca rthaginian constitution.

223 Cumulation expect the majority of the attention to be paid to the judicial and legislative functions of indefinite tenure and only secondarily to the definite executive functions. It is clear that citizenship can be studied in its most common form, but to treat it as a set of differences within a genus would ignore the

fact that the second form is a perversion of the first. The genus arrangement would neither capture citizenship in its fullest sense, nor would it call upon the explanatory principles central to understanding the deficient citizenship as deficient. Now, the series of citizenships is in some important respects different from the series of souls. It is a perfective series: the definition of the first form of citizenship is logically prior and is somehow contained in the definition of the second on the basis of the 'better and worse' relationship (ef. Met. B.3 999a13-14). Moreover, the citizenships are not arranged by ontological addition, nor by natural priority; rather Spartan and Carthaginian citizens are included as citizens on the basis of a qualification to the first form of citizenship. In spite of these differences, the common account of the souls is vacuous for the same reasons. Though the second account of citizenship will cover all cases, we should first explain democratic citizen-

ship and its legislative and judicial functions, since that is where the real citizenship power resides, then turn to the executive functions of Spartan citizenship and their relationship to the authoritative functions. Similarly,

Aristotle does not deny that there is a general account of the soul, he only says that it is absurd to overlook an account that will treat the peculiar

nature of the serial objects. Though 'the actuality of the potentially living body' is common to all the souls, it only explains inseparability of the soul and body. What are most important for explanations are the particular faculties of the soul and their per se relations among one another. If the members of the series do not form a strong generic unity, what makes them a Single group, that is, what are the principles of extending and limiting the series? First, each requires a non-nindom addition to the

member before it. The prior member is the precondition for the posterior member. DA III.12 provides a more detailed account of the faculties in the series: nutritive soul is first, because it is necessary for all living embodied things. As such, it can be treated as an independent and per se subject. Taste is a sort of touch and is relative to nutriment, which is tangible body. For this reason, taste and touch presuppose nutrition (which is now relative to them) and are next in the series, first among the senses. Imagination does not occur without sensation, nor thought without imagination. In

this way a prior faculty can be treated both per se and as related to a posterior through hypothetical necessity: the relations of hypothetical necessity establish the order and explain the reasons for that order.

224 Aristotle's Theory of the Unity of Science Second, we need something that will limit the series at the beginning and the end. After all, what prevents something causally significant and logically prior to the first member from being included in the soul series? For example, just as nutritive soul is prior to sensitive soul, so the natural

change of simple bodies is prior to the nutritive soul. Why should the natural change of simple bodies not be such a member? To say that this natural change is not life is to beg the question, since life is said in many ways and the only thing binding homonyms together is their serial order, in which natural change also participates. It is clear that the series is generated, but not limited, by logical potential containment. The limits of the series come from the posterior commonality that the members of the series generate, specifically from the material component. Natural change

of simple bodies cannot be included in the series, because simple bodies are not organic. Every faculty of the soul per se must be in an organic body. The common account, then, provides a common feature that limits

the series both at the beginning and at the end. For there is no activity that is logically prior to nutrition that requires an organic body, and there is no activity logically posterior to embodied intellect that in its own right requires an organic body. Nevertheless, 'having an organic body' cannot be the genus of soul, because the genus must be the genus of the form, not the matter. 'Having an organic body' is not what the soul is. The cumulative soul series, then, introduces us to a new form of organization among subject matters. The subjects are generated by a series

of additions. The additions are ontological, in the sense that one faculty is added to another faculty, but the relationship between the members is one of natural priority and hypothetical necessity, that is, the posterior faculty requires the existence of the prior. The members of the series share a common account that is not the account of their genus, but rather of their material correlate. Nothing prevents such subjects from having a genus,

but it is unlikely that the genus will explain much that the first member of the series does not.

Friendship Aristotle trears friendship both in the Eudemian Ethics and the Nicomachean Ethics. In both works he distinguishes three kinds of friendship, those based on virtue, pleasure, and utility. In the Eudemian Ethics Aristotle characterizes the relationship between these three kinds as focal, but in the Nicomachean version he speaks in terms of similarity (op.oiwp.a and Ka(J' O,uoLoT17Ta). The Ka8' o,umoT11Ta solution is characteristic of many

discussions in the EN, and has close affinities to cumulation and analogy.

225 Cumulation There has been much discussion as to whether Aristotle changed his mind about the relationship between the kinds of friendship. I think he did, but not in the way or for the reasons often attributed to him. I interpret the shift not in terms of a general chronological development away from focality, but as a realization that the focal analysis of friendship does not do justice to the phenomena. 23 1. Eudemian Ethics and the Problems

of Focal Friendship

In the Eudemian version Aristotle argues at length for a focal arrangement of the ends of friendship and, therefore, of the friendships themselves.24 The argument we are concerned with appears in EE VII. 1-3, of which the following is part: [W}e must attempt to .gain clear distinctions, starting from the following principle. The desired (OP€KT()V) and the wished for (f3ovA71TOV) is either the good or the apparent good. Now this is why the pleasant is desired, for it is an apparent good; for some think it such (OOKt:L), and to some it appears such (~aiVf.TaL), though they do not think so (om,V) . For appearance and opinion do not reside in the same part of the soul. It is clear, then, that we love both the good and the pleasant. (VII.2 1235b24-30)

Before this passage Aristotle discussed the opinions of others (ooKOvvm) and the aporiai; now he lays down a principle that states that the object of desire (OpEKTOV) and wish (f3ovl\~TOV) is either a good or an apparent good. From this principle and the fact that the pleasant is an apparent good, Aristotle concludes that both the good and the pleasant are objects of desire. 23 So also the conclusion of Price 1989, 148: '[WJhile the EHdemian Etllies offers an explicit statement (of focality) that is clearly less than successful and satisfactory, the Nicomaellean offers a less explicit analysis that seems much more apt to the subject-matter ... ' See his chap . 5 for a significantly different analysis of the focal relationship. 24 The details of the argument have not been carefully studied by those who have been concerned with the question of focality. Owens (1989) makes no mention of this section, and speaks of the focal relationship in terms of imitation (136-7). Berti sees the Significance of the argument, but treats it only briefly (1971, 176). Moreover, he says that just because a focal relationship holds benveen the three objects of friendship, there must also be a focal relationship between the friendships themselves. Rowe (1971, 57-60) sees no difference in purpose between the nvo passages, but considers the EN presentation a misleading version of the EE.

226 Aristotle's Theory of the Unity of Science He next introduces a second principle: some goods are good with-

out qualification, others are good to somebody (1235b30-32). Through an induction he argues (1235b33-1236a7) that what is pleasant without qualification is good without qualification." And since he has already laid down in the first principle that what is pleasant to someone is good to that person, he can conclude that there are two kinds of pleasant things, ~bv a7rAw< and ~M ny"~ of which the first is identical with the a.yaeov a7rAw< and the second with the aya80v

TLVt.

In detail Aristotle's argument goes something like this: 1.

PRINCIPLE:

x is OPEKTOV and f3oVATJTOV,

iff x is aya80v

or x is $aWOJ.l.EVOV

a.yaeD". 2. Additional premiss:

x is ~M, iff x is q,awDp.EVov a.yaeD" (whether x is actually a.yaeD" or not)

3. Therefore

if x is

4. and, since

if x is a.yaeD", x is OPEKTD" (from

5. Therefore

(if x is a.yaeD", x is OPEKTD") and (if x is ~M, x is 0pEKTOV)

6.

some aya80v is aya80v

PRINCIPLE:

~avl x is

0PE/(TOV

a7TA(JYi!

PRINCIPLE)

some is aya86v

nVL

7. From induction:

x is ~av o.:trAw'i, iff x is aya80v arrA.ws

8. (an interpretation of 2)

x is ~ov

TLVL,

iff x is aya6lov

HIlt

Aristotle has established a focal relationship between the good and the pleasant, since the pleasant can be defined as a function of the good. If something is pleasant without being absolutely good, then it is pleasant

25 The structure of the argument is not entirely dear. He needs to argue that there is a certain kind of ~M that is both r,ov tt1TAw!> and aya80v cbr'\'wS', and especially that there are psychic as well as physical pleasures that fall into this category. He argues from the obvious case that what is advantageous to a healthy body is aya8ov, to what is pleasant to a health body is pleasant without qualification, and finally to what is pleasant to a healthy soul is pleasant without qualification. There is no explicit connection made between the pleasant and the good until the end of the passage, and this is stated as a conclusion: 'To [sensible and good adults] that which suits their habit is pleasant, and that is the good and noble' (1236a5-7) .

227 Cumulation because it is apparently good." Although both the pleasant and the good are objects of desire, they are not coordinate species of desirables. The good is prior, while the pleasant is posterior and dependent on the good. By establishing a focal relationship between the objects of friendship Aristotle prepares the way for a focal interpretation of the friendships themselves. Since pleasure is definable in terms of the good - for it is the apparent good, if it is not the good itself - pleasure is said to be focally related to the good (VII.2 1236a15- 33): There must, then, be three kinds of friendship, not all being so named for one thing or as species of one genus, nor yet having the same name quite by mere accident. For all the senses are related to one which is the primary, just as is the case with the word 'medical'; for we speak of a medical soul, body, instrument, or act, but properly the name belongs to that primarily so-called. The primary is that of which the definition is contained in the definition of all/7 e.g. a medical instrument is one that a medical man would use, but the definition of the contained is not implied in that of 'medical man.' Everywhere, then, we seek for the primary. But because the universal is primary, they also take the primary to be universal, and this is an error. And so they are not able to do justice to all the phenomena of friendship; for since one definition will not suit all, they think there are no other friendships; but the others are friendships, only not similarly 50. But they, finding the primary friendship wiJI not suit, assuming it would be universal if really primary, deny that the other friendships even are friendships; whereas there are many species of friendship; this was part of what we have already said, since we have distinguished the three senses of friendship - one due to excellence, another to usefulness, a third to pleasantness.

Later he explains further (VIl.2 1236b17-26): But those whose love is based on pleasure do not seem to be friends, when we look carefully, because their friendship is not of the primary kind, being unstable, while that is stable; it is, however, as has been said, a friendship, only not the primary kind but derived from it. To speak, then, of friendship in the primary sense only is to do violence to the phenomena, and makes one assert paradoxes; but it is impossible for all friendships to come under one definition. The only alternative left is that in a sense there is only one friendship, the primary; but in a sense all 26 Although apparent x's are not regularly listed as focal terms, we can compare the focal way in which that which is not known may be said to be known, Met. Z.4 1030a33-34. 27 This is to accept Bonitz's emendation of 1fucn for ~J.Ltv .

228 Aristotle's Theory of the Unity of Science kinds are friendship, not as possessing a common name accidentally without being specifically related to one another, nor yet as falling under one species, but rather as in relation to one and the same thing.

It is clear here why the medical things are not one species or species of one genus. In spite of their per se relations, they are different kinds of things, substance (man) and non-substances (actions, events, etc.). But the application of the principle here to friendship is much more problematic, and has been used to support the theory that the EE is earlier than the EN, which rejects the focal relationship in favour of mB' Ol'-o
28 Fortenbaugh (1975, 59-60) has said that it is difficult to construe the three friendships in the 7fPOS ElJ arrangement. He suggests that the E£ illustrates and explains focal meaning but does not apply it directly to friendship, because it does not work. '[TJhe Eudemian Ethics does not go on to apply this analysis to the different kinds of friendship. Having stated that the focal logos must appear in the other definitions, the Eudemian version does not show how the definition of perfect or primary friendship is involved in the definitions of other kinds of friendships.' He suggests that the friendships of the EN are analogically related, claiming oddly as the reason that the three kinds of friendship do not perform the same function. Walker (1979) argued that the EN did not present an analogical arrangement. 29 For a recent defence of the focal arrangement, see Ward 1995.

229 Cumulation children or brutes, but to the adult is really pleasant; at least, when we remember both we choose the latter. And as the child or brute is to the adult man, so are the

bad and foolish to the good and sensible. (VII.2 1235b33-1236a2)

Aristotle implies a division into two kinds of desirables: those goods and pleasures that are natural and not peculiar to an individual in aberrant condition, and those that are both cpaLVO/lEVa aya86. (apparently good) and aya86. TLV' (good to someone). The examples provided imply that cpavTaIT{a incorrectly affirms the not-good object to be good. Thus, an immature person will mistake the pleasant for the good. He must mistake his pleasure friend for a virtue friend. Now, if the pleasant is to be focally related to the good, pleasure must contain the definition of good in it. But equally there are many pleasure friends who can accurately identify the basis of their friendship. There is no reason to suppose that every person must say of his pleasure friend that he thought he was a virtue friend and intend by 'virtue' what the word is defined to mean. We do not have to be deluded or bad to have a pleasant friend whom we do not think to be virtuous. If this is so, the focal relationship between pleasure and good breaks down. Aristotle is not wholly unaware of this problem. He treats virtue and pleasure friendship together and makes it clear that bad men are not capable of virtue friendship. Owing to their debility the pleasure they derive is perverted: Nothing prevents [bad men's] loving with the other kinds [0£ friendship]; for owing to pleasure they put up with each other's injury since they are incontinent.

(modified ROT; VII.2 1236b15-17)

The harm they do one another is a result of their perversion. Such a view, however, makes it impossible for a good man to pursue a purely pleasure friendship, something Aristotle makes room for at the end of the chapter: For the bad may be pleasant to one another, not qua bad or qua neither good nor bad, but (say) as both being musicians, or the one fond of music and the other a musician, and inasmuch as all have some good in them, and in this way they harmonize with one another. (VIL2 1238a35-38)

The pleasure friendship that a good man enters into cannot be for merely the apparent good, for he would not in that case be good. Conversely, the pleasure friendship that the bad man shares with the good man is

230 Aristotle's Theory of the Unity of Science not merely an apparent good, since 'all have something of the good' (1238b13-14). In order to save the phenomena, then, Aristotle assimilates pleasure friendships that are not actually perverted to virtue friendships by identifying the grounds of pleasure in some limited virtue. What is the result if we reject the focal principle in its present fonn? If we treat good and pleasure as independent ends but preserve the relative/ absolute distinction for each in its own right, we eliminate the basis of

the focal relationship. And, as we shall see, this is precisely what happens in the EN account. Clearly, though, Aristotle intended this argument to be the basis of his claim that the friendships are focally related. In order for the argument to succeed, the cpawoJ.Lwou aya80v must appear to the bad man to be virtue, but in fact be pleasure; he must mistake pleasure for virtue. Since virtue

is pleasurable, Aristotle may have supposed that the mistake would not be infrequent.

The characterization of the useful friendship also presents a problem for the focal relationship. The EE seems to take the dependency of the useful on the good as obvious, but it is clearly not the same kind of dependency as that of the pleasant. For, as we saw, pleasure friendship was construed as a

kind of sick virtue friendship. A friendship is useful, however, because it is a means to other ends, like pleasure and virtue. Now, utility friendship is useful for many things, among them virtue and pleasure friendships. But utility friendship is useful for other goods and pleasures besides friendship, since friendship is not the only locus of virtue or pleasure. Although one can easily argue that the useful is focally related to the pleasant and the virtuous (and if the pleasant is itself focally related to the virtuous, then the useful is always ultimately focally related to the virtuous), the utility friendship is not focally related to the pleasure or virtue friendship. For the definition of utility friendship does not potentially contain the definition of pleasure or virtue friendship, even though it may potentially contain the definition of pleasure or virtue. In spite of Aristotle's attempts, neither

utility friendship nor pleasure friendship can convincingly be brought into a dependency relationship with virtue friendship.'o Pleasure friendships can be made focally dependent only if they are perversions of virtue friendships, and utility friendships cannot be subordinated focally to virtue friendships at all. 30 Even the pleasure associated with virtue is different from the pleasure pursued as an end. So, for example, Aristotle asks (1.5 1216a33-37) whether for the good life it will be necessary to add pleasures, or whether it will be pleasurable in another way.

231 Cumulation 2. The Nicomachean Version In the EN Aristotle makes no explicit mention of analogy or focality of friendship. But, just as in the EE, EN VII/'2 says that the problem of friendship can be solved if we first come to know the purposes of friendships, and by knowing the purposes we shall be able to make the distinctions. Since the purposes of friendship differ in species, so do the friendships differ in species (VIII.3 1156a6-8)31 The most notable feature of EN VIII.2 is Aristotle's dismissal of the focal relationship between the ends of friendship (1155b17-27): The kinds of friendship may perhaps be cleared up if we first come to know the object of love. For not everything seems to be loved but only the lovable, and this is good, pleasant, or useful; but it would seem to be that by which some good or pleasure is produced that is useful, so that it is the good and the pleasant that are lovable as ends. Do men love, then, the good, or what is good for them? These sometimes clash. So too with regard to the pleasant. Now it is thought that each loves what is good for himself, and that the good is without qualification lovable, and what is good for each man is lovable for him; but each man loves not what is good for him but what seems good, This however will make no difference; we shall just have to say that this is that which seems lovable.

Aristotle assumes from the beginning that there are three ends of friendship, the good, the pleasant, and the useful, and asks whether one loves the good or what is good for oneself. Although his analysis of the problem considers only the good, the pleasant could be easily substituted. He implies that the ends are to be treated ,eparately for the purpose of his analysis, and makes no attempt to connect or relate the pleasant and the good. In this way he treats the good and the pleasant as independent objects of love and, as a result, eliminates the basis for the focal arrangement. As for utility friendship, it is almost brushed aside, this time not because it is easy to fit into a focal arrangement (although it is), but because it is not an end in itself. This separate treatment for the three objects of love is picked up again in chapter 3, where Aristotle considers the three kinds of friendship in terms of their ends. Virtue friends love each other for themselves, but pleasure and utility friends abstract some feature from their friend that is of interest to them. The pleasant aspects of another person are abstracted from the whole person, and are not considered as logically dependent on 31 bta
CPtll.~CTHS

apa Kat

at cptll.{at. Tpla b~ TO. T11S CPtll.iM

232 Aristotle's Theory of the Unity of Science the whole person or on virtue friendship, which has as its object the whole character of the other (1156a10-16). Pleasure and utility friendships are considered as abstractable parts of complete friendship. Thus, Aristotle's efforts in the EE to construe pleasure as dependent on the good are overturned, and pleasure is treated as an independent end alongside virtue. A focal arrangement on this basis is no longer possible.32 In the place of a focal analysis Aristotle arranges the friendships in a manner that in several respects is similar to the cumulative arrangement of the souls. First, he provides a general account that covers all the cases (me' EmITTOV, 1156a8-10) but that fails to be a definition: [W]ith respect to each of the aforementioned objects there is a mutual and recognized love, and those who love each other wish each other well in that respect in which they love one another (ad apa d)VOE~V clAi\~i\O~S' KUL f3ovAf.(J"ea~ Taya8a /J.r, Aav8avovTuS' at' Ell n TWV Elprfl.LEvwV). VIII.2 1156a3-5

In spite of the fact that he is able to give a general account, he clearly says that pleasure and utility friendships are only incidentally friendships (1156a16-17).33 They are incidental because one wants the friends' good, not for their own sake but in order that they may continue to be a source of profit or pleasure to oneself. That is not to say that pleasure friends do not wish each other well, but they do so insofar as they are pleasant to each other. The friend's good, then, may either be defined in terms of oneself Oust as one is a friend to wine, in order that it may be preserved for oneself), in which case it is the friend's good only incidentally, or it may be defined in terms of one's friend, for his own sake. 34 This distinction makes clear that the general definition contains at least one -ambiguous term, en' EV TL TWV €ip1JJ1.€vWV and this casts doubts on the generic status of the definition. 35 Second, in the EN Aristotle both reverses and alters the dependency we found in the EE, so that pleasure and utility friendship will be prior to virtue friendship in the series. No longer is virtue friendship contained in pleasure friendship, instead pleasure friendship is contained in virtue 32 Gauthier and lolif (1959, ii, 686) quOte the EE passage on. focal meaning without mentioning the differences between the two presentations. They suppose that the similarity mentioned at 1157a32 (V yap aya.8olJ n Kat O},wtOlJ n. TaUT!! $ii\m) is the kind of similarity discussed in EE, which is certainly incorrect. 33 KaTa (J"V}J.f3Ej37JK6~

TE

01) at $!ALa! aUral ELn-W.

34 This is contrary to the opinion of Walker, who holds that the definition states the necessary and sufficient conditions for all kinds of friendship (1979, 185). 35 Cf. Phys. VIl.4 248b17-19 and the discussion above on the soul.

233 Cumulation friendship. The nature of the containment has also changed. The term 'pleasure friendship' is not contained in the definition of virtue friendship, but pleasure friendship is nevertheless implied in virtue friendship, and can be proved to belong to virtue friendship because of the essential attributes of virtue friendship. So at EN VIII.3 1156b12- 17, Aristotle says: And each [virtue friend ] is good without qualification and to his friend, for the good are both good without qualification and useful to each other. So they are pleasant; for the good are pleasant both without qualification and to each other, since to each his own activities and others like them are pleasurable, and the actions of the good are the same or like.

Whether or not this argument is sufficiently articulated to constitute a proof, it is clear that virtue friendship is pleasant and useful because of its own nature. The virtue friendship is not a pleasure friendship in the way a pleasure friendship is a pleasure friendship, since a virtue friendship is not pursued for pleasure, but it is nonetheless pleasant, and presumably more pleasant than a pleasure friendship. In a similar way, the definition of the sensitive soul does not explicitly contain the definition of the nutritive soul, though it implies the existence of the nutritive souL Likewise, too, the nutritive soul is not the final cause of the animaL as it was for the plant, but rather is set in some causal relation, namely necessary condition, to the sensitive soul. Third, the series are also similar with respect to ontological priority and posteriority. Just as the nutritive soul can exist without the sensitive soul, but the sensitive soul cannot exist without the nutritive souL so there can be a pleasure friendship without it being a virtue friendship, but a virtue friendship must be a pleasure friendship. At the same time, there are features of the friendship series that are more difficult to assimilate to cumulation of the soul type. Clearly, the utility and pleasure friendship are not serially related to one another, but only to virtue friendship. Again, Similarity (0I"0'OT'1< 1156b33- 1157a4) figures largely in Aristotle's description of the relationship between perfect (virtue) friendship and pleasure friendship, and this would be more appropriate within a perfective series: This kind of friendship, then is complete both in respect of duration and in all other respects, and in it each gets from each in all respects the same as, or something like what, he gives; which is what ought to happen between friends. Friendship for the sake of pleasure bears a resemblance (of.LoiwJ.W.) to this kind; for good people too are pleasant to each other. So too does friendship for the sake of utility; for

.

- -- - -

234 Aristotle's Theory of the Unity of Science the good are also useful to each other. Among men of these sorts too, friendships are most permanent when the friends get the same thing from each other.

VIII.6 (1158b5- 11) gives a similar description: II]t is from their likeness and their unlikeness to the same thing that they are thought both to be and not to be friendships. It is by their likeness to the friendshi p of excellence that they seem to be friendships (for one of them involves pleasure and the other utility, and these characteristics belong to the friendship of virtue as well); while it is because the friendship of virtue is proof against slander and lasting, while these quickly change (besides differing from the former in many other respects), that they appear not to be friendshipsi Le. it is because of their unlikeness to the friendship of virtue. (modified ROT)

The likeness and unlikeness are based on three sets of factors that serve to determine friendships: the general account, the purposes of friendship, and the characteristics (Tp07TO< ) of the complete friendship .'6 The general account establishes their common claim to the title, while their purposes differ. The purposes, in turn, entail certain characteristics that the complete friendship has most completely and others share more or less." The friendships are even described as differing by the more and the less, in spite of the fact that they are speCifically different (VIII .11155b13-16). The Similarity among the characteristics of friendships, then, is a deduced result of the 36 These three sets fonn a

SOrt

of tree. The general definition contains three factors: 1.

IlEt EVVOEtii aA'\~'\otS' Kat !3ovAE(!"8aL TayaOci 2. J.l.~ Aav8civoVTa~ 3. OL' ill TL TooV Elp1JJ.l.f.vwv.

The last is divided into 1. virtue; 2. pleasure; 3. utility. Virtue friendship is then characterized by (i) durability, (ii) age-group considerations, (iii) living together, (iv) needing a long time to fonn, (v) getting the same thing from one another, (vi) unsusceptibility to slander, (vii) between people who are similar, and (viii) who trust each other. 37 The Magna Momfia ILll (1209a19-35) gives an explanation that combines elements of the EE and the EN accounts: And these forms of friendship, that of the good, the pleasant, and the useful ... hang in a way from the same point. JUSt so we call a knife surgical, a man surgical, and knowledge surgical ... Similarly ... the fri endship of the good which is based on the good, the friendship depending on pleasure, and that depending on utility ... while they are nm actually the same, they have still in a way the same sphere and the same origin ... [TJhe friendship of the virtuous ... is a compound of all these, of the good and the pleasant and the useful. Clearly, the author of the MM combines the definitional inclusion (from the medical example) and association by accumulation. There is no reason why they can not apply to the same objects, but they do not explain one another.

235 Cumulation purposes. For this reason, these similarities are secondary and need not be thought to establish any sort of rival order among the friendships: they are posterior to the purposes. They are discussed at length, because Aristotle is interested in explaining why pleasure and utility friendships are called friendships (1157a25-32), in spite of the fact that he considers them to be incidentally friendships. On balance, then, Aristotle's analysis of friendship in the EN has strongest affiliations with cumulation. He is able to give an account of why one friendship is more, another less, like friendship properly so called on the basis of the logically prior purposes, and these purposes most closely resemble the order of inclusion among the souls. By these organizational means Aristotle is able to provide a more convincing and plausible account of the nature of friendship than he had in the EE. Series in which there are prior and posterior members manifest a variety of forms . The souls and the friendships, when viewed serially, are generated through logical and ontological additions and they progress in order of perfection. As such, they are basically cumulative series. For their logical additions are not diminutions or perversions of the first member, but rather completions. In other series, like that of citizenship, the order is based on logical but not ontological inclusion: the first member is not ontologically prior to the second member. Instead, the terms of the series are related by the addition of an element that represents a qualification and diminution of the first member. In all cases, though, it is the additions that give the series their distinctive scientific form. For each member individually serves as a principle of explanation for analogically common features, and the first member serves as the causal explanation for all the properties that derive from it and that all the other members share in because of their possessing that member.

The Place of Theology in the Science of Being Our findings concerning cumulation may help clarify a famous problem in metaphysics, the place of theology in the science of Being. Metaphysics r discusses general metaphysics but does not include any consideration of theology. E .1, by contrast, makes theology the centrepiece of the science of Being qua Being. 38 The question 'arises, then, whether these are compatible positions. If Aristotle meant what he clearly appears to mean in E.l, then he is probably overestimating the perfective aspects of the series of Being 38 For a brief summary of the controversy see Patzig 1960-61, 185- 7, and Frede 1987b, 84.

236 Aristotle's Theory of the Unity of Science and is granting too large a role to theology. There is no question that in K1 he intends theology to have the central place in the science of Being (1026a23-32): One might indeed raise the question whether first philosophy is universal, or deals with one genus; i.e. some one kind of being; for not even the mathematical sciences are all like in this respect, - geometry and as tronomy deal with a certain particular kind of thing, while universal mathematics applies alike to all. We answer that if there is no substance other than those which are formed by nature, natural science will be the first science; but if there is an immovable substance, the science of this must be prior and must be first philosophy, and universal in this way, because it is first. And it will belong to this to conside r being qua being - both what it is and the attributes which belong to it qua being .

Both Frede and Patzig view the relationship between sensible substance and god (non-sensible substance) as focal; Patzig, insofar as god is the cause, that is, the prime mover, for sensible substance, and Frede because god is form and pure actuality, and therefore more abstract than sensible substance, though containing that feature which is substance first and foremost. 39 What is said of it qua Being will, therefore, apply as well to concrete sensible substance, which in turn will be treated as a subordinate science. 'Why would it be the task of the theologian to consider these matters [i.e., general metaphysics]?' Frede asks. 'There are two possible explanations. The first is that since these matters have to be discussed somewhere, and since they are most naturally discussed in the context of ontology, it will be the task of the theologian to deal with them, since it is his task to do ontology. But there is another possible explanation which ties this fact to Aristotle's claim that first philosophy is universal, because it is first. Since it is first, and since these principles and notions are unive rsal, first philosophy will be the first place where they are used. Hence, it will be the task of the theologian to introduce them: 40 There are important distinctions between these views, and each is open to particular objections. Patzig's view that god is cause, the prime mover of all things, implies that god is useful in the explanations of sensible substances and is adapted to these substances, just as Aristotle suggests in A.4-S. Accordingly, the definition of god will contain the definition of sensible substance, and god will be secondary to sensible substance. This 39 So also Owens 1978, 298: 'In studying thi s definite nature, one studies the Being found in everything else.' 40 Frede 1987b, 93.

237 Cumulation is not to say that god cannot be focally primary in some relation, but as prime mover god will be derivative.

Frede, by contrast, claims that god, being pure form and actuality,

will be treated prior to sensible substance in the order of the science. All those attributes that belong to Being qua Being will be treated first when god as form is treated. For this reason the science of form as well as the principle of non-contradiction (PNC) and principles such as unity will be treated under theology. Frede notes the parallel Aristotle adduces between metaphysics and mathematics to support his claim. But there are

some problems with Aristotle's parallel. The study of proportion, universal mathematics, considers attributes that are common to all magnitudes and can be abstracted in conception. When theorems of proportion are proved,

they are proved of the genus, general magnitude, and can be applied to the specific instances of magnitude, geometry and astronomy. God, by contrast, is a separate substance and not just the sum of common attributes

of sensible substance. God has peculiar attributes, pure actuality, thought thinking itself eternally, and so on, that are discussed in /\, and that sensible substances do not share. Similar difficulties arise for Frede's claim that theology will consider the principle of non-contradiction. For PNC does not hold of god as such, nor even of actuality as such. Now, there is no question that Aristotle claims that theology is the science of Being qua Being, and universal because it is first . But it is equally clear that he must be overstating the case, and may be assimilating theology to the role of the primary member of a strong perfective series, like ends

and means, in which the good of the means is defined in terms of the good end. 41 If this is so, there are a couple of respects in which his account in E.l is off the mark. There is no question that the substances form a series of

prior and posterior - god, sensible substances; and that god is the most abstract, lacking matter and change (the Metaphysics for the most part treats substance with matter, but not with change). I suggest, though, that for the purposes of the science of Being qua Being this series should be likened to the cumulative soul series, vegetative, sensitive, intellectual, in which conceptual and ontological additions are made to each member in order to generate a series of objects that share the same category. As we saw, what is

said commonly of all living things, namely, that the soul is the actuality of the potentially living organic body, is not said just of vegetative soul only nor is it said of the other kinds of soul in virtue of vegetative soul. Rather 41 Compare also Aristotle's comment in the EE's discussion of friendship: 'But because the universal is primary, they also take the primary to be universal, and this is an error' (VII. 2 1236a23-25).

238 Aristotle's Theory of the Unity of Science it is said of all souls in virtue of each kind of soul, and it is a conclusion

derived equally from the nature of the vegetative, sensitive, and intellectual souls. We may interpret the kinds of Being and the general attributes of Being, like PNC, in a similar manner. In the series god, sensible substance,

conceptual and ontological additions are made, but the general attribute PNC does not belong to sensible substance in virtue of god, but rather it belongs in virtue of the nature of sensible substance. Now it may be argued that the order of excellence is reversed in the two series: the series vegetative, sensitive, intellectual increases in order of excellence while the series god, sensible substance decreases. But in fact, this just strengthens the point. For god is separate and unchanging essence and actuality. As

a result, PNC will belong to god if it belongs to anything. But PNC also belongs to Beings that do not meet the stringent qualifications of god. In fact, it applies to anything definite, substance or non-substance, in virtue of whatever their definition is. Aristotle's favourite example in

r,

man as

a biped animal, indicates that PNC will hold even of. definition expressed in terms of the matter of a substance. Moreover, Aristotle nowhere claims

that PNC holds in virtue of god or pure actuality; rather he makes clear in APo 1.10 and r.3 (1005.22- 29), that PNC is common by analogy, just as the common definition of soul is common by analogy.

The example of general and special mathematics mentioned at the end of E.1 is .lso relevant, though not in the way Aristotle appears to use it. The study of PNC belongs to the science of Being at the general and universal level, and so corresponds to universal mathematics. But the

specific branches of mathematics (geometry and astronomy) are based on ontological principles that form a series. Geometry considers the plane or

solid, astronomy adds motion. Correspondingly, god and sensible substance form an ontological series, god concerning form alone, sensible substance concerning form together with matter. Just as general mathematics (theory

of proportion) does not hold generally in virtue of its holding specifically of geometry (for there can be proportion in locomotion), so general metaphysics (PNC) holds of all Beings qua what they are and not in virtue of god or pure actuality.42 PNC holds of Being in an even more abstract sense than god. There is another respect in which Aristotle's E.l account differs from his usual doctrine. He claims that if separate and unchanging substance does not exist, physics will be the first science. But this does not follow from what he says about abstraction elsewhere. For if there were only 42 The fact would be especially dear in the series arithmetic and geometry, since general mathematics holds for both rational and irrational quantity.

239 Cumulation isosceles triangles or even bronze isosceles triangles, 2R would still not

belong to them in virtue of bronze or isosceles (APo 1.5 74a16). Aristotle clearly has ways of talking about sensible substance abstracted conceptually from change even if it is not actually separated, as he says at Met. M.3 1077b17-30. Likewise, god need not exist in order for PNC and general metaphysics not to be included in physics. For these reasons Aristotle would have been better off organizing Being in accordance with the cumu-

lative pattern rather than the focal and perfective pattern that Patzig and Frede envision.

Conclusion: Analogy, Focality, and Cumulation Aristotle once accused Speusippus of representing nature like an episodic

tragedy, on the grounds that he had made each hypostasis independent and isolated from every other (Met. N.3 1090b19-20). His own theory of the subject-genus, however, was perhaps even more vulnerable to this

charge. Accordingly, Aristotle developed the doctrine of abstraction together with analogy, focality, and cumulation to provide a set of interlocking and mutually dependent techniques for overcoming the isolation of the subject-genus. In spite of the fact that these techniques receive little attention within the formal presentation of the APo, it is clear that they can be expressed best within that theory and especially within the fundamental notions of genus and essential connections. Without sacrificing

the integrity of the autonomous genus, these techniques allow for the inclusion of the relevant and necessary external objects and causes within a science as the well as the connections between autonomous genera. Focality is, of course, the primary relation, being identical with per se predication. It provides a flexible description of normal science in both its core and extended aspects. Focally derivative items, which surround a core

subject-genus, both reveal the nature of the core subject and may also be semi-abstracted so as to become subjects in their own right. These new subjects, nevertheless, remain part of the science of the core. Any per se

(2) predicate, for example, male and female which belong to animal, may have properties proved of them per se, and these proofs will form a part of the extended science of animal. Focality, then is the primary means of

unifying a science and displaying the unity of the components of a science. Analogy allows Aristotle to remain within the limitations of the qua-requirement, and yet consider commonalities between different but related genera. Analogy resolves the tension between qua and per se requirements within the same science, since the genera in which analogies occur must be related in virtue of some abstractable commonality. The

240 Aristotle's Theory of the Unity of Science nature of this commonality varies. In lower ge'nera, the commonality is often some aspect of form, and is related to each genus by a common relation, as, for example, the functions in the biological works are common among various parts. Among higher genera, where no genuine commonality is available, some sort of serial order supplies the per se relations necessary for the unity of science. Focality provides one such series. The analogy of potentiality in A.4-S is arguably backed by such a focality. The focal relations take many different forms, including the causal relations characteristic of normal science and the medical example; but we also find the relations of imitation and deficiency, which are especially useful in backing analogies. For objects so related are of the same basic kind and therefore amenable to analogical comparisons. Such is the basis of the scala naturae in which one genus, man, forms a normative kind in terms of which other genera are explained. The imitation and deficiency relation is not, as I have argued, an essential feature of analogy, but only one of the means by which two analogous genera can be related. Owen suggested that the relationship between the souls is focal, on the grounds that the definitions of the souls exhibit definitional inclusion and are related by 7fporr$f(n< and acpaipErr«.43 He is certainly right that cumulation exhibits some focal characteristics. We find, besides these additions, relations of hypothetical necessity among the souls discussed in DA III.l2. But the cumulative soul series is not focal insofar as the primary purpose of cumulation is not to bring one object into an explanatory relationship with the primary object, in spite of the fact that this is a necessary condition for cumulation. Although the souls do exhibit definitional inclusion, the n+ 1 th member of a series does not include the nth member for the purpose of explaining the nth member. Nor are cumulative objects included in the science only to the extent to which they are useful for the primary term, as focally derivative objects are; each member of the series is treated as a subject in its own right with its own per se predicates. Again, an important criterion of a focal science is that all members have their shared name in virtue of the first member. This may also be true of imitative or perfective series, but since the kinds of souls are called soul in virtue of the highest faculty they possess, this series cannot be called focal in the proper sense. 44 Ontological and logical priority alone are not enough to create a focal term. The first term must also be that in 43 Owen 1960, 192n37. 44 Because cumulation is a fusion of analogy and focahty, Rodier (1900, 218) was partly correct to say that the kinds of soul are analogically related, and Owen (1960) partly correct to say that they are focally related.

241 Cumulation virtue of which all subsequent terms are called by the same name. When these three criteria are taken together, it becomes impossible for a series of the soul type to be focally related. Cumulation also has some analogical characteristics. Like analogues, cumulative subjects are all in the same category; focally related subjects are not; and all share some per se attribute and not just by relation. Souls are all actualities of organic bodies, friendships are mutual and recognized bonds of affection. The result of the cumulative TrpoO"$'O"t< is not the creation of a genus network around a subject, but a proliferation of parallel subjects, which share attributes analogically and in virtue of common essential elements, for instance, the assimilation of the nutritive, sensitive, and intelligible by that which has the capacity to receive them. Souls are per se things and are treated in their own right and not as relative to the first member of the series. Cumulation differs from biological analogy because in biological analogy there must be some absolutely common element to which the analogues are all per se related, and which is semi-abstractable, but which, given the concrete subject matter is not abstracted. This semi-abstractable element is causally significant and distinct. In cumulation, by contrast, . there is not a single common cause to which the members are all related; their commonality is posterior and proved from different and specific causes. Like metaphysical analogues, members of cumulative series are gathered together because of their mutual focal relations of definitional inclusion. Since members of cumulative series are not per se related to some common and logically prior item, they do not need to be related to anything more abstract than themselves in order to be analogically related. For this reason they are well adapted to operate at the most general and abstract levels of Aristotle's ontology. Indeed, analogues, precisely because they require a distinct abstract can never be the ultimate form of scientific unification, but instead always rely on focality or cumulative series. Finally, these three techniques themselves can be seen to form a sort of cumulative series: focality, analogy, cumulation. A new qualification is added at each stage in order to create an additional form of unification. To the per se relation between genera that is characteristic of focality we add a proportional identity in order to create analogy, and the per se relation among analogical genera is further qualified by progressive ontological and logical additions in order to create cumulation. Together these techniques contribute to a style of philosophy and science that is distinctively Aristotelian. For Aristotle combines that rigour so admired among us moderns, that isolates a subject matter for study and seeks to understand it in its own right together with the synoptic vision of

242 Aristotle's Theory of the Unity of Science cosmic unity through hierarchical and progressive abstraction. From these techniques also emerges a certain flexibility, according to which several modes of unification can be used on the same group of objects to different effects. Aristotle, with his interest in explaining the phenomena and solving aporiai, maximizes thereby his ability to explain. These techniques are most properly expressed in the formal language of essential relations and demonstration, and for this reason Aristotle can provide a unified view of the world while avoiding the nebulous and metaphorical expression of the Platonists.

BIBLIOGRAPHY

Texts and Translations Barnes, J. 1984. The Complete Works of Aristotle. The Revised Oxford Translation (Bollingen Series LXXI.2). Princeton: Princeton University Press. {ROT] Bekker, L 1831. Opera Aristolelis. Academia Regia Borusica. Berlin: G. Reimer. Minio-Paluello, L. 1949. Aristotelis Categoriae et Uber de Interpretatione. Oxford: Clarendon Press. Ross, W.D. 1964. Aristotelis Analytica Priora et Posteriora. Oxford: Clarendon Press. Ross, W.D . 1958. ATistoteiis Topica et Sophistici Elenchi, Oxford: Clarendon Press. Ross, W.D. 1950. Aristotelis Physica. Oxford: Clarendon Press. Allan, D.J. 1936. Aristotelis de Caelo. Oxford: Clarendon Press. Fobes; F.H. 1967. Aristotelis Meteorologicorum Libri Quattuor. Hildesheim: Georg alms Verlagsbuchhandlung. Ross, W.O. 1956. Aristotelis de Anima. Oxford: Clarendon Press. Hett, W.s. 1975. Aristotle: On the Soul, Pama Naturalia, On Breath. Cambridge: Harvard University Press. Peck, AL. 1965. Aristotle: Histori~ Animalium I, Books I-III. Cambridge: Harvard University Press. - 1970. Aristotle: Historia Animalium II, Books IV-VI. Cambridge: Harvard University Press. Salme, D.M. 1991. Aristotle: History of Animals, Books VII- X. Cambridge: Harvard University Press. Peck, A.L., and E.S. Forster. 1983. Aristotle: Parts of Animals, Movement of Anima/s, Progression of Animals. Cambridge: Harvard University Press. Peck, AL. 1942. Aristotle: Generation of Animals. Cambridge: Harvard University Press.

244 Bibliography Jaeger, W. 1957. Aristotelis Metaphysica. Oxford: Clarendon Press. Tredennick, H'J and G. Cyril Armstrong. 1935. Metaphysics X-XIV; Oeconomica; and Magna Moralia. Cambridge: Harvard University Press. Bywater, I. 1894. Aristotelis Ethica Nicomachea. Oxford: Clarendon Press. Walzer, R.R., and J.M. Mingay. 1991. ATistote/is Ethim Eudemia. Oxford: Clarendon Press. Ross, W.D. 1957. Aristotelis Politica. Oxford: Clarendon Press. Alexander Aphrodisiensis. 1891. In Aristotelis Metaphysica Commentaria. Ed. M. Hayduck. Berlin: G. Reimer. Euclid. 1883-1916. Opera omnia. Ed. LL Heiberg and H. Menge. Leipzig: Teubner. Proclus. 1873: In primum Euelidis elementorum {ibrum commentarii. Ed. Gottfried Friedlein. Leipzig: Teubner.

Secondary Literature Ackrill, J. 1978. 'Aristotle on "Good" and the Categories.' In J. Barnes, M. Schofield, R. Sorabji, eds, Articles on Aristotle, 2: 17-24. New York: St Martin's. Annas, ]. 1976. Aristotle's Metaphysics Books M and N. Clarendon Aristotle Series. Oxford: Clarendon Press. Apostle, H. 1981. Aristotle's Posterior Analytics. Grinell: Peripatetic Press. Aubenque, P. 1978. 'Les origines de la doctrine de l'analogie de l'etre. Sur l'histoire d'un contresens.' Etudes Phi!osophiques: 3-12. Balme, D. 1961. 'Aristotle's Use of Differentiae in Zoology.' In Symposium Aristotelicum II: Aristote et les problemes de methode, 195-212. Louvain: Publications Universitaires. - 1962. 'yevo) and etoo) in Aristotle's Biology.' Classical Quarterly n.5. 12: 81-98. - 1972. Aristotle's de Partibus Animalium 1 and de Generatione Animalium 1. Clarendon Oxford Series. Oxford: Clarendon Press. - 1987a. 'Aristotle's Use of Division and Differentiae.' In A. Gotthelf and J. Lennox, eds, Philosophical Issues in Aristotle's Biology, 69-89. Cambridge: Cambridge University Press. - 1987b. 'Aristotle's Biology Was Not Essentialist.' In Gotthelf and Lennox, eds, Philosophical Issues in Aristotle's Biology, 291-312. Barnes, ]. 1994. Aristotle: Posterior Analytics. 2nd ed. Clarendon Aristotle Series. Oxford: Clarendon Press. Berti, E. 1971. 'Multiplicite et unite du bien selon EE I 8.' In P. Moraux and D. Harlfinger, eds, Untersuchungen zur Eudemischen Ethik. Akten des 5. Symposium Aristotelicum, 157-84. Berlin: de Gruyter. Bolton, R. 1976. 'Essentialism and Semantic Theory in Aristotle: Posterior Analytics II, 7-10: Philosophical Review 85, 514-44.

245 Bibliography

- 1978. 'Aristotle's Definition of the Soul: De Anima 11,1-3.' Phronesis 23: 258-78. - 1987. 'Definition and Scientific Method in Aristotle's Posterior Analytics and Generation of Animals.' In A. Gotthelf and J. Lennox, eds, Philosophical Issues in Aristotle's Biology, 120-66. Cambridge: Cambridge University Press. - 1994. 'Aristotle's Conception of Metaphysics as a Science,' In T. Scaltsas, D. Charles, and M.L. Gill, eds, Unity, Identity, and Explanation in Aristotle's Metaphysics, 321-54. Oxford: Clarendon Press. - 1995 . 'Science and the Science of Substances in Aristotle's Metaphysics Z: Pacific Philosophical Quarterly 76: 419-69. Bonitz, H. 1853. 'Ober die Kategorien des Aristoteles.' Sitzungsberichte der Wiener Akademie 10: 591-645. - 1961. Index Aristotelicus. Berlin: de Gruyter. Bremmer, J. 1983. The Early Greek Concept of the Soul. Princeton: Princeton University Press. Broadie, S. 1991. Ethics with Aristotle. New York: Oxford University Press. Burnyeat, M. 1987. 'Platonism and Mathematics. A Prelude to Discussion.' In A. Graeser, ed., Mathematics and Metaphysics in Aristotle. Proceedings of the 10th Symposium Aristotelicum, 213-40. Bern and Stuttgart: Verlag Paul Haupt. Burnyeat, M., et a1. 1979. Notes on Book Zeta of Aristotle's Metaphysics. Study Aids Monograph no. 1. Sub-Faculty of Philosophy: Oxford. - 1984. Notes on He of Aristotle's Metaphysics. Study Aids Monograph no. 4. Sub-Faculty of Philosophy: Oxford. Burrell, O.B. 1973. Analogy and Philosophical Language. New Haven: Yale University Press. Cartwright, N., and H. Mendell. 1984. 'What Makes Physics' Objects Abstract?' In J. Cushing, C. Delaney, and G. Gutting, eds, Science and Reality, 134- 52. Notre Dame; University of Notre Dame Press. Charles, D. 1990. 'Aristotle on Meaning, Natural Kinds and Natural History.' In D. Devereux and P. Pellegrin, eds, Biologie, log/que et metaphysique chez Aristote, 145-67. Paris: Editions du Centre National de la Recherche Scientifique. - 1994. 'Matter and Form: Unity, Persistence, and Identity.' In T. Scaltsas, D. Charles, and M.L Gill, eds, Unity, Identity, and Explanation in Aristotle's Metaphysics, 75-105. Oxford: Clarendon Press. - 1997. 'Aristotle and the Unity and Essence of Biological Kinds.' In W. Kullmann and S. Follinger, eds, Aristotelische Biologie: Intentionen, Methoden, Ergebnisse, 27-42. Stuttgart: Franz Steiner Verlag. Charlton, W. 1970. Aristotle's Physics Books 1, II. Clarendon Aristotle Series. Oxford: Clarendon Press.

246 Bibliography Cherniss, H. 1944. Aristotle's Criticism of Plato and the Academy. Baltimore: Johns Hopkins Press. Cleary, J. 1985. 'On the Terminology of "Abstraction" in Aristotle.' Phronesis 30: 13-45. - 1988. Aristotle on the Many Senses of Priority. Journa l of the History of Philosophy Monograph Series. Carbondale and Edwardsville: Southern Illinois University Press. - 1995. Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics. Philosophia Antiqua Series, vol. 67. Leiden: £.J. BrilL Cobb, R.A. 1973. 'The Present Progressive Periphrasis and the Metaphysics of Aristotle! Phronesis 18: 80-90. Code, A. 1986. Aristotle's Investigation of a Basic Logical Principle. ' Canadian Journal of Philosophy 16: 341-57. - 1996. 'Owen on the Development of Aristotle's Metaphysics.' In W. Wians, ed., Aristotle's Philosophical Development: Problems and Prospects, 303-25. Lanham, Md.: ROWlnan and Littlefield. Cohen, S. Marc. 1992. 'Hylomorphism and Functionalism.' In M. Nussbaum and A. Rorty, eds, Essays on Aristotle's De Anima, 57-73. Oxford: Clarendon Press. Coles, A. 1997. ' Animal and Childhood Cognition in Aristotle's Biology and the Scala Naturae,' In W. Kullmann and S. Follinger, eds, Aristotelische Biologie: Intentionen, Methoden, Ergebnisse, 287-323. Stuttgart: Franz Steiner Verlag. Cook, K. 1989. 'The Underlying Thing, The Underlying Nature and Matter: Aristotle's Analogy in Physics 1.7: Apdran 22: 105-19. Cook Wilson, J. 1904. 'On the Platonic Doctrine of Q.UVIl-{3A.y/TOt a.PL81l0i.' Classical Review 18: 247--60. de Corte, M. 1939. 'La definition aristotelicienne de l'ame.' Revue Thomiste 45: 460-508. Dancy, R. 1975. Sense and Contradiction: A Study in Aristotle. Synthese Historical Library, vol. 14. Dordrecht and Boston: D. ReideL - 1983. 'Aristotle and Existence.' Synthese 54: 409-42. Demoss, D., and D. Devereux. 1988. 'Essence, Existence and Nominal Definition in Aristotle's Posterior Anafytics II.8-lO.' Phronesis 33: 133-54. Detel, W. 1997. 'Why All Animals Have a Stomach. Demonstration and Axiomatization in Aristotle's Parts of Animals.' In W. Ktillmann and S. Follinger, eds, Aristotelische Bioiogie: Intentionen, Methoden, Ergebnisse, 63-84. Stuttgart: Franz Steiner Verlag. Ferejohn, M. 1980. 'Aristotle on Focal Meaning and the Unity of Science.' Phronesis 25: 117-28. - 1991. The Origins of Aristotelian Science. New Haven and London: Yale UniverSity Press. I

247 Bibliography Fortenbaugh, W.W. 1966. 'Nicomachean Ethics, I, 1096b26-29.' Phrone,i, 11: 185-94. - 1975. 'Aristotle's Analysis of Friendship: Function and Analogy, Resemblance, and Focal Meaning.' Phronesis 20: 51-62. Frede, M. 1987a. 'Categories in Aristotle.' In M. Frede, Essays in Ancient Philosoph y, 29-48. Minneapolis: University of Minnesota Press. - 1987b. 'The Unity of General and Special Metaphysics: Aristotle' s Conception of Metaphysics: In Frede, Essays in Ancient Philoso phy, 81-95. - 1994. 'Aristotle's Notion of Potentiality in Metaphysics 0: In T. Scaltsas, D. Charles, and M .L. Gill, eds, Unity, Identity, and Explanation in Aristotle's Metaphysics, 173-93. Oxford: Clarendon Press. Frede, M., and G. Patzig. 1988. Aristoteles 'Metaphysik Z': Text, Ubersetzung und Kommentar. Munich: Verlag C.H. Beck. Furth, M. 1988. Substance, Form and Psyche: An Aristotelean Metaphysics. Cambridge: Cambridge University Press. Gauthier, R.A., and J.Y. Jolif. 1959. L'ethique a Nicomaque. Louvain: Publications Universitaires. Gill, M.L. 1989. Aristotle on Substance: The Paradox of Unity. Princeton: Princeton University Press. - 1997. 'Material Necessity and Meteorology IV 12.' In W. Kullmann and S. Fellinger, eds, Aristotelische Biologie: [ntentionen, Methoden , Ergebnisse, 145-61 . Stuttgart: Franz Steiner Verlag. Goldin, O. 1996. Explaining an Eclipse: Aristotle's Posterior Analytics 2.1-10. Ann Arbor: University of Michigan Press. Gomez-Lobo, A. 1989. 'The Ergon Inference.' Phro"e,i, 34: 170-84. Gotthelf, A. ' Notes towards a Study of Substance and Essence in Aristotle's Parts of Animals ii-iv.' In A Gotthelf, ed., Aristotle on Nature and Living Things, 27-54. Pittsburgh and Bristol: Mathesis Publications and Bristol Classical Press. - 1987. ' First Principles in Aristotle's Parts of Animals.' In A Gotthelf and J. Lennox, eds, Philosophical Is sues in Aristotle's Biology, 167-98. Cambridge: Cambridge University Press. - 1997. 'The Elephant's Nose: Further Reflections on the Axiomatic Structure of Biological Explanation in Aristotle.' In W. Kulhnann and S. Fijl!inger, eds, Aristotelische Biologie: Intentionen, Methoden, Ergebnisse, 85-95. Stuttgart: Franz Steiner Verlag. Graeser, A , ed. 1987. Mathematics and Metaphysi cs in Aristotle. Proceedings of the 10th Symposium Aristotelicum. Bern and Stuttgart: Verlag Paul Haupt. Graham, D. 1987. Aristotle's Two Systems. Oxford: Clarendon Press. Granger, H. 1985. 'The Scala Naturae and the Continuity of Kinds.' Phronesis 30: 181-200.

248 Bibliography Grene, M. 1974. ' Is Genus to Species as Matter to Form? Aristotle and Taxonomy.' Synthese 28: 51-69. Grice, P. 1988. 'Aristotle on the Multiplicity of Being.' Pacific Philosophical Quarterly 69: 175-200. Hamlyn, D.W. 1968. Aristotle's de Anima, Books II and III. Clarendon Aristotle Series. Oxford: Cla rendon Press. - 1977-8. 'Focal Meaning.' Proceedings of the Aristotelian Society n.s. 78: 1-18. Heath, T.L. 1949. Mathematics in Aristotle. Oxford: Clarendon Press. - 1956. Euclid. The Thirteen Books a/The Elements. 2nd ed. New York: Dover. - 1981. A History of Greek Mathematics. New York: Dover. Hesse, M. 1965. 'Aristotle's Logic of Analogy.' Philosophical Quarterly 15: 328-40. Hicks, R.D . 1907. Aristotle: de Anima. Camb ridge: Cambridge University Press. Husain, M. 1981. 'The Multiplicity in Unity of Being qua Being in Aristotle' s pros hen Equivocity.' New Scholasticism 55: 208-18. Ide, H. 1992. 'Dunamis in Metaphysics IX.' Apeiron 25: 1-26. Irwin, T. 1981. 'Homonymy in Aristotle.' Review of Metaphysics 34: 523-44. - 1982. 'Aristotle's Concept of Signification.' In M. Schofield and M. Nussbaum, eds, Language and Logos: Studies in Ancient Greek Philosophy, 241-66. Cambridge: Cambridge University Press. - 1990. 'Th e Good of Political Activity.' In G. Patzi& ed., Aristoteles' 'Politik', Akten des XI Symposium Aristotelicum, 73-98. Gottingen: Vandenhoeck and Ruprecht. Judson, L 1997. 'Aristotle on Fair Exchange.' Oxford Studies in Ancient Philosophy 15: 147-75. Kenny, A 1978. The Aristotelian Ethics. Oxford: Clarendon Press. Kirwan, C. 1993. Aristotle's Metaphysics Books r, 6, E. 2nd ed. Clarendon Aristotle Series. Oxford: Clarendon Press. Klubertanz, G. 1960. St Thomas Aquinas on Analogy: A Textual Analysis and Systematic Synthesis. Jesuit Studies. Chicago: Loyola University Press. Kosman, A 1968. ' Predicating the Good.' Phronesis 13: 171-4. - 1984. 'Substance, Being and Energeia.' Oxford Studies in Ancient Philosophy 2: 121-49. - 1987. 'Animals and Other Beings in Aristotle.' In A Gotthelf and J. Lennox, eds, Philosophical Issues in Aristotle's Biology, 360--91. Cambridge: Cambridge University Press. Kraut, R. 1989. Aristotle on the Human Good. Princeton: Princeton University Press. Kullmann, W. 1974. Wissenschaft und Methode: Interpretationen zur aristote lischen Theorie der Naturwissenschaft. Berlin and New York: de Gruyter.

249 Bibliography

- 1990. 'Bipartite Science in Aristotle's Biology.' In D. Devereux and P. Pellegrin, eds, Biologie. logique et metaphysique chez Aristote, 335-47. Paris: Editions du Centre National de 1a Recherche Scientifique. Kung, J. 1981 . 'Aristotle on Thises, Suches and the Third Man Argument.' Phronesis 26: 207-47. - 1982. 'Aristotle's "de Motu Animalium" and the Separability of the Sciences.' Journal of the History of Philosophy 20: 65-76. - 1986. 'Aristotle on "Being Is Said in Many Ways.'" History of Philosophy Quarterly 3: 3-18. Lear, J. 1980. Aristotle and Logical Theory. Cambridge: Cambridge University Press. - 1982. 'Aristotle's Philosophy of Mathematics.' Philosophical Review 91: 161-92. LeBlond, I.M. 1945. Aristote, philosophe de fa vie: Le livre premier du traite sur les Parties des Animaux. Paris: Aubier, 1945. - 1973. Logique et methode chez Aristote. 3rd. ed. Paris: J. Vrin. Lennox, J. 1980. 'Aristotle on Genera, Species and "the More and the Less.'" Journal of the History of Biology 13: 321-46. - 1985. 'Demarcating Ancient Science: A Discussion of G.E.R. Lloyd, Science, Folklore and Ideology: The Life Sciences in Ancient Greece.' Oxford Studies in Ancient Philosophy 3: 307-24. - 1986. 'Aristotle, Galileo, and "Mixed Sciences.'" In W.A Wallace, ed., Reinterpreting Galileo, 29-51. Studies in Philosophy and the History of Science, vol. 15. Washington: Catholic University Press. - 1987a. 'Divide and Explain: The Posterior Analytics in Practice.' In A Gotthelf and J. Lennox, eds, Philosophical Issues in Aristotle's Biology, 90-119. Cambridge: Cambridge University Press. - 1987b. 'Kinds, Forms of Kinds, and the More and the Less in Aristotle's Biology.' In Gotthelf and Lennox, eds, Philosophical Issues in Aristotle's Biology, 339-59. Leszl, W. 1970. Logic and Metaphysics in Aristotle. Padua: Editrice Antenore. Lewis, F. 1991 . Substance and Predication in Aristotle. Cambridge: Cambridge University Press. Liddell, H.G., and R. Scott. 1996. A Greek-English Lexicon. Revised and augmented by H. Jones. Oxford: Clarendon Press. [LSJ] Lloyd, AC. 1962. 'Genus, Species and Ordered Series in Aristotle.' Phronesis 7: 67-90. Lloyd, G.E.R. 1987. Polarity and Analogy. Bristol: Bristol Classical Press. Reprint of Cambridge: Cambridge University Press, 1966. - 1990. 'Aristotle's Zoology and His Metaphysics. The status quaestionis. A Critical Review of Some Recent Theories.' In D. Devereux and P. Pellegrin, eds,

-

--

-

---

250 Bibliography

Bioiogie, logique et metaphysique chez Aristote, 7-35. Paris: Editions du Centre National de 1a Recherche Scientifique. Lones, T. 1912. Aristotle's Researches in Natural Science. London: West, Newman and Co. Loux, M.J. 1973. 'Aristotle on the Transcendentals.' Phronesis 18: 225-39. - 1991. Primary Ousia: An Essay on Aristotle's Metaphysics Z and H. Ithaca: Cornell University Press. Lovejoy, AO. 1964. The Great Chain of Being. Cambridge: Harvard University Press.

J. 1981. 'On the Generation and Corruption of the Categories.' Review of Metaphysics 34: 662-8l. Matthews, G. 1992. 'De Anima 2. 2-4 and the Meaning of Life: In M. Nussbaum and A. RaTty, eds, Essays on Aristotle's De Anima, 185-93. Oxford: Clarendon Malcolm,

Press. McKirahan, R.D. 1978. 'Aristotle's Subordinate Sciences.' British Journal for the History of Science 11: 197-220. - 1992. Principles and Proofs: Aristotle's Theory of Demonstrative Science. Princeton: Princeton University Press. Meikle, S. 1995. Aristotle's Economic Thought. Oxford: Clarendon Press. Menn, S. 1992. 'Aristotle and Plato on God as Nous and as the Good.' Review of Metaphysics 45: 543-74. Mignucci, M. 1975. L'Argomentazione Dimostrativa in Aristotele: Commento agli Analitici Secondi . Padua: Editrice Antenore. Moravcsik, J. 1967. 'Aristotle on Predication.' Philosophical Review 76: 80-96. Mueller, I. 1970a. 'Homogeneity in Eudoxus's Theory of Proportion.' Archive for History of Exact Sciences 7: 1-6. - 1970b. 'Aristotle on Geometrical Objects.' Archiv filr Geschichte der Philosophie 52: 156-71. - 1982. 'Aristotle and the Quadrature of the Circle.' In N. Kretzmann, ed., Infinity and Continuity in Ancient and Medieval Thought, 146-64. Ithaca: Cornell University Press. Muskens, G.L 1943. De vocis anaiogias significatione ac usu apud Aristotelem. Groningen: J.B . Wolters. Nussbaum, M. Aristotle's De Motu Animalium. Princeton; Princeton University Press. Nussbaum, M., and H. Putnam. 1992. ' Changing Aristotle's Mind.' In M. Nussbaum and A. Rorty, eds, Essays on Aristotle 's De Anima, 27-56. Oxford: Clarendon Press. Owen, G.E.L. 1960. 'Logic and Metaphysics in Some Earlier Works of Aristotle.' In G.E. L. Owen, Logic, Science and Dialectic. Ithaca: Cornell University Press, 1986.

251 Bibliography - 1965. 'Aristotle on the Snares of Ontology.' In Owen, Logic, Science and Dialectic. - 1966. 'The Platonism of Aristotle.' In Owen, Logic, Science and Dialectic. - 1978-9. ' Particular and General.' In Owen, Logic, Science and Dialectic. Owens, J. 1978. The Doctrine of Being in the Aristotelian Metaphysics. 3rd ed. Toromo: Pontifical Institute of Mediaeval Studies. - 1989. 'An Ambiguity in Aristotle, EE VIl.2 1236b23-4.' Apeiron 22: 127-37. Patzig, G. 1960-1. 'Theologie und Ontologie in def "Meta physik" des Aristoteles.' Kant-Studien 52: 185- 205. Peck, A.L. 1965. Aristotle, Historia Animalium. Vol. 1. Cambridge: Harvard University Press. - 1983. Aristotle, Parts of Animals. Cambridge: Harvard University Press. Pellegrin, P. 1986a. Aristotle's Classification 0/ Animals: Biology and the Conceptual Unity of the Aristotelian Corpus. Trans. A Preus. Berkeley: University of California Press. - 1986b. ' Les fonctions explicatives de I'Histoire des animaux d' Aristote.' Phronesis 31: 148-66. - 1987. 'Logical Difference and Biological Difference: The Unity of Aristotle's Thought.' In A Gotthelf and ]. Lennox, eds, Philosophical Issues in Aristotle's Biology, 313-38. Cambridge: Cambridge University Press. Philippe, M.-D. 1948. " Aq,atpEuls. 7Tpou8EUlS. XWpi(HV dans Ia phiiosophie d' Aristote.' Revue Thomiste 48: 461-79. - 1969. 'Analogon and Analogia in the Philosophy of Aristotle.' The Thomist 33: 1-74. Preus, A. 1983. 'Eidos as Norm in Aristotle's Biology.' In J. Anton and A. Preus, eds, Essays in Ancient Greek Philosophy II, 34
252 Bibliography Ross, W.D. 1914. Review of Brentano, Aristoteles Lehre des Menschlichen Geistes, . Mind n.s. 23: 289-9l. - 1924. Aristotle's Metaphysics. Oxford: Clarendon Press. - 1936. Aristotle's Physics. Oxford: Clarendon Press. - 1949. Aristotle's Prior and Posterior Analytics. Oxford: Clarendon Press. Rowe, c.J. 1971. The Eudemian and Nicomachean Ethics: A Study in the Development of Aristotle's Thought. Proceedings of the Cambridge Philological Society, Suppl. 3. Scaitsas, T. 1994. Substance and Universals in Aristotle's Metaphysics. Ithaca: Cornell University Press. Shields, C. 1999. Order in Multiplicity: Homonymy in the Philosophy of Aristotle. Oxford: Clarendon Press. Smyth, H.W. 1956. Greek Grammar. Rev. Gordon M. Messing. Cambridge: Harvard University Press. Sprague, R.K. 1975. 'Aristotelian Periphrasis: A Reply to Mr. Cobb.' Phronesis 20: 75-6. Thompson, 0 ' Arcy W. 1929. ' Excess and Defect: or the Lit tle More and the Little Less.' Mind 38: 43-55. - 1940. Science and the Classics. Oxford: Oxford Un iversity Press. - 1961. On Growth and Form. ed. J. Bonner. Cambridge: Cambridge University Press. Thorp, J.W. 1974. 'Aristotle's Use of Categories.' Phronesis 19: 238-56. Tiles, J.E. 1983. 'Why the Triangle Has Two Right Angles Kath ' Hauto.' Phronesis 28: 1-16. Tuozzo, T.M. 1995. 'Aristotle's Theory of the Good and Its Causal Basis.' Phronesis 40: 293-314. Walker, A.D.M. 1979. 'Aristotle's Account of Friendship in the Nicomachean Ethics.' Phronesis 24: 180-96. Ward, J.K. 1995. 'Focal Reference in Aristotle's Account of
253 Bibliography - 1997a. 'Speusippus on Knowledge and Division.' In W. Kullmann and S. Follinger, eds, Aristotelische Biologie: Intentionen, Methoden, Ergebnisse, 13-25. Stuttgart: Franz Steiner.

- 1997b. 'Analogy in Aristotle's Biology,' Ancient Philosophy 17: 335-58. Witt, C. 1989. Substance and Essence in Aristotle: An Interpretation of Metaphysics VII-IX. Ithaca: Cornell University Press. Woods, M. 1992. Aristotle: Eudemian Ethics, Books 1, II, and VI1l. 2nd ed. Clarendon Aristotle Series. Oxford: Clarendon Press.

INDEX LOCORUM

Cat.

1 3 5 5 6 6 7 8

1.12- 15 1b16 2.34--b5 3.22-28 5.38-b10 6.19- 25 6.36-37 11.15

150n23 62n18 151n28 138 41n40 38n36 181 165

21.29-32

117n2

D1

1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.6 1.6 1.7

11

1.7

1.7

73b9-10 73b10-16 73b26-32 73b32-33 74.12-13 74.16-17 74.17-25 74.35-b4 74b8-10 75.28-29 75.38-39 75.39-b2 75a42-b1

APr

1.39

49b3--5

117n2

72.14--24 72.16- 17 73.24--25 73.24--27 73.34--b16 73.34--37 73.37-b3 73b4--5 73b5-10 73b6-8

80 26 19n8 15 16 16 16 21 16 149n22

APo

1.2 1.2 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4

1.7 1.7 1.7 1.7 1.9 1.9 1.9 1.10 1.10 1.10 1.11 1.12 1.13

75b10--11 75b12-20 75bl4--17 75b37-76.2 75b37-38 76.4--7 76.9-15 76.37- b2 76b16-19 77.26-35 77.40--b6 78b32-79.16

150 16 17n4 17n4 17n4 18, 239 24 30 16n2 30 21- 2 20 18n7, 126 21,90 21-22 33n26 22

21

18 32-3 157, 238 26, 91 81 26 33n26 33n26

256 Index Locorum 1.22 1.22 1.22 1.28 128 11.4 11.4 11.11 11.13 11.13 11.13 11.13 11.14

IU7 11.17 11.17 11.17 11.17 11.17 11.18 11.19 Top. 1.5

1.5 1.9 1.9 U5 1.15 1.15 1.18 IV.6 V.2 V.8 VI.4 VI.4 VI.6

83a2- 17 83b13-17 83b19-20 87a38 91,18- 21 91bl-7 96b5--6 97.6-19 97.34-37 97b7-15 98a20--23

99.1-16 99.8- 10 99a15- 16 99.16--37 99.37- b7

101b39102.1 102.31-b3 103b20--39 107.3-17 107b13- 18 107b19 108b6 128a26-29 130.39 138b23-26 141b15-18 142b2--4 143a29-32

126n7 183 19n7 21 31 19n8 164n41 123 158n36 6n1 158n36 210 83, 84, 91,99, 188 212 93 28 83,91 94 94 97 109

117n2 221n21 143, 153 146-7 201 40n38 62n18 219 140nl0, 142 117n2 182 174n51 117n2 143n15

VI.6 VI.6 VI.8 VI.9 VUO VI.11

144,31-b3 144b31- 145al 146,36- bl 147b13- 14 148,25- 26 149al-3

137- 8 131nl0 181 117n2 210 117n2

165.35- 37 165b12-17 173bl-11 181b37-182a2

198 138 138 32 198

184a23- 25

183n12 177-8 193n24 166 186 191 187 187 187 204 180n6 188 180

SE 1 3 13

31 34 Phys. U 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.8 1.8 1.8 1.8 1.9 11.2

190b7-8 191,6--7 191.7- 12 191a12- 13 191a17- 27 191a27-29

11.2 11.2 11.2 11.2 II.2 11.2 lll.1

191b4-10 191b15- 16 191b27-29 192a31- 32 193b22194.12 193b26--32 193b32-33 193b34 194al-12 194.7-15 194b9 2OOb32-201a3

IV.l IV.8 V.2

209,9 214b22- 23 226,26- 29

30 19n7 30n22 30 35 31 181 40n37, 181 101n12 101n12 79n42

257 Index Locorum VnA

39-41, 212

VnA

24Sb17-19

40,49,

Vn.4 Vn.4

249.21-25 249a29-b26

232n35 40 41

26Sb17-19 299,13-17

23n14 31, 154

333a20-34

46n49

372b34373,5 373,6-16 373,16-19

34 35 35

DC 1.2 IIJ.I

GC 11.6 Mete. III.3

III.3 III.3

DA 1.1 I.l 1.1 I.l I.l I.l 1.5 11.1 11.1 11.1 II.l

n.3 n.3 11.3 n.3 11.3 nA 11.4 1I.5 11.8 n.s 11.9 11.9 11.11 1II.l0 1IJ.12

414b19-33 414b19 414b32-33 415al-11 415a11-12 415,14-23 415a23-b7 417bS-9 420a30-b4 420bl-4 421,16-20 421,17-bl 423,12-15 433b19-21

214 209 209

215 209n 209 204 193n23 104 82n46 S2n46 104 69n29 50 223, 240

Sens.

5

443b3-12

104

454bl4-23 455b32-33

72

467a6-S

96

468,9-12 468a13-17 468b28-30 469b21-22 470.19-20

6S,72 67 75 95 95

478b32-33 479b19-26 480.23-b20

95 95 101

486.5-14

80

Somn .

402,6-7 402bl-8 402b3-5 402b9-403,2 403,3-b19 403,25-b19 410a13 412.7-8 412a4-5 412b4-9 413a8-9

11.1 11.2

413a11-20 413a22-23

11.2 11.2 11.2 11.3 n.3

413a31-32 413b24-27 414.12-28 41416-14 414b16-19

51 208 213 208 209 31n23 136n7 180n6 210 209

209, 209n2 210 209, 211-12 209n 209n 211 209 209n

1 2

72

Long.

6 Juv.

1 2 3 5 6 Resp.

17 20 21

HA 1.1

258 Index Locorum 1.1 1.1

1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.2 1.4

1.4 1.6 1.6 1.6 1.12 11.1

11.1 11.1 11.1 11.12 11.15 11.17 I1I.1 111.9 I1I.11 111.16 II1.19 III.19 IY.1 IV.3 IV.5 IV.8 IV.8 IV.11 V.4

486.14487.10 486.14-b22

81 53-4, 55n4, 62n18 486.20-21 60 486.21-23 38 486b5 38,79 486b14-16 61 486b17 65n21 486b20 70 102 486b21-22 486b24-487.1 60n13 55n4, 488b29-32 68 489.19-22 71 489.23-26 67 490b10-12 93 491.14-19 55n4 79n42 491.19 493.12-16 67n27 497b6-12 62 497b1S-20 70 497b26-27 70 497b33-498.2 67 503b29-32 67 506.15 112n25 508.16 112n25 510.21-23 112n25 517.6-10 66n24 517b21-26 66n24 519b26-30 67 520b1S-19 71n33 520b25-33 69 523b27-29 64n20 112n27 527b22-24 530b31-33 68 112n27 533.28-30 534b12-15 64n20 538b8-9 103 112n27 540bl-3

VI.12 VII(VIII).l VII(VIII).1 VII(VIII).2

566b12-13 588.25-31 588b4-13 589b1S-19

64n20 73 111-12 101

PA 1.1 1.1 1.1

1.1 1.1

1.1 1.1

639.15-29 639.15-19 639.29-b3 639b5-10 640.10-19 640.34-35

1.2-4

1.4 1.4 1.4

644.12-23 644.14-16

1.4 1.4 1.5 1.5 1.5 11.1 11.1 11.1 11.1 11.1 11.1 11.2 112 11.2 112 11.2 11.3 11.3 11.4 11.7 11.7 11.8

644.22-23 644.23-27 645b6 645bS-10 645b20-28 646.13-24 646b20-22 646b30-34 647.14-21 647.14-19 647.24-33 647b29-35 648.2-7 648.4-8 648.4-5 648b2-8 650.34-35 650.2-8 651.17-18 652b23-25 653.10-12 653b35654.19

644.1~23

7n1 129n9 19n7 48n53 36n33 76 215 74 78 69 55n4, 65n21 63n19 67n26 101 71n34 55n4, 72 80 85 107n17 106n15 131 105 59 103 73 71n34 95n5 71n34 132 69 72 72 84

259 Index Locorum

11.8

653b35

11.8 11.8 11 .9 11.9

653b36 65435-9 65538-10 655312-17

11.9 11.9 11.9

655317-28 655323-34 655332

11.9 11.9

655333 655b2--4

11.9

655b2

11.9 11.9 11.9 11.9 11.10 11.12 11.13 11.14 11 .14 11.15 11 .16 11.16 I1I .1

655b4--15 655b4--5 655b8 655bll 656b26-29 657318-23 65833-10 65836-7 658b2- 7 658bl4--15 658b35-36 659b23-27 661b3--
IlI A

I1I .5 I1I.5 111.5 III.5 111.5 III.6 III.6 111.6 IV.2 IVA

669.24--32 669b8- 12 677325-35 67838-9

65n21, 83 57 102 131 131, 84 83 69 57, 65n23, 84 65n21 69, 107n17 65n21, 66n24 71 70 66 65n21 131 101 131 102 131 131 70 59 70 55n6 71 198 100 101 67 101 102 100, 102 95 71n34

IV.5 IV.5 IV.5 IY.5 IV.5 IV.5 IV.5 IY.5 IV.8 IV.8 IV.10 IV.10 IV.10 IV.10 IV.10 IV.10 IV.10 IV.ll IV.ll IV.ll IV.12 IV.12 IV.12 IVJ2 IV.12 IV.12

678331-34 679315-23 679b15 680315 68139-15 681315-28 681b28-30 681b33-34 683b28 684333-35 686324--68732 686325-28 686b2D-31 686b31-68731 68738-23 687b6 68832--4 690bl4--16 691316 691317-19 692b3-9 692b13 693b4--13 693b1D-13 693b13-14 693b26694312

100 83 56n7 55n6 112 113 71 71 56n7 100 113 100 113 72

114 55n6 70 48n52 70 102 61-2 55n6 100 48 90

695b17-19 696b2-8 696bl6-20 696b24--31

48 101 100 84 102 132

1 1 6 7

69831-7 69834 700b4--
49-50 108 50 50

1

70435-9

48

IV.13 IV.13 IV.13 IV.13 IV.13 MA

lA

260 Index Locorum 1 18 19

704b9-11 714b3- 7 714b20-23

49 70n31 49

716b5- 9 717.4-6 725.5 726bl-5 735.16-26 737.36- b4 739.18-20 741b11-15 742.18-b17 743bl8-25 745b2-9 753b35- 754.3 756.32 76la24-32 779.2-4 782.14-20 783b2-8

112n27 112n27 198 107 106 108 68 75n37 75 75 166n45 68,72 112n25 60n14 73 103 69, 103

B.1 B.2 B.2 B.2

982.1- 3 982.25-28 985blO-13 992.18-19 995b18- 24 995b26-27 996bl4-22 997.21-22 997.25-33

159 31n24 79n42 221n20 165 165 148n21 18n7 136n6, 158n38

B.3 B.3 B.3 B.3 B.3 B.3 f.

998b9- 21 998b22-28 998b23-24 999.6-14 999.13-14 999.16-23 1003.21-22

6

GA 1.2 1.2 Ll8 Ll9 ILl 11.3 11.4 11.5 11.6 11.6 11.6

lll.2 111.5 IIL11 V.l V.3 V.3 Met.

A.l A.2 AA A.9

B.l

6, 137 140n10 216 223 220n18 122, 157

f.2 f.2 f.2 f.2 f.2 f.2 f .2 f.2

1003.35- 36 1003b2-3 1003b5- 14 1003b5-6 1003b6-10 1003b8-10 1003b8 1003bl4-15

f.2 f.2 f.2

1003b16- 17 1003b17 1003b221004.2 1003b22-25 1003b32-36

f .2 f .2 f.2 f.2 f.2 f.2 f.3 f .3 6.2 6.6 6.6 6.6 6.6 6.7 6.7 6.8 6.11 6.11 6.14 6.18 6.21 6.28 6.28 6.28 6.30 £.1

1003b33- 34 1003b35-36 1004.5 1004.6-9 1005.22- 29 1005.26-27 1014.1-3 1016bl- 3 1016b1 1016b6-11 1017.22-30

1019.3 1019.11-12 1022.31-32 1022b15-18 1024.36-b3 1024b6-9 1024b9-16 1025.30-32 1025b7-13

197n30 145 117 135n5 163 125, 157 166 120, 183n 135n5 197n30 166n44 166 166, 166n43 167 168, 171 136n7 135n5 238 26n20 20n10 170 168 170n49 169 170 148n21, 204n47 16n1 220 218 142n14 19n8 79n42 215 74n35 142n12 18, 18n7 159

261 Index Locorum E.1 E.1

E.2 E.2 E.2 E.2 2 .1 2.1 2.1 2 .1 2.1 2.1 2.1

1025b3G-1026.6 1025b341026.6 1026.23-32 1026.33 1026bl4-21 1026b27-33 1028.1G--15 1028.10 1028.18-20 1028.20 1028.20-31 1028.27

2 .1 2.1 2.1 2 .1 2.1 2.3

1028.28-29 1028.29-30 1028.35-36 1028bl-2 1028b2-4 1029.20-26

2.3

1029.23-24

2.4 2.4 2.4 2.4 2.4 2.4 2.4 2 .4 2.4 2.4 2.4 2.4 2.4 2.4 2 .4 2.4

1029b14 1029bl6-18 1029b22-27 1029b22 1030.14 1030.17-27 1030.17-23 1030.17 1030.23-27 1030.25-28 1030.27-32 1030.29-b3 1030.33-34 1030b3-4 1030b8-12

31n23 209n 236 136n7 155n33 155n33 185n14 148 136n7 150 151n27 149 150, 151n26 151n28 150, 159 150 149, 153 157 180n6, 204n23 185n13, 204 189 151 154n32 152 152 152 152 149 152 156n33 160 160 116, 153 227n26 160 166n43

2.4 2.5 2.5 2.5 2.5

1030b11

2.5 2.5 2.5 2.7 2.9 2 .10 2.10 2.10 2.11 2 .11 2.12

103101- 3 1031.2-5 1031.7-11 1032b2- 5 1034.30-32 1035.2 1035bl4-22 1035bl6-18 1036.26-b3 1036b3G--32

2.12 2.12 2.16 H .2 H.2 H.2 H.2 H.2 H.3 H.3 H.4 H.4 H.6 H.6 H.6 8.1 8.1

1038.3-9 1038.18-21 1040b16

8.1 8.1 8.6

1030b18-24 1030b2G--21 1030b23-26

1042.4-5 1042b25 1043.2-7 1043.19-21 1043.29- b4 1043.34-37 1044.25-31 1044b8-20 1045.14-25 1045.14-17 1045.36- b5 1045b27-32 1045b361046.1 1046.11-13 1046.17-19

136n7 139 155 150 117n2, 155 155 156 155 166 126n7 204n47 82n45 118n3 18n6 118n3 74, 137n8, 220 74n35 143n15 166n43 143 188 136n7 182 204n47 190n19 51n57 107n17 127 74n35 140,142 169 150n24 189 190 190n19 177-8, 188

262 Index Locorum

8.6 8.6 8.6 8 .6 8.7 8.8 8 .8 8.8 8.10 L1 L1 L1 L1 L1 L1 L2

1.2 L2

1.2 L3 L3

1048a30-b9 1048.37- b4 1048b6-9 1048b8 1049.29-30 1049b12- 17 1050.21-23 1051.34 1052.31-34 1052.33-34 1052bl- 19 1052b7- 16 1052bl8-20 1052b31-32 1053b20-21 1053b22-24 1054.3-4 1054.14 1054.26-29 1054b3-6

1.4 1.4 1.4 1.8 K.l K.12 1\.4-5

1055a6-7 1055.35-38 1058.21-26 1059b31-34 1068b18- 20

1\.4 1\.4 1\ .4 1\.4 1\.4 1\.5 1\.5 1\.5 1\.5 1\.5 1\.10

1070.31-33 1070.33-b10 1070bl-2 1070b12-13 1070bl6-21 1071.2-3 1071.15-17 1071.26 1071.29-35 1071.34-35 1075.14-15

191 193 192 193 185 131 192 118n3 136n7 168 169 166n45 179 172, 173 172 141 166n43 215n9 136n7 174n51 171 61n16 38 169n48 74n35 136n6 142n14 177, 204n47, 240 183 179 136n7 180 178 185 184 178, 179 184 183, 185 51n56

M.2 M.3 M.3

1077b4-11 1077b17-30 1078.5-8

M.3 M.3 M.7 N.3

1078.14-16 1078.31-b5 1081b8-10 1090b19-20

EN 1.6 1.6

1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7

1096.17-23 1096.23-29

IV.3 V.5 V.5 V.5 V.5 V.5

1096.31-34 1096b8-14 1096bl4-16 1096b16-25 1096bI7- 18 1096b24-25 1096b26-31 1096b26-29 1096b30-31 1097.3-8 1097al6-18 1097b2 1098a7-17 1098al6-17 1102.1 1104b8-9 1106b361107.2 1123b20 1133.7-29 1133al6-18 1133b7 1133b18-23 1133bI8-20

V.5 V.ll VIL3

1133b23-26 1138.4-b14 1147a5-6

I.7

1.7 1.12 11.2 11.6

31n24 29, 239 19n7, 158 36 23n15 218n14 239

216, 217 195, 200, 201 203 197 198n38 195, 197 198 198n38 197 194-5 195 200 200 198 203 199 199 199 199 199 43 45n47 45 43 43n43, 44n46 45 5 95

263 Index Locorum VIII.1 VIII.2 VIIl.2 VlIl.3 VIIL3 VIIL3 VIIL3 VIIL3 VIllA VIII .4 VIIl.6 X.1 X.4 X.5 X.8

1155b13- 16 1155b17-27 1156a3-5 1156a6-8 1156a1G-16 1156al6-17 1156b12-17 1156b331157a4 1157a25- 32 1157a32 1158b5- 11 1174b31- 33 1175b361176a1 1178b31-32

234 231 181, 232 231 232 232 233 233 235 232n32 234 199 200 200 199

MM 11.11

1209a19- 35

234n37

1216a33- 37 1217b25-34 1218al- 9 1218b16-24 1235b24-30 1235b27-29 1235b301236a7

230n30 201 216 195-6 225 228

EE L5 L8 L8 L8 VII.2 VII.2 VII.2

226

VII.2 VII.2 VIL2 VII.2 VII.2 VII.2 VII.2 VII.2 VII.2 VII.2 VII.10 VIL13 VII .15 VII.15 Pol. L9 L9 L9 LlO 11.5 IILl IILl IILl IILl IILl IV.1 V.3

1235b331236a2 1236a5-7 1236a15-33 1236a15-22 1236a21-22 1236a23-25 1236b15- 17 1236b17-26 1238a35- 38 1238b13- 14 1243b30- 35 1246a26-31 1249a21-b25 1249b9- 13

1257a6- 18 1257al4-17 1257b35 1258a38-b8 1264b4-6 1275a30- 33 1275a33-34 1275a34-b5 1275b5-6 1275b18-19 1288b12 1302b331303a2

229 226 227 117 144 237n41 229 227 229 230 45n47 43n42 204 144

41- 2 42 47 47 5 222 101n12 216, 221 222 222 101n12 59n12

GENERAL INDEX

abstraction 30, 239; addition and 31, 154, 178, 188, 240; in biology 82; from change 193-4; degrees of 15, 38 (see also semi-abstraction); among friendships 231; general cause and 47, 51; genus-species chain vs., 87; inappropriate 47, 105; mathematical 10, 29, 154; outside mathematics 30; other views of 30021; per se/qua and 29, 39, 51; pure 14; among souls 209; from substances 154 Academy 5- 6, 13 accident 8; good as 203; per se 19; science of 143,151, 155n33 activity 193 actuali ty, absence of analogy among kinds of 180. See also potentiality adaptation of terms to subject-genus 26, 90, 92 addition, ontological 224, 235. See also abstraction; cumulation affection (mii17)f'aj, 79, 83, 85 Alexander Aphrodisiensis 138n9, 154, 194n26 alternating proportion, theorem of 24-9. Sec also mathematics; universal

ambiguity. See homonymy analogy 10,53-115,239; absence in Cat. and Top. 77; biological demonstration and 89-115; common cause among 88,95- 7, 101- 8; continuous 200; demarcation of genus and 56- 8,91, 183; flexibility and fixity in 60, 67-8, 86, 183; foca lity and 12,175,189, 240 (sec also focality); function in 10 (see also function); of goods 200-3; between greatest kinds 61; in imperceptible cases 71; in lower genera 239; other views of 56-9 (sec also realist view; relativist view); place in speciesgenus-analogy and wholes-parts systems 77-86, 108; relative position and 69; role in APo 89-99; semiabstraction and 128; among subjectgenera 26-8, 88; ubiquity in biological works 53, 53n1; among whole animals 60. See also Being; common cause; good; potentiality; soul appetite 50 application argument 19, 35, 106; adaptation and 26, 106; metabasis and 23; mixed science and 33 Aquinas, Thomas 12

266 General Index artefact 186

ascidian 113 auditory passages 100 autonomy 8, 33 axiom 9, 26, 91

composition of parts 80-2, 108. See also wholes-parts system conclusion, demonstrative 18 connatural spirit 50 connection, techniques of 4, 239-42.

See also analogy; cumulation; focality Cook Wilson, J. 217

babbling 138 balding 103 Balme, D. 55, 92

core science 144-5; of Being 155-7,

barter 42 Being: difficulties in interpreting the science of 136; and foeality 12, 142-3; genus of 136-43; internal

coupled terms 156- 7 crafts, analogy among the 200

unity of 169; One and 166-71, 174; prior to genesis 76. See also demonstration, in the science of

Being; metaphysics Berti, E. 195 bifocality 166, 190n19. See also focality

171; extended and 155,189, 194 (see also extended science)

cumulation 13,214-24,240-1; analogy and 13, 241; focality and 13, 207, 240-1; of friendship 232; of god 235-9; at high levels of abstraction 241; means and ends and 207; scala naturae and 207; of soul 214-24

biological works, organization of

dating of EN and EE 225

48n51, 81, 108, 129 {3ios. Sec way of life blood 69, 71, 100, 103, 107 blood-vessel 71, 100 bone 69, 83, 93 brain 71

defence, parts for 131 definition: in accordance with the name 211; empty 223; in Euclid 27;

breast 67 bronze triangle 239

capitalism 47 carnivore 131 cartilage. Sec bone categories: analogy among 175, 182;

among goods 202-4; One and 171; in the science of Being 141-2,

144--65, 183 coextension. See extension; noocoextension commensurability 15, 38, 40-4, 46n49,

49 common cause 49-50

generic 180, 191, 209-12, 221, 223, 232; matter in the 213, 224; nominal and real 182; of relative terms 181;

unity of 130, 140 definitional inclusion 117, 240; in accidental compounds 151-3; with ends and means 195; in focal conclusions 125; and homonymy

120; potential 215, 222, 233; problems with 145 demonstration 7, 15, 34; accidental

22; analogy in 90-2, 100; in the biological works 90; conclusions

of 18, 210; Euclidean 34; of focal facts 123, 196 (see also linguistic predication); and focality 195; at general and specific levels 25-8; of natural facts 123, 196 (see also

267 General Index natural predication); parts of 34; in the science of Being 136, 158, 164 difference and otherness 78 Dionysius 210 division: dichotomous 74, 220; genus as subject to 9n7, 11, 21; by multiple differentiae 74. See also species-genus-analogy system doctor. See medicine as example dualizer lID, 113 dunamis. See potentiality ear 131

eggshell 72 embedded terms 32-6 embryology 58, 75 ends 230. See also means and ends essence 151-5 Euclid 24-9, 33-7 eudaimonia 129, 199 evolution, theory of 130 exchange 43-5 explanation: asymmetry in 97; external and internal 130-1; flexibility in 114; generic and specific 105 (see also demonstration, at general and specific levels). See also middle term extended science 144-6, 156-7; of Being 165, 171. See also core science extension 158; of animal parts 61; in demonstration 91; as part of definition 98. See also non-coextension eye 131 familiarity (yvwP'fWV) 108, 191, 210 feather 69, 102 Ferejohn, M. 134 figures, series of 214. See also series; soul flesh 67

focality, 11, 116-74; analogy and 12, 176, 193, 200, 205, 239 (see also analogy); in biology 129; demonstrations and 122; in EE 225-31; in EN 197, 231; homonymy and 120, 240; perfective series and 208; predications in 159-64; relation of, broken 192; relations of 118, 145, 197; in the science of Being 12, 134-74, 177; subordinate science and 135; transitivity of 125, 157; as two-step process 144; various cases of 44, 148, 194, 230-1. See also bifocality; normal science food 132 formal cause 98 formalist view of analogy. See relativist view Form Numbers 217 form as substrate 185. See also substrate Frede, M. 161, 236 friendship 224-35; accidental 232; complete 234; non-cumulative features of 233; objects of 225, 231 function(s): analogy among 72-4,213; general and specific 44; similarity, difference, and 82 functionalist view of analogy. See realist view general account. See definition, generic Generation of Animals, role of 48n5l. See also biological works generation of parts, order of 75 genus: ambiguity in term 54-5, 78; Aristotelian vs. Platonic 216-20; of Being, see Being, genus of; and commensurability 38; demarcation of analogy and, see analogy,

268 General Index demarcation of genus and; and difference 79, 142; of series 215-16; and species 138, 220. Sec also division; focality; subject-genus gill 101 Gill, M.L. 193 god 204, 235-9 good 194-206; " accident 203; apparent 225-9; and categories 204-5; foeality of 195, 206; god as focus of 204; independence of 231; potentiality and 204 Gotthelf. A . 56 greatest kind (}liyWTO/.l yivos) 61 hair 69-70, 102, 131 halo 34 happiness. Sec eudaimonia health 157 heap 183; Being as 138-40; unity of 171 hearing 104 heart 71 homonymy 5, 40, 94, 160, 195-{;, 210-12; of Being 148, 201; in definitions 40, 181, 212, 232; and foeality 119-20, 134; of good 201; of potentiality 190 honour 199 hoof 69-70 horn 107 hylomorphism 80-6; and abstraction 47 ichor 69 incidental. Sec accident incommensurable number 217 incomplete abstraction. See semiabstraction induction 188, 191 instrumental parts of locomotion 48

intelligence 73, 103 in terdisciplinarity 130, 145 internal unity 168, 172-3 interpretation of Aristotle's corp us as unity 4 irrational quantities 27 joint 50 kind-crossing. See metabasis knowledge, relational 5-6 Kullmann, W. 56 land animal 131 linguistic predication 118,124. See a/so natural predication locomotion, animal 39, 47-8, 73; abstraction in 47; four-point theory of 48 longevity 94-7, 211; and analogy 97 lung 101 manufactured goods 39 many 173. See a/so One material cause 98 mathematics, universal 10, 237-8. See also alternating proportion matter: definition in terms of 213; genus as 58, 74; logical vs. physical 76; as substrate 185. Sec also potentiality me,ming 98, 121 means and ends 205, 237; as focally related 196-7 measure 166, 172-4; and essence 172 medicine as example 11, 119, 144 metabasis 9-10, 21-2, 32-3, 87; and application argument 23; between closely related genera 22-4; and scala naturae 110-14 metaphor 177, 184

269 General Index metaphysics: general 236; as normal science 161-2; and predication relations 163. See also Being

middle term 94--5, 159 mind . See nous minor term, focus as 126

mixed science 31-7 money 47 more and less 58, 69, 79, 84, 101-2; and scala naturae 110 mouth 72 Muskens, G.L 56

nail 70 names 117; generic 24, 32; lack of 68,

84, 93, 109 natural dependence 150 natural predication 159,162-4; identity

of focal and 164 necessity 8, 20, 157, 159 need lxPEia) 43- 5 non-coextension of terms 107 non-contradiction, principle of 237- 8. See also axiom; principle non-substance 145, 156. See also accident; category; substance normal science 118-19, 144. See also foeality normativity 109, 113

nous 200, 209, 212 offices, indefinite 222 One 166- 74; categories of 169 (see also categories); as divisible 173n51; internal and relational 168, 171; measure as essence of 172 (see also measure); science of 166. See also Being opposites 166 orthodox view of analogy. See realist view

otherness 78; and animal composition

81 Owen, G.E.L 116, 134, 175, 190, 194 Owens, j. 176 packing 36 paronymy 8n5, 127n8, 170 particulars 7 parts of animals: corresponding to whole animals 61, 76, 84; as essential 100; order of generation of

75 Patzig, G. 236 Pellegrin, P. 55, 63- 6, 73-4, 92, 110 perfective series. See series, perfective per se 4, 8, 11, 41, 45, 81, 188; accident 19; goods 198; predication and abstraction 15, 31; predication and analogy 86-7; predication and confusion of terms 42; predication

and focality 119-22, 124, 146-8, 192, 196; predication and metabasis 22-3; predication and qua 40,

90, 98, 107, 135; predication and subordinate science 135; specific,

predications 16-17, 149, 154, 161; tension between qua and 32, 37, 53, 109, 128, 239. See also qua perversion 228-9, 235

Plato 5,136,140,143,177,195- 6,200, 202, 205, 218-19, 242 pleasure 199, 226-32 Posterior Anaiytics, importance of 4 potentiality 177-94; analogy and 191,

205; compared with good 204; different kinds of 178; focality and 191; in persistence and change 190; as a principle 177, 180; and the science of Being 194 pounce. See bone practical syllogism 50

270 General Index practical wisdom 199 precausal stage of inquiry 108 predicables, four 147 predication, vs. predicate 161. See also linguistic predication; natural predication, per Sf, qu.a principle 7, 80, 159, 178-9 priority 150, 218, 220; in friendship series 232; natural 183, 185, 215, 220, 223, 233; ontological 161-2, 232 Proclus 25n18 proper (OiKEtOV) 41

proportional analogy 43. See also alternating proportion qua 4, 8, 81, 86; abstraction and 29-30; analogy and 11, 86; locality and 122, 126; metabasis and 22-3; tension between per se and 32, 37, 53, 109, 128, 239. See also per se

realist view of analogy 56, 92; in potentiality 177-8, 186; resolu tion with relativists 98. See also relativist view recursive unification 13n13. See also cumulation relational unity 168, 171 relative terms, definition of 181 relativist view of analogy 57, 59, 82, 92, 177, 179; resolution with realists 98. See also Balme; Pellegrin; realist view relevance criterion, focal relation as 125 rest, point of 50 restriction of demonstrative terms 92. See also adaptation Robinson, D. 195 root 72

Same 168, 171 scala naturae 109-15, 240; analogy and 58, 111; lack 01 explanatory power Ill, 114; more and less and 112, 115; psychological capacities and 112 scales 69-70, 102 Selachia 132 self-predication 218-19 semen 107 semi-abstraction 10, 14, 38, 51-2, 158, 183, 241; and core and extended science 129; and subject genus 51-2. See also abstraction sensation 131 separability 185, 211 series: first member of 220; and focality 207-8, 214; 01 locality, an~logy, and cumulation 241; of Form Numbers 217; genus of 216, 221; kinds 01 235; limiting the 224; perfective 207-8, 222, 235; species in 221; 01 substances 237 sight 200 Similar 168, 171 similarity 208, 224, 233. See also more and less sleep 73 snub 154, 156; ambiguities of 38; and bandy 32; distinct from accidental predication 155; and focality 144; and mathematical abstraction 31; and mixed science 35; and per se 31 soul 208-24; analogical account of 208, 210-14; compared with figures 214-15; cumulative account of 208, 214-24; defined by actualiry and potentiality 212; as primarily intellectual 213; problems concerning 208; relations among faculties of 223;

................................

.,

271 General Index

serial order of 214; traditional concept of 213; universal account of 208. See also series species-genus-analogy (SGA) system 77-86, 108; different from dichotomy 78; hierarchy of 77; reasons for the system 86; relation to wholes-parts (WP) system 81-2 Speusippus 5, 239 sponges 113 subject-genus, 14, 20-1, 30, 239; absence of species in 54; and analogy 10; core and extended 128; different from divisionary genus 54, 118; different from substrate 127; and explanation 7; identity conditions of 14, 20-1; Euclid and 25; isolation of 3, 9; multiplicity of, in mixed science 33; principles in 26, 50; problems with 3. See also genus subordinate science 9, 37. See also mixed sciences substance 151, 170, 184. See also Being; metaphysics; non-substance substrate 149, 185-7; form and matter as 185; of non -substance 150; pre-existing and coexisting 186 subtraction. See abstraction UlJVn-At:'iV 198 superordinate science. See subordinate science; mixed science syllogistic 107. See also demonstration talons 69 taxonomy 55, 57 teeth 68 teleology, universal 133 theology 235-9. See also god theorem 211, 233. See also demonstration, conclusions of third-man argument 140

Ti. E(rn. See what-is-it

Timaeus 133 touch 104 trade, retail 42, 47 traditional language 78, 107 traditional view of analogy. See realist view transitivity. See focality, transitivity of trunk 70 underlying thing. See substrate universal: and cause 7, 97; and focality 120; and qua 17; science 3, 6, 7, 13 unity: accidental 170; within greatest kind 61; internal and relational 168, 172- 3. See also One universal predication 159, 162, 164. See also nat ural predication; linguistic predication usury 47 value 41, 200. See also exchange; trade virtue 109; friendship 228-30, 231-5 water animals 131 way of life (/3io,) 48, l30 wealth 42; and abstraction 43 what-is-it (Ti. fun) 147, 149 whole animals 60. See also parts of animals wholes-parts system 80, 107; and cause 86; and function 81; and position 81; relation to species-genus-analogy sys tem 81. See also species-genusanalogy system womb 68,72 Woods, M. 218

PHOENIX SUPPLEMENTARY VOLUMES

1 Studies in Honour of Gilbert Norwood edited by Mary E. White 2 ArbitH of Elegance: A Study of the Life and Works of C. Petronius Gilbert Bagnani

3 Sop hocles the Playwright S.M. Adams 4 A Greek Critic: Demetrius on Style C,M.A. Grube

5 Coastal Demes of Attica: A Study of the Policies of Kleisthcncs C.W.]. Eliot 6 Eros and Psyche: Studies in Plato, Piotinu5, and Origen John M. Rist 7 Pythagoras and Early Pythagorean ism l.A. Philip

8 Plato's Psychology T.M. Robinson 9 Greek Fortifications F.E. Winter 10 Comparative Studies in Republican Latin Imagery Elaine Fantham 11 The Orators in Cicero's 'Brutus'; Prosopography and Chronology G.V. Sumner 12 'Caput' and C%nate: Towards a History of Latc Roman Taxation Walter GoHart

13 A Concordance to the Works of Amrnianus Marcellinus Geoffrey Archbold 14 Faffax opus: Poet and Reader in the Elegies of Propertius John Warden

15 Pindar's 'Olympian One': A Commentary Douglas E. Gerber 16 Greek and Roman Mechanical Water-Lifting Devices: The History of a Technology John Peter Oleson

17 The Manuscript Tradition of Propertius James L. Butrica 18 Pannenides of Elea Fragments: A Text and Translation with an Introduction edited by David Gallop

19 The Phonological Interpretation of Ancient Greek: A Pandialectal Analysis Vit Bubenfk

20 Studies in the Textual Tradition o/Terence John N. Grant 21 The Nature

0/ Early Greek Lyric: Three Preliminary Studies

R.t. Fowler

22 Heraclitus Fragments: A Text and Translation with a Commentary edited by T.M. Robinson

23 Th e Historical Method of Herodotus Donald Lateiner 24 Near Eastern Royalty and Rome, 100-30 Be Richard D. Sullivan

25 The Mind of Aristotle: A Study in Philoso phical Growth John M. Rist 26 Trials in the Late Roman Republic, 149 BC to 50 BC Michael Alexander

27 Monumental Tomb s of the Helleni stic Age: A Study of Selected Tomb s from the Pre-C lassica l to the Early Imperial Era Janos Fedak 28 The Local Magistrates of Roman Spain Leonard A. Curchin 29 Empedocles The Poem of Empedocles: A Text and Tran slation with an Introduction edited by Brad Inwood 30 Xenophanes of Colophon Fragments: A Text and Translation with a Commentary J.H. Lesher

31 Festivals and Legends: The Formation of Greek Cities in the Light of Public Ritual Noel Robertson 32 Reading and Variant in Petronius: Studies in the French Humanists and Their Manuscript Sources Wade Richardson 33 Th e Excavations of San Giovanni di Ruoti, Volume 1 Alastair M. Small and Robert J. Buck

34 Catullus Edited with a Textual and Interpretative Commentary by D.ES. Thomson

35 The Excavations 0/ San Giovanni di Ruoti, Volume 2: The Small Finds c.J . Simpson, with contributions by R. Reece and

J.J. Rossiter

36 The Atomists: Leucippus and Democritus Fragments: A Text and Translation with a Commentary by c.C.W. Taylor 37 Imagination of a Monarchy: Studies in Ptolemaic Propaganda KA Hazzard 38 Aristotle's Theory of the Unity of Science Malcolm Wilson