Aristotle’s Theory of the Unity of Science 0802047963, 9780802047960

Table of contents :
Title......Page 3
Contents......Page 5
Acknowledgments......Page 7
Abbreviations......Page 9
Introduction......Page 11
1. Genus Abstraction and Commensurability......Page 24
2. Analogy in Aristotles Biology......Page 63
3. Analogy and Demonstration......Page 99
4. The Structure of Focality......Page 126
5. Metaphysical Focality......Page 144
6. Mixed Uses of Analogy and Focality......Page 185
7. Cumulation......Page 217
Bibliography......Page 253
Index Locorum......Page 265
General Index......Page 275
Backmatter......Page 283

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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. M A L C O L M W I L S O N 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 xxxvui Tome supplementaire xxxvm

MALCOLM WILSON

Aristotle's Theory of the Unity of Science

UNIVERSITY OF TORONTO PRESS Toronto Buffalo London

www.utppublishing.com (c) 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 supplemental, 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. I. Title. II. Series: Phoenix. Supplementary volume (Toronto, Ont.) ; 38. B485.W54 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 (BPIDP).

CONTENTS

ACKNOWLEDGMENTS ABBREVIATIONS

INTRODUCTION

Vll

ix

3

CHAPTER 1: GENUS, ABSTRACTION, AND COMMENSURABILITY 14 Demarcating the Genus 15 Abstraction 29 1. Speed of Change 39 2. Value 41 3. Animal Locomotion 47 CHAPTER 2: ANALOGY IN ARISTOTLE'S BIOLOGY 53 Problems with Analogy 53 1. Fixity of Analogy 60 2. Difficult Cases 67 3. Analogues and the More and Less 69 4. Analogues and Position 69 5. Analogy of Function 72 6. Genus as Matter 74 A Solution 77 A Challenging Case 83 Analogy and Abstraction 86

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 Per Sc 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 of 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

BIBLIOGRAPHY INDEX

243

L O C O R U M 255

GENERAL

INDEX 265

175

ACKNOWLEDGMENTS

My first thanks go to my teachers at Berkeley, Tony 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 material published in 'Analogy in Aristotle's Biology,' Ancient Philosophy 17 (1997).

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ABBREVIATIONS

Works of Aristotle APo Posterior Analytics APr Prior Analytics Cat. Categories DA de Anima DC de Caelo DI de Interpretatione EE Eudemian Ethics EN Nicomachean Ethics GA Generation of Animals GC Generation and Corruption HA History of Animals 1A Progression of Animals Juv. On Youth, Old Age, Life and Death Long. On Length and Shortness of Life MA Movement of Animals Met. Metaphysics Mete. Meteorologica MMagna Moralia PA Parts of Animals Phys. Physics PN Parva Naturalia Pol. Politics Resp. Respiration SE Sophistical Refutations Sens. Sense and Sensibilia Somn. de Somno Top. 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

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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. I 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, focality, and cumulation, of which the last three are the special concern of this book. I intend to study these techniques both at a specific and a general level. I 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 fundamental 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 perform 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 fully 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 so 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 that 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.ll 1138a4-b!4). Similarly, Plato's universalization of virtue, which is manifested in the Republic's inclusion of women in the leadership of the state (451d-e), prompts Aristotle to distinguish between men's and women's tasks and therefore between their virtues (Pol. II.5 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. In his later work, Plato studied a second form of relational knowledge. In 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 Forms 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. In order to know anything, therefore, one must know everything.1 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 11.13 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 common, the less one retains of the particular kinds. And yet what a thing is specifically 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.2 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.I, where Aristotle draws the distinction between the specialized expert and the generally 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. 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.5 When terms are so related, they are said to be per se (naO1 avro) or essentially related. Only essentially related terms may be joined in a demonstrative premiss, and a string of such premisses will 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 •fi (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 modern 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 characteristic form. 4 These issues will be discussed in greater detail in chapter 1 below. 5 In relating terms within definitions Aristotle allows for some paronymy, i.e., 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 /xera/3acri? 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.8 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 (i.e., 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, focality, and cumulation operate. Analogy, strictly speaking, is a proportional relationship between four terms (A is to B as C is to D), 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.9 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. 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 observation, 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 irpos tv \fy6/j.fvov 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 (6v}. 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 (owi'a). 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 term (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.'11 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 theologiae I.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.13 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 focality, 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.'

1

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 (aaipe ee£r7? virap^L 8wajuei TO TrpOTepou), 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 bvva.fj.ti that this containment is not explicit definitional containment. This is also clear from the examples: the 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 least in these examples. The prior member can exist independently of the posterior, but the posterior cannot exist without the prior (415al-ll). 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 (cf. PA I.I 640a34—35). Nutrition, therefore, is not present in the essence of sensation, but is necessitated by it. In the geometrical 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 the general account of the series, for Aristotle says, '[Tjhere might be a common

9 Cf. Met. 1.2 1054a3^1, where the triangle is the unit measure of rectilinear figures.

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 ££ 1.8 121831-9, EN 1.6 1096al7-23, and Met. B.3 999a6-14,10 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.l 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 (yupicnov} 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 double11 ... 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 1096al7-23 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 context 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 do-uju/SAryrot, 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.'12 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; cf. 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 them.13 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 posterior, and not just among Form numbers. 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. 1019all-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/ 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 Aristotelian metaphysical framework for the argument we need only change the meaning of yupiffTOv 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, 860all-21) identifies a use of ytopifav meaning 'ratione et notione distinguere/ used principally for the function that the differentia discharges: TOV 18101; TTJ? ovcrias (KOLOTOV Koyov TOLLS TTfpl e/caoToy ouceuus 8ia$opats %0a/^ey (Top. 1.18 108b6). According to this use XOO/JIOTOZ; 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 (rov irpwrov Trportpov), 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 (cf. A. 11 1019a3ff.). 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. 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. 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. Z.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 Cherniss 1944, 513ff. 18 For these characteristics of a Platonic genus, see Met. B.3 999al6-23. 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 soul.20 Posterior members are not TTOLO. 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. 1 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.l 1275a34-b2 Aristotle discusses the definition of the citizen: But we must not forget that things of which the underlying things (uTTOKei'jueya) differ in kind (TOJ ei6et), one of them being first, another second, another third, have, when regarded in this relation (17 rotaura), 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 (77 roiavra.}, 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 (juaAicrr' 1275a33-34): 20 Cf. Met. A.9 992al8-19 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 (e£ou