How Aristotle Gets By In Metaphysics Zeta (Oxford Aristotle Studies Series) [1 ed.] 9780199664016, 0199664013

Table of contents :
Cover
Contents
Introduction
1 An Oblique Approach to Substance
2 Some Alien Presences
3 Some Unexpected Absences
Part One: The Shape of Zeta
1 The Hitch-Hiker’s Guide to Metaphysics Zeta
The Approach to Substance in Zeta
1 Metaphysics Zeta 1: A Minimum Metaphysical Theory
2 The Definition of Substance: The Agenda of Zeta, and a First Look at Levels
The Three Segments of Zeta: A Bird’s-Eye View
3 Substance and Subjects
4 Substance and Essence
5 Substance and Universals
The Anti-Platonism of Zeta, and Some Other Participants in the Debate
6 A Place for Polemics
7 Expanding the Dramatis Personae
Two Constraints on the Account of Substance? Levels and Non-Linearity
8 Levels
9 Non-Linearity: Inaccessibility and the Common Conclusion Assumption
10 The Logic of Non-Linearity
Some Alternative Argumentative Strategies
11 “Mapping” the Old Onto The New, and A Use For Abductive Argument
Part Two: Substance as Subject
2 Subjects in Metaphysics Zeta 3
1 Sources of the Received View: Aristotle’s Categories, and the Early Philosophers of Nature
2 Aristotle’s Target in Zeta 3
3 The Distribution of “Received” and “Partisan” in Zeta 3; On “Stripping Away”
4 The Shift from “Received” to “Partisan”: the Cross-Theoretical Identification Between the Result of Stripping Away and Matter
5 The Trouble with Matter
6 Bare Substrates and Bare Substrate Ontology
7 The Homonymy of Matter, and Some Difficulties for Metaphysical Predication
8 Conclusion
Part Three: Substance as Essence
3 A Start on Essence in Metaphysics Zeta 4
1 “How (Informed) People Speak” About Essence: Two Points of Contact with the Tradition
2 Beyond Received Views: Partisan Developments
3 How to Talk About Essence: Ownership versus Content
4 A First Approach, Conducted Logik(omitted)s: Essence and “What a Thing is per se”
5 A Second Approach to Essence: the Connection with Definition
6 Does a Compound of a Substance with an Accident have an Essence?: Essence and the Thisness Test
7 Two Conditions on Definition and Essence: Unity and Primacy
8 Grades of Being, of Essence, and of Definition
Appendix: Greek Hoper and the Pseudo-Cleft Constructions in English
4 Sameness, Substitution, and Essence (I): Zeta 5, the SE, and “A Nose by Any Other Name”
The Puzzles of Essence, and an Apparent Discrepancy
1 The Three Puzzles in Zeta 5
2 What Aristotle Knows About Snub in the SE
How to Make Room for the Puzzles in Zeta 5
3 The No-Solution Solution
4 Accidents and Compounds
5 Contextual Definition
6 Making Room for the Puzzles in Zeta 5: the Issue of Validity
Back to the SE
7 Double Trouble
8 Saying the Same Thing Again Again
Sameness and Substitution
9 The Puzzles, Sameness, and Definition
10 The Puzzles and Some Principles of Sameness
11 Sameness and Definition: Substitution and the Extended Sameness Test
The Zeta 5 Puzzles Revisited, and a Defence of Babbling
12 The Remaining Strategy
13 A Nose By Any Other Name: Substitution and Reformulation in the Three Puzzles
14 In Defence of Babbling
Afterword: Reservations and Retractions
15 Does Aristotle’s Argument Hit Too Wide a Target?
16 Does the Argument Hit No Target At All?
17 Systematic Considerations
5 Sameness, Substitution, and Essence (II): The SE, and the Pale Man Argument from Zeta 6
Some Background Ideas
1 Aristotle’s Hierarchy of Essences, and “Things that are the Same as Their Essences”
The Pale Man Argument
2 Things that are Not (Essentially) the Same as Their Essences: the Pale Man Argument
3 So Many Arguments, So Many Ways To Go Wrong
Referential Opacity and the Pale Man Argument
4 Referential Opacity, and the Fallacy of Accident
5 From the Fallacy of Accident to the Non-Sameness Result: the Supporting Argument
Referential Opacity and the Theory of Essence
6 “Under a Description”
7 Ownership versus Content Again
8 Composite Essences and Their Owners
9 Conclusion
6 Plato as Friend: Is There Room for Plato in an Aristotelian Theory of Essence?
Purity in the Engagement with Plato
1 The Basic Argument for Sameness
2 Plato and the Elaboration of the Basic Argument
“Severance”: How Platonic Separation is not a Target
3 “Severance” and Its Consequences: 1031b3–11
4 A Fresh Argument for Identity: Severance and a Principle From the Theory of Izzing and Having
Goodbye to Severance, and in Defence of Uniformity
5 The Applications of Uniformity: Fallacy, or True Platonic Doctrine?
6 Fallacy Again, or More True Doctrine?
7 Aristotle on How Plato’s Forms are Inessential to His Argument
7 Substance as Essence: The Shift to “Partisan” Mode in Zeta 10 and 11
1 Zeta 10 and the Transition to “Partisan” Mode
2 A Partisan Question in Zeta 11
3 On How Aristotle Manages the Shift from the Tradition to the Partisan Point of View (i): The Full-Expansion Condition on Definition, and the Drive to Form as Primary Substance?
4 On How to Manage the Shift from the Tradition to the Partisan Point of View (ii): The Full-Expansion Condition on Definition, and an Isomorphism Between Theories?
5 Some Conclusions
Part Four: Substance as Universal
8 Substance and Universals (I): Plato as Foe: Setting the Stage in Zeta 13
1 The Programme of Zeta 13
2 The Platonic View of Universals in Zeta 13–16
“No Universal is a Substance”
3 Zeta 13, 1038b8–15: The Primary Argument
4 Does Aristotle Play Fair with Plato in the Primary Argument?: The Primary Argument and the Argument of Zeta 6
5 The Limits of the Primary Argument
6 An Ad Hominem Objection to Aristotle: the Problem of Friendly Fire
7 Zeta 13, 1038b16–23: A Reprise of the Primary Argument
8 Zeta 13, 1038b15–16: On Substance and Predication
9 Zeta 13, 1038b34–1039a3: Universals and the This–Such Distinction
“No Substance can have Actual Substance as Its Parts”
10 Zeta 13, 1038b23–29, 29–30: A Substance and Its Parts
11 The Problem of Friendly Fire Again
12 Some General Results, 1038b30–34
13 Lines, Numbers, and Democritean Atoms: 1039a3–14
14 The Closing Dilemma of Zeta 13: More on the Structure of Universals, 1039a14–23
Individuals and Their Kinds: Aristotle’s Alternative to Plato
15 A Closer Look at Kinds
16 Individual and Kinds, and How the Form is Predicated of the Matter: (i) An Account of Statement Predication
17 Individuals and Kinds, and How the Form is Predicated of the Matter: (ii) The Metaphysical Analysis of Kinds
18 An Injection of Theory
19 Some Pluses and Minuses
Appendix: Mutual Exclusivity and Some Versions of Compatibility
9 Substance and Universals (II): Plato on Genus, Species, and Differentia
1 The Assumptions that Make Plato Vulnerable
2 Aristotle’s Dilemma
3 “The Genus is Numerically the Same in the Different Species”
4 “The Genus is Not Numerically the Same in the Different Species”
5 Two Final Negative Consequences
10 Substance and Universals (III): Zeta 15 and 16, and Plato’s Fundamental Mistake
1 “Received” and “Partisan” Mode in Zeta 15
2 An Aristotelian Condition on Definition?
3 The Revised Aristotelian Condition
4 A Comment on Aristotle’s Silence, and the Constructive Dilemma (CD) Strategy Revisited
5 The Critique Continued in Zeta 16
6 A Final Jab at Plato, and a Summary of Conclusions in the Segment
Appendix: Definition, Substance, and Universals: A Puzzle, and Some Speculative Conclusions
Part Five: Back to the Definition of Substance: The End-Game
11 The Posterior Analytics, and a Fresh Approach to Defining Substance
1 The Search for Substance: Are We There Yet?
2 Substance as a Cause
3 From the An. Po. to the Metaphysics
4 Some Questions of Fit
5 On Why Aristotle Does Not Mean for the Fit to be Exact
6 Causes and the Definition of Substance
7 Conclusion
12 Aristotle on the Positive Contributions of Zeta
1 The Retrospective in Eta 1
2 A Closing Note About Levels
Bibliography
Index
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B
C
D
E
F
G
H
I
K
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P
Q
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Z
Index Locorum

Citation preview

How Aristotle gets by in Metaphysics Zeta

Mosaic by Ralph Carlin Flewelling, from the Hoose Library of Philosophy, University of Southern California. Photograph by Dietmar Quistorf.

“WITH A LITTLE HELP FROM HIS FRIENDS”

OXFORD ARISTOTLE STUDIES General Editors Julia Annas and Lindsay Judson also published in the series The Powers of Aristotle’s Soul Thomas Kjeller Johansen Aristotle on the Apparent Good Perception, Phantasia, Thought, and Desire Jessica Moss Teleology, First Principles, and Scientific Method in Aristotle’s Biology Allan Gotthelf Priority in Aristotle’s Metaphysics Michail Peramatzis Doing and Being An Interpretation of Aristotle’s Metaphysics Theta Jonathan Beere Space, Time, Matter, and Form Essays on Aristotle’s Physics David Bostock Aristotle on Meaning and Essence David Charles Time for Aristotle Ursula Coope Aristotle on Teleology Monte Ransome Johnson On Location Aristotle’s Concepts of Place Benjamin Morison Order in Multiplicity Homonymy in the Philosophy of Aristotle Christopher Shields Aristotle’s Theory of Substance The Categories and Metaphysics Zeta Michael V. Wedin Aristotle’s De Interpretatione Contradiction and Dialectic C. W. A. Whitaker

How Aristotle gets by in Metaphysics Zeta Frank A. Lewis

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Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Frank A. Lewis 2013 The moral rights of the author have been asserted First Edition published in 2013 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available ISBN 978–0–19–966401–6 Printed in Great Britain by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.

Preface Aristotle’s Metaphysics Book Zeta is widely regarded as the text in which he presents the details of his fully-developed theory of “substance”—his account of the basic entities on which the reality of things in the sublunary world must be based. In line with this, earlier writers have been interested most of all in the “bottom line”—the views Aristotle ends up with in his own formal, “official” account of substance, in which are featured the distinctive Aristotelian concepts of matter, (Aristotelian) form, and form–matter compounds (these last include the “middling-sized objects” of our ordinary experience). Examples of this approach include my Substance and Predication in Aristotle (Cambridge University Press, 1991). This “full throttle”, “Aristotle’s developed theory”, approach faces a significant obstacle that commentators have increasingly come to appreciate. The obstacle is that fully two-thirds of Zeta is devoted not to Aristotle’s own theory, but to the views of others—where these “others” include not only the likes of Democritus and Socrates the Younger, for example, in cameo appearances, but also to a significant extent one or another of Aristotle’s own other selves in the Organon.1 In the texts that make up the Organon, famously, the notions of form and matter distinctive of Aristotle’s most developed theory in Zeta do not appear; at the same time, these texts represent a body of work that has a great deal in common with the work of Aristotle’s contemporaries above all in Plato’s Academy. Unsurprisingly, then, the most prominent of the alien presences in Zeta is that of Plato himself. Predictably, Plato frequently appears as a target in Aristotle’s discussion. At other times, less expectedly, Plato is friend, not foe, and is co-opted as spokesman for views that mutatis mutandis Aristotle himself can readily accept. Why does Aristotle suppress so many of the details of his own “partisan” theory, and devote so much space to the views of Plato and others, or one of his own other selves in other texts? Aristotle’s discussion of views that may not have a place in his own “official” theory—at least, not without significant revision—is part of the phenomenon of the different levels present in Aristotle’s work, and especially notable in Zeta. Of the two levels, the one is devoted to the official Aristotelian theory, including the distinctive notions of (Aristotelian) form and matter, and the other to various “received” views, even the received informed views of others and of his own other selves, in works that are 1 “Aristotle’s own other selves”: I am tempted to write “perhaps former selves”. But I avoid “developmental” or “chronological” hypotheses in part for fear of the loop from perceived interpretive need to developmental hypothesis and back to interpretation. I am mindful also of the reminder in Burnyeat (2001), that since the corpus we study today was not published in his lifetime, in principle Aristotle had the opportunity to go back and forth between works at will. We cannot, therefore, assume in the case of the Categories as opposed to Metaphysics Zeta, for example, that “simpler” means “earlier”.

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innocent of the apparatus of form and matter.2 The different levels reflect the distinction already noted between the passages in which Aristotle sets out his own views, propria persona, and those many places in Zeta where the views under discussion may not be (or may no longer be) authentically his. The distinction between levels, and the repeated infusion of views that are not part of Aristotle’s official theory, are a large part of what makes Zeta the complex entity it is universally recognized to be. One further point about the received views that form part of Aristotle’s discussion should be made at the outset. Aristotle will not hold that because a view originates with another, it is not for him worthy of serious attention. On the contrary, these are views philosophers generally—perhaps even Aristotle himself in other works—will subscribe to, and as such they deserve serious discussion, even if in the end they are rejected or amended to some significant degree. Various parts of Zeta, as we shall see, attest to how seriously Aristotle attends to the fit between “received” views, and the details of his own “partisan” theory. In the present work, accordingly, I am interested less in the conclusions in his own “official” or “partisan” theory that (I take it) Aristotle must be committed to—but says so little about in Zeta—and interested more in the details of how he interweaves the philosophical tradition and his own “partisan” theory, as he works through the agenda he has set himself en route to the formal conclusions of Zeta, to be found above all in its final chapter, 17. To express my interests slightly differently: how is it, if commentators (present writer included) understand Aristotle’s final views as well as they have sometimes claimed to, that so often they have so little idea of how what he is doing in a given passage contributes to his larger conclusions? So my approach to Zeta here is, I hope, more sensitive to the context and to Aristotle’s own concerns. Devotees of Zeta will already know that the dense thickets of argument in its seventeen chapters will not respond kindly to broad generalities about their contents—not, at least, in the absence of a serious attempt to find a way through at least some significant portion of the philosophical terrain. At the same time, it is not my intention to give a blow-by-blow account of every argument in Zeta. For the occasional complexities in what follows, part of the responsibility is mine, and part Aristotle’s—in what proportion, I leave it to the reader to decide. The Introduction sets out the major voices—of others, and Aristotle’s own in other works—that resonate in the different chapters of Zeta. In Part One, The Shape Of Zeta, I discuss some general points regarding Aristotle’s attack on his project. I will argue that Aristotle’s goal is to produce a definition of substance—better, a definition of primary substance and of the substance of a thing; for this reason, a large portion of his discussion is dominated by “received” views of how such a definition should go. The first order of business, accordingly, will be Aristotle’s review in Zeta 1 of what he supposes are significant themes in the philosophical tradition as to the contents of a 2 For more on the terminology attached to the division in levels in the secondary literature, see Chapter 2, Section 2, and Chapter 1, n. 34.

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minimum metaphysical theory within which a definition of substance finds its place, followed in Zeta 2 by a review of traditional candidates for (primary) substance in Zeta 2, and in the opening lines of Zeta 3, by a list of traditional options for the desired definition. As we shall see, the list in the agenda passage of Zeta 3 shapes proceedings in much of what follows in Zeta. Later chapters of Zeta offer a blend of Aristotle’s critical scrutiny of the deliverances of the tradition concerning the agenda items of Zeta 3, together with (in lesser amount) sketches of his own “partisan” views, and their fit for better or worse with the tradition—often with the benefit of a friendly amendment of Aristotle’s devising. It has been suggested that various principles, labelled “levels” and “non-linearity”, govern proceedings in these later chapters; these principles require early discussion. I also present a bird’s-eye view of the different segments motivated by the different definitions of substance Aristotle finds in the philosophical tradition, and add some remarks about the different thinkers who find a place there. Later parts of the book—Substance as Subject (Part Two), Substance as Essence (Part Three), and Substance as Universal (Part Four)—follow the course of Aristotle’s discussion through the different strains he has identified in received views about substance. (It will be noted that Aristotle’s original agenda of four “received” characterizations of substance in the event shrinks to three; see Chapter 1, n. 18.) This will bring us to the end of the penultimate chapter, 16, in Zeta. At this late point we may reasonably ask: if so much of Zeta is occupied with the philosophical tradition—mostly in critical vein—and if so few of Aristotle’s own developed views are on display, what is left of Aristotle’s deepest metaphysical thoughts, which Zeta is so often thought to contain? It is sometimes said that Aristotle’s positive conclusion in Zeta, where one can be found, is that form is the substance of a thing and is (primary) substance. But if this is his conclusion, it is at best orthogonal to the announced topic of the book: it purports to settle the “Application Problem”, telling us what counts as primary substance and the substance of a thing—but leaves to one side the details of the actual definition that might produce this result. We owe to Richard Rorty the contrarian question: how far does the conclusion that form is primary substance actually get us? Plato would say his forms are the basic entities—the primary substances. Aristotle would say that his are. Does it all come down in the end to just (let us say) the different existence conditions for Platonic and for Aristotelian forms? I will argue that the answer to the Application Problem—that (Aristotelian) forms are the primary substances—falls out directly from the successful definition of (primary) substance, but that this answer is not after all the main conclusion to Zeta. Aristotle does not see the status of forms as primary substances as, in the first place, a consequence of his definition. The status of his forms, rather, is a “given” that serves as a constraint on a successful definition. This is a result his definition must give, if the definition is to be acceptable. I say more about this style of argument in the Introduction and in Chapter 6, Section 6. In Part Five I try to work out the details of what I suppose is the actual conclusion to Zeta, as offered in its final chapter, 17, where Aristotle gives his own, authentic

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definition of (primary) substance and of the substance of a thing. In Zeta 17, even while abandoning the “received” candidates for substance from the agenda passage in Zeta 3, Aristotle continues to rely on outside help of a sort, and he is more than happy to endorse the views he is using. The outside views in question come from his own Posterior Analytics. Aristotle brings from the An. Po. a conception of demonstration in which the middle term identifies the cause of a given event-type; this causal notion is taken over in Zeta 17 in the definition of the substance of a given individual thing as the cause of its being. I will suggest that Aristotle’s definition is best thought of as representing the property of being a (primary) substance or being the substance of a thing as, in modern dress, a second-order functional property of (Aristotelian) forms, in virtue of their role as the cause of being for compound material substances. On this rendering of Aristotle’s views, the property of being the cause of being for things is a role property, and it is realized in a given form by the set of causal properties appropriate to that very form. So the definition of primary substance as the cause of being for a thing will apply across the board, to all forms alike, even while different forms have different sets of realizer properties, varying with the range of things that have a form as their substance. In this story, facts about a given (Aristotelian) form—its existence conditions, its relations with other items in the ontology, its place as the essence of things—all contribute to qualifying that form to perform as the substance of a thing. But the role that forms must play in order to count as the substance of a thing and hence as a (primary) substance remains constant, across the variety of different compound material substances and the variety of forms that are the cause of their being. I end the book with a brief discussion of Aristotle’s own review of what he thinks he has accomplished over the course of the discussion in Zeta.

Acknowledgements This book was written over a period of some years, and earlier versions, all or in part, of Chapters 1, 4, 6, and 8 have already been published.3 Other chapters have been read at various venues, and I have benefited from comments of the members of the audience on each occasion. Different versions of the material in Chapter 1 were offered to audiences at Oxford, Providence (where Mary Louise Gill was commentator), and Los Angeles. I am grateful to Myles Burnyeat for permission to refer to his then unpublished Map of Zeta (= Burnyeat 2001) on these different occasions. A version of Chapter 3 was read at a conference, “Aristotle on Definition and Essence”, at Oriel College, Oxford, in Spring 2010; and that same source was, indirectly, the stimulus for reshaping Chapter 11 into its present form. I am greatly indebted to David Charles for the invitation to this and to other conferences in Oxford over the years. Chapter 4 was presented to audiences at the University of Colorado at Boulder, and at the symposium on “The Essential Aristotle”, with Michael Wedin and Mary Louise Gill, at the Pacific Division Meetings of the American Philosophical Association; Chapters 4 and 5 together were given as the Hesperia Lectures at the University of California at Davis. Chapter 6 was read at a Conference on Substance and Essence at Oxford University, and later to an audience in Los Angeles. An early draft of what is now Chapter 8 was read at Brown University, where Mary Louise Gill was again commentator. Chapter 8 also borrows material from a paper read at the conference “Aristotle on Predication”, at Rutgers University, and again at the meetings of the American Philosophical Association in Chicago. At this distance from at least some of these occasions, I can now do no more than list the friends and colleagues who have come to my aid in different ways. They include Ara Astourian, Robert Bolton, Myles Burnyeat, Victor Caston, David Charles, Alan Code, Paolo Crivelli, Norman Dahl, Kit Fine, Mary Louise Gill, Gareth Matthews, Henry Mendell, Kathrin Koslicki, David Manley, Amanda Printz, Jeff Pryor, Jan Szaif, and Michael Wedin. I also acknowledge the help of the anonymous advisers for

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I am glad to acknowledge permission granted by the respective copyright holders for the following previously published material: “The Hitchhiker’s Guide to Metaphysics Zeta”, Proceedings of the Boston Area Colloquium in Ancient Philosophy, Vol. XV (1999) 2000, and for “Predication, Things, and Kinds in Aristotle’s Metaphysics”, Phronesis, 56.4 (2011), both published by Koninklijke Brill NV; “Friend or Foe?: Some Encounters With Plato in Aristotle Metaphysics Zeta”, The Modern Schoolman, LXXX (May 2003); a review of Myles Burnyeat, A Map of Metaphysics Zeta, Mind, 113.449 (2004), 158–64, and “A Nose By Any Other Name: Sameness, Substitution, and Essence in Aristotle Metaphysics Z5”, Oxford Studies in Ancient Philosophy, XXVIII (2005), 161–99, both published by Oxford University Press; and “Is There Room for Plato in an Aristotelian Theory of Essence?”, in Georgios Agnostopoulos, ed., Reason and Analysis in Ancient Greek Philosophy, published by Springer SBM in the book series Philosophical Studies Series.

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Ocford University Press. Especial thanks go to John Malcolm for his typically trenchant and helpful comments on an earlier draft of the entire book. I am grateful to all for the help they have given me, and extend my apologies to those others whose contributions, which I will have taken advantage of at the time, have now receded from memory.

Contents Detailed List of Contents Introduction

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Part One: The Shape of Zeta 1 The Hitch-Hiker’s Guide to Metaphysics Zeta

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Part Two: Substance as Subject 2 Subjects in Metaphysics Zeta 3

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Part Three: Substance as Essence 3 A Start on Essence in Metaphysics Zeta 4

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4 Sameness, Substitution, and Essence (I): Zeta 5, the SE, and “A Nose by Any Other Name”

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5 Sameness, Substitution, and Essence (II): The SE, and the Pale Man Argument from Zeta 6

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6 Plato as Friend: Is There Room for Plato in an Aristotelian Theory of Essence?

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7 Substance as Essence: The Shift to “Partisan” Mode in Zeta 10 and 11

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Part Four: Substance as Universal 8 Substance and Universals (I): Plato as Foe: Setting the Stage in Zeta 13

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9 Substance and Universals (II): Plato on Genus, Species, and Differentia

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10 Substance and Universals (III): Zeta 15 and 16, and Plato’s Fundamental Mistake

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Part Five: Back to the Definition of Substance: The End-Game 11 The Posterior Analytics, and a Fresh Approach to Defining Substance

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12 Aristotle on the Positive Contributions of Zeta

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Bibliography Index Index Locorum

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Detailed List of Contents Introduction 1 An Oblique Approach to Substance 2 Some Alien Presences 3 Some Unexpected Absences

1 2 4 5

Part One: The Shape of Zeta 1 The Hitch-Hiker’s Guide to Metaphysics Zeta The Approach to Substance in Zeta 1 Metaphysics Zeta 1: A Minimum Metaphysical Theory 2 The Definition of Substance: The Agenda of Zeta, and a First Look at Levels The Three Segments of Zeta: A Bird’s-Eye View 3 Substance and Subjects 4 Substance and Essence 5 Substance and Universals The Anti-Platonism of Zeta, and Some Other Participants in the Debate 6 A Place for Polemics 7 Expanding the Dramatis Personae Two Constraints on the Account of Substance? Levels and Non-Linearity 8 Levels 9 Non-Linearity: Inaccessibility and the Common Conclusion Assumption 10 The Logic of Non-Linearity Some Alternative Argumentative Strategies 11 “Mapping” the Old Onto The New, and A Use For Abductive Argument

9 10 10 16 21 21 21 22 24 24 26 28 29 32 34 37 37

Part Two: Substance as Subject 2 Subjects in Metaphysics Zeta 3 1 Sources of the Received View: Aristotle’s Categories, and the Early Philosophers of Nature 2 Aristotle’s Target in Zeta 3 3 The Distribution of “Received” and “Partisan” in Zeta 3; On “Stripping Away” 4 The Shift from “Received” to “Partisan”: the Cross-Theoretical Identification Between the Result of Stripping Away and Matter

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5 The Trouble with Matter 6 Bare Substrates and Bare Substrate Ontology 7 The Homonymy of Matter, and Some Difficulties for Metaphysical Predication 8 Conclusion

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Part Three: Substance as Essence 3 A Start on Essence in Metaphysics Zeta 4 1 “How (Informed) People Speak” About Essence: Two Points of Contact with the Tradition 2 Beyond Received Views: Partisan Developments 3 How to Talk About Essence: Ownership versus Content 4 A First Approach, Conducted Logiko¯s: Essence and “What a Thing is per se” 5 A Second Approach to Essence: the Connection with Definition 6 Does a Compound of a Substance with an Accident have an Essence?: Essence and the Thisness Test 7 Two Conditions on Definition and Essence: Unity and Primacy 8 Grades of Being, of Essence, and of Definition Appendix: Greek Hoper and the Pseudo-Cleft Constructions in English 4 Sameness, Substitution, and Essence (I): Zeta 5, the SE, and “A Nose by Any Other Name” The Puzzles of Essence, and an Apparent Discrepancy 1 The Three Puzzles in Zeta 5 2 What Aristotle Knows About Snub in the SE How to Make Room for the Puzzles in Zeta 5 3 The No-Solution Solution 4 Accidents and Compounds 5 Contextual Definition 6 Making Room for the Puzzles in Zeta 5: the Issue of Validity Back to the SE 7 Double Trouble 8 Saying the Same Thing Again Again Sameness and Substitution 9 The Puzzles, Sameness, and Definition 10 The Puzzles and Some Principles of Sameness 11 Sameness and Definition: Substitution and the Extended Sameness Test The Zeta 5 Puzzles Revisited, and a Defence of Babbling 12 The Remaining Strategy

69 71 74 74 76 83 84 87 90 92 95 97 97 102 104 105 106 107 108 110 110 112 113 113 114 115 117 117

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13 A Nose By Any Other Name: Substitution and Reformulation in the Three Puzzles 14 In Defence of Babbling Afterword: Reservations and Retractions 15 Does Aristotle’s Argument Hit Too Wide a Target? 16 Does the Argument Hit No Target At All? 17 Systematic Considerations 5 Sameness, Substitution, and Essence (II): The SE, and the Pale Man Argument from Zeta 6 Some Background Ideas 1 Aristotle’s Hierarchy of Essences, and “Things that are the Same as Their Essences” The Pale Man Argument 2 Things that are Not (Essentially) the Same as Their Essences: the Pale Man Argument 3 So Many Arguments, So Many Ways To Go Wrong Referential Opacity and the Pale Man Argument 4 Referential Opacity, and the Fallacy of Accident 5 From the Fallacy of Accident to the Non-Sameness Result: the Supporting Argument Referential Opacity and the Theory of Essence 6 “Under a Description” 7 Ownership versus Content Again 8 Composite Essences and Their Owners 9 Conclusion 6 Plato as Friend: Is There Room for Plato in an Aristotelian Theory of Essence? Purity in the Engagement with Plato 1 The Basic Argument for Sameness 2 Plato and the Elaboration of the Basic Argument “Severance”: How Platonic Separation is not a Target 3 “Severance” and Its Consequences: 1031b3–11 4 A Fresh Argument for Identity: Severance and a Principle From the Theory of Izzing and Having Goodbye to Severance, and in Defence of Uniformity 5 The Applications of Uniformity: Fallacy, or True Platonic Doctrine? 6 Fallacy Again, or More True Doctrine? 7 Aristotle on How Plato’s Forms are Inessential to His Argument

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7 Substance as Essence: The Shift to “Partisan” Mode in Zeta 10 and 11 1 Zeta 10 and the Transition to “Partisan” Mode 2 A Partisan Question in Zeta 11 3 On How Aristotle Manages the Shift from the Tradition to the Partisan Point of View (i): The Full-Expansion Condition on Definition, and the Drive to Form as Primary Substance? 4 On How to Manage the Shift from the Tradition to the Partisan Point of View (ii): The Full-Expansion Condition on Definition, and an Isomorphism Between Theories? 5 Some Conclusions

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Part Four: Substance as Universal 8 Substance and Universals (I): Plato as Foe: Setting the Stage in Zeta 13 1 The Programme of Zeta 13 2 The Platonic View of Universals in Zeta 13–16 “No Universal is a Substance” 3 Zeta 13, 1038b8–15: The Primary Argument 4 Does Aristotle Play Fair with Plato in the Primary Argument?: The Primary Argument and the Argument of Zeta 6 5 The Limits of the Primary Argument 6 An Ad Hominem Objection to Aristotle: the Problem of Friendly Fire 7 Zeta 13, 1038b16–23: A Reprise of the Primary Argument 8 Zeta 13, 1038b15–16: On Substance and Predication 9 Zeta 13, 1038b34–1039a3: Universals and the This–Such Distinction “No Substance can have Actual Substance as Its Parts” 10 Zeta 13, 1038b23–29, 29–30: A Substance and Its Parts 11 The Problem of Friendly Fire Again 12 Some General Results, 1038b30–34 13 Lines, Numbers, and Democritean Atoms: 1039a3–14 14 The Closing Dilemma of Zeta 13: More on the Structure of Universals, 1039a14–23 Individuals and Their Kinds: Aristotle’s Alternative to Plato 15 A Closer Look at Kinds 16 Individual and Kinds, and How the Form is Predicated of the Matter: (i) An Account of Statement Predication 17 Individuals and Kinds, and How the Form is Predicated of the Matter: (ii) The Metaphysical Analysis of Kinds 18 An Injection of Theory 19 Some Pluses and Minuses Appendix: Mutual Exclusivity and Some Versions of Compatibility

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9 Substance and Universals (II): Plato on Genus, Species, and Differentia 1 The Assumptions that Make Plato Vulnerable 2 Aristotle’s Dilemma 3 “The Genus is Numerically the Same in the Different Species” 4 “The Genus is Not Numerically the Same in the Different Species” 5 Two Final Negative Consequences 10 Substance and Universals (III): Zeta 15 and 16, and Plato’s Fundamental Mistake 1 “Received” and “Partisan” Mode in Zeta 15 2 An Aristotelian Condition on Definition? 3 The Revised Aristotelian Condition 4 A Comment on Aristotle’s Silence, and the Constructive Dilemma (CD) Strategy Revisited 5 The Critique Continued in Zeta 16 6 A Final Jab at Plato, and a Summary of Conclusions in the Segment Appendix: Definition, Substance, and Universals: A Puzzle, and Some Speculative Conclusions

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Part Five: Back to the Definition of Substance: The End-Game 11 The Posterior Analytics, and a Fresh Approach to Defining Substance 1 The Search for Substance: Are We There Yet? 2 Substance as a Cause 3 From the An. Po. to the Metaphysics 4 Some Questions of Fit 5 On Why Aristotle Does Not Mean for the Fit to be Exact 6 Causes and the Definition of Substance 7 Conclusion 12 Aristotle on the Positive Contributions of Zeta 1 The Retrospective in Eta 1 2 A Closing Note About Levels

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Bibliography Index Index Locorum

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Introduction In Metaphysics Book Zeta, Aristotle’s announced topic is the definition of substance (Greek ousia), where the substances are (as a first take) those basic entities on which in his view the reality of objects in the sublunary world must be based. The suggestion that certain items in the ontology are basic, however, will not constitute the definition Aristotle is looking for; for him, the definition must convey what about the substances qualifies them as basic. This last question receives different answers, varying with the entities that in a given context he counts as basic. In Zeta, Aristotle inherits the notion of substance from the received tradition, including his own discussion of substance in the Categories. But some crucial modifications are in the wings. In the less complex ontology of the Categories, this man, Archimedes (say), or this horse, Affirmed, are among the primary substances—the entities in virtue of which there exist all the other items in the ontology—while the kinds, man, horse, and the rest, are ranked as secondary substances. Meanwhile, the notion of the substance of a thing is altogether absent.1 All this (and more) is swept away in Zeta. In Aristotle’s official theory in Metaphysics Zeta, three different kinds of things will count as substances: (Aristotelian) form,2 matter, and the compound material substance, which has the first two as constituents. And among the three different kinds of item that, in one way or another, count as substances in the sublunary world, an (Aristotelian) form is the cause of being for and, hence, the substance of a given individual substance, so that Aristotle’s forms are now the primary substances. In all of Zeta, Aristotle’s interest in defining substance is, in effect, the project of defining the notion of primary substance, where it will be his forms that

1 In fact, the Categories cannot accommodate the notion of the substance of a thing, see Furth (1978), 631. Aristotle argues in Categories 5 that individual substances are the primary substances, on the basis of the existential dependence by kinds on the individuals of which they are metaphysically predicated. To admit the substance-of relation, where secondary substances are the substance of individual substances, would be to introduce overtly the point that individuals themselves are essentially dependent on their kinds. The difficulty is not that the two notions of dependence contradict each other—they do not—but that they deliver different items—individual substances, their kinds?—as primary substances. This is to relativize the notion of primary substance—it will be relative to this or that criterion for substance—beyond endurance. The notion of primary substance is, of course, linked to different notions of priority in different works. But to impose them simultaneously destroys the notion of primary substance (“the one and only first substance”) altogether. 2 “(Aristotelian) form”, as opposed to Plato’s; see, for example, Physics B1, 193a30–31, b3–5.

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satisfy the definition he gives in the final chapter of the book. Meanwhile, the kinds of the Categories do not appear on the list of substances at all. Of the three kinds of substance recognized in the body of Metaphysics Zeta, as we have seen, Aristotle settles on the (Aristotelian) forms of natural things as his choice for the primary substances, and his forms satisfy the definition of substance—properly, primary substance, or the substance of a thing—that emerges in the final chapter of Zeta. But it is not part of his project to define substance as it applies to compound material substances: this use of term, “substance”, is (I suppose) left as a byproduct of the definition he gives. That is to say, compound material substances count as substances, thanks to the relevant form that is their substance and, hence, is properly primary substance. Aristotle’s project of finding a definition of (primary) substance gets under way in earnest in Zeta with a review of received views at the beginning of Zeta 3 (1.4 below). His work in the body of Zeta on the various options on offer in Zeta 3, however, is all preliminary to the “new start” and the authoritative definition in the final chapter, 17, of Zeta. When in Zeta 17 Aristotle arrives at his definition of (primary) substance as a cause of a certain sort, he argues that his definition has the result that Aristotelian form qualifies as primary substance. This result, as I see it, is not unexpected. The definition is not needed in order to generate the result, for the status of Aristotle’s forms as the primary substances is determined, before the definition of primary substance is put before us in Zeta 17. The order in which these points emerge will be no surprise, if as suggested in the Preface above, it is at best orthogonal to the announced topic of Zeta to settle the “Application Problem”—telling us which entities they are that count as primary substance and the substance of a thing. Instead, Aristotle’s principal goal is to produce the definition of (primary) substance, which (I suppose) is to be judged in part by its success in identifying the appropriate entities as the primary substances. We will have more to say (in Chapter 1, Sections 1.3 and 1.7, and in Chapter 11) about the relation in Zeta 17 between Aristotle’s answer to the Application Problem and the final, successful definition of primary substance.

1 An Oblique Approach to Substance By the end of Zeta, I will argue, Aristotle has achieved the definition of (primary) substance he wants, and the route to the definition, arguably, is confirmed in the retrospective in the opening chapter of the following Book Eta. The body of Zeta together with Eta 1 (in combination also with the remaining chapters of Eta and the discussion of potentiality and actuality in Book Theta, which will not be our subject here) are famously where the details of his fully developed theory of substance are supposedly to be found. Appropriately, then, a good deal of effort on the part of many writers has gone into the task of setting out—not without controversy—what are variously taken to be Aristotle’s considered views as he proceeds towards a definition of substance in Zeta.

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Yet—in what aficionados of this text will recognize as a major understatement— much remains unclear. Even the strategy Aristotle follows in reaching his views is far from evident. The agenda which he sets himself at the beginning of Zeta 3, and which dominates subsequent chapters, is fashioned around “received” views of substances— views that come from the philosophical tradition. His agenda is quoted as 1.4 below, and anticipated here: 1.4 Substance is said, if not in more ways, at least chiefly in four: that is, (i) the essence and (ii) the universal and (iii) the genus seem to be the substance of each thing, and fourth of these, (iv) the subject. Zeta 3, 1028b33-6.

None of the views in 1.4 is necessarily Aristotle’s own—so which of them, if any, does Aristotle himself endorse? Do these lines offer disjunction of options—either a subject, or the essence of something, or a universal of some kind—or a conjunction: something that is both a subject and an essence and a universal? 3 To achieve a single notion of substance in the end, do some “received” characterizations get to stay, in their original form or (more likely) rewritten in some way, while others have to go? Finally, we will find that the list is hardly comprehensive, and a more promising conception of substance emerges in the final chapter 17 of Zeta, once Aristotle’s review of his initial agenda is done. The uncertainties of the agenda Aristotle sets himself in Zeta 3 are only the beginning. The individual entries in Aristotle’s agenda, as we saw, are not original with him. And the unwinding of the agenda in later chapters is along similar lines. In line with the oblique approach initiated in Zeta 3, Aristotle devotes fully two-thirds of the rest of Zeta not to his own developed theory of form and matter, but to the views of others, and to a significant extent the views of his own other selves in the Categories, Topics, de Sophisticis Elenchis, or Analytics, which are all form-and-matter-free. The most prominent outside presence, however, is that of Plato. Frequently, Plato is a target in Aristotle’s discussion (even if, as often as not, he is not mentioned by name). At other times, less expectedly, Plato is in the role of friend, not foe, and Aristotle appears to suppress his own views and uses Plato as mouthpiece for views that, transcribed into the terms of his own theory, Aristotle would happily endorse. Why does Aristotle hide behind Plato’s skirts in this way? For all the difficulties to which his reticence gives rise, the temptation is almost irresistible to scrutinize Aristotle’s critique of others in the hope of unearthing the views that are authentically his. What plausibly might his views be? And of the views that are plausibly his, which would survive the critique he offers of other philosophers—and how? The secondary literature does not lack for attempts to spell out different candidates for Aristotle’s finished views. But even if we can imagine a convergence 3 On the shrinking of Aristotle’s agenda down to three from the original four entries at the beginning of Z3, see this chapter, nn. 18 and 54, and for more discussion of the topics raised in this paragraph, see Chapter 1, Sections 2 and 10.

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of opinion on these matters, a nagging question remains. In general, we may worry, how is it that however confident we may feel about this or that detail of Aristotle’s final conclusions, the interpretation of so many individual passages and their contribution to Aristotle’s larger project can still seem so mysterious? Our target in what follows is Aristotle’s metaphysical views in the context in which he himself sets them—as in part the outgrowth of what he sees as the philosophical tradition, but also as in part a reaction against the views of his philosophical peers. A standing constraint on any account must always be the philosophical reasons—the justification—Aristotle would or does give for his conclusions. In the present work, however, our primary focus is on the manner of Aristotle’s exposition; in particular, on how as a means to advance his own metaphysical conclusions, he presses hard on the continuity of one sort or another between his views and the views of others. In the remainder of this Introduction, I review in more detail the diversity of authors and views that make an appearance in Zeta (the “alien” presences in Section 2). As counterpoint to this, it will also be useful to mention some of the ways in which Aristotle is silent about the details of his own theory (these are the unexpected “absences” from Zeta in Section 3). The extent to which Aristotle withholds material that one might naturally think belongs in his account of his own theory indicates yet again the complexity of the route he follows to his desired conclusions.

2 Some Alien Presences Of all the subtleties in how Aristotle’s account of substance unfolds in Zeta, perhaps the most striking is the unexpected alien presences there. My word, “alien”, covers a range of possibilities. Sometimes the visitor to Zeta is Aristotle himself, from some other of his works, and the presence is “alien” in only the weakest of senses, marking the fact only that these works are innocent of the apparatus of form and matter that is central to Aristotle’s full-blown theory in the relatively small portion of Zeta where it can be found. The presence of Aristotle’s other selves at times is entirely benign, as with the variety of moves set out in the Topics and used to effect in the discussion of essence in Metaphysics Zeta 4. In other cases, as with the appearance of the subject criterion for substance from the Categories in Metaphysics Zeta 3, the result is a correction of the Aristotelian “other self”. And at other points in the discussion of essence, Aristotle apparently misapplies rules laid out and discussed in the Topics and in the postscript to the Topics in the SE. On this score, it may seem as if the Aristotle of the SE stands as foe in relation to certain parts of Zeta; in some (but not all) cases, I will argue, where the SE suggests corrections to proceedings in Zeta, the result is to advance rather than impede Aristotle’s cause in Zeta. In any event, it will be of interest to sort out how the rules in question contribute to (or, pessimistically, confound) the project or projects under way in Zeta. The most productive contribution of all from outside, however, is that of Aristotle’s An. Po, whose use of demonstration to explain and define event-types—thunder,

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eclipses, and so on—is taken over in Metaphysics Zeta 17 to suggest a scheme for explaining the constitution of individual substances, and for saying what it is to be the substance (singular) of individual substances. As we shall see, this is the chapter in which Aristotle achieves his goal of giving a definition of substance. There remain the more obvious alien presences, where the views of some philosopher other than Aristotle are brought into the discussion. The most frequent intruder by far is Plato, who is frequently a target in the Metaphysics, but on other occasions a friend. Friendship apparently is on Aristotle’s mind in Zeta 6, where he takes up a nexus of ideas involving the “substance as essence” assumption which motivates the segment, and works towards the conclusion that entities that are suitably primary are the same as—even identical with—their essences. For all his approval for this result, however, the strategy Aristotle follows in arguing for it is strikingly “arm’s length”: the assumptions of the argument and its conclusion alike are tailored to the Platonic theory of forms—a theory which overall he decisively rejects.4 I suppose that the engagement with Plato in Zeta 6 is entirely friendly and for Aristotle benign. Aristotle co-opts Plato in this chapter in the way he co-opts other philosophers elsewhere, in the search for “big tent” principles that are ontologically neutral—that hold across ontologies (Chapter 6). Notably, however, points on which he and Plato agree in Zeta 6 will be turned against Plato in the discussion of “substance as universal” in Zeta 13 (Chapter 8, Section 8.4). Plato is a target many times over in the discussion of universals in Zeta 13 and related chapters. The most conspicuous attack on Plato’s theory of forms comes in Zeta 14, which attacks the Platonic view of how universals—here, Platonic forms—are related to one another. In this, ironically, Plato may be an accessory to Aristotle’s arguments: in style and even in theme, the chapter bears loose resemblances to the first half of Plato’s Parmenides, where Plato directs criticisms of his own against one or another version of a theory of forms. Plato’s views also come under attack en passant in Zeta 15 and 16.

3 Some Unexpected Absences Along with the presence of Plato and of Aristotle’s own “other selves” from other texts, and the cameo appearances of others, there are also significant absences from large stretches of Zeta. As Burnyeat (2001) is the latest to emphasize, there are different “levels” in Aristotle’s account, distinguished by the absence or the presence of Aristotle’s own distinctive ontology of form and matter. The “partisan”, distinctively Aristotelian parts of Zeta include parts of Zeta 3; Zeta 7 through 9 (but the consensus now appears to be that these chapters along with 12 are an intrusion, so they do not properly belong in the tally);5 Zeta 10 and 11; Zeta 15 and 16 (this is Burnyeat’s count: 4

Ross is nicely trenchant on Aristotle’s procedures here: he is quoted in the epigraph to Chapter 6. Reasons for thinking these chapters not part of Aristotle’s original design are given in Burnyeat (2001), 29–38 (Z7–9) and 42–4 (on Z12). 5

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I tend to think that these last two chapters are only mildly dusted with the official Aristotelian theory); and finally Zeta 17. In other places, Aristotle is concerned with views he finds in the philosophical tradition—views whose authenticity for him may not be immediately obvious. In this connection, think again of Zeta 6. The use of Plato in the discussion of essence here—Plato’s unexpected presence—is one side of the coin; Aristotle’s reluctance to speak propria persona, in the terms of his own ontology, is the corresponding absence that marks the other side. It would be good to have a clearer picture of Aristotle’s reasons for suppressing the details of his own ontology in such cases. It would be good also to understand the “fit” Aristotle evidently takes for granted between the results of the two kinds of discussion. Why should the details about subjects, a thing’s essence, or about what is universal to what—all from the philosophical tradition, but with no direct comment on whether from one or from many sources—converge on a single coherent set of notions in the favoured Aristotelian ontology? This question is particularly acute given the Non-Linearity Assumption from Burnyeat (2001), which holds that each segment of Zeta (beginning at Zeta 3, 4, 13, and 17 respectively) constitutes a “fresh start”, so that no assumptions or results in Aristotle’s theory obtained in one segment are valid still in another. If the segments are as discrete as this, why think that they combine to yield a single, unified conception of substance in Aristotle’s official theory of form and matter? In the event, I will suggest, the different conceptions of substance from the agenda passage in Zeta 3 all fail as definitions of substance. But the failure is no disaster, for two reasons. In the first place, their failure helps clear the way for what Aristotle regards as the correct definition in Zeta 17. At the same time, second, the mere presence of these different conceptions in the philosophical tradition for Aristotle suggests that they should not be entirely scrapped. The notion of essence has the strongest claim to being retained in the official Aristotelian conception of substance (although as before, not part of the definition); but he may wish to accommodate in some way the remaining notions as well (Chapter 12). As so often, however, the details are absent from the text, and remain largely a matter of conjecture.

PART ONE

The Shape of Zeta

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1 The Hitch-Hiker’s Guide to Metaphysics Zeta My main interest in the pages that follow is in elements of the strategy that guides Aristotle’s different attempts on the notion of substance in Metaphysics Zeta. To some extent, my remarks are inevitably a compromise. I cannot talk exclusively about strategy, to such a degree of abstraction that I say nothing about the actual contents of Zeta. On the other hand, this is not the occasion for a survey of the entirety of Zeta in all its awesome complexity. So I shall settle for dividing my attention between the two kinds of topic. In the present chapter I begin (Section 1) with Aristotle’s summary in Zeta 1 of what any sound metaphysical theory will look like; his account is presented in largely neutral terms, but with more than a passing nod to the views of his own Categories. In the remaining sections of the chapter I discuss various aspects of how as I see it the overall argument of Zeta proceeds, beginning (Section 2) with the project of defining substance, and with the agenda for most of the rest of Zeta that Aristotle announces at the beginning of Zeta 3. His agenda is drawn from the philosophical tradition, and like much of the ensuing discussion stays clear of his own more developed views, which emerge in full throat only in the final chapter, 17, of Zeta. The distinction between his developed theory and the views he finds in the tradition is a matter of levels, which I discuss in Section 2 and again in Section 8 below. It may be helpful at this point (Sections 3–5) to give an overview of what I take to be the overall drift of the three segments of Zeta in which Aristotle pursues the agenda he has set for himself in Zeta 3. Next (Sections 6 and 7), I revisit the issue of the other participants in the debate under way in Zeta—Plato and (no less strong a presence) Aristotle’s own other selves from other texts. Thereafter, I turn again (Sections 8–10) to the methodological principles that do—or that may—govern Aristotle’s procedures in Zeta: levels, and the divide already noted between “received” views and Aristotle’s developed, “partisan” theory; and what I take to be the more controversial question of Non-Linearity (the term is from Burnyeat 2001). Finally (Section 11), I sketch some alternative assessments of Aristotle’s argumentative strategy in the body of Zeta. Later chapters will revisit various topics in Zeta in greater detail. But it will be good to start with the general picture.

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THE APPROACH TO SUBSTANCE IN ZETA

1 Metaphysics Zeta 1: A Minimum Metaphysical Theory As we have already seen in the Introduction, Aristotle’s discussion in the body of Zeta casts its net widely, to include not only Aristotle’s own other selves in the Categories and elsewhere in the Organon, but also the work of other philosophers—above all, that of Plato and his fellow Platonists. In Zeta 1, by contrast, the main ideas in large part—with a handful of signal exceptions1—occupy common ground with the metaphysical theory presented in the Categories. In this latter work Aristotle’s views are remarkably complex, but they are still relatively simple in comparison with the more elaborate views under construction in the Metaphysics. It will be useful to have the relevant notions from the Categories before us from the start. Conspicuous entries in the ontology of the Categories include individual substances, for example, Archimedes or Coriscus, and the various non-substances that are their accidents, being musical, generosity, being seated, and the rest. In addition to individual substances, which Aristotle will count as primary substances, we find also various secondary substances—man, animal, and the rest—that are the kinds under which the individual substances fall. (We will return to the primary/secondary distinction—more generally, to Aristotle’s idea of the different grades of being—shortly.) Similarly, the various lowest-level non-substances, generosity, and the rest, fall under their own nonsubstance kinds, with the different labels, “quality”, “quantity”, and so forth, at their head.2 More controversially, Aristotle’s ontology also makes room for accidental compounds—absent from the Categories but present elsewhere in the Organon and in the Metaphysics—constructed out of individual substances together with their various accidents, taken one at a time: Archimedes seated, the one approaching, and so on.3 1

Here, I think of what I take to be the appeal to the substance of a thing (1028a14–18; see Introduction, n. 1); the hint of core-dependent homonymy (a18–20, Chapter 3, Section 8); and the appearance of accidental compounds (a20–29, this chapter, n. 3). 2 The correct status of the labels, “substance”, “quality”, and so forth is not obvious. It is often assumed that the category heading—substance, for example—is the highest level of classification you can reach in that category. As you go up the classificatory tree in the category of substance, the universals at each level are progressively less revealing about the content of the relevant kind. We learn less about a thing when told that it is an animal than when told it is a man, less still when told that it is a living creature. But (on the present story) we learn least of all when we are told just that it is a substance. There is an alternative to this picture. Ordinarily, we think that we are saying something about the content of the kind as we move among the different rungs of the classificatory tree. But we do not say anything about the content of the kind when we call an item a substance (or a primary substance, or one or another grade of secondary substance), or a quality, and so forth. These labels attach to different trees, or to the different levels on a given tree: this is the level labelled, ‘primary substance,’ for example; this is the level for (one or another grade of ) secondary substance. Or if we are looking at the traditional “ontological square”, the labels are as much part of the square as are the vertical and horizontal lines we use to draw it. Call labels of this kind “formal”, as opposed to the “contentful” notions that are part of—and so diagrammed within—the categorial scheme. For further discussion, see Wedin (2000), 35–6. 3 Accidental compounds are the subject of Accidental Compound Theory (ACT hereafter), discussed in Lewis (1982, 1991) and Matthews (1982). In ACT, the accident, ç, is metaphysically predicable of the individual substance, a, and the accidental compound, a + ç, exists if and only if, in fact, ç is (metaphysically) predicated

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The Categories also includes an elaborate scheme of metaphysical predication, in which substance and non-substance kinds alike are (metaphysically) predicated of the items that fall under them, and its accidents are (metaphysically) predicated of the individual substance.4 In this connection it will be useful to say that an individual substance Has its various non-substance accidents, but that it Is its various substantial kinds: thus, Archimedes Is (a) man, but he Has pallor. This handy device, due to Code and Grice, inverts for the benefit of English speakers Aristotle’s own claims in the Categories, that the kind, man (a secondary substance), is said of the individual substance, Archimedes, while his various accidents, pallor, generosity, and so on, are in him.5 Lastly, absent from the Organon altogether and absent too from Metaphysics Zeta 1 (as from other parts of Zeta where the focus is on the received tradition), is the analysis of individual substances, Archimedes and the rest, as compounds of form and matter, or form–matter compounds.6 Because they are distinctive of Aristotle’s own “partisan” theory, form–matter compounds will not appear in Zeta until the partisan portions of Zeta 3. Zeta 1 will, however, make reference to accidental compounds (this chapter, n. 3), which are also featured in the Organon, although not in the Categories portion of that set of works. This is a raw list of items in Aristotle’s Organon ontology, and incomplete at that. But one general feature of his ontology bears mentioning, not least because it is relatively alien to current thinking. This is the idea that different kinds of items in the ontology are assigned different grades of being. In line with this, part of the very idea of being a substance, for Aristotle, includes a notion of primacy over entities that are not substances. More than this, the primacy is such that items in the non-substance categories, which have a lesser grade of being, stand in a relation of ontological dependency on substances—more precisely, on individual substances.7 If Aristotle’s ontology also of a. The parent substance, a, is accidentally the same as—but not identical with—the compound, a + ç. As I read Aristotle, accidental compounds will enter the discussion shortly in Zeta 1 (passage 1.2 below). His terms for accidental compounds include “compounds by way of the other categories” (kata tas allas kate¯gorias suntheta, Z4, 10029b22–7, M2, 1077b4–9) and “things spoken of by virtue of an accident” (to¯n legomeno¯n kata sumbebe¯kos, Z6, 1031a19, cf. hosa kata sumbebe¯kos, b24). Other examples of accidental compounds are in 3.11 below from Z4; see also the examples collected in Chapter 5, n. 11. 4

Our contemporary notion of predication is linguistic predication, in which a predicate—a linguistic item—is predicated of a grammatical subject. Alongside a counterpart (more or less) of this linguistic notion, we find in Aristotle the very different notion of metaphysical predication, which is a relation between items in the ontology. In the favoured cases studied in the Categories, we can read the ontological relations that make true a given linguistic predication directly off the sentence itself: the sentence is true just in case the relevant entity is metaphysically predicated of the correct subject entity. The relations of Having and Izzing are varieties of metaphysical predication. 5 Code (1980, 1986); see Categories 2–5. 6 In talking of form–matter compounds as compounds, I am following Aristotle’s talk of individual substances as a “this-in-this” (tode en to¯ide) or as “what is out of these” (to ek touto¯n) or as a “composite” (sunolon) or a “composite substance” (sunole¯ ousia). Thus, I will say that for some matter, m, and form, ł, a = m + ł. This unpacking of individual substances is not found in the Organon; it is introduced in the Physics, and present in full force in the “partisan” parts of Metaphysics Zeta. 7 This picture is subject to considerable complication. In the Categories, for example, Aristotle allows that within the category of substance, the individual substances are primary and their kinds are the secondary

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includes accidental compounds, these will be ranked in ontological standing behind their two constituents, the individual substance and its various accidents. It also bears repeating that once form and matter are admitted to the ontology, primacy will shift from the individual substance to its constitutive form, which later chapters of Zeta make clear is the substance of the thing, and the cause of its being. But this is a story that, properly, must be postponed to the later, “partisan” portions of Zeta. With these preliminaries out of the way, we may turn to the details of the discussion in Zeta 1. The agenda of Zeta is driven by the need for a definition of substance, first announced, with unaccustomed rhetorical flourish, at the end of Zeta 1: 1.1 And moreover, what is sought after both long ago and now and always, and always puzzled over: what is being?—is just the question, what is substance? (for this some say is one, others more than one, and of the latter, some say it is limited, others unlimited); for which reason it is for us too to investigate most of all, and primarily, even so to speak exclusively, concerning that which is in this way [= substance], what it is. (1028b2–7, following Furth’s translation, cf. 2, 1028b31–2, 17, 1041a6)

Why the notion of substance is central to metaphysics is explained in Zeta 1, which sets out the minimal set of features that any good metaphysical theory should exhibit.8 substances. In Metaphysics Zeta, this competition between the particular and the general (Owen [1978–9] (1986), and this chapter, n. 13) continues, subject to the necessary adaptations—not only, as in the Categories and in early chapters of Zeta, between the “this” (the individual substance, Archimedes, say) and his kind (his “what a thing is”, or ti esti), but later in the “partisan” parts of Zeta, with the introduction of (Aristotelian) form and matter (this chapter, n. 6), between the individual and his form. On this last point—the competition between the individual substance and his constitutive form—the usual reading of Aristotle is that the form, but not the individual, counts as primary substance. 8 The word “metaphysics” is firmly ours by now, and in one mainstream use it picks out the study of reality in general (something like what Aristotle himself calls the study of being qua being). But the very term “metaphysics” is a product of Aristotelian scholarship. We owe our use of the term to the point in the history of scholarship in antiquity, most likely some time after Aristotle’s death, when the work of his that we know under the title Metaphysics—previously untitled, for all we can tell—acquired the label, “the work that comes after the physical works” (ta meta ta phusika, in Greek). The significance of the term intended by those who introduced it is uncertain. Much, of course, depends on the sense of “after”. At a minimum, perhaps, (i), there will be a certain pedagogical priority to mastering the basic concepts of Aristotle’s natural philosophy—to the study of the changeable objects in the natural, sublunary order—in particular, to mastering the concepts of matter and form, which Aristotle introduces in Physics A and B to explain how change can take place. On this view, it is only after work in natural philosophy that we should dive into the study of being that, in the Metaphysics, leads in the end to what Aristotle terms “first philosophy” or “theology”, and the study of the Unmoved Mover, which counts as God for Aristotle. (And if we are thinking of pedagogy, then Aristotle would warn that the works that comprise the Organon require study before even the works of natural philosophy.) Alternatively, somewhat differently, (ii), we might think that the mysteries of metaphysics, and especially the eventual goal of understanding the nature of God or the Unmoved Mover, will not be discovered until we first learn more about the concepts that explain the natural world. The point, then, will be not so much pedagogy as the order of discovery: in this spirit, as Aristotle remarks more than once, we should start with what is better known to us, and only thereafter move on to what is better known—more intelligible—by nature. The idea that the truths of metaphysics are more intelligible by nature reminds us, (iii), that there are also systematic reasons for thinking that, for Aristotle, natural philosophy comes before metaphysics. The notions of matter and form are central to Aristotle’s explanation of change and coming to be in the natural world; and

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Two features stand out over all others: we distinguish different grades of being, distributed variously over, most notably, substances (the primary beings) on the one hand, and the non-substances on the other; and entities of the second sort stand in a relation of dependency on entities of the first sort. Both ideas also have a place in Aristotle’s Categories, as we have seen. Zeta 1 fills in various details. In the theory it describes there are many kinds of being, signifying “what a thing is” and a “this” on the one hand, and quality, quantity, and the other things predicated in this way on the other. Of the different kinds of being, “what a thing is” is primary, and signifies substance; and everything else is a being, just because it is a quantity or a quality and so forth of what is in this first, privileged way.9 The nature of the relation of dependency by the non-substances on the substances is the subject of the first of many puzzles to appear in Zeta: 1.2 For this reason [sc. on account of the previous talk about dependency], someone might even raise the puzzle whether walking and being healthy and sitting each of them signify a being [Ross’s text], and likewise too for everything else of this sort; (a22) for none of these either is by its nature per se (“in respect of itself ”), or is capable of being separated from the substance, but rather, if anything, it’s the walker (“the walking ”) that belongs among the beings, and the sitting and the healthy . These latter are more evidently beings,10 because there is something which is for them a determinate subject (and this is the substance and the particular), which is just what is made manifest in this sort of predication; for the good or the sitting are not said without this. (a29) It is clear, then, that it is thanks to (dia) this [substance] that each of those other things is, so that that which is primarily, i.e. not is something, but is simpliciter, would be substance. (1028a20–31, following Furth)

Like the references to received views dotted throughout Zeta, the puzzles that are distributed throughout the book signal the dialectical character of much of Aristotle’s discussion. The moral of the present puzzle is that the dependency in question is not a relation of compositional dependency—the dependency of a whole on its parts, like the

they are central too to the analysis of being among the objects of the sensible world in Metaphysics Zeta and Eta. And when we move beyond being in the sensible world to the account of non-sensible, unchanging being—the being of the Unmoved Mover—the central notion (on the usual account) is that of form by itself, while the notion of matter drops away. As we move through the different orders of being in this way, the concepts of natural philosophy are extended and adapted (or, it may be, discarded) as Aristotle fashions his account of what lies outside the sublunary world altogether. The word “substance” is also ours; it translates Aristotle’s word, ousia, which is an abstract noun connected with the family of Greek words for our English, to be. Provisionally, we may think of the substances as the basic realities: more clarification will come from Aristotle’s own efforts to define the notion. 9 “in this first privileged way”: the phrase reproduces Aristotle’s own, but the back-reference, which grammatically picks up the previous talk of “what a thing is”, would better invoke the rival notion of substance latent in the passage as individual substance, as noted later in this section. 10 I have been nudged into this reading of the Greek, contrary to Furth (“seem more to be beings”— speaking perhaps with the vulgar?), by a remark in discussion by Alan Code.

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dependency of the walking thing (a compound of a substance with an accident) on the underlying substance that walks.11 The non-substances are not per se beings—they cannot exist independently of everything else; in particular, they cannot exist apart from substance (a22–4). Each non-substance is, thanks to (dia, a29) substance, which is primary, unqualified being, in contrast to qualified secondary being. There are different modes of primacy—in time, in knowledge, and in definition (1028a31–b2)—all of which should converge on the same class of entities. (Whether they do in fact so converge is, to say the least, disputed.) Finally, the project of inquiring into substance is a restricted version of what philosophers have been doing all along: the traditional question, What is being?, can be replaced by the narrower question, What is substance? For, the successful study of what is primary will bring knowledge of everything else along in its wake: 1.3 In every case knowledge is properly of what is first (kurio¯s tou pro¯tou he¯ episteme¯ ), that on which the others depend, and on account of which they are spoken of . If then this is substance, it is of substances that the philosopher would have to grasp the principles and causes. (ˆ2, 1003b16–19)

In all of this there are certain things Aristotle is not doing. First and foremost, he is not at this point in Zeta pressing on us his own preferred ontology of form, matter, and compound material substance. It would be a mistake to attempt a proleptic reading of Zeta 1, and without further ado to set about fitting form, matter, and the rest directly into the framework that the chapter establishes. For example, Aristotle notes that one kind of being “signifies what a thing is and a this” (1028a11–12), and if we look outside Zeta 1, to Physics B7, for example, we find that he glosses what a thing is by “form” (to ti estin kai he¯ morphe¯, Physics B7, 198b3). But we should not read this identification into the argument of Zeta 1. The main business of the chapter is to explore various (roughly) structural features which prima facie any respectable metaphysical theory must have, and the kinds of roles things will play there, in themselves and with respect to one another. It is left to other parts of Zeta and to Eta to say which entities in Aristotle’s own preferred ontology play the roles in question. I am arguing here against appealing to what we know in the end is the “official” Metaphysics theory of form, matter, and form-matter compound, before Aristotle himself brings these into the discussion. As we will see shortly, we may have reason to resist the “proleptic” reading of Zeta, not just in the opening chapter, but for large stretches of the book.

11

For the accidental compounds that are the subject of Aristotle’s puzzle; see this chapter, n. 3 and the accompanying text. The very construction of an accidental compound, from an accident and its parent substance, requires that a relation between these two constituents (and the concomitant notions of dominance and dependence) has already been achieved.

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At the same time, second, we must also resist the retrospective reading of Zeta 1. The chapter is clearly weighted towards the ontology of substances, accidents, and kinds from the Categories (but with a healthy dose added of Metaphysics ˆ2 on the dependence by non-substances on substance).12 But the Categories ontology is present in the chapter only provisionally, as a frame for some of the structural features Aristotle thinks belong in any proper theory of substance. It is not part of the agenda of the chapter to argue that all such features are properly accommodated in the Categories ontology. On the contrary, the Categories ontology does not well accommodate them all. For example, no single item in the Categories both is a “this” and gives the “what is it” of a thing; and no single item both gives the “what is it” of a thing and also is that on which non-substances depend for their being (this chapter, n. 9). Prima facie, these are all individually, perhaps even jointly, legitimate demands on the primary beings in one’s metaphysical theory—not just Aristotle’s own metaphysical theory, but anyone’s; and it will be the task of later chapters to determine whether they are accommodated better in the new theory of form, matter, and the rest.13 Finally, Aristotle does not in Zeta 1 mean to fix once and for all the domain of objects that it is the business of metaphysics to explain.14 By starting out from the ontology of the Categories, Aristotle is in effect following his own later advice, and sticking to the agreed-upon substances—perceptible substances—which are “better known to us” (Zeta 3, 1029a33–b12, cf. H1, 1042a24–5). By setting these out for study and explanation in later chapters, he is laying the groundwork in Zeta for a shift elsewhere to a different domain of entities which, when we can explain them properly, will be “better known by nature”.15 In Zeta (but not in the Categories), the explanation of perceptible substances leads to matter and, especially, form. But as Aristotle repeatedly emphasizes,16 the study of form in the natural world is in turn the springboard for the inquiry into the form that is not part of nature, and is the proper subject matter for theology (if the traditional view is right that the Prime Mover is pure form).

12

Metaphysics ˆ2, 1003a33–b19, cf. the retrospective summary at ¨1, 1045b27–33; see also this chapter,

n. 1. 13 For the “what is it” of a thing, see for example the discussion of definition in chapters Z4 and 5 on essence. Dependency, along with related questions of what to count as primary and what as secondary, is a recurring theme in Zeta: see again Z4 and 5, for example, and the discussion of priority in Z10, 1035b33ff. and 1036a12ff. For (Aristotelian) form as a this, see Z3, 1029a28, and H1, 1042a29; also ˜8, 1017b25, ¨7, 1049a35, ¸3, 1070a11, 13–15, and GC A3, 318b32. According to Owen (1978–9) 1986, Aristotle argues in Zeta that the demands of thisness and of what a thing is can be jointly satisfied by one and the same set of entities in his own theory. 14 For a contrary account, see Bolton (1995) 1996, passim. 15 If this is correct, then (contrary to Bolton (1995) 1996) the contrast between what is best known to us, and what is best known by nature, is not between the domain of particular substances introduced in Z1, and the apparatus of form, matter, and compound, in terms of which these are explained in later chapters. 16 Passages often read in this way include Z2, 1028b28–32; 3, 1029b3–12; 11, 1037a10–17; 16, 1040b27– 1041a3 (see 10.6 and 10.7 below); and 17, 1041a7–9.

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The transition from the metaphysics of perceptible substance to that of various eternal non-sensible substances is anticipated in a number of places in Zeta,17 and culminates in the study of the unmoved movers of theology in Metaphysics Lambda. The official topic of Zeta and Eta, meanwhile, is primary substance and the substance of a thing, as these apply in the realm of perceptible substances.

2 The Definition of Substance: The Agenda of Zeta, and a First Look at Levels After announcing his project of defining substance at the end of Zeta 1, Aristotle begins with a list of what other philosophers have taken to be the substances in Zeta 2 (he revisits the list of popular candidates and revises it in light of his own views at the beginning of Zeta 16). He reasserts the need for a definition rather than a list at the end of Zeta 2. Thereafter, the agenda for the rest of Zeta is largely set at the beginning of Zeta 3, with a survey of notions variously thought to be constitutive of the notion of substance: 1.4 Substance is said, if not in more ways, at least chiefly in four: that is, the essence and the universal and the genus seem to be the substance of each thing, and fourth of these, the subject. (Zeta 3, 1028b33–3618)

Aristotle’s very statement of his agenda is stunningly vague in crucial ways. His list in 1.4 comes from the philosophical tradition; none of the views is necessarily his own: so which of them, if any, does Aristotle himself endorse? Do the opening lines of Zeta 3 offer rival conceptions of substance—either a subject, or the essence of something, or a universal of some kind? Or are they separately partial characterizations that in the mind of their originator(s)—perhaps even in Aristotle’s own eyes—yield a unified and coherent view: a view of something that is both a subject and an essence and a universal? And is the list comprehensive, or—as we are warned in 1.4, and indeed find in the body of Zeta 3 and, most importantly, in the last chapter of Zeta—are there other conceptions of substance yet to come? These uncertainties aside, the candidates for defining substance in 1.4 and Aristotle’s favoured definition in Zeta 17 have an important feature in common. The preliminary attempts from the philosophical tradition all attempt to specify the role that an entity must play to qualify as primary substance: it must be a subject to other items, or it must be the essence of certain things, or universal to certain things. I emphasize that these are all role properties. Aristotle does not here hand us a list of items that count as primary

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See this chapter, n. 16. The idea that the substance of a thing is its genus is quietly dropped from the reprise of the Z3 list at the beginning of Z13 at 1038b2–3, see further, this chapter, n. 54. In the later list, Aristotle also supposes that the “received” view that the individual is a substance has been covered by the discussion of subjects in the body of Z3. 18

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substances but, rather, gives us a recipe for identifying such items. However, the recipe in each case needs further examination. Zeta 3 at best gives us only a down-payment on the search for a definition, and it will be up to later chapters of Zeta to tell us more about the nature of the role indicated in each case. So, for example, to define the substance of a thing as its essence introduces a term, “essence”, in the definiens that is itself undefined and in need of further explanation. We will want to explore these different notions before we can decide to what extent, if at all, they are suitable role properties by which to define or otherwise understand the property of being a substance (or the substance of a thing) that we are after.19 As things turn out, in the contest for being the appropriate role property by which to define the substance of a thing, the winner is not on the Zeta 3 list at all. It is, instead, the property of being the cause of being for individual things, introduced formally in Zeta 17. At the same time, in the retrospective in H1, some “received” characterizations from 1.4 may get to stay, although not as part of the definition, and not perhaps in their original form but subject to revision in some way. The specification of substance as a subject is taken up in Zeta 3; substance as essence occupies Zeta 4 through 6 and 10 and 11; and finally. the discussion of universals takes place in Zeta 13 through 16. In this list of chapters of Zeta, I skip over chapters 7 through 9 and 12, now widely regarded as relevant but as interpolations in the original design of the book (whether their interpolation is Aristotle’s doing, or that of a later editor, remains unknown).20 Again, my main focus will be on how in the three main segments of Zeta Aristotle carries out the agenda he sets himself at the beginning of Zeta 3. Finally, Aristotle presents his own solution to the definition of substance in Zeta 17; this chapter stands apart from the discussion of the Zeta 3 agenda in earlier chapters. Zeta 17, together with Aristotle’s concluding summary in H1, will be the subject of my last two chapters, 11 and 12. As we have already seen, the different accounts of substance set out in the agenda passage in 1.4 and explored in later chapters of Zeta are received views, and Aristotle’s own attitude to each is not immediately apparent. Discussion of the different conceptions of substance in these chapters is embedded in the theories, most notably, of Plato, but also of other philosophers, above all of Aristotle’s own self in other texts, and we hear of these conceptions well in advance of any reference to Aristotle’s more developed views elsewhere in Zeta. Before we go further, it will be helpful to fix on labels for the two halves of Aristotle’s discussion. We will say that the discussion in the body of Zeta operates on two levels. At one level, Aristotle is concerned with ideas he finds in the philosophical tradition; he will use “metaphysically unloaded” or

19

In the main text passim, I talk of the different attempts to define substance in terms of essence and the rest; but it is not clear that the result of Aristotle’s discussion will be to produce more than necessary and sufficient conditions for substance—and in some cases, it may produce less. 20 See Introduction, n. 5.

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“non-partisan” views of his own and of others21 as a platform from which later to convert those others to his own, distinctively Aristotelian theory of form and matter. The second level is that of the “official”, “in-house”, or “partisan” theory of form and matter, to which Aristotle wishes to convert the others. As a working hypothesis, then, I suppose that Aristotle contrives large stretches of Zeta so that they stay clear of the final conclusions for which he is headed, and instead deal exclusively with material from the philosophical tradition that is innocent of the details of his own official theory. Now, Aristotle has available to him a large repertoire of received views, of varying degrees of authenticity from his point of view, that stop well short of the official Metaphysics doctrine of form and matter. Plausibly, large parts of this tradition have already been incorporated, even refashioned, within his own work in other texts; so we will include in the philosophical tradition quoted in Zeta much that in its present form is due to Aristotle’s “other selves” in texts outside Metaphysics Zeta. But I rank the views of Aristotle’s “other selves” alongside “received views” from other sources, subject to the provision that, as with the views that are due to others, these views too count as “received” in the intended sense, only if they make no essential use of Aristotle’s more developed views in parts of Zeta and elsewhere. So, for example, in Zeta 10 Aristotle quotes the view from the de Anima, of form as the substance of the ensouled, and as the form or essence of a certain sort of body (1035b14–16); but the “other self ” quoted here is steeped in the theory of (Aristotelian) form and matter, and it is not welcome outside the partisan portions of the chapter. For my purposes, my use of “received” throughout excludes views from other Aristotelian texts in which the theory of form and matter is already present. In each of the three segments of Zeta, discussion for much of the time is in terms exclusively of received views, which make no essential use of material that would beg the question in favour of Aristotle’s own preferred, “official” theory.22 Different received views will be variously adopted, co-opted, modified, or rejected. But a context that contains so much as a single assumption that makes essential use of form and matter counts as part of the official theory, and so falls outside the scope of “received views”. Where we are to draw the boundaries between contexts at the different levels will be a matter for discussion in the relevant chapters here. It is no surprise that Aristotle wishes to locate his views in the larger philosophical context he owes to his contemporaries and to his predecessors. It is also not surprising that he will think that those views must variously be adapted or emended—even outright rejected—as he proceeds to his own, “partisan” conclusions. The gradualist 21 Discussion that is “non-partisan” in the sense I intend will not beg the question against Plato and in Aristotle’s favour. But I emphasize that the use of the term means only that Aristotle does not deploy the views distinctive of his own theory—but not that there is no contention to be found in passages that I call “non-partisan.” On the contrary, there is an abundance of contention in Zeta, by no means all of it conducted from a platform of full-blown Aristotelian theory. 22 For more on purity, see Chapter 6.

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approach to the intricacies of his own theory is not unique to Zeta.23 In the account of change in Physics A, for example, for large stretches of the book Aristotle mines his predecessors in natural philosophy for the notions of subject and of opposite, and only late in the game makes the connection between these notions from the philosophical tradition and his own concepts of form and matter. Plato, meanwhile, enters the story at the very end in A9, where Aristotle suggests that by failing to distinguish matter and privation, Plato failed to recognize the full complement of items needed for a successful account of change. In Metaphysics Zeta, the engagement with Plato is more immediate, but the policy remains the same: not to confront Plato from the start with the details of Aristotle’s own views, but to open the discussion on the basis of what he can reasonably think of as common ground—from received or accredited views that do not obviously beg the question against Plato. Similarly in the de Anima, the definition of soul, which Aristotle announces is his target at the beginning of the first chapter, is deferred to the “new start” (palin d’ ho¯sper ex huparche¯s epanio¯men, 412a3) at the beginning of the second book in B1. In between we find extended discussion of a multitude of Aristotle’s forerunners, and different themes in their treatment of the soul, with prominent place given to Plato, who comes in for extended criticism. In all this, apart from fleeting mention of form and matter in the discussion of the different roles of body and soul in A2, (Aristotelian) form and matter make no appearance until chapter B1. The “new start” here recalls the last, and definitive “new start” (after the different and lesser “new starts” that initiate earlier segments of the book) in Metaphysics Zeta 17. In part, then, in Zeta as elsewhere, Aristotle is motivated by a sense of his place within the wider philosophical tradition. But he also sees the contemporaries who hold views different from his own as candidates for conversion to a properly Aristotelian theory. And to make the case for conversion compelling, Aristotle must start his debate with others on terms that they will not flat-out reject from the start. For this reason, it is important that the border between “received” and Aristotle’s own “partisan” views be observed throughout. The discussion in the body of Zeta 3, as we shall see, is sufficiently brief that the two levels are uncomfortably intertwined, and need more than usual care to keep apart. In the other, more protracted segments of Zeta, the distinction between levels is more easily managed. It is tempting to compare the stepwise way in which Aristotle reveals his own views in Zeta with the compressed version of the same procedure in the opening chapter of Physics B. Aristotle’s target there is the nature of natural objects. First, he

23

The same approach characterizes the entire body of books by Aristotle collected under the title Metaphysics, of which Zeta is a part: “There is every reason to suppose that Book A formed the first part of Aristotle’s course of metaphysical lectures. It is quite in his manner to begin with an historical inquiry”, Ross, 1924 I, xv.

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gives a list of things we ordinarily suppose are natural, or have natures, to get our initial ideas fixed. There follows a definition of the nature of a thing, as an internal principle of its behaviour. Finally, he explains which items in the ontology answer to the specification given: the form and the matter of a thing both qualify, to different degrees, as its nature. It may seem that Aristotle is headed on this same three-step strategy in Zeta: first, the list or lists (this is the survey in Zeta 2); second, the definition (this is the role of the different notions assembled in the agenda passage, 1.4 above, of Zeta 3); and third, presumably, the application to the “house” ontology of form and matter. In fact, however, the parallel between proceedings in Zeta and in Physics B1 is far from exact. In the first place, the attempt to establish a definition of substance in Zeta is for most of the time inconclusive: no genuine definition is forthcoming until the last chapter of Zeta. Only the view that the substance of a thing is also its essence—a necessary and sufficient condition for substance, but not its definition—appears to survive unscathed, and no authentic definition of substance appears until Zeta 17, where the definition, which Aristotle now endorses, is completely new. Not even the second step in evidence in the Physics, then, is attained in these earlier chapters of Zeta. A fortiori, there is no move there to the expected third step: if there is no successful definition of substance in these earlier chapters, there can be no route from a definition of substance to an answer to the application problem—to the problem of saying which items in his distinctive Metaphysics ontology count as primary substance. This is not to say that the view of (Aristotelian) form as primary substance is not on the table at various points in these chapters—but it is not the product of a definition of substance. The fact that no successful definition of substance is in prospect in these earlier chapters suggests that the result that forms are the primary substances can be obtained without the benefit of a definition of substance. To the contrary, when Aristotle offers a last and definitive definition of substance in the last chapter of Zeta (Chapter 11), the support goes in the opposite direction, from the view of form as primary substance, to the success of the definition that yields this result. For Aristotle, it is a condition on a successful definition of substance that it have this “partisan” consequence, that (Aristotelian) form is primary substance. We will return to the topic of levels later in this chapter (Section 8). First, however (Sections 3–5), I offer a brief survey of the three segments of Zeta which set out from the different received views of substance set out in the agenda passage, 1.4, in the beginning lines of Zeta 3. After this survey, in Sections 6 and 7 I look briefly at the other characters, Plato and others, in the drama that makes up Metaphysics Zeta. The last four sections, 8–11, of this chapter are reserved for a discussion of two very different readings of the argumentative strategy that governs Aristotle’s work in Zeta.

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THE THREE SEGMENTS OF ZETA:

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3 Substance and Subjects Aristotle sets out his agenda for the body of Zeta in the opening lines of Zeta 3; the remainder of the chapter takes up the “received” view of substances as subjects. Aristotle argues that the subject criterion under the current definition of subject—one Aristotle himself sponsors in the Categories—leads in the more developed ontology of the Metaphysics to a single, wrong candidate, namely matter, for primary substance. He also tells us that his theory recognizes three kinds of substances, form, matter, and form–matter compound, and that of the three, form is primary substance, while matter is ranked last. But he obtains this last result quite independently of the subject criterion;24 to the contrary, he uses the result to trump the deliverances of the criterion in its received form. Meanwhile, how, or even whether, form counts as a subject is left altogether up in the air. In this segment Aristotle’s concern seems to lie more with a critique of the received criterion for substance, than with using the criterion to reveal what counts as primary substance in his own theory. Zeta 3 is discussed in greater detail in Chapter 2.

4 Substance and Essence In the case of the view of the substance of a thing as its essence—taken up in the second segment, which covers Zeta 4 though 6 together with 10 and 11—it appears that Aristotle largely concurs with the received view and with various consequences he draws from it. While the connection between the notions of substance and essence is close, however, it is not so close as to yield a definition of substance as essence. Aristotle’s hospitality towards the received view is enough, however, to raise the worry that the segment provides equal support for his own “partisan” views and for those of his longtime opponent, Plato. In a variety of ways, the received view, along with such important consequences as the sameness of a (primary) thing with its essence (Zeta 6, 1031a28 ff, cf.10, 1036a1–2, 11, 1037a33–b7), cash out with equal ease in Plato’s and in Aristotle’s ontology. So it is not immediately obvious how the discussion of “received” views in Zeta 4 through 6 promotes distinctively Aristotelian conclusions in the ensuing “partisan” discussion in Zeta 10 and 11. In the event, Aristotle establishes no firm definition of the essence of a thing in the preliminary discussion in Zeta 4 through 6. And as noted, while the connection

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This is contrary to Burnyeat’s “common conclusion” assumption, Section 9.

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between the notions of substance and essence is close, it does not yield a definition of substance as essence (or of the substance of a thing as its essence). Finally, in the “partisan” chapters 10 and 11, Aristotle makes no effort to apply what characterization of essence he has to establish that the (Aristotelian) form of a thing counts as its essence, much less that because the form of a thing is its essence, for that reason it is the substance of the thing, or is primary substance. On the contrary, he asserts, without argument, only that soul is primary substance (Zeta 11, 1037a5); at best, we are left to infer from this and our knowledge from the De Anima that its soul is the form of a living thing, that the form of a living thing is primary substance.25 The segment on essence is discussed in greater detail in Chapters 3–7. In Chapter 3 I review Aristotle’s initial discussion of essence: its background in the Organon, the connection Aristotle reaffirms in Zeta 4 between the topics of essence and of definition, and Aristotle’s contrasting exclusive and inclusive views as to which kind of entity qualifies as having an essence. Chapters 4 and 5 (on the arguments in connection with snub in Zeta 5, and the Pale Man argument of Zeta 6) are concerned with Aristotle’s relations with his other self in the SE—a text which provides the logic that drives various arguments in the segment. Chapter 6, on the sameness of each primary thing with its essence in Zeta 6, is concerned with Aristotle’s relations with Plato, and with ways in which he and Plato largely see eye to eye. Chapter 7, finally, looks more closely at the relation between Zeta 4 and 6 and their sequel in Chapters 10 and 11, where mention of form and matter is not out of court.

5 Substance and Universals In the account given in Section 4 I suppose that Aristotle accepts the received view that the substance of a thing is its essence: essence and the related notion of definition genuinely have a place in the new, “partisan” theory of substance, and the role the two notions play there mirror in certain ways the role they have in the “received” theories with which Aristotle began. In the final segment of Zeta set in motion by the Zeta 3 agenda, however, on substance and universals, he is busy once more dismantling the received view that supposedly is the starting point of the segment. Aristotle is clear from the start that he rejects Plato’s account of substances and universals (Aristotle at first leaves the author(s) of the view he rejects anonymous, but Plato is surely his primary target). His critique is fashioned around two restrictions on the class of substances: (i) no universal can be a substance; and (ii) no part of a substance can be a substance.

25 For the view, controverted in Section 11 and subsequent chapters, that Aristotle’s conclusion in Zeta is that (Aristotelian) forms are the primary substances, see Rorty (1973), mentioned in the Preface above, and Burnyeat (2001).

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If, in fact, Aristotle’s own forms are both primary substances and universals (Aristotle is silent here, as he must be, since the discussion is in “non-partisan” mode), the details must be quite different from anything in Plato’s theory in light of conclusion (i) above. But if Aristotle rejects the opening, Platonic account of substances and universals, and if his criticisms do not extend to saying how Plato’s account is to be corrected, how can the starting point of the segment be the source of positive conclusions in the following, “partisan” chapters of the segment? Our best move may be to recalibrate our take on Aristotle’s position at the beginning of Zeta. Aristotle waxes rhetorical at the end of Zeta 1 that the primary task of Zeta is to find a definition of substance (1.1 above), and Zeta 2 closes with a demand for the “sketch” of an answer to the question, What is substance?26 The agenda at the beginning of Zeta 3 (1.4 above) takes up the task by setting out various notions commonly thought to be constitutive of substance. Suppose that some if not all of these “received opinions” come from outside, and that alongside his interest in promoting his own theory, including the idea that (Aristotelian) form is primary substance, Aristotle means to test the truth of his theory against received opinions. At the same time, such tests are accompanied by the proviso that a failure of fit between received opinions and Aristotelian theory may best be remedied by some emendation or qualification of the former in their received form. In this spirit, in the discussion of essence in Zeta 4 and on, Aristotle is anxious to show that he is to a significant degree in harmony with the received characterization of substance. But in Zeta 3 on subjects, as in the segment on universals that begins with Zeta 13, his main interest is in criticizing the received view in its existing form, and—to the frustration of his modern commentators—any positive agenda regarding his own theory is very much to one side. Despite his scepticism about a Platonic view of universals, however, it is possible to find in the later chapters of the segment the hint of a theory of universals that is free of the burdens of Platonism. In Zeta 15, for example, Aristotle argues of a variety of items, all of them particulars, that (a) they are substances and, hence, prima facie candidates for definition, but that (b) they are after all indefinable. Plausibly, then, he would hold that a thing is a (primary) definable, only if it is in some way both a substance and a universal. On this reading, the discussion in Zeta 13 through 16 forces a revision in rather than the outright abandonment of the received (Platonic) view that substances can be universals. A policy of revision rather than rejection, as we have seen, may also be appropriate in the case of the view of substance as a subject discussed in Zeta 3.

26 Burnyeat (2001), 13–15, argues that the “sketch” demanded at the end of Z2 is met later in Z3 by the “sketch” at 1029a7–9 of substantial being afforded by the primary subject criterion. I am supposing that the demand of Z2 is answered in Z3 by the full range of options in 1.4, see this chapter, n. 49.

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THE ANTI-PLATONISM OF ZETA, AND SOME OTHER PARTICIPANTS IN THE DEBATE

6 A Place for Polemics As the survey in previous sections suggests, Aristotle keeps firmly in the background any interest in arguing from the various opinions of record about substance on offer in Zeta 3 in order to establish central tenets of his own, “official” theory of substance. For large stretches of text, he is silent about his own proprietary views about substance, and his arguments proceed in broadly “non-doctrinaire” terms taken from his own Organon, or from his philosophical friends and rivals. In places, the discussion is entirely friendly, and results that appear desirable in their original setting among the received views have relatively easy counterparts in his “official” theory of form and matter. In other cases, various puzzles that arise among the received views, and have a resolution at that level, can be resolved with equal success in the “official” theory of form and matter. In both kinds of case, Aristotle’s purpose apparently is to confirm his own theory, by showing that it is able to reproduce what is successful in the views it is intended to supersede. In other places, Aristotle’s discussion brings to light difficulties and inconsistencies in the received views. Here, his intent is mainly polemical, and as far as the details of his own, positive views go, he is at his most oblique. All the same, it is not hard to imagine ways in which he can bring the various opinions of record about substance into a form which is not only internally consistent, but which will cohere with his own official, “partisan” theory. In many parts of Zeta it is easy to see Plato as the (unnamed) target of Aristotle’s criticism of received views. But it is worth considering the possibility that Zeta is antiPlatonic not just on an occasional basis, over isolated points of controversy, but on a global scale. It is not beyond reason to see Plato’s hand in the initial received opinions (1.4 above) that set up most of the discussion in Zeta. For all Aristotle tells us directly, the three views that structure the body of Zeta are each attributable to different authorities, and do not even pretend to add up to a single coherent notion of substance. At the same time, there is evidence that two, perhaps even all three, are due, directly or indirectly, to the same author. We have Aristotle’s word elsewhere for the view that Plato’s forms are the essences of their participants;27 and in Zeta 13 he seems to suggest that the origins of the view of substance as a universal are to be found in Plato (“in certain quarters,” tisin, 1038b7, from 8.5 below).28 Finally, the view of substance as a subject, in the form in which it is considered in Zeta 3, is due at least in part to the Categories. In the Categories, arguably, Aristotle corrects a Platonic view on which 27

Metaphysics A6, 988a8–11, 7, 988b4–5, M5, 1080a1. But this is not always his view: see, for example, Z4, 1030a13–14. 28 For the identification with Plato, see Ross (1924) II, 209, and for the larger background in Plato, FredePatzig (1988), II, 244.

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(Platonic) forms are primary because they are privileged subjects of a certain sort.29 If so, then Plato is ultimately one source—perhaps, only one among many—for the view of substance as a subject as well. If in the end Plato is the author of—or more cautiously, subscribes to—all three received views, this does not guarantee the truth of any of them, much less that together they make up a single coherent theory in the way that Plato presumably will have hoped. The first casualty is the attempt to define substance in terms of subjects. As Zeta 3 shows, the conception of subject in the Categories can no longer stand the light of day. The problem is not that the subject criterion is inconsistent with the view of substance as essence, or as a universal, but that it works out badly applied to the new “official” theory of form, matter, and form–matter compound.30 In this case, Aristotle will use the new theory to correct a received view, with help from other, presumably more authoritative constraints on substance, namely, separability and thisness, both of which figure in the “big tent” outline in Zeta 1 of features that belong in any good theory of substance. The received view of substance as subject in Zeta 3 is inconsistent in yet other ways with Aristotle’s views both in Zeta 3 itself and in other chapters of Zeta. Thus, as we have already seen (Section 4), the received view, that substance is that of which everything else is said, while it itself is predicated of nothing further, is juxtaposed in Zeta 3 with Aristotle’s official view, that substance—that is, in the official view, (Aristotelian) form—is predicated of matter. In Zeta 13, meanwhile, Aristotle at first sight says, apparently agreeing with Zeta 3’s first thoughts, that a substance is not predicated of anything (1038b15, included in 8.9 below)—how then can a substance be universal to anything, as Aristotle surely thinks it must be, let alone predicated of matter, as he repeatedly says it is? Here, I take it, Aristotle’s view is that the situation is untenable, given Plato’s account of substance, predication, and universals—but perhaps not, given an Aristotelian view. In Zeta 13, arguably, Aristotle’s purpose is to oppose the Platonic view that a substance is universal to, and hence, also predicated of, the very things of which it is the substance. Opposition to this view of Plato’s leaves ample logical and conceptual room for the contrary position which (in broad terms) I suspect is Aristotle’s, that an item can be simultaneously universal to one set of things, and the substance of another. So Aristotle’s views about substance and predication are ruled out on Plato’s view, and

29 Plato and the Aristotle of the Categories agree that primary substances are subjects—even, primary substances because they are subjects—but disagree radically over the details: see Lewis (1991), 72–3, and Chapter 8, Section 15. But I know of nothing in Aristotle’s text that directly supports this view of the Platonic background of the subject criterion; support is absent, for example, from the discussion of received accounts of substance, including substance as ultimate subject, in Metaphysics ˜8. 30 But is the subject criterion in fact inconsistent with the view of substance as a universal? Perhaps yes, on a Platonic view of universals, but no on an Aristotelian view; see the paragraphs immediately following in the main text.

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ruled out too on the received view of Zeta 3—but on an official Aristotelian view, they may not be. At the same time, Aristotle may well mean to point out a tension between the received views of the substance of a thing as both the essence of, and also universal to, the very thing[s] of which it is the substance. Once again, the story involves controversy with Plato. In the discussion of essence, Aristotle appears to endorse the governing assumption, which I take it originates with Plato, that one thing is the substance of another just in case the first is the essence of the second. At the beginning of Zeta 13, Aristotle takes up a Platonic view of universals expressly modelled after this view of essence: thus, one thing is the substance of another just in case the first is universal to the second. Later in the chapter, the parallel with the discussion of essence is explicitly set aside (1038b16–17, included in 8.8 below). Rather, as we have seen, it may be that the substance of a given thing is universal to an altogether different set of things. Again, from views he and Plato hold in common about essence, Aristotle extracts an assumption in the Primary Argument in Zeta 13 that he directs against Plato’s view of universals. Arguably, the shared conclusion of Zeta 6, asserting the identity of things that are suitably primary with their essences (Chapter 6), is needed to help establish the Partial Functionality assumption that is central to Aristotle’s case in the Primary Argument against Plato’s view of universals in Zeta 13 (Chapter 8, Section 3–5). If this account can be made out (I postpone the details until Chapter 6), then the resources of the discussion of essence in Zeta 4 and following are deeply implicated in the opening account of substances and universals in Zeta 13. On the reading I will offer, Aristotle holds that Plato is part right—right about the connection between substance and essence—part wrong—wrong about how substances are also universals. And in Zeta 13, as I see it (Chapter 8), he uses what he finds to be right about Plato’s views to overturn what he thinks is wrong about them.

7 Expanding the Dramatis Personae Plato is notable among the outside figures whose views come under scrutiny in Zeta, but he is not alone. Equally striking among the unexpected presences in Zeta is that of Aristotle himself—the Aristotle of the Topics or the SE, it may be, or of the Categories, or the Posterior Analytics, or (glancingly) the Physics. Views from all of these catch Aristotle’s interest in the discussion of “received” views in different non-partisan parts of Zeta. As in the case of Plato, the character of Aristotle’s engagement with his alter egos runs the gamut, from outright approval (Zeta 17 and the Posterior Analytics) to disapproval (Zeta 3 on the subject criterion vis-a`-vis the Categories and Physics).31 31 With respect to his engagement in Zeta with various of his own “other” selves in other texts, Aristotle is apparently willing to follow his own advice: “If we cannot find anyone else to argue with, we should argue with ourselves”, Topics ¨14, 163b3–4. The citation is from Burnyeat (2001), 103.

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At various places in Zeta, above all in the discussion of essence in Zeta 4–6, Aristotle relies heavily on modes of arguing familiar from the Topics and SE. The presence of these other selves at times is entirely benign, as with the variety of moves set out in the Topics, and used to effect in the discussion of essence in Metaphysics Zeta 4. But the presence of Aristotle from the Topics and the SE can also be disconcerting, as in the puzzles of essence in Zeta 5. In the SE, Aristotle puts together a set of puzzles he himself there regards as defective; despite this, a more elaborate version of the puzzles appears in the discussion of essence in Metaphysics Zeta 5. In Zeta 5 Aristotle is seeking additional support for the view that “only substances” can have a definition or an essence in the full sense, by giving reasons to think that items like the snub or snubness, which are not substances, do not do so. The more spectacular of the puzzles he uses to prove his point involve reduction to “babbling” (adoleschein), also featured in the SE: for example, if (the) snub = hollow nose, then snub nose = hollow nose nose, and if snub = snub nose, then snub nose = snub nose nose . . . and so on ad infinitum. This is material that Aristotle apparently discards in the SE, and it sits oddly, to say the least, in the middle of the discussion of substance in Metaphysics Zeta. The Pale Man Argument that appears in the segment on essence in Zeta 6 raises similar questions. The Argument involves the (mis)application of logical principles sanctioned by the Topics in support of a conclusion Aristotle endorses, even as he declares the Argument itself invalid. In the discussion of substance as a subject in Zeta 3, meanwhile, the Aristotle of the Categories enters the discussion only to meet with outright rejection. Aristotle argues that the subject criterion for substance which dominated the Categories, in the new metaphysical context where form and matter are now in play, promotes matter—the least likely of the three candidates, form, matter, and the form–matter compound—as primary substance. (Zeta 3 also engages, and casts a sceptical eye on, the tendency in Physics A but corrected in B1, to think of matter as the primary candidate for the nature of a thing.) Of major importance, finally, the Aristotle of the Posterior Analytics takes centre stage in the closing chapter, 17, of Zeta, where Aristotle draws on the Analytics conception of substance as a cause in order to underwrite a major “new start” after the different segments set in motion by the agenda of Zeta 3. In the complementary account in Eta 2, Democritus is cited for the idea of the differentiae of being which, suitably expanded and adapted, provides an analogue for Aristotelian form as the actuality of sensible substances. It is not hard to imagine that Plato too has a place in the ancestry of the causal account of substance under way in these chapters. Aristotle finds clear benefits in the engagement with the views of others. Despite the negative results of Zeta 13–16, for example, the encounters with Plato in Zeta are not invariably fruitless. Plato is a philosophical friend, not a foe, in the discussion of the sameness of a thing with its essence in Zeta 6. There is also a positive side to Plato’s view

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of substance as a cause, which in Zeta 13 Aristotle links to a failed view of universals.32 Plato’s idea is revived in the “new start” in Zeta 17, where it is married to Aristotle’s own analysis of causes from the Posterior Analytics. This new start leads to an account of substance that sticks, and that may even show how to salvage what is good from the remnants of the received views that dominated the approach to substance in the body of Zeta. Once the account of substance is secure, as I would argue it is by the end of Eta 1, Aristotle is free to pursue the application to his own “partisan” theory of form, matter, and form–matter compound in the remainder of Eta. (Here, as we have seen, Democritus takes his place as a forerunner of the Aristotelian theory of form.) Aristotle’s is a view of substance that allows that a material substance can have (metaphysical) parts; and Eta ends with Aristotle’s best account of how such parts combine to make a genuine unity. At the same time, Aristotle tells us, it is the lack of such an account that is to blame for the problems over unity for which he has been chiding Plato. Once the definition of substance is in place, and its authenticity against the background of received opinions is established in Zeta 17 and in the retrospective in Eta 1, the main item of unfinished business is surely the discussion of unity which takes place in Eta 6. In the present book, our interest is in Zeta and our discussion will end with the retrospective in Eta 1. This review of the contents of the three segments leaves one large set of issues still in need of attention. In the recent literature, two major assumptions, Levels and NonLinearity, have been thought to govern the structure and contents of the arguments Aristotle sets out in Zeta in pursuit of his initial agenda. I discuss these two assumptions in Sections 8–10. In the concluding Section 11 I offer some preliminary remarks about possible alternatives to the story that the second, Non-Linearity assumption recommends.

TWO CONSTRAINTS ON THE ACCOUNT OF SUBSTANCE? LEVELS AND NON-LINEARITY Two major structural peculiarities—at best, only hinted at in Aristotle’s text—have been thought to constrain large parts of the argument of Zeta.33 One assumption is that of levels, two in all—the one lodged in “received” views from the philosophical tradition, the other representing Aristotle’s “official” or “partisan” theory of (Aristotelian) form, matter, and form–matter compound.34 The second assumption, Non-Linearity, 32

Chapter 8, Section 2, and Chapter 8, n. 6. The two assumptions I am about to describe are the centrepiece of Burnyeat (2001): while versions of the distinction in “levels” appear in the earlier published literature (this chapter, n. 36), Burnyeat’s is by far the most extended and most vigorous treatment. 34 Burnyeat (2001) labels the two sides of the distinction between levels, “logical” and “metaphysical”. The term “logical” follows Aristotle’s logiko¯s in Z4, 1029b13 (in 3.4); other occurrences in Zeta are at Z4, 1030a25, and Z17, 1041a28 (see also ek to¯n logo¯n, in the retrospective at H1, 1042a12–13). If Aristotle’s 33

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is constructed out of Aristotle’s reference to the “fresh starts” that introduce each new segment based on the agenda he sets out for himself at the beginning of Zeta 3. I take up the two assumptions in order in Sections 8–10.

8 Levels After the preliminaries in Zeta 1, Aristotle turns in Zeta 2 to a list of candidates for substances offered up by the philosophical tradition. The tradition is again in evidence in Zeta 3, where we find a collection of “received” views that purport to give the definition of substance, or of the substance of a thing. Thereafter, the first order of business in each segment of Zeta is to work up the “received” criterion for substance it inherits from the opening of Zeta 3; in line with their origins, Aristotle’s initial discussion of the different criteria runs in terms of “received” opinions, while his own views are largely suppressed. Two segments contain multiple chapters, and discussion of his own “official” theory of form and matter is reserved for later chapters of the segment; in the case of the single chapter, 3, devoted to substance as subject, the two levels weave in and out of the discussion throughout. The separation between the two parts of his inquiry—on the one side, the appeal to the philosophical tradition, and on the other, his “partisan” views, where the official theory of form and matter belongs—is signposted only lightly, if at all, by Aristotle himself.35 The tradition delivers views commanding different degrees of credibility in Aristotle’s eyes. Received views as a group will include data regarding “how we speak”. Of received views, some, perhaps the majority, will be accredited received views, with the authority of Plato or some other figure not identical with Aristotle. Others, finally, will be accredited because they belong to Aristotle himself, in passages (principally from the Organon) that do not include reference to form and matter. In this taxonomy, ideas fall guidance over the term logiko¯s is uncertain, he gives no guidance at all as to an appropriate label for the remaining level. Burnyeat, 19–24, has much to say of help in understanding the different uses of logiko¯s in Aristotle (other, more recent reviews appear in Chiba (2010) and Peramatzis (2010)). Even so, the use of the term by Aristotle, not to mention his commentators, is complex, and invites controversy. There is even disagreement in the literature even as to how much of Zeta Aristotle means to mark off by the term—even, perhaps, only the first half of Z4. Disagreement over the different meanings of logiko¯s in Aristotle should not distract from a central theme of the present book: namely, that for large tracts of Zeta, Aristotle is canvassing the work of others, or of his own other selves, for ideas that are not (or not yet) framed in terms of the full apparatus of the official Metaphysics ontology of form and matter. Hence, not only the “Friends” of some chapter headings below, but also philosophical foes, with room too for Aristotle’s own “other selves”. In place of Burnyeat’s “logical”, then, I talk of Aristotle’s appeal to how people speak and, in particular, of his interest in what informed people have to say, where “informed people” may include even Aristotle’s other selves in contexts where form and matter are not mentioned. For further discussion, see Section 2. I will sometimes use the label “partisan” for passages that draw on Aristotle’s “official” theory of form and matter, and “non-partisan” for places where he withholds the specifics of his own developed views: discussion that is “non-partisan” in the sense intended will not beg the question against Plato and in Aristotle’s favour. As before, however (this chapter, n. 21), a passage that is non-partisan in this sense may still be quite contentious. 35

See this chapter, n. 34.

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under the rubric of “received views”, not so much because of their provenance as because they are conceptually independent of Aristotle’s “partisan” views in the theory of form and matter. Then again, we find views that belong in Aristotle’s “in-house”, full-blown theory because they make essential use of the notions of matter and form. Aristotle’s own, developed theory will not rely on form and matter alone, and may well also accommodate a variety of received views, the latter adjusted as needed to warrant their place in the fullblown authentic Aristotelian theory. But it does not go the other way: the collection of received views from which Aristotle’s argument begins in the three segments of Zeta may not include material from Aristotle’s “partisan” theory of form and matter, on pain of begging the question against the philosophers Aristotle means to convert to his own views. However lightly mapped by Aristotle himself, the division between the two kinds of inquiry just described has come to seem an obvious feature of the terrain in Zeta.36 Aristotle’s reticence in Zeta about his own theory of form and matter and the resulting difference in “levels” require explanation in ways that go well beyond what is given in the text. Aristotle’s purpose in working through the views of others may well be primarily tactical. He means to engage his audience and, in particular, to engage the Platonist, and to bring his current or perhaps former colleagues in the Academy around—to convert them—to his own metaphysical point of view.37 So we are to think of him as edging his way forward towards his own favoured theory, but starting from concepts familiar from the philosophical tradition—even concepts from his own Organon (say), large parts of which the Platonist along with everyone else can accept because they are instrumental but theory-neutral. In the event, the engagement with Plato can go forward in ways that ways that are friendly, and also in ways that are not. In some chapters—the discussion of essence in Zeta 6, for example—Plato is friend, not foe, as Aristotle argues for his thesis that each primary thing is the same as its essence. By couching his argument in Zeta 6 in terms of an alien Platonic ontology, Aristotle is able to restrict his sameness thesis to primary substances, as required, while remaining non-committal on which the primary substances are in his own ontology. Later in Zeta and in Eta, however, he is perfectly clear that his forms are the primary substances, and subject to the identity result of Zeta 6.38

36

For the difference in levels, under different labels and with varying emphases, in addition to Burnyeat (2001), see Bostock (1994), 116, Ferejohn (1994), and Code (1997). Not every recent commentator is convinced by the distinction in levels. One hold-out is Wedin (2000), who argues strongly for a “proleptic” view (my term) of Aristotle’s account. Thus, for example, when in Z4 Aristotle assigns genous eide¯—“species of a genus”?—to the slot he devises for things that are suitably primary, Wedin argues that by genous eide¯ he must mean (Aristotelian) form. (He has precedent here in Lewis (1984), rightly criticized in Burnyeat (2001).) But the stronger the arguments that Aristotle meant that his forms are the primary substances, the more unlikely it becomes that he did mean it—but simply failed to say so. 37 So Burnyeat (2001), 125. 38 For the arguments of Z6, see Chapters 5 and 6.

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In the case of Zeta 6, Aristotle has no doubt reasons of strategy, even of drama, for making common cause with Plato, while keeping his own theory in the background.39 Elsewhere, however, his intent is more that of philosophical critic, with Plato as his especial target. So there is a persistent polemical undertone to Zeta, and we will return to the polemical side of Zeta frequently in what follows. I have described a division between passages rooted in a framework of received views, from which mention of matter and form is excluded, and the “partisan” framework of Aristotle’s official theory. As already noted, the boundary between the two is one-way: Aristotle is always free to reach from a later “partisan” passage into a previous passage rooted in the philosophical tradition, but no passage that deals in terms of received views may use results from any “partisan” one, on pain of losing its status as independent of the official Aristotelian theory. One interpretative caveat results from the prohibition against importing the “partisan” into the discussion of received views: it will be premature to try to settle in-house disputes about matter or form in the passages of the latter sort—e.g., does Zeta 6 or 13 (both chapters that carefully avoid discussion of Aristotle’s own “official” theory) require a conception of form as particular, or as general?—since the very concept of (Aristotelian) form is excluded here.40 But in a “partisan” passage, the results of a preceding passage that gets its impetus from “received” views are always fair game. Indeed, a major point of the division between levels is to provide a body of received views, variously adapted for their new context as later inquiry proceeds at the “partisan” level. Given the differences between the two levels, should we anticipate difficulties in accomplishing the shift from the first level to the second, “partisan” one? Even in passages where the focus is on received views, Aristotle is interested in how a given condition on substance applies in the ontology of others—most conspicuously, in Plato’s. But once the condition has been properly worked-up, we might reasonably expect that he will ask how to apply it in his own distinctive ontology of form, matter, and form–matter compound. At the same time, if in each segment of Zeta Aristotle applies a different criterion for substance, we must ask how in the end the different applications mesh. If the different criteria, after suitable adjustment, belong together in a single coherent theory, will there be some single kind of item in Aristotle’s preferred theory that all the applications in the different segments in unison pick out as primary substance? We may also hope for some conceptual unity behind the different criteria. In this way, the application problem within a segment, taken across segments, mutates into the problem of unity. What measures does Aristotle take to assure us that the work of the different segments is unified in the appropriate way?41

39 40 41

“reasons of strategy”: see Chapter 6 below. Burnyeat (2001), 28–9, 46, 55; see the remarks about “proleptic” readings of Z1, Section 1. I say more on the topic of unity across segments in Section 2 and in Chapter 12.

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This question takes on a greater urgency on one current account of Zeta. As each of the later segments of Zeta begins, Aristotle describes himself as going back to the initial list in Zeta 3 for the next item of business.42 This is sometimes paraphrased by saying he is making a “fresh start”;43 and this in turn has been taken to mean that we may not expect the argument of Zeta to be cumulative from one segment to the next. The restriction is surprising, not to say controversial; it is the Non-Linearity assumption, and our topic in the following two sections.

9 Non-Linearity: Inaccessibility and the Common Conclusion Assumption As we have seen, the three main segments into which the body of Zeta divides are constructed around the received views announced in Aristotle’s agenda (1.4 above) at the beginning of Zeta 3. The Non-Linearity assumption that supposedly governs the argument of the three segments has two components. In each segment, first, the two levels work together in such a way that “each of his [Aristotle’s] four starting points leads . . . to the same conclusion: substantial being is form”.44 At the same time, second, each segment proceeds to that conclusion independently: no assumption made or result obtained within one segment of Zeta is to be carried over into any other segment. In particular, as we shall see, the received view about substance that motivates a given segment cannot be carried over into any other segment.45 (One set of views, however, presumably is exempt from Non-Linearity: these are the common stock of assumptions—exclusive of the agenda items from Zeta 3—drawn from the philosophical tradition at large, which do not rely on the distinctive Aristotelian notions of form and matter, and so are sufficiently neutral that they may appear anywhere in any segment.) Both of the requirements that together make up Non-Linearity require attention. I begin with the Common Conclusion assumption. A majority of commentators would agree that for Aristotle, Aristotelian forms are primary substances in Metaphysics Zeta and Eta. It is less clear that Aristotle explicitly states this as the conclusion to each of the three segments into which Zeta divides. On the contrary (Section 11), he may use his view of that forms are primary substances as a means for confirming (or disconfirming) a given proposal for the definition of substance. It is still less clear—indeed, it is contrary 42

Thus at the beginning of the second segment on essence and the beginning of the third on universals: “Since at the start we distinguished (en arche¯i dieilometha) by how may we define substance, and one of these appears to be the essence”, Z4, 1029b1–3; “Since our inquiry is about substance, let us go back again (palin epaneltho¯men)”, Z13, 1038b1–2 (for translation and meaning in context, see Burnyeat, Chapter 8, n. 3). Notably, however, Z17 gives us a more radical new start, without any reference back to Z3. 43 The “fresh start” language is in Ross (1924) I, lxxvii, xciv. 44 Burnyeat (2001), 4–5, my emphasis. 45 Non-Linearity does not require that the results of earlier segments be junked, but only that they may not be presupposed. Even this, however, may be more than Aristotle’s language of “going back” to the original list (this chapter, n. 42) requires.

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to the case—that identifying forms as the primary substances is the conclusion of Zeta as a whole. Recall that the task Aristotle sets himself in the opening chapters of Zeta is to define substance (1.1 above). It is this project—the project of defining substance (singular) or, better, the substance of things—that is Aristotle’s main aim in Zeta, and I will suggest that his answer is plain to see in the closing chapter, Zeta 17 (Chapter 11). By comparison, identifying the class of things that count as (primary) substances is of secondary importance.46 We may also find surprising the “Inaccessibility” requirement, also part of NonLinearity, to the effect that assumptions (and results obtained on their basis) in effect in the “partisan” portions of one segment of Zeta are not accessible at any other segment. According to the Common Conclusion requirement, as we have seen, whichever of the three received characterizations of substance we choose, the same conclusion follows, revealed in the second, “partisan” half of each segment: primary substance is (Aristotelian) form. Bating our doubts above over whether this is Aristotle’s common conclusion, why would he deny himself the benefits of a cumulative argument in order to prove it, and opt instead for Inaccessibility?47 The reply that Aristotle’s policy is, “Do this four times in a row”, not “Do this the same way four times in a row”,48 underestimates Inaccessibility, as well as the objection to it. Multiple arguments for the same conclusion can be different, even interestingly so, without having to meet the requirement that no “partisan” segment can borrow (“partisan”) material from any other. To highlight the difficulties with Non-Linearity, I offer a sketch of how the overall argumentative strategy of Zeta would have to go, if the Inaccessibility and Common Conclusion clauses of Non-Linearity were genuinely in force there. The essentials of the resultant view, I hope, will be relatively clear. The view has the further helpful

46 Plausibly, Aristotle begins his search for a definition of substance with a preliminary definition (along with a preliminary idea of the class of entities that answer to it). One view might be simply that the substances are the basic entities, than which nothing is prior; Aristotle’s review of received views at the beginning of Z3 (1.4 below) offers the promise of a more developed account. His work in the body of Zeta on the various options offered in Z3 leads towards the “new start” and the full-blown definition in the final chapter of Zeta, where the substance of a thing is defined as the cause of its being. In this procedure, it is tempting to hear echoes of the An. Po., and the thought that scientific inquiry will begin with a preliminary account of what a term means, together with some grasp of the class of entities that answer to the term; see Bolton (1995) 1996, 249–50. 47 Burnyeat suggests that Non-Linearity, which involves reaching the same conclusion independently several times over, serves the “pedagogical aim” that underlies the methodological peculiarities of Zeta. But this does not address the issue of unity raised three paragraphs above in the main text. Equally important, the different attempts are not based on independent but equally firmly established starting points—on the contrary, Aristotle puts some effort into discrediting two of his three starting-points, at least in the form in which he receives them—so that there is no clear sense in which one argument reinforces another, see further Section 4. 48 Burnyeat (2001), 81, n. 7, responding to Lewis (1999) 2000 and Wedin (2000).

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feature that it is clearly wrong. Getting straight on where the main fault lines lie may help us see better the form Aristotle’s arguments in fact take.

10 The Logic of Non-Linearity I begin by noting again what seems a striking omission at the very beginning of Aristotle’s definitional project. Aristotle sets out the promised outline of his project at the beginning of Zeta 3:49 repeating 1.4 above, 1.4 Substance is said, if not in more ways, at least chiefly in four: that is, the essence and the universal and the genus are thought to be the substance of each thing, and fourth of these, the subject.

Astonishingly, he omits to tell us whether these different characterizations of substance complement each other, or whether instead they compete. As we have already seen (Introduction, Section 1, and this chapter, Section 2), we are left to decide whether these are potentially rival conceptions of substance, or whether they are separately partial characterizations of what together adds up to a single unified notion—something that is (in certain ways) both a subject and an essence and a universal.50 Given Aristotle’s silence on these questions,51 the safer course is to suppose as a working hypothesis that 1.4 gives us a disjunction of options. If we suppose that disjunction in this case is inclusive, our hypothesis is consistent with finding that more than one criterion applies, or even that all apply in harmony together; but this is not required. So the argumentative strategy we are attributing to Aristotle begins with nothing more than a disjunction of propositions each of which—even, perhaps, more than one of which—may in some way or another be constitutive of the notion of substance.52 Add to this the Common Conclusion and Inaccessibility assumptions above, and we seem committed to the standard technique for arguing from a disjunction: namely, that of Constructive Dilemma (“CD” hereafter). On this picture, the three segments of Zeta arrange themselves into three separate sub-derivations, each taking as its lead assumption a different disjunct from the original disjunction, and all three driving to 49 “promised outline”: hupotuposamenois, Z2, 1028b31. The definition of subject gives one part of the outline (Z3, 1029a7–8, tupo¯i eire¯tai ti pot’ estin he¯ ousia), but the complete outline encompasses the full range of options offered in the first sentence of Z3; see this chapter, n. 26. 50 If, as I am inclined to think, the received views all originate with Plato (Section 6), this does not guarantee the truth of any of them, much less that together they make up a single coherent theory. If in Aristotle’s eyes the different views do not cohere together, he may prefer to take them one by one, rather than try out their conjunction. 51 I cannot see that Aristotle resolves these questions in the survey in ˜8 either: his introductions to the different strands in ousia—allon de tropon; eti . . . ; eti . . . ; and kata duo tropous . . . —give no guidance on the matter. 52 I say “constitutive of the notion of substance” because, however intended by their author or authors, the different options in 1.4 may not succeed as definitions of (primary) substance, and at best may be only constraints on a definition, offering necessary and sufficient conditions on the notion of substance, for example.

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the same conclusion, that (Aristotelian) form is primary substance. As standardly with CD, the conclusion follows from the original disjunction, providing it follows from each of the disjuncts in the different sub-derivations. The standard requirements on CD assure us that Non-Linearity is satisfied in the argument: the disjunct that heads a given sub-derivation, along with any lines in the sub-derivation that are derived from it, are inaccessible at lines that lie outside that sub-derivation. In particular, it is inaccessible at the other sub-derivations. As a consequence, the order in which the different subderivations appear is immaterial.53 Excluding the guiding views given in 1.4, however, the “received” views from the tradition at large constitute a prior set of assumptions, accessible at all three sub-derivations alike.54 Aristotle’s text fails to match the blueprint suggested by the CD account in almost every particular. But if the CD account correctly represents the logical strategy behind Non-Linearity, and if the CD account fails, it appears that Non-Linearity fails along with it.55 An initial objection to the CD account is that Aristotle gives us little or no reason to accept the initial disjunction. The initial range of options is handed on by the philosophical tradition and so worth initial consideration—but does it exhaust all the likely possibilities? Could it be that—does it even turn out that—none of these attempted definitions is correct, and the truth about substance lies somewhere else entirely?56 Other objections may cut a little deeper. First, if Aristotle is driving towards the common conclusion that (Aristotelian) forms are primary substances, the required subderivations for this conclusion will need various ancillary premisses—that forms are subjects (in line with the definition of subject); or that forms are essences, or that they are universals (following the definitions of essence and universal). Does Aristotle explicitly 53 Burnyeat (2001), 15–16, asks if there is any significance to the order of the different segments of Zeta; but on the CD account, if there is any significance, it will be rhetorical, not logical. The observation about order is due to a remark in conversation by Kit Fine, who offered it as a comment on Non-Linearity. 54 Finally, notice that the option from Z3 that the substance (of a thing) is a genus is quietly dropped from the disjunction that heads up the argument; see this chapter, n. 18. It may help to think of the third disjunct, that substance is a universal, as incorporating two options, that either substance is a species or it is a genus. On this understanding, listing substance as genus as a separate disjunct amounts to supposing that either substance is a species or a genus, or it is a genus; which simplifies to just: substance is either a species or a genus. That is, as before, substance is a universal, where the possibility that substance is a genus is included as one of the available options. This is how Aristotle sets up the argument of Zeta; it is also how he proceeds in Z13–16, on substance as universal, where he devotes chapter 14 to the special case of substance as genus, which gets separate mention again at H1, 1042a13–15. 55 Burnyeat (2001), note, p. 82, agrees in finding CD unpalatable as an account of the form of Aristotle’s argument. Pace Burnyeat, however, failing the CD account, I can think of nothing that would motivate the inaccessibility component of Non-Linearity. 56 Aristotle acknowledges from the start that other characterizations of substance are available: “substance is spoken of, if not in more ways, at any rate in four above all” (my emphasis, from 1.4 above). Again, separation and thisness—not on Aristotle’s initial list of four—threaten to displace the subject criterion in Z3. And Z17 finds a “new beginning” in the idea that substance is a cause of some kind. It is not obvious how this last characterization of substance is related to those cited at the beginning of Z3, and so not obvious whether or not it invalidates the initial disjunction: see Chapter 12, Section 1.

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state the needed claims? And if so, does he use them as premisses in the relevant subderivations, as the CD strategy requires; or are they (all or some of them) things he believes true, without ever setting them in the context of the arguments indicated? But do all three segments in Zeta in fact have a single common conclusion? That form is primary substance is certainly Aristotle’s considered judgement, and it appears in each segment (although very obliquely in the segment on universals). But (again) it is one thing to be able to locate the relevant statement in the required stretch of text, and quite another to find it set out as conclusion to an argument along the lines of the different sub-derivations given above. More serious still, as we have seen (Section 9), Aristotle can hardly think that the assertion that form is primary substance satisfies the search for the definition of substance that is the announced target of Zeta. At most, he has an interest in showing that it is a consequence of whatever of worth survives of this or that definition he inherits from the philosophical tradition, that (Aristotelian) form is primary substance. At stake here, however, is not the status of Aristotelian form, which is not in doubt, but rather the prospects of the would-be definition. The technique of CD fits this interest in definition rather poorly. CD is a technique for arguing from a disjunction to a given conclusion, no matter from which disjunct you argue. This style of argument is appropriate when you are indifferent to—or simply do not know—which disjunct is true, and the whole point is to reach the conclusion on the basis of the original disjunction alone. But while (as we have seen) Aristotle says little to justify the original disjunction, he is hardly non-committal about the individual disjuncts—that is, about the would-be definitions that motivate the different segments of Zeta. To the contrary, his discussion in each segment may well settle whether the relevant definitional claim is true, or whether it should be rejected outright, or retained but modified in some way. The technique of CD simply does not offer a mechanism for evaluating the different disjuncts it features, in the way Aristotle evidently wants. This brings us to the last, and decisive, reason for rejecting the CD account. On the most plausible reading, two of the three segments of Zeta (on subjects, and on universals) cast doubt on the received view that, on the CD account, acts as primary assumption in the relevant sub-derivation. So he cannot use the received view, in the very form in which he received it, as primary assumption in the sub-derivation the CD account requires—for, that view is the very one he takes himself to be refuting. Perhaps Aristotle knows how to replace the idea he means to discredit with his own, positive view. But the details here are speculative, and as things stand, the sub-derivation lacks a primary assumption, and cannot even get started. I have devoted space to criticizing the CD account, because it appears to offer the best, if not the only correct, way of applying the Inaccessibility and Common Conclusion assumptions included in Non-Linearity. As I see it, both assumptions fail; if this is correct, the CD account and Non-Linearity fail too, and both are well lost. But the assumption about levels emphatically stays; indeed, it does some of the work that might otherwise be attributed to Non-Linearity. In certain cases, instead of Non-

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Linearity restricting inferences from one segment of Zeta to another, the distinction in levels is what inhibits the injection of material from a “partisan” passage to a passage that is by design neutral with respect to Aristotle’s “official” theory. For example, the conclusion in Zeta 11 that Socrates’ substance is his (Aristotelian) form is absent from the discussion of substance and universals later in Zeta 13. But we have not Non-Linearity (as Burnyeat 2001, 46, suggests), but the distinction in levels, to thank for this. The discussion in Zeta 13 runs at the level of received views, and the entry of form is reserved for the “partisan” phase of the discussion, when and if that ever comes to pass. Non-Linearity, in this instance at any rate, is an epiphenomenon, and it is the distinction in levels that drives the account. Again, there is the apparent discrepancy between Zeta 13, where Aristotle appears to say that a substance is not predicated of anything, and the view expressed in Zeta 3, that substance is predicated of matter. But we will not need Non-Linearity to seal off Zeta 13 from the relevant part of Zeta 3: the difference in levels—the “partisan” in this part of Zeta 3, the discussion of received views in 13—by itself is enough to do this. To be sure, the two views appear together in the body of Zeta 3 itself—but they are distributed between “received” and the “partisan” parts of the chapter. We are not to import Aristotle’s own “partisan” views into the “received” side of things; and received views are always subject to revision before they can suitably find a home in the official theory. So the salient question becomes, is the received view (that substance is not predicated of anything) open to modifications that might render it friendly to Aristotle’s own “official” theory?57 If previous arguments are correct, the different segments of Zeta are not subject to the constraints of Non-Linearity, while the assumption of levels remains firmly in place. Discussion of levels and of the structure of Aristotle’s arguments more generally is reserved for the body of the present volume. In the remainder of the present chapter (Section 11) I say more about the argumentative strategies that animate the discussion of the different “received” views flagged in the agenda passage in Zeta 3.

SOME ALTERNATIVE ARGUMENTATIVE STRATEGIES

11 “Mapping” the Old Onto The New, and A Use For Abductive Argument On the CD account discussed in the previous section, the body of Zeta contains a series of received views purporting to define (primary) substance or the substance of a thing, all of them marching to the same ultimate conclusion. No matter which received view

57 The modifications I have in mind to received views about (metaphysical) predication are discussed in Chapter 8 and its Appendix.

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(or views) we listen to, the definition that results points to the same conclusion, that forms are the primary substances. It does not bode well for an account along these lines that Aristotle doubts the correctness of two of the received characterizations of substances, while the third characterization in terms of essence, while successful, does not rise to the level of a definition. So it is hard to see how the different received views heading the different segments of Zeta together drive towards a single overall conclusion concerning what entities count as the primary substances. On the contrary, taken jointly or even separately, the guiding ideas of the different segments are not needed in order to generate this conclusion, for it is already either assumed or argued for on independent grounds in the body of each segment that (Aristotelian) forms are the primary substances. What, then, of the announced topic of the different segments of Zeta: namely, to produce a definition of (primary) substance? While the hope that the different notions listed in the Zeta 3 agenda will yield a definition turns out to be unrealistic, Aristotle remarks more than once on their relevance to the study of substance (see, for example, 6.1 and 8.2 below), and they contribute to the eventual definition in various ways that he goes some way to explaining in Zeta 17 and in the retrospective in Eta 1 (Chapters 11 and 12). It is also no secret that Aristotle works those various notions hard in the segments that precede Zeta 17. Each is put under intense scrutiny; in particular, the discussions of essence and universals introduce a number of distinctions and raise a variety of questions and puzzles with which the tradition must come to terms. But these same distinctions and puzzles also await Aristotle in the “official” theory within which his finished definition of substance in Zeta 17 is embedded, and the resolution of the puzzles again offers the hope of progress. Even in the absence of a successful definition in the earlier segments of Zeta, then, there is still the possibility of a number of positive outcomes. It will be a task for Zeta 17 and the retrospective in Eta 1 to fit the notions of essence, universal, and subject into the immediate context of Aristotle’s official definition of Zeta 17. Meanwhile, the various puzzles surrounding the notions of essence and universal give Aristotle the opportunity to press the virtues of his official theory, by showing that it can meet those puzzles with at least the same degree of success with which they can be handled in the philosophical tradition. In the final chapters 10 and 11 of the segment on essence, for example, he supports his theory by showing that it does the work it is supposed to do, where the expected work is broadly settled by features of the cluster of “handed-down” theories that figure in his preliminary, “non-partisan” discussion. We begin in the earlier chapters in the segment with the connection between essence and definition, and the different levels at which each notion can apply; and move in the opening parts of Zeta 10 to various questions about definition, and the answers we are inclined to give them—nowhere going beyond the boundaries of a framework from which appeal to Aristotle’s “official” theory of form and matter is by design excluded. Then in the body of Zeta 10, Aristotle goes on to show how our answers within the

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framework of “received” views are matched at the “partisan” level by how those same questions are resolved, as well or better, in his own theory of form, matter, and form– matter compound. On this showing, a main concern in Zeta is how to “map” the received theories featured in earlier chapters onto the new “official” theory. Aristotle can justify the transition from old theories to new, if he can show that various fundamental features of the theories that are his starting-point are properly reproduced in the theory that supersedes them.58 It is not the aim to use “received” views, one at a time (NonLinearity), to buttress the single conclusion that form is primary substance; the aim is rather an holistic one, to support an entire new theory by showing that at various points it can do the work its predecessors were able to do. All the more urgent, then, to show that the promising ideas that emerge at the level of received views can be reproduced or improved on, or even rationalized, in his own preferred theory. When it comes to his “official” definition of (primary) substance in Zeta 17, however, Aristotle’s aims are more ambitious. Aristotle means to suggest that his definition of substance replaces altogether the rival attempts at definition scouted in the Zeta 3 agenda. His definition best among its rivals yields the needed result, that (Aristotelian) forms are the primary substance. More accurately, none of the rival attempts at definition succeeds, so that his is the only sustainable route to the needed conclusion. Thanks to this more ambitious style of argument, the relative weakness of the received views for Aristotle need be no disadvantage. On the contrary, if Aristotle can show that the most widely considered alternatives falter (the alternative attempts at definition introduced in Zeta 3 and discussed at length in the body of Zeta),59 then the definition given in Zeta 17 is arguably the best among its potential rivals. We may imagine him arguing as follows: If the definition of primary substance as the cause of being for individual substances is correct (it is the best compared to its potential rivals reviewed in the body of Zeta), then (Aristotelian) forms are the primary substances. Forms are the (primary) substances.

Therefore: The definition of primary substance as the cause of being for individual substances is correct.

Aristotle does not argue here from the definition of (primary) substance to its application identifying (Aristotelian) forms as the primary substances. On the contrary, the argument works in the opposite direction, from the view of forms as the primary

58 Perhaps Burnyeat would not disagree: “Aristotle invites his readers to see how at the metaphysical level of discourse one can get confirmation and a clearer understanding of conclusions independently reached at the logical level” Burnyeat (2001), 41. 59 “The most widely considered alternatives”: en tetarsi ge malista, “chiefly at least in four,” Z3, 1028b23–4, from 1.4 above.

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substances, in support of the definition that makes them so. And the argument does not aspire to deductive validity; it is an abductive form of argument and consists of inference to the best explanation, where the aim is rather the degree of probability of the conclusion.60 Otherwise put, the theme already present in the body of Zeta, that (Aristotelian) forms are the primary substances, tends to confirm the new idea in Zeta 17, that (primary) substance, or the substance of a thing, should be defined as the cause of being for that thing.

60 The notion of abductive reasoning is due to Pierce; see Hilpinen (2004), 644–53, and Chomsky (1972), 171–2.

PART TWO

Substance as Subject

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2 Subjects in Metaphysics Zeta 3 In the body of Metaphysics Zeta 3, Aristotle begins work on the agenda 1.4 above, repeated here, which he has set himself at the beginning of the chapter: 1.4 Substance is said, if not in more ways, at least chiefly in four: that is, the essence and the universal and the genus seem to be the substance of each thing, and fourth of these, the subject. (1028b33–6)

His target in this chapter is the subject criterion for substance, which he tests against the official theory of (metaphysical) predication in the Metaphysics.1 One main purpose of his discussion, then, will be to find how well, or how badly, the “received” view of substance as a subject and the “partisan” Aristotelian theory of (metaphysical) predication fit together. If, however, as I suspect, the fit is bad, he is here in no mood for reconciliation, and says nothing about how the subject criterion might be accommodated in his own finished theory. As Aristotle reports the received criterion, 2.1 The primary subject (to hupokeimenon pro¯ton)2 is thought above all to be substance.3 (Z3, 1029a1–2)

where by (primary) subject, we are to understand 2.2 That of which the others [as often in Greek, he means: all the others] are said, but it itself is no longer said of anything else. (1028b36–7, cf. 1029a8–9)

1

For (metaphysical) predication, see Chapter 1, n. 4. For ‘primary’ (pro¯ton) in ‘primary subject,’ cf. pro¯to¯i, a16, and also perhaps to eschaton, a24. Aristotle’s explanation makes it clear that ‘primary’ here has to do with the position an item occupies in the theory of (metaphysical) predication. In the body of Z3, contrary to his official theory, Aristotle imagines that there can be chain of (metaphysical) predications, in which each item is predicated of its immediate successor; in such a chain, the terminal item in the chain would count as primary subject: that which itself is predicated of nothing further but (given the further assumption that the predication relation is transitive) of which everything else in the chain is predicated. The use of “primary” here is not the use of “primary” in “primary substance”, where Aristotle is occupied with quite different questions involving ontological priority and posteriority. 3 I translate “is thought above all” (taking malista with dokei)—marking the primary subject criterion as the majority view—rather than “to be substance above all [= primary substance?]” (taking malista with ousia). We find much the same choice at 1029a29–30 (in 2.16 below), which I resolve the same way (this chapter, n. 31). 2

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3

According to what we may suppose is Aristotle’s official, “partisan” theory of (metaphysical) predication, meanwhile, 2.3 . . . the rest are predicated of the substance, but it of the matter. (1029a23–4)

Other texts for the partisan Aristotelian theory appear later in Zeta and in Theta:4 2.4 is subject in two ways (hupokeitai dicho¯s), either being a this, as the animal to its affections, or as the matter to the actuality. (Zeta 13, 1038b4–6) 2.5 For that of which and [= i.e.] the subject (to kath’ hou kai to hupokeimenon) differ in this, by being either a this or not being ; for example, what is subject to the affections is man, both body and soul [= the compound of body and soul], and the affection is the musical or pale . . . In all cases of this sort, the subject (to eschaton) substance; but in the cases that are not like this, but what is predicated is a certain form and a this (eidos ti kai tode ti to kate¯goroumenon), the subject (to eschaton) is matter and matter-like substance. (¨7, 1049a27–30, 34–6)

For the sake of a uniform terminology, let us say that its accidents are (metaphysically) predicated of the compound material substance, while form is (metaphysically) predicated of matter. Canonically, the upper half of this scheme contains a single level, while the lower half comprises a whole hierarchy of coincident matters each worked up by form into a compound that serves in turn for the next increment of form. This half of the scheme is bounded by prime matter at the bottom,5 and by the proximate matter of a compound material substance and its substantial form at the top. In Zeta 3, as we shall see, this lower half is simplified so as to contain a single level of matter and form, similar to the way in which the upper half contains just a single level containing compound material substances as subjects to their various accidents.6 In the meeting of the “received” (the subject criterion for substance) with the “partisan” (the theory of metaphysical predication) described in the previous two paragraphs, there will be conflict. The partisan prevails: the received view must bend, if it does not break, and in this segment at least, the received has very little leverage against the weight of true Aristotelian theory. There are signs elsewhere, however, that Aristotle will opt for accommodation, suggesting that his choice for primary substance, namely (Aristotelian) form, is after all in some appropriate way a 4

With the passages quoted, see also B1, 995b35; cf. B4, 999a33–4, H2, 1043a5–6. The attribution of a notion of prime matter to Aristotle is a continuing item of controversy; for one recent account, see Lewis (2008). 6 It is a curiosity of Aristotle’s discussion in Z3, as elsewhere, that while he is clear about the entities that enter into a relation of metaphysical predication—an accident and an individual substance, a form and matter—he is not clear about what results from the interaction in each case. In the lower half of the scheme, where form is predicated of matter, the result is apparently a form–matter compound: the individual substance, Socrates (say), or some lower-level form–matter compound. But when an accident is (metaphysically) predicated of an individual substance, being seated of Socrates (say), the result is not an accidental compound—the one seated, or seated Socrates (Socrates + seated)—but a structured entity—Socrates’ being seated—that is alternately truth-bearer and truth-maker for the linguistic predication, “Socrates is seated”. For further discussion, see this chapter, Section 1, nn. 13 and 14, Chapter 8, Sections 15–19, and Lewis (2011). 5

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subject.7 In Zeta 3 itself, however, the contrast between the “received” and the partisan is stark. Before turning to the details of the encounter between the two points of view, we look first at some different possibilities as to the source of the received view on the one side of the dispute.

1 Sources of the Received View: Aristotle’s Categories, and the Early Philosophers of Nature In the body of Zeta 3, once his list of received opinions about substance is on the table, Aristotle takes up his first (and apparently most popular) candidate: a thing is thought above all to be a (primary) substance if and only if it is a primary subject. But if this is a received view, received from whom? On one natural account, the source is Aristotle himself in the Categories, where according to Aristotle, 2.6 It is because the primary substances are subjects for everything else that they are called substances most strictly. (Categories 5, 2b37, my emphasis, cf. 2a34–5, b15–17)

By subject in the statement of the subject criterion in Zeta 3, as we have seen (2.2 above), Aristotle means that of which all the others are said, but it itself is no longer said of anything else. So the Categories and Zeta 3 alike hold out the prospect of a single kind of items that are subjects to all predicables. But if this works out smoothly in the Categories, the result in the Metaphysics will not be so happy, leading at best (Aristotle suggests) to the unacceptable result that matter is the sole kind of substance. The moral of the story, apparently, is that a criterion for substance that performed well in the Categories is no longer so obviously suitable in the new metaphysical context of the Metaphysics. A reading of other texts, however, might lead one to think that the idea of substance as a subject is rooted not in the Categories, or not only there, but (also) in what may seem a quite different place, in Aristotle’s interpretation of his predecessors among the Presocratic philosophers of nature. In Physics B1, Aristotle brings his own theory of matter and material causes to bear on the attempts by the Presocratics to explain the natural world in terms of its basic material constituents—the four elements; or fire; or atoms and void. On accounts of this kind, a thing’s nature and, hence, its substance are to be identified with its most basic material constituents: 2.7 Hence fire, earth, air, and water have been held to be the nature of things, some people choosing just one for this role, some several, and some making use of all. Those who fix on some such element or elements represent it or them as the entire substantial being (te¯n hapan ousian), and say that other things are merely affections, states, or dispositions of these. (Physics B1, 193a21–26, following Charlton’s translation)

7

See this chapter, n. 15 and Chapter 12, n. 11, with Lewis (1991), 301–4.

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As Aristotle goes on to explain, the favoured element or elements comprise “the primary underlying matter for each thing” (he¯ pro¯te¯ hekasto¯i hupokeimene¯ hule¯, a29). The same reading of the Presocratics appears in Metaphysics B5: 2.8 Most thinkers and the earlier thinkers (hoi men polloi kai hoi proteron) held that body is substance and being, and that all other things are modifications of this, so that the principles of bodies are the principles of beings. (Metaphysics B5, 1002a8–11)

The views Aristotle puts in the mouths of his Presocratic materialist predecessors are a remarkable blend of his own ideas and the raw material he finds in the Presocratic accounts of nature and natural processes.8 Aristotle’s ideas emerge in their clearest form over the course of the first two books of the Physics. In Physics A7, we find two sets of results: first, a statement of the principles involved in change generally, including accidental change, but above all in coming to be and perishing; and, second, the related account of the metaphysical constitution of the things liable to coming to be and perishing.9 In the account of change and the account of metaphysical constitution alike, the same three principles are involved: the underlying nature or “what underlies” (to hupokeimenon), which is subject to contraries, also identified (in isolated “partisan” appearances) as the form, and as the lack or privation of the form.10 A final legacy of Physics A7 is the question: which of the constituents of a thing that come to light in the account given is to count as the nature or substance of the thing—its form or its matter? (The question at A7, 191a19–20, is answered at B1, 193b6–7.) Traces of these different issues can be found in Aristotle’s report of Presocratic concerns in 2.7 and 2.8 above: the topic of change is implicit in his report, but issues of the basic material constituents of things, and of what to view as the substance of things, are on the surface. Aristotle’s distinctive contribution is to thread these different concerns together into a single line of theory. The theoretical apparatus he brings to bear has its origins in a place that is out of reach (in doctrine as well in time) to the Presocratics, in the theory of (metaphysical) predication in Aristotle’s own Categories. The notion of a subject is prominent in the Categories, along with the relation of (metaphysical) predication between an accident (an item from a non-substance

8 This is not to say that (with some minor exceptions) Aristotle’s appeal to the Presocratics crosses the line from “received” views to his own “partisan” theory of (Aristotelian) form and matter. But his discussion of his predecessors, no less than his appeal to his own other selves in other works, is highly “Aristotelian” in colouring, even if it stops short of his own “partisan” ontology. 9 In Physics A7, Aristotle moves virtually without notice from the account of coming to be and passing away to the analysis of the constitution of objects that change in these ways. The use of the first as a route to the second has sometimes been doubted (Frede (2000), 12–14), but I will not pursue these doubts here. 10 In terms of the divide between “received” and “partisan”, Physics A deals almost but not quite entirely with received views, while in Physics B1, Aristotle moves in steps to his own, partisan views featuring matter and form. The theory of matter and form appears almost tangentially in Physics A until the final chapter, A9. In Physics B1, Aristotle moves in three steps to his own partisan theory, beginning with a survey of received views about what counts as a natural object, to a definition of the nature of a thing (as an internal principle of its behaviour), to finally an assessment of the ways in which his matter and form variously satisfy that definition—with primacy going to a thing’s form.

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category) and an individual substance as its subject. The innovation of the Physics is the invitation to apply these notions, in effect, one step down from anything contemplated in the Categories, in the service of accounts of what it is for a thing to come into being or to perish, and of the basic material constituents of things that are liable to these kinds of change. Can Aristotle successfully co-opt the notion of subject at home in the account of (metaphysical) predication in the Categories, to do duty in these new ways? After all, the Categories is innocent of natural philosophy: analysis stops with individual substances, and there is no trace of the questions addressed in Physics A7—no causal analysis of how individual substances come to be or perish, and no theory of their internal constitution as compounds that result from (metaphysically) predicating one thing of another, much less their constitution as compounds of form and matter. At the same time, even if Aristotle can reasonably employ the notion of a subject of (metaphysical) predication from the Categories in the accounts of coming to be and perishing and of the metaphysical constitution of perishable things, questions of what in the constitution of a thing to count as its nature or substance are at first unresolved. According to Aristotle in Physics A7, in a brief excursion into partisan mode, “it is not yet clear whether the form or what underlies is substance” (191a19–20). In Physics B1, where the discussion has turned firmly partisan, much the same two candidates for substance, form, and what underlies, are on offer, and Aristotle has an answer to the choice between them. He outlines two views of what serves as the nature of a thing, defined as an internal source of (typical) behaviour for the thing. One candidate is the Presocratic one—a thing’s basic material constituents, that is, “the primary underlying matter for each thing” (193a29), count as the “nature and substance of ” a thing (a9–10, my emphasis), while “all other things are merely affections, states, and dispositions of these” (a25–6, from 2.7 above). Aristotle’s own view parts company with the Presocratic choice. The second and, in his eyes, the stronger choice for the nature of a thing (mallon . . . phusis, b6–7), and again (presumably) for its substance, is (Aristotelian) form. And of course, matter and form together are what make up the things due to nature (to d’ ek touto¯n, b5–6). Aristotle is less forthcoming on the choice between form and “what underlies” in the account of substance in his metaphysical dictionary, Metaphysics D. In D8, he once more records two strains in the notion of substance, corresponding roughly to the two options from the Physics, but this time he does not adjudicate between them. We have—one strain—three cases centred on the notion of a subject or what underlies (to hupokeimenon). The subject criterion applies directly, (i), to the obvious Presocratic candidates, namely, the four elements,11 and also to whole animals, gods, and their parts:

11 Of course, the elements play a prominent role in Aristotle’s own physical theory, but the Presocratics are brought firmly into the story in Physics B1; see the discussion in the main text immediately below and especially B1,193a14–28.

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2.9 Spoken of as substance are the simple bodies such as earth and fire and water and whatever else of this sort, and in general bodies and the animals and divinities constituted form these, and their parts: these are all called substance because they are not said of a subject (ou kath’ hupokeimenou legetai) but everything else is said of them. (Metaphysics ˜8, 1017b10–14)

Thereafter, the criterion applies obliquely, (ii), to the causes of being that inhere in such things that are not said of a subject (b15–16); and even, (iii), to the parts present in such things (b17–21), which define or demarcate them, are thises, and do not get destroyed with the destruction of the whole (they are “naturally prior”, by the notion of priority Aristotle ascribes to Plato at ˜11, 1019a1–4).12 As to the other strain: Aristotle lists (iv) the essence of a thing, which he lines up with Aristotelian form. Aristotle is silent in ˜8 as to how to adjudicate between the two strains in the notion of substance—which takes precedence over which?—possibly because he largely confines itself to recording what he regards as, at bottom, (merely) the received notion or notions of substance. The combination in 2.9 of what appear to be certain Presocratic choices for substance with the subject criterion from the Categories again raises questions about the different conceptions of subject that appear side by side in the passage. As we wondered in connection with the Physics, how does the notion of a subject that appears in the Categories, with its attendant apparatus of (metaphysical) predication, fit together with the notion of a subject as part of the metaphysical constitution of perishable natural objects? So it is appropriate to ask, as Aristotle himself asks in Metaphysics Zeta 3: can the scheme of (metaphysical) predication from the Categories tolerate the downwards extension Aristotle engineers, from the subject to accidents in the Categories, to the underlying subject in the account of change and the objects that change, where the apparatus of form and matter is now brought into play? If the notions of subject at work variously in the Categories and in the Physics are fundamentally different,13 then we risk a loss of coherence in the two-tier scheme of (metaphysical) predication in the Metaphysics (2.3, 2.4, and 2.5 above) that is put together out of them—its upper half cut from the same cloth as (metaphysical) predication in the Categories, its lower half

12 Aristotle offers as an example for case (ii) the role of soul in the animal (b16), so the idea relies on his own psychological works. The idea that a thing’s substance is the cause of being for that thing is developed in above all in Metaphysics Z17 (Chapter 11); it is something of a stretch to connect this with the subject criterion, as Aristotle does in D8. Meanwhile, for the cases included under (iii), compare the mathematizing Platonists of B5 (see 2.14 below). It is perhaps worth adding that while I group Aristotle’s cases (i) through (iii) under the notion of subject, a different alignment is given in Ross (1924) I, ad loc., so that cases (ii) through (iv) alike fall on the side of form. 13 By “fundamentally different notions” I have in mind what used to be called (in a totally different use of the word “logical” from that introduced by commentators to reproduce Aristotle’s logiko¯s, Chapter 1, n. 34 above) an improper mix of “logical” and “physical” notions of subject, Cook Wilson (1926), I, 159–66, cf. Ross (1949), 70–1. On the opposite side of the debate, Kung (1978) argues that Aristotle sees no serious distance between the notions of logical subject and subject of change.

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employing the notion of subject rooted in the analysis of change and of the objects that change in the Physics.14 It seems clear that Aristotle himself, at least provisionally, supposes the two notions do cohere. The list of examples in 2.9 above from Metaphysics D8 includes not just the typical Presocratic choices, the four elements and the rest, which are the underlying subjects of change, but also things counted as substances by the Categories interpretation of subject as the basic subject of metaphysical predication: animals, gods, and their parts (for this last, see Categories 5, 3a29–32). Suppose, then, that the Categories notion of subject fits well with the Presocratic notion of subjects as the basic material constituents of the world that persist through change—so that these (whatever a given Presocratic philosopher supposes them to be) are the substances and even the substance of things. A more urgent question remains: how well suited is the subject criterion for substance in the context of Aristotle’s own account of change and the objects that change and, more generally, the context of the larger ontology of (Aristotelian) form and matter? In the relatively limited ontology of the Categories, individual substances count as primary substances by virtue of the fact that they are subjects for everything else—alike for their kinds, and for their accidents and the kinds under which those accidents fall. But in an ontology in which form and matter are added to the mix, will the “basic subject” criterion for substance pick out a suitable set of items as primary substance? Even, will it pick out anything at all? Given the uncertainty whether the subject criterion can succeed as applied to Aristotle’s own “partisan” theory, it will be no surprise if in Zeta 3 the subject criterion in its received form is Aristotle’s target in the chapter. This will be our topic in the next section.

2 Aristotle’s Target in Zeta 3 In this segment of Zeta the received view from which discussion begins is not a foundation on which further results can be built. On the contrary, in Zeta 3 Aristotle rejects the view; from it no positive results follow, either in general or for Aristotle’s own theory. His primary concern is to show that the subject criterion, as defined, leads in his own theory to a single, wrong candidate for substance. He cannot, then, simultaneously be applying the criterion approvingly, to press the conclusion that (Aristotelian) form is primary substance. To be sure, he also tells us that his theory recognizes three kinds of substances, form, matter, and form–matter compound; of the three, form is primary substance (1029a5–7 and 29–33 from 2.16 below). But he obtains this last result quite independently of the subject criterion; to the contrary, he uses it to trump the (uncertain) deliverances of the criterion in its received form. In this segment, Aristotle’s concern seems to lie more with a critique of the received criterion 14 As before (this chapter, n. 6), however, the notion of (metaphysical) predication, and the corresponding notion of a subject, are applied to quite different effect in the two parts of Aristotle’s scheme; see Chapter 8, Sections 15–19, and especially the summary in that same chapter, n. 75.

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for substance than with using the criterion to reveal what counts as primary substance in his own theory. It seems likely that in Aristotle’s view there is a version of the subject criterion for substance to be salvaged from Zeta 3 that will not succumb to the objections lodged against the version of the criterion on offer in that chapter. On some other version of the criterion, primary substances—in Aristotle’s official theory, Aristotelian forms—will be subjects.15 But he nowhere, in Zeta 3 or elsewhere, explains the new version of the criterion which gives the desired result.16 While Aristotle’s intent towards the subject criterion for substance is altogether negative in Zeta 3, it would not be right to conclude that no positive claims are made in the chapter. On the contrary, we learn that substance is thought to be above all a this and separate (2.16 below)—two further received views about substance, otherwise unannounced in the chapter, which he uses there to call the subject criterion into question.17 Again, he sets out his own ontology of form, matter, and form–matter compound; of the three, he tells us, if the form is prior to and more of a being than the matter, the same reasoning will make it also prior to the compound (a2–7).18 At the same time, thanks to the requirements of thisness and separability, form and the form– matter compound are thought to be substance to a greater degree (mallon) than the

15 1029a2–3 may tell us that his forms are subjects, without further explanation, if the reference of toiouton at a2 is to “the primary subject” or to “substance taken as the primary subject” in the preceding sentence. Such, at any rate, appears to be the verdict of the Metaphysics more generally. Aristotle appears to say that the criterion does apply “in a way” to form (H1, 1042a26–9, cf. Z3, 1029a2–3); at the same time, the discussion in ˜8 is evidence that he is willing to show an extreme flexibility in the variety of cases the subject criterion can cover: see, for example, case (ii) in #1 above (˜8, 1017b14–16), where he finds a way of bringing the cause of a thing’s being, in particular, in the case of a living thing, its soul, under the rubric of subject. In the De Anima, he appears to rule against the view of soul (which is the form of living things) as subject. Work as subject accrues instead to the form–matter compound; and commentators often say that form is a subject in virtue of its role in setting up the individual substance as a viable subject for accidents. For more discussion, see Granger 1995, 135–59 and 177–85. 16 Aristotle leaves altogether undone in Z3 one further piece of business regarding the subject criterion in the form in which it is used in the chapter, namely the stipulation that a subject in the required sense “itself is no longer said of anything else,” 1028b37. This stipulation can hardly survive the discussion of Z3; but if the received view of substance as subject is not reformed, and if in the official theory of (metaphysical) predication, form is (metaphysically) predicated of matter, how could Aristotle also maintain that (Aristotelian) form is primary substance? The question is close to the surface in Z13, 8.9 below; I defer discussion to Chapter 8, Section 8. 17 Sources for thisness as a feature of substances include, along with 2.16 below, Categories 5, 3b10–13, An. Po. A4, 73b7, Metaphysics B5, 1001b32, and 2.4 above from Z13; once form emerges as the choice for primary substance, we find that (Aristotelian) form is a this, Chapter 1, n. 13 (and for what not to count as a this, see Categories 5, 3b13–21, SE 22, 178b37–9, and Metaphysics Z13, 1038b35–1039a3 [= 8.10 below]). Separability should be thought of in conjunction with Aristotle’s distinctions among the different kinds of priority, Categories 12, especially priority by nature, for which see also Metaphysics ˜11, 1019a1–4; for the combination, see for example Metaphysics Z1, 1028a31–34. Famously, Aristotle says that in calling his forms separate, Plato attaches separation to entities of the wrong kind; 10.6 in Chapter 10, Section 6, and M4, 1078b30–34. He regards his own, Aristotelian forms as separate only in account, Physics B1, 193a5, Metaphysics H1, 1042a29. 18 Aristotle’s statement at a5–7 is conditional in form, but it is hard not to think that he means to assert the antecedent; see Chapter 6, n. 13.

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matter; but the compound is posterior and clear, as is the matter, “in a way”; while the front-runner, form, is the most puzzling of all (2.16 below). Side by side with the negative conclusion of the chapter, then, Aristotle is willing to assert a significant number of positive claims. But most of the latter are unargued. If they are not directly supported, on what basis does he assert them? A large part of the answer here involves the source from which the various propositions come—whether from Aristotle’s own theory, or from elsewhere. Some, that is, are partisan—drawn from the “official” theory of form and matter—but others, like the subject criterion itself, are included because of their place in—or at least their compatibility with—the philosophical tradition. The distribution of partisan and “received” passages at different points in Aristotle’s discussion, in particular, the place of “stripping away” in the “partisan”/“received” divide, is our next topic.

3 The Distribution of “Received” and “Partisan” in Zeta 3; On “Stripping Away” The conception of substance as subject put under scrutiny in this segment of Zeta is a received view: it is part of the philosophical tradition, even if that tradition is located in other works of Aristotle himself (the Categories), or derives from Aristotle’s own interpretation of his Presocratic predecessors (the Physics)—or even draws on both sources. In any event, the conception belongs on the “received” side of the “received”/“partisan” divide. Appropriately, therefore, the initial discussion of the subject criterion is not evidently driven by partisan considerations. Aristotle imagines that the subject criterion, as refined by the definition in 2.2 above and repeated at 1029a7–9, is best implemented by means of the philosophical “stripping away” (aphairesis) carried out in 2.11 below. Stripping away, I will suppose, is not a partisan procedure—not ideologically driven.19 As to the process of “stripping away”, after his restatement of the subject criterion at a7–9, Aristotle describes the procedure he has in mind, prefacing his description with the appropriately sceptical remarks: 2.10 But this cannot be all, for it is not enough, for this itself [= the very statement] is unclear, and what is more (a10), it turns out that matter is substance. (a9–10) 2.11 (immediately continuing 2.10). For if it is not substance, what else is escapes us: for when everything else is stripped away, it seems that nothing is left;20 for, on the one hand (a12), the other things are affections and effects and powers of bodies, but on the other (a14), length and depth and breadth are particular quantities but not substances (for, the how much is not substance), but rather that to which these belong primarily, that is substance. But yet (a16)

19 It is perhaps a stretch to set stripping away on the side of “received” views, but the procedure has precedent in Metaphysics B5, see 2.14 below, in what seems a review of different metaphysical options quite generally, with (again) no hint of a distinctively Aristotelian slant on things. 20 For the “else”, see 2.12 below; see Schwegler (1847) IV, 43, and Dancy (1978), 394.

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length, breadth, and depth being stripped off, we see nothing remaining, except if there is such a thing as what is determined by these . . . (a10–18) 2.12 (immediately continuing 2.11) . . . so that it must seem that matter alone is substance, to those who look at things in this way [sc. by way of the subject criterion, in combination with stripping away as a means for implementing it]. (a18–19)

Or again (a few lines later in the chapter), 2.13 For those who theorize along these lines, it results that matter is substance. But this is impossible. (a26–7)

At the very outset in 2.10, even before stripping away begins, Aristotle expresses reservations about the subject criterion. In part, he complains that he finds the criterion itself unclear. He also has reservations over where he sees the application of the criterion is headed: If the criterion is to be believed, matter, or better, as in 2.12,21 matter alone, turns out to be substance. We will return below to Aristotle’s reservations about the unclarity of the subject criterion, and about the fact that, as a proposed criterion for substance, it delivers what he finds to be the wrong result (2.10, 2.12, 2.13 above). Meanwhile, on the “received”/“partisan” divide, it is worth noting that Aristotle’s (“partisan”) objections to seeing matter as the sole kind of substance are at two removes from the process of stripping away. Criticisms of this sort, from the vantage point of Aristotle’s own theory, require first and foremost the cross-theoretical identification of the result of stripping away, reached by an argument that appears to be metaphysically neutral, with this or that kind of item within the partisan, Aristotelian ontology of form, matter, and form– matter compound. Second, for reasons drawn partly but not, perhaps, exclusively from within Aristotle’s own theory, there are objections to thinking that the relevant kind of item, in fact, matter, can be substance, much less the only kind of substance. In the remainder of this section we focus on the device of “stripping away”, which is Aristotle’s chosen means for applying the subject criterion for substance. Stripping away as a method for identifying substance has a precedent in Metaphysics Beta 5, where the target is again “being (to on) and what are the substances of the things that are”: 2.14 A puzzle connected with these [= a variety of Pythagorean and/or Platonic claims] is whether numbers and bodies and planes and points are substances or not. If they are not, it baffles us to say what being is and what are the substances of the things that are. For modifications and movements and relations and dispositions and ratios do not seem to indicate the substance of anything; for all are predicated of a subject, and none is a this. And as to the things which might seem most of all to indicate substance, water and earth and fire and air, of which composite bodies consist, heat and cold and the like are modifications of these, not substances, and the body which is thus modified alone persists as something real and as a substance (a3–4). But, on the

21

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other hand, a body is surely less of a substance than a surface, and a surface less than a line, and a line less than a unit and a point. For a body is bounded by these; and they are thought to be capable of existing without body, but a body cannot exist without these. This is why, while most of the philosophers and the earlier among them thought that substance and being were identical with body, and that all other things were attributes of these, the more recent and those who were held to be wiser thought numbers were the first principles. (B5, 1001b26–1002a11, following the Revised Oxford Translation.)

Aristotle does not use the term “stripping away” here, and he does not explicitly state the subject criterion for substance; but his procedure is much like that of Zeta 3. As in Zeta 3, he distinguishes modifications from their subject: first, the ordinary run of modifications and movements and relations and dispositions and ratios, that are predicated of a subject and are not a this (b29–32). Then again, once we arrive at the four elements, out of which ordinary bodies are constructed and “which are thought above all to signify substance” (b32–3), we separate these into various modifications, heat, cold, and the like, and the body that is so modified, so that this last alone remains as a being a being and a kind of substance (ho¯s on ti kai ousia tis ousa, 1002a3–4). From this point, however, we part company with Zeta 3 and proceed to surfaces, lines, points and units—bypassing the world of the Presocratic materialists, and heading instead for that of the geometrizing and mathematizing Platonists. In Beta 5 Aristotle says nothing to justify directing the search for substance away from what is (metaphysically) predicated of a subject, and towards the subject of what is so predicated. In Zeta 3 the subject criterion is expressly on the table, and he offers stripping away as possibly the only way of implementing the subject criterion. Given the deficiencies of the criterion, “it turns out that matter is substance”. As he explains in 2.11 above, excerpted here, From 2.11 For if it is not substance, what else is escapes us: for when everything else is stripped away, it seems that nothing is left.

And so, despite the pessimism of this last remark, once the stripping way has been done, we have the for Aristotle unacceptable result (repeating 2.12 and 2.13 above) that 2.12 . . . it must seem that matter alone is substance, to those who look at things in this way. 2.13 For those who theorize along these lines, it results that matter is substance . . .

In these passages, as in the rest of Zeta 3, nothing about the stripping away—at least, nothing Aristotle is willing to own up to22—is ideologically driven. In order to find “that of which everything else is said, while it is said of nothing further” he assumes above all that predication here is metaphysical predication, and that a (metaphysical) 22

I have in mind the happy coincidence between the two-step example and the simplified two-stage theory of (metaphysical) predication later in the chapter. In the discussion of (metaphysical) predication in ¨7, by contrast, the multi-stage character of the lower half of the scheme is implicitly acknowledged, 1049a19–36 (not so, however, in Z13, 2.4 above).

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subject of (metaphysical) predication is in a certain way independent of what is (metaphysically) predicated of it. I will assume that the independence is modal: a statue (Aristotle’s example) is red (say), but it might not have been.23 Aristotle states the independence assumption at a24–6 in the passage that follows: 2.15 For, there is something of which each of these is predicated, whose being is different from that of each of the predicables (for, the others are predicated of the substance, but it of the matter [ta men gar alla te¯s ousias kate¯goreitai, haute¯ de te¯s hule¯s]), (a24) so that the ultimate in itself is neither of a certain kind nor of a certain quantity nor anything else: indeed, not even the negations either, for these too will belong accidentally. (1029a21–6, my emphasis)

Given a notion of (metaphysical) predication governed by independence, even if a statue is red, heavy, and fragile, we can still distinguish the redness, heaviness, and fragility from the statue to which these attributes belong. This is not to say that the statue is not after all red, or heavy, or fragile. But it might not have been: the redness (say) and the statue are distinct items in Aristotle’s ontology, and they can be separated in thought even if, in fact, the one is (metaphysically) predicated of the other. But once we have separated in thought the statue from its redness and the rest, it seems that attributes of dimension remain, which are essential to the statue and cannot be separated from it in the same way. If these further properties of length, breadth, and depth are the attributes of some other subject, however, and not of the statue itself, then they can be pared from that further subject, which is “what is bounded by these.”24 That is, perhaps, following Physics D 1 and 2, indeterminate extension.25 This reasoning represents Aristotle’s best attempt to apply the subject criterion for (primary) substance; the criterion itself is “received” in character, and its application too is presumably free of any ideological commitments that Aristotle’s own theory of form and matter might bring. Thus, the notion of (metaphysical) predication, together with the independence assumption, is no more than the notion of Having, which the Aristotle of the Categories has in common with Plato. Again, the ontological assumptions Aristotle must make if the procedure of stripping away is to go forward are also on the “received” side of the ledger, and do not go beyond the subject-attribute ontology of Plato and of Aristotle’s Categories (with the addition perhaps, as we shall see, of accidental compound theory, which appears elsewhere in the Organon, in the philosophical dictionary in Metaphysics ˜, and in other texts). But the initial application of the subject criterion must and does stay clear of the more developed ontology that is Aristotle’s own in the Metaphysics. It is a later, and separate, step in the argument of Zeta 3 for Aristotle to line up the result of stripping away—a result whose credentials are 23 For the modal view, see Aristotle’s “in itself ”, italicized at a24 in 2.15 below in the main text. For the independence assumption, a.k.a. Owen’s “hatstand” theory of (metaphysical) predication, see Owen (1970) 1986, 249; see also Chapter 8, Section 2. 24 This is Aristotle’s “shift of subject” manoeuvre, Lewis (1991), 289. 25 Physics D1, 209a4–6, 2, 209b7–11, see Dancy (1978), 394–6, and Lewis (1991), 291.

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entirely free of commitment to the Aristotelian theory of form and matter—with elements in the partisan theory of form and matter. The “partisan” interpretation of the results of stripping away, which he identifies with matter, is predicted (disapprovingly) in 2.10 above, and reported again, once the stripping away is done, in 2.12 and 2.13 above. I have suggested that the process of stripping away in Zeta 3 is free of any partisan Aristotelian content. This, however, tells us only what the procedure is not. Beyond this negative characterization, is the procedure even coherent? A ready objection to bare substrate theory in general runs as follows. “If a given statue (say) is red and round, then the statue is (subject to) round, and (subject to) red; why on earth say that something else—not the statue, but a bare substratum—is subject to the redness or to the roundness?” A standard reply to this objection is quite different from the two-step argument Aristotle sets out in Zeta 3. On the standard line—one, I take it, that would be alien to Aristotle—we add the assumption that the statue is a whole that includes its various attributes as constituents. Given this assumption, being red is already part of the being of the statue—redness is one of its many parts—so by the independence assumption noted earlier in this section, the redness cannot after all be (metaphysically) predicated of the statue; it must be predicated instead of some other subject which is properly independent of it. Repeat this reasoning for all the other attributes we associate with the statue, and we reach the bare substrate (supposing only one is needed) that is the true subject to them all. This argument leads in the end to the same “bundle-plus-bare-substrate” view that results from the stripping away Aristotle describes in Zeta 3, but the two arguments are not the same. Aristotle does not assume from the start that the various attributes we associate with the statue are its parts; instead, his view at the beginning is rather the “veneer” theory of properties described by Anscombe: “as if the substance were the lump of underlying material, and the properties a veneer or a barnacle-like cluster of dependent quasi-substances stuck on to the substance.”26 As a result, at the first stage of stripping away in Zeta 3, the statue apparently is present all along as subject to the various attributes, redness and the rest, and the idea that some other item is their true subject emerges only later, after a second step of stripping away. But difficulties remain even at the first stage of stripping away. “If the statue is red and round, then the red statue is (subject to) round, and the round statue is (subject to) red; similarly, if we claim merely that the statue is red, is it not (again) the red statue that is (subject to) red?”27 Aristotle will deny that the red statue is subject to roundness, (even) 26 Anscombe and Geach (1961), 16. In the “cluster” or “veneer” theory of properties, the substance itself is the recipient of the “barnacle-like cluster” Anscombe describes—but it is not a part of the cluster. Similarly, for Aristotle the structured entity that gets dismantled in the process of stripping away is not the statue, but (I will argue) the accidental compound of the statue with each of its accidents. 27 See Stahl (1981): “Thinking away all the properties of an F, including its F-ness, does not make it a non-F. Thus . . . [given the question, What is it that is potentially all the things I have thought away?] an

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to redness, and so forth. The statue is, but the red statue is not, a proper subject to roundness. Yet the statue is (we supposed) red, so that apparently the statue is identical with the red thing, or with the red statue. So is the statue round, or not? And if it is not, then we are well on the way to the view of a bare substrate as a “featureless bearer of properties” that rightly earns ridicule in the textbooks. In fact, however, stripping away should not require that redness, roundness, and the rest are after all false of the statue. And Aristotle can even make it palatable that the statue is, but the red statue is not, subject to the attribute of roundness, redness, and the rest. His argument here requires not just the standard ontology of individual substances and attributes, but also, thirdly, the compounds of the first two. These are accidental compounds like Socrates seated, musical Socrates and so on; or, with the “+” sign to indicate the operation of compounding, Socrates + seated, Socrates + musical, and the rest. Socrates + musical is accidentally the same as its parent substance, Socrates; but the two are not identical. In Accidental Compound Theory (ACT) it is strictly speaking improper to say that the red statue is round, or the round statue red—even if it is straightforwardly true that the statue itself is both round and red.28 The two cases can differ, because in ACT, the statue and the red statue are not identical, but only accidentally the same. In ACT, the red statue is a compound of an individual substance with an accident—it = the statue + red—and in the one-step model of (metaphysical) predication that prevails in the Categories and Topics, the statue is subject to redness and subject to roundness, and there exist corresponding compounds of the form, the statue + red, the statue + round; but round is not (metaphysically) predicated of the statue + red, and there are no “iterated” compounds of the form, (the statue + red) + round, or even, (the statue + red) + red. So Aristotle can look to the Organon for an ontology that includes individual substances, their accidents, and compounds of individual substances with their accidents (one by one)—but no compound subjects and no iterated compounds; and in this context, the substance, the statue, is again independent of the redness that is (metaphysically) predicated of it, as the project of stripping away requires. So much for the first step in stripping away. More work is needed, however, if we are to reach the full-scale “bare substrate theory” which the argument of Zeta 3 calls for. Aristotle’s move is to reapply the same technique as before, this time to the body and its attributes of (determinate) extension that jointly constitute the statue: if the statue is the product of (metaphysically) predicating this-or-that specific length, breath, and depth of indeterminate extension, then the attributes that are essential to the statue

answer of the form ‘the F’ or ‘that F’ will do”, 178, my emphasis. If Stahl’s second sentence is right, then presumably stripping away will end where it begins, with the statue—namely, on his view, the red thing. 28 For ACT, see Chapter 1, n. 3. What I call “strictly speaking improper”, namely “reiterated” compounds, musical just Coriscus, and the rest, are allowed in Extended ACT (Lewis (1991), 108–14); but they can always be eliminated in favour of the resources of Core ACT by itself.

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(which would not exist without that very shape) can still be stripped away—but stripped from some other, lower-level subject to which they are accidental.29 At this second stage of stripping away, we strip away the attributes of dimension from their subject. Having isolated the statue that is subject to one set of properties, we have now reached a second subject, which is subject to its own distinctive set of properties. Does this give the desired result, that a single subject underlies all the properties we have encountered so far? Aristotle simply assumes, but does not argue, that having analysed the statue as (in effect) a compound of subject and its attributes, this new, second subject inherits all the properties that we formerly ascribed to the statue, so that we have reached a single subject for all predicables, itself predicated of nothing further. And once he has dropped his reluctance to engage the assumptions of his own “official” theory, Aristotle will offer an argument within his theory that attempts to line up the single subject that is supposedly the end-product of stripping away with elements of his own ontology.

4 The Shift from “Received” to “Partisan”: the Cross-Theoretical Identification Between the Result of Stripping Away and Matter After the act of stripping away has been performed, the question remains: how does the result of the stripping away envisioned in 2.11 line up with Aristotle’s official ontology of form and matter? Aristotle turns to this question in 2.12 (cf. 2.10 and 2.13 above): if we investigate things in this way, it must appear that matter is the sole (kind of) substance. Aristotle goes on to give reasons in support of the cross-theoretical identification between the result of stripping away and his concept of matter. Consider the scheme of (metaphysical) predication that consists of a substance and its attributes in the upper half, and matter and form in the lower half—this, I take it, is (with some simplification) Aristotle’s official, partisan theory of metaphysical predication in the Metaphysics (2.3, 2.4, and 2.5 above): here, perhaps, matter is that of which everything else is predicated, and its being—like the being of the subjects revealed in the different steps of stripping away earlier in the chapter—is revealed as other than that of the various items predicated of it (this is the independence assumption from 2.15 below). If we follow this line of reasoning, then as predicted, the subject criterion for substance leads to the conclusion that matter, even matter alone, is substance. Provisionally, let us grant that Aristotle’s matter is a wholly unsuitable candidate for the role of primary substance, or of the only substance (the unsuitability of matter is taken up in Section 5). Aristotle’s ultimate target in the chapter is the subject criterion that apparently produced these results. But responsibility for the unwanted results does not lies solely with the subject criterion, or even with the criterion in tandem with the 29

For the move to a new, lower-level subject, see this chapter, n. 24.

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process of stripping away that Aristotle uses to implement it. To obtain the consequence that matter is (the only) substance, we must also suppose that the result of stripping away can properly be identified with matter in the official Aristotelian scheme. The truth is that Aristotle is not unequivocal that the cross-theoretical identification succeeds: “For if this [= matter] is not substance, it escapes us what else is” (2.10 above, my emphasis). There is good reason for Aristotle’s hesitation here. Aristotle’s official scheme of (metaphysical) predication finds a role for matter as subject: there are different levels of matter in the lower half of that scheme, where matter at each level is subject for the next increment of form, and matter at the very bottom—a.k.a. prime matter—is subject to the entire complement of form that lies above it. But it does not follow that matter, even prime matter, is subject for everything. In particular, the individual substance is subject to its accidents; and Aristotle has yet to show that these migrate away from the individual substance as their subject, and instead have matter, better, prime matter, as their true and proper subject. (We noted a comparable gap in the “non-partisan” half of Aristotle’s argument in the final paragraph of Section 3.) Aristotle tries to close the gap with the “transitivity” argument in 2.15 above, excerpted here: From 2.15 (a21) For, there is something of which each of these is predicated, whose being is different from that of each of the predicables (for, the others are predicated of the substance, but it of the matter [ta men gar alla te¯s ousias kate¯goreitai, haute¯ de te¯s hule¯s]) . . .

In lines a21–24, Aristotle argues from the two premisses that (a) various attributes are predicated of the substance, while (b) it is predicated of the matter, to the conclusion that (c) there is a single subject, namely, matter (in any more fully-developed scheme with multiple layers in the lower half, prime matter) of which everything—attributes and substance like—is predicated. If the (metaphysical) predication relation is transitive, and if there is no equivocation in the terms in the two premisses, the conclusion follows. In fact, however, Aristotle glosses over the fact that the attributes are (metaphysically) predicated of the compound material substance, while it is substance in the sense of form that is (metaphysically) predicated of the matter.30 So the inference fails, for want of a single univocal middle term, and Aristotle’s hesitation over the place of matter here suggests he is aware of the deception. But it is not wanton fraud on his part: it is simply the best he can do in locating a counterpart to the end-product of stripping away in his own ontology. In fact, no such counterpart exists. So Aristotle has two levels of objection to the “received” subject criterion, in the form in which he finds it: applied to his own

The ambiguity in “substance” is disguised by the use of what purports to be the pronoun of crossreference—“the others are predicated of the substance, but it of the matter”—where “substance” refers to the compound material substance but, despite the apparent cross-reference, “it” refers instead to substance in the sense of form. 30

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metaphysical theory, at best, it makes the wrong kind thing substance; but he has reason to suspect that in his theory it fails to pick out anything at all.

5 The Trouble with Matter Suppose that, despite the doubts expressed in Section 4, matter is the proper partisan counterpart in Aristotle’s theory to the rock-bottom subject apparently brought to light by the procedure of stripping away, so that matter emerges as the sole candidate for substance. Alas, the identification of substance with matter is at odds with other acknowledged features of matter in the official Aristotelian ontology, and with what we know about other elements of that ontology. As we have already seen (the penultimate paragraph of Section 2), form and the compound material substance both count as substances to a greater degree than does the matter. Again, according to two other received opinions about substance—neither of them included in Aristotle’s opening list, and neither defended further in Zeta 3—separability and thisness belong most of all to substance, and on these two counts both form and the compound of form and matter come out ahead of matter by itself. So matter is not the sole kind of substance: to the contrary, there are three kinds of substance, and of these matter is ranked as the least: 2.16 (the immediate continuation of 2.13 above) . . . for in fact separate and this seem above all to belong to substance,31 for which reason, the form and what’s “out of ” the two [= the compound material substance] would more seem to be substance than the matter. (a30) The substance that’s “out of ” the two, though, I mean the one that is “out of ” the matter and the shape, should be set aside, for it is posterior, and clear; and the matter too is in a sense evident; but the third has got to be investigated, for that is most puzzling. (1029a27–33)

If, then, a version of the subject criterion for substance is to stand, as Aristotle appears to think it must, proceedings in Zeta 3 show that it cannot stand in the received form cited at the beginning of the chapter (2.1 and 2.2 above).

6 Bare Substrates and Bare Substrate Ontology The argument of Zeta 3 shows Aristotle attempting to accommodate a bare substrate ontology within his own metaphysical theory, in order to find there the basic subject required by the subject criterion for substance. Even if his ontology could be seen as a bare substrate ontology that contains a “subject for everything” in the way the subject criterion requires, however, it turns out on other grounds that the criterion is not a good criterion for substance—it is trumped by other criteria that point not to matter,

31 “Seem above all to belong to substance”: I take the malista with the dokei: according to the majority tradition these two, separability and thisness, outrank the subject criterion as this is understood in Z3.

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as the subject criterion does, but to Aristotelian form. As I interpret Aristotle, therefore, the subject criterion in its received form cannot stand. But there may seem to be a difficulty. In the argument just sketched, the subject criterion is overturned, in essence, in the following way: given the bare substrate ontology of the sort Aristotle sets out in Zeta 3, the subject criterion identifies the wrong kind of item as primary substance; so the subject criterion, “as is” at any rate, must go. At this point (we might think), the opportunity has come for Aristotle to change sides, and tell us that the subject criterion, in its present form, is after all acceptable, and that the bare substrate ontology is what must be surrendered. But it would be a mistake to conclude that he finds no bare substrate ontology of any form acceptable. On the contrary, I will suppose, he is firm in thinking that we should accept a bare substrate ontology, suitably contrived. (Meanwhile, the subject criterion also may survive, but differently applied, or in some suitably amended form.) If it is correct that Aristotle accepts a version of bare substrate theory, are we to suspect him of an unannounced reversion to Platonism? Plausibly, in Aristotle’s theory of (metaphysical) predication in the Categories, individual substances Are members of their kinds and Have their various accidents, and Being is logically prior to Having.32 These views seem directed precisely against a bare substrate ontology of the kind represented by the Receptacle in Plato’s Timaeus. Having in the Categories rejected a Platonic version of bare substrate theory, is Aristotle now committed to an Aristotelian counterpart of that very same theory in Zeta 3? There are two reasons why this is not so. In the first place, Aristotle does not endorse (what we may think of as) the rampant or full-blown bare substrate theory on display in Zeta 3; this is the result of a flawed argument (the transitivity argument in 2.15 above), as he must surely have known. It is present there, as I see it, only provisionally, as the best he can make of a bad job in applying the subject criterion within his own ontology. Second, we need to distinguish between rampant or full-blown substrate theory, and an ontology like the one I suppose is authentically Aristotle’s, that includes a bare substrate, modulo the appropriate qualifications. On the conventional story, Aristotle’s concept of prime matter is that of a subject to various layers of form, none of which belong to it essentially. This is not to say that the prime matter is not after all subject to various modifications, but only that—although it never occurs without modifications—none of these is essential to it. But in contrast to the version of bare substrate theory Aristotle cobbles together in Zeta 3, prime matter in the official theory belongs firmly in the lower half of the scheme of (metaphysical) predication, and only there.33 It may be that prime matter is the ultimate subject of which all the layers of a thing’s constitutive form are (metaphysically) predicated. But it is the individual substance, not 32

The theory of Izzing and Having is due to Code and Grice, Chapter 1, n. 5. The place of prime matter in Aristotle’s metaphysical theory is the subject of ongoing controversy; for a defence, see Lewis (2008). 33

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matter of any level, that is the subject to a thing’s accidents. So the ontology does not contain a subject for everything, and it is not a full-blown bare substrate ontology. In particular, Aristotle does not revert to the (full-blown) bare substrate ontology of Plato’s Timaeus.34

7 The Homonymy of Matter, and Some Difficulties for Metaphysical Predication I suggested in the last section that Aristotle’s theory of (metaphysical) predication makes room for prime matter at the very bottom—something that is a bare substrate, which has no features in its own right, even while it may be the bearer of one or more forms (but none of the accidents) that lie above it in Aristotle’s scheme. On this point, Aristotle’s partisan theory seems to line up well with the “non-partisan” operation of stripping away at the centre of the argument of Zeta 3, which requires at each level a subject that is suitably independent of the items (metaphysically) predicated of it. That is, the relation between a subject and what is (metaphysically) predicated of it must be accidental, if the predicable is to be stripped away from its subject in the way Aristotle envisions: at every level, it is not part of the nature of the subject, or essential to it, that it have the predicables it does. At first sight, prime matter in the official theory fits well with this: it is merely the extreme case, where the subject has no predicables that can be regarded as part of its nature, or as essential to it.35 We have already seen (in Section 4) that the complexities of Aristotle’s official theory outstrip the appeal of the apparent match between prime matter and the result of “stripping away”. The picture is made more complicated in yet another way. In the story on the “received” side of the ledger in Zeta 3, stripping away is possible, because the relation between a subject and what is (metaphysically) predicated of it is accidental: only if this independence condition between what is (metaphysically) predicated and its subject is met, can stripping away ever take place. But Aristotle elsewhere gives us reason to think that the relation of predication between matter and form in his official, “partisan” theory is not similarly accidental. The difficulty—suppressed in the

34 On this story, Aristotle’s official theory is more along the lines of the “double bundle theory”—core bundle and peripheral sub-bundle, but with prime matter added to convert the core bundle into an example of bare substrate theory—set out in Van Cleve (1985), 99–100. For more discussion of the distinction between rampant bare substrate theory, and the version of bare substrate theory that I take to be Aristotle’s, see Lewis (2008), 144–5. 35 More cautiously, prime matter has no essential occurrent properties, leaving room for its potentially having various features—it is capable of receiving elemental contraries, two at a time. Prime matter will also have essentially the second-order functional property of being prime matter. Perhaps only essential properties that are occurrent and purely qualitative are excluded: we should presumably leave room for its being essential to the prime matter that is a constituent of one form–matter compound—my chair (say)—that it not be simultaneously a constituent in another—my desk. For discussion, see Lewis (2008), nn. 5 and 19.

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discussion in Zeta 336—comes from Aristotle’s notion of the homonymy (in certain cases) of matter. In the case of the paradigmatic individual substances, namely, living things, the various stuffs and structures that are the thing’s matter, above the level of the four elements, are none of them a true so-and-so—a true sense-organ, a true organ for locomotion, and so on—in the absence of the ability to play the appropriate functional role within the living thing. Thus, for something to count as a human body (say), it must be a body with the relevant organs; and if these various organs each deserves its name, it must be the living human organ, and part of a living human body. So the soul of the human being must be present to the body for it to qualify as matter for the person. That is, the living body and its organs cannot exist without the relevant form or soul. But if the form or soul is (metaphysically) predicated of the living body and its organs, the relation in this case must be essential, and the independence condition for (metaphysical) predication fails. If this is right, various consequences follow—some of a general sort, and others that directly affect the argument of Zeta 3. To begin with the general point: in cases where the flesh and bones of the living creature must have the relevant form or soul (or else be only homonymously flesh and bones), the two halves of the scheme of (metaphysical) predication cannot be alike to the degree that Aristotle apparently would have us believe. It will not be right to think that the Metaphysics offers a two-tier scheme involving a single predication relation, in which Socrates’ matter (say) Has the relevant form or soul, in exactly the way that Socrates himself Has his various accidents, pallor, and the rest. The relation between Socrates’ matter and his soul cannot be the accidental relation of Having, if his matter cannot exist without his soul. These general difficulties point to troubles for the argument of Zeta 3. Aristotle’s argument portrays (metaphysical) predication as holding accidentally between a subject and its predicables. The relation must be accidental, as we have seen (in Section 4), if on the “non-partisan” side the stripping away is to be performed successfully. But if, on the partisan side, the relation is not accidental, as the homonymy of matter seems to suggest—if (metaphysical) predication here is not simply the converse of Having— then the operation of stripping away has no counterpart on the partisan side, and the entire strategy of the chapter is at risk. At the same time, homonymy suggests a quite immediate reason for doubting that matter is a serious candidate for primary substance—even the only substance. Aristotle’s notion of the homonymy of matter seems to make matter dependent for its very being on the form that is (metaphysically) predicated of it. This dependency in turn undercuts the idea that matter could be primary substance, or the sole substance, in an even more obvious way than is done by Aristotle’s own trumping of the subject criterion with the aid of the thisness and separation requirements.

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But the difficulty is brought to the fore in Maudlin (1990).

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Alternatively, perhaps, the dependency by matter on form makes precise the way in which matter fails the separateness condition: matter can hardly be capable of separate existence—its existence cannot be independent of the existence of anything else—if it is dependent on form in the way the doctrine of homonymy apparently requires. Can it be right that the homonymy of matter impinges on the argument of Zeta 3 in the ways described? During the process that has led up to the birth of a given living animal (say), as Aristotle tells the story in the biology, a variety of structures will count as matter, each built on top of its predecessor by way of a fresh increment of form or soul, taking us ever closer to the living body of the animal when the creature is born. In this process, a succession of potentialities for each next stage of development is realized, as each level of matter serves as the “before-matter” for the more developed stuff or structure that comes next. As always, the potentiality in the matter at the lower level may fail to be realized: so it is essential to matter at a given level that it have the potentialities it does, but it is accidental to matter at that level that those potentialities be realized. The fact remains that once the matter has been worked up to become part of some higher-level item by acquiring some new increment of form, the potential in the before-matter for that form has now been actualized. Once the before-matter has been made part of that higher-level item, it will exist at a higher level of actuality thanks to the newly acquired form, and cannot exist without it. The form in question might never have been acquired; but once acquired, it is extrinsic, but also essential, to the matter to which it belongs37 and cannot be removed, even in thought. On this account, stripping away applied inside Aristotle’s official theory asks us, per impossibile, to imagine the living body (say) that currently serves as the proximate matter for the living creature, as itself existing without the form of the living creature, which is essential to it. Instead, we can only “unwind” as it were the development of the creature, to focus on the different before-matters that later were worked up to become the living body that is the matter of the finished creature. Unwind sufficiently many times, and we may end up with prime matter. But this is diachronic analysis, tracing the history of transformations in the increasingly complex stuffs and structures that count as matter at different stages in the development of the living thing. “Stripping away”, on the other hand, addresses the constitution of a thing at a time (or its stable constitution over some stretch of time); if stripping away is to go forward, it must be the case that what is predicated of a subject (at a given time) is independent of the subject (at that time), so that we can peel its constituent form away from an item, leaving behind the part that serves as its matter. In Aristotle’s “official” theory of matter, however, his notion of homonymy seems to show that the stuff or structure that serves as the matter of a thing cannot exist outside the thing, or without the form to which it serves as subject; and stripping away as it is envisioned in Zeta 3 seems impossible.

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“extrinsic, but essential, to”; see Lewis (1994).

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These complexities associated with the homonymy of matter fall squarely on the partisan, Aristotelian side of the ledger. So they should not be taken to suggest that the procedure of “stripping away” itself is inherently flawed. Rather, the homonymy of matter adds to the reasons for thinking that the version of the subject criterion due to the tradition and the procedure of stripping way that accompanies it—which if not traditional, is at the least non-partisan—are not well-suited to fit the complexities of Aristotle’s official theory.

8 Conclusion The application of the subject criterion in Zeta 3, supposing that the application succeeds at all, points in the direction of a conclusion that is contrary to Aristotelian doctrine. Of the three kinds of substance, Aristotle warns us in the chapter that matter is the weakest. The result that, instead, matter is primary substance constitutes a reductio, not necessarily of the subject criterion however formulated, but of any version of it that uses the Categories notion of a basic subject. The theory of (metaphysical) predication in effect in the Categories presents us with a monolithic conception of the subject of (metaphysical) predication: individual substances are the subjects for everything else, kinds and accidents alike.38 And if the criterion is influenced, even dominated, by the Presocratic notion of a thing’s basic material constituents—in Aristotle’s account, an underlying subject—here again there is a clear sense in which a single set of basic material constituents (whether these are one or many in kind) serve as subjects for everything else. The effect of a criterion for substance based on this monolithic view of the subject of (metaphysical) predication is disrupted in Zeta 3 by the fact that it is applied within an essentially different metaphysical context, containing the two-tier scheme of (metaphysical) predication, with form predicated of matter below, and accidents predicated of individual substances above. Here, despite Aristotle’s best efforts (the transitivity argument in 2.15, Section 4), no single subject for everything is to be found. Instead, there are two irreducibly different kinds of subject to two very different kinds of predicables. We will also find—on top of the disruption introduced by the homonymy of matter (Section 7)—significant complications in the application of the relation of (metaphysical) predication to a compound material substance and its accidents on the one hand, and its application to matter and form on the other (Chapter 8, Sections 15–19). Different parts of the discussion in Zeta 3 fall on different sides of the “partisan”/ “non-partisan” divide. The Categories-cum-Physics subject criterion for substance belongs on the “non-partisan”, “received” side of the ledger, and the initial working out of the criterion by means of stripping away is similarly “non-partisan”. But the 38 For the monolithic conception of the subject of (metaphysical) predication in the Categories, see Lewis (1991), 63–73.

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ultimate downfall of the subject criterion is to be traced to its poor fit with Aristotle’s own ontology—in particular, the prevailing theory of (metaphysical) predication in the Metaphysics, in combination with the “thisness” and “separability” requirements, which are themselves not clearly partisan or clearly non-partisan. In this mix of the “partisan” and the “non-partisan”, one lesson of the chapter is surely a warning that the shift from the one level to the other does not always go smoothly.

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PART THREE

Substance as Essence

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3 A Start on Essence in Metaphysics Zeta 4 With Metaphysics Zeta 4, Aristotle takes up a second item from the agenda passage 1.4 (repeated here) from the beginning of Zeta 3: 1.4 Substance is said, if not in more ways, at least chiefly in four: that is, the essence and the universal and the genus seem to be the substance of each thing, and fourth of these, the subject. (Z3, 1028b33–6)

Accordingly, his topic in this new segment of Zeta is how the notion of the essence of a thing contributes to the larger project of “giving the what-is-it”—that is, of giving a definition—of substance. Thus (the opening lines of the chapter), 3.1 Since at the start we went through how many ways we define substance, and of these one seems (“is considered”) to be the what it was to-be [= the essence], this needs to be thought over. (Z4, 1029b1–3)

In 1.4, Aristotle writes of taking essence as one of the candidates for the substance of a thing, so we are best thinking of the project he describes in 3.1 as that of asking whether the substance of a given thing is to be defined as the essence of that thing. Now, what we are to take as a thing’s essence is a matter of specifying the role that one set of entities will play with respect to another in our ontology. To a certain extent, then, the notion of essence can stay constant across ontologies. The very notion is hardly proprietary to Aristotle, and while various details are filtered through his own Organon, the approach to the topic he adopts in Zeta 4 seems firmly “non-partisan”. At the same time, once he has adapted and applied the notion within his own theory, the result will most certainly be distinctively his. As will seem typical of his treatment of “received” views, we may expect that what Aristotle selects from among the deliverances of the philosophical tradition will yield a conception of essence that, appropriately reworked, is well-adapted to his own notion of essence in the context of his official, “partisan” theory. In Aristotle’s official, partisan ontology, Aristotelian form will be in a certain way the essence of the individual substance, Archimedes (say); and in a different way, the essence of itself (Aristotle takes up this latter idea two chapters below in Zeta 6). A first task, however, is to delineate the notion as it applies independently of his own

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“official” theory—conspicuously in these chapters, its application to the ontology of the Organon, which is innocent, for example, of Platonic and Aristotelian forms alike and, hence, is to a large degree neutral between Plato and Aristotle. (But there will be a direct, and what I take to be a friendly appeal to Plato and Plato’s forms in Zeta 6 in Chapter 6.) As we saw in Chapter 1, the ontology of Aristotle’s Organon includes individual substances, Archimedes, Coriscus, and the rest, and their kinds, man, animal, and so forth; together with the various non-substances, generosity, being seated, and so on, that are accidents of the individual substances. More controversially, his ontology also makes room for accidental compounds, constructed out of individual substances together with their various accidents, taken one at a time: thus, a + ç, or, if you like, Archimedes seated, the one approaching, and the like. In all of this, one general feature of the ontology of the Organon bears emphasizing again. These different kinds of item are assigned different grades of being in the ontology. Part of the very idea of being a substance, for Aristotle, includes a notion of primacy over non-substances, which have a lesser grade of being, and stand in a relation of ontological dependency on substances.1 Accidental compounds, meanwhile, come in third, behind their two constituents, the individual substance and its various accidents.2 We will also find differing views, reflected in the Categories and Topics, and also in some of the puzzles in Metaphysics Beta, about the status of kinds—highest genera, lowest species— and the associated differentiae: how these are to be ranked, not just among themselves, but also in comparison with individual substances.3 Along with the different grades of being just noted, we shall see that Aristotle also recognizes more or less robust notions of essence. It is a hallmark of essence, Aristotle will argue in Zeta 4, that strictly speaking, essence belongs to entities that are properly one and primary; entities with a lesser degree of unity need not apply. The idea that only entities that are primary can have an essence in the proper sense, raises a puzzle that Aristotle addresses in Zeta 6. If an item is primary and also has an essence, what standing shall we give to that essence? The essence of a thing, Aristotle thinks, is also its substance; so surely a thing’s essence must be prior to the thing. How, then, can the thing itself be primary? The only answer is to suppose that a primary substance and its essence are identical, so that neither is prior to the other. As it turns out,

1 Since this was written, notions of ontological priority and dependency have entered contemporary discussion of Aristotle, see Koslicki (2008) and Peramatzis (2011). 2 This ranking among entities has recently been controverted in Code (unpublished). 3 On the status of differentiae, up or down, see Granger (1984). The status of kinds generally comes significantly under review between the Categories and the Metaphysics. There is also disagreement about whether to promote highest genera over lowest, or vice versa: see, for example, Metaphysics B3, 998b14– 999a23 (reverberations of this controversy are to be found at various points in Zeta; see, for example, 3.21 with Chapter 3, n. 49).

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Aristotle suggests that single items from the non-substance categories too—pallor, generosity—are also identical with their essences.4 At the same time, Aristotle will allow that entities that are not primary in the ontology— conspicuously, accidental compounds like the pale man5—do have an essence, but in some less-than-first-class way; in their case, we are to think that they are not the same as their essences. In Zeta 5 and 6, Aristotle continues to press the exclusive notion of essence, even while allowing that other, more relaxed cases also exist. Entities of lesser grade are disqualified in a variety of ways from having an essence in the first-class way. The essence of a pale man, for example, is, presumably, composite, cobbled together from the essence of pallor and the essence of man.6 These two last are terminal essences—for them, as before, the only possible candidate for their essence is: themselves. Aristotle tells us at the end of Zeta 5 what he takes himself to have accomplished in the two chapters, 4 and 5, together (the appearance of the summary in this position is a reminder that the chapter divisions are not due to Aristotle, and that he most likely thought of Zeta 4 and 5 as forming a unit): 3.2 It is plain, then, that [i] definition is the formula of the essence, and [ii] the essence is either of substances alone, or of them chiefly and primarily and simpliciter. (Zeta 5, 1031a11–14, translation by Furth)

1 “How (Informed) People Speak” About Essence: Two Points of Contact with the Tradition I have argued that in large parts of Zeta, Aristotle appeals to the philosophical tradition in which he finds himself, while staying well away from the particulars of his own, partisan metaphysical theory. Chapter 4 of Zeta, where Aristotle begins his discussion of essence, is typical of this oblique, “non-partisan” approach to his larger project of

4

This claim is difficult to reconcile with other things Aristotle says about what qualifies an item to be the same as its essence in the required sense; but I will not take on these difficulties here. For discussion, see Wedin (2000), 264–5, 282–3. 5 At the same time, the individual substance, Archimedes (say), is demoted in Zeta from his status as primary substance in the Categories, and kinds are no longer substances at all. But these demotions are occasioned by the introduction of form and matter—a development which is to be kept out of the nonpartisan passages in Zeta. Accordingly, individual substances make only a last-minute appearance in the penultimate sentence of Zeta 6, where they are the topic of a “sophistic puzzle” (and they are not identified as form–matter compounds, as in Aristotle’s “official” theory). Kinds, meanwhile, are given a starring role at Z4, 1030a10–14; see Chapter 3, n. 49; this, presumably, is in line with the “non-partisan” approach of these chapters, and takes its cue from Metaphysics B3, 998b14–999a23. Finally, it worth emphasizing that, as becomes clear in the summary at the end of Zeta 11, where Aristotle no longer shies away from his own partisan theory of form and matter, individual substances like Archimedes, who comes with matter, do not here count as primary substances, and so like the pale man (the compound of Archimedes it may be with the accident, pallor) will not be identical with their essences. For this point, see Chapter 6, nn. 20 and 57. 6 1032b12–13. Accidental compounds have essences “only in a throwaway sense of the word”; Matthews (1990), 259, n. 7. For more discussion, see Chapter 5, Section 12, and for a dissenting view, Code (unpublished).

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defining substance. So the chapter seems an obvious occasion to trace the sources in others, or in Aristotle’s own other selves, for the “received” views that he thinks relevant to understanding how the notion of essence bears on the inquiry into substance. Aristotle’s sources include his own Organon, but he will also appeal to a line of thought that goes back to Socrates. First, in terms borrowed from the Organon, we say that 3.3 And first, let us say some things about it logiko¯s,7 that the “what it is to be for each thing” is what it is said per se. (1029b13–14)8

As we shall see (in Section 4), this characterization provides a somewhat uncertain guide to the topic. A second, and historically if not conceptually prior route to essence, lies through Socrates’ What is it? question. On this approach, Aristotle’s notion of essence is fashioned around a complete answer, in order, to the question, What is it?, of a given thing; as for Socrates, the What is it? question is also a request for definition, again answered, on some Aristotelian accounts, by citing genus and differentia, “in order”.9 Appropriately, then, the topic of definition enters early on in the discussion in Zeta 4, where it is treated as equivalent to the notion of essence. The Socrates of the Platonic dialogues sets two conditions on his What is it? question. First, we want to know what a thing Is, not what it Has:10 in the language of the Euthyphro, we want to know the essence (ousia) of the holy, not one or other of its accidents (a pathos). Second, as Socrates struggles repeatedly to explain, the items he asking to have defined are general items: the holy (appropriately understood), not this or that holy thing. Accordingly, a complete answer to the question, What is man? (say), gets the answer, man Is a rational animal, let us suppose, where rational animal (“what man Is”) is the definition and the essence of man.

This is the first of the only three appearances of the Greek logiko¯s in all seventeen of the chapters of Zeta (for the two other occurrences of Aristotle’s logiko¯s in Zeta, see Chapter 1, n. 34). There is some dispute as to whether the extent of the discussion that is conducted logiko¯s and initiated at the beginning of Z4 is cancelled by the remarks at 1030a27–28 shortly after the second logiko¯s at a25, or whether, as argued in Burnyeat (2001), 22–3, the discussion extends to the end of Z6. There is an extended discussion of the different possible readings of Aristotle’s term in Burnyeat, 19–25; see also Chiba (2010) and Peramatzis (2010), and Chapter 1, n. 34 and this chapter, n. 20. 8 See also this chapter, n. 22 and the discussion of the locutions, “x is per se1 y” and “x is per se2 y”, in Section 4. 9 For Aristotle, the definition of a thing is defined in terms of its essence, and its essence defined in terms of a proper answer to the What is it? question, this chapter, nn. 43 and 44. Some answers may be incomplete, and so will not render the essence or the definition of a thing. Aristotle can also place his own conditions on what will count as a satisfactory response to the What is it? question in a given context; see Charles (2000), chapter 10, section 10.3. 10 This is again the handy Code–Grice idiom, Chapter 1, n. 5. 7

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Suppose now—disregarding Socrates’ advice—we drop a level, and ask the What is it? question not of man, but of Archimedes. We now have the answers to two What Is it? questions to negotiate: Archimedes Is a man, and man Is . . .

Thus, Archimedes has as his essence the essence of man, where Archimedes Is a man.11 We ask of Archimedes, What Is Archimedes?; and then ask of the entity, man (his lowest kind), we cite in answer, What Is man? The answer to this second question, fully articulated, gives the complex entity that is Archimedes’ essence: The essence of Archimedes: Archimedes Is (a) man [unarticulated], and man Is (a) rational animal (say).

Finally, in the absence of an answer to the question, What is man?, we can cite simply “what it is to be a man” (ti e¯n anthro¯po¯i einai, or to anthro¯po¯i einai), which is a place-filler answer to fall back on when we do not know the full content of the relevant definition. I return to Aristotle’s method for specifying essences in Section 3. Aristotle’s various attempts at defining the essence of a thing in terms drawn from the philosophical tradition weave in and out of a discussion of the connected topic of which things have an essence in the first place—in particular, what level of things have an essence. There is, first, the exclusive, “black-and-white” view:12 only those things that are suitably primary can have an essence, and nothing else can. Later in the chapter he takes a more relaxed, inclusive view, and allows a reduced (and related) notion that applies in other cases. Once Aristotle has introduced this second topic—the different kinds of entity that have an essence, and their different levels—are we to think that the search for a definition with which the chapter began has been abandoned, with no clear resolution? Does Zeta 4 ever reach a definition of the essence of a thing? A better view, perhaps, is that in place of a single, perhaps authoritative definition of essence, Aristotle is content instead with a different approach to his topic. In place of a single definition, he will want to locate the notion within a wider cluster of ideas— What a thing is per se, or what we say in answer to Socrates’ What is it? question, or the like—already established as part of the philosophical tradition. Ultimately, it may be, these different ideas all take in each other’s washing—there is no stepping outside the circle, to fix the notion of essence in independent terms. But the purpose of the project 11

Better: Archimedes has as his essence* the essence (no asterisk) of the lowest kind, man, such that Archimedes Is a man. Rational animal (say) is the essence of Archimedes’s essence, but only the essence* of Archimedes himself (the distinction is from the Metaphysics, and is not evident in the theory of Izzing in the Categories; for details, see Lewis (1984), 117–18, and (1991), 312, n. 10, and 340–1, n. 72; see also Chapter 8, Sections 5–6). The distinction invites reservations about cross-level cases of sameness in substance: Archimedes and Euclid, perhaps, are the same in substance because they share the same essence*; but the entity that is the essence [no asterisk] of Archimedes’ essence, is the essence* of Archimedes himself. So to say that Archimedes and his essence “have the same essence” (even if the assumption is correct, that the essence of X is identical with X) elides an important difference between the two cases. 12 The use of the phrase “black-and-white” in this context is due to Dancy (1978), 394.

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may be exactly this, to specify the place the notion occupies within the circle of “received” terms already to hand.13

2 Beyond Received Views: Partisan Developments In other, more developed accounts on offer in later chapters of Zeta, Aristotle explicates talk of individuals and their kinds, not in terms of the taxonomic notions of genus and species, but with an account of the (Aristotelian) form that typifies the kind. On this picture a thing’s essence is its (Aristotelian) form, and essence or form is that thanks to which a given matter constitutes a thing of the relevant kind (11.6, 11.9, from Zeta17; Chapter 11). Aristotle’s name for an essence again may be a temporizing one, picking out the essence by way of its lowest kind: “what it is to be for (a) house”, or “to be for ice”, or “to be for (a) threshold”. When the definition of a thing is fully spelled out, it is in terms of matter and form: “to be for (a) threshold” is for bricks and timbers to be situated in a certain way (H2, 1043a7–8, cf. 1042b26–7), “to be for ice” is for water to be solidified in a given way (1043a9–10, cf. 1042b27–8). But Aristotle keeps considerations of this sort carefully out of the discussion in these early chapters of Zeta.

3 How To Talk About Essence: Ownership versus Content Aristotle has two, in theory independent, ways of specifying an essence: by way of its owner, most obviously in English, “the essence of Archimedes”; and by way of its content: “the essence, man”, or as I shall say, “the essence as of man”.14 In his own distinctive jargon, Aristotle seems at times to have exclusively ownership in mind. For example, in his initial characterization of essence in Zeta 4, we read in 3.3, repeated here: 3.3 The "what it is to be for-each-thing" is what it is said per se. (1029b13–14)

The dative—“for-each-thing”—points in the direction of ownership, if only because in the balance of the sentence, we are given a recipe for discovering content: it is whatever the thing is said to be per se. For example (Aristotle continues), 3.4 What is “the for-you to be”? Not “the for-musical to be”, for you are not per te musical.

On the present point, despite differences over the details, I find myself on common ground with Peramatzis (2010), 47–9. 14 I adapt this device from Jenkins (2008), 124. Handy though the device is, I will use it only to make clear how I am understanding Aristotle at a given point, and not to replace his terminology. My motive in not replacing his language is not just purity: it may well be that the ambiguity latent in his terminology is not only the cause of some of our difficulties in reading him, but also accounts for some of the slides that appear to bedevil his arguments in the chapter. For this latter point, see the suspicions voiced in Section 4 (d). 13

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In 3.4, Aristotle’s “the for-you to be” identifies an essence through its owner, and goes on to ask about a suitable content. Notice, however, that when he casts about for an answer, he uses an expression of the same form, “the for-musical to be”, now to specify an essence by way of its content:15 not an essence with the right content for that owner, as it turns out, since the essence as of musical is something you fail to be per te. In Aristotle’s “what it is to be for-each-thing” or “the for-each-thing to be”, both of which occur frequently, the demonstrative pronoun gives no guide as to content. I suspect the same is true where an essence is specified by means of a proper name. Thus, the essence, “what it is for-Socrates to be”, like “being for-you” above, most likely is not an individual essence, Socrateity (the essence as of Socrates), but the general essence, “what it is for (a) man to be”, a.k.a. the essence as of man.16 So there need be no link between how the owner of the essence is specified and the content of the essence. Other cases may be similar. For example, on some accounts, “what it is for-pale-man to be” is the essence that has the pale man as owner, and is just the essence, “what it is for-(a)-man to be” (the essence as of man), which is also the essence that Socrates owns, supposing that he is the pale man in question.17 If so, then again, there is no immediate inference from ownership to content. But we may also specify an essence in a way that does take notice of its content. Because Greek lacks our clear distinction between definite and indefinite articles, however, it is not easy in a given case to tell whether the essence is specified via its owner—“what it is for-(the)-[or this-] man to be”—or via its content, “what it is to be for-(a)-man.” Most often, perhaps, the best hypothesis is that Aristotle specifies an essence by way of ownership and content combined. Consider his (abbreviated) “the for-man to be”. Here, arguably, the dative—“for-man”—points in the direction of ownership, while the general term—“for-man”—speaks to content.18 It may often be, then, that Aristotle’s language for essence specifies the content of an essence simultaneously with the specification of its owner.19 The owner is this man here, and the content of the essence in question is the (unarticulated) notion, man.

I take it that the dative “for-musical” in specifications of essence by content is by agreement with the dative for the (often unspecified) owner: “the to be (for-)musical [dative]”. 16 See Metaphysics ˜18, 1022a26, Z6, 1032a8, cf. Ross (1924) I, xcv, n. 1, and for the as of jargon, this chapter, n. 14. 17 So Halper (1989), 76–80, cited by Dahl (1999), n. 15. I part company with these views on two points. I do not agree (a) that ‘the pale man’ is just another way of referring to Socrates (this reading is contrary to ACT, Chapter 1, n. 3). On view (a), it will follow by the Indiscernibility of Identicals, that the pale man and Socrates have the same essence—unless (b) we suppose that the locution, “X owns the essence, E”, is referentially opaque at subject-position. For scepticism about both (a) and (b), see Chapter 5. 18 Hence the expansion in Frede-Patzig, “what it is for-(a)-man to be (a) man”, where both owner and content are addressed; see also Barnes (1994), 174. 19 I adopt this hypothesis in the absence of any finer-grained analysis of the Greek. Thus, in “the for-man to be” I do not know whether ‘man’ is subject—“the for-the-man to be ”—or predicate—“the to be a man”. While these come to the same thing in the end, the first suggests that the content of the essence is to be inferred from the specification of its owner, but the second, that ownership is 15

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The difficulties in distinguishing designations of essence by way of owner, from designations by way of content, and perhaps also from designations of owner and content together, make the opening parts of Zeta 4, discussed in Section 4, more than usually difficult to decipher. I will try to explain my choice of interpretation as we go along.

4 A First Approach, Conducted Logiko¯s: Essence and “What a Thing is per se” Aristotle’s first attack on the notion of essence starts from a condition set out at length in the Organon (and present in other texts): namely, that the essence of a thing is what it is per se (3.3 above, included in 3.5 below, and see this chapter, n. 22). But because expressions of the form, x is per se y, have more than one meaning, as the Organon explains, the condition is open to counter-example. Aristotle passes under review various amended statements of essence, and introduces and illustrates a non-circularity condition on statements of essence, which now double as statements of definition; here, he attempts to correct an earlier example with the help of the “rule of subtraction” from the Topics. At the same time, incidental to matters of philosophical substance, but far from trivial, will be the business of untangling the quite difficult terminology in Aristotle’s discussion of essence. The discussion divides naturally into four parts: 3.5 (incorporating 3.3 above). And first, let us say a few things about it logiko¯s [“in terms of how informed people speak”?],20 namely, that the what it was to be for-each-thing is what it is said per se (“in virtue of itself,” Greek kath’ hauto). For, the for-you to be is not the formusical to be; for you are not musical per te (“in virtue of yourself ”). So, is what you are per te. (1029b13–16) 3.6 (continuing 3.5). Yet not all of this [not all of what a thing is per se is (or is part of ) its essence]; for not per se in the way that pale is to surface [we do not mean “per se” in the way that surface is per se pale], because the for-surface to be is not the for-pale to be [= the essence as of pale is not the essence of surface]. (b16–18) 3.7 (continuing 3.6). Nor again the combination of both, namely the for-pale-surface , because the thing itself [= surface]21 is added. (b18)

inferred from the specification of content. I am tempted to the first view; but my “simultaneously with” in the main text is intended to avoid the choice between the two. 20 I adopt here the least “loaded” interpretation of the vexed term logiko¯s, which has some support in Aristotle’s later reference in the chapter to “how people speak”, 1030a27–8. Other, more robust readings of the term are discussed at length in Burnyeat (2001), Chapter 1, n. 34, see also this chapter, n. 7. 21 My translation retains the Greek auto ( Jaeger, with Ab and Alc), but with the force of haute¯ ( J), or aute¯ (Al ªæ). The point is that, either way, we end up with a compound essence.

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3.8 (continuing 3.7). Therefore, the formula in which the thing will not be present, but which formulates it, this the formula of what it was to be for-each-thing, so that if the for-palesurface to be is the for-smooth-surface to be, then the for-pale and for-smooth to be are the same and one. (b19–22)

(a) In the passages 3.5–3.8, Aristotle imagines a series of attempts at characterizing the notion of the essence of a thing. I being with 3.5, repeated here: 3.5 And first, let us say a few things about it logiko¯s [“in terms of how informed people speak”?], namely (b13), that the what it was to be for-each-thing is what it is said to be per se (“in virtue of itself ”). For, the for-you to be is not the for-musical to be; for you are not musical per te (“in virtue of yourself ”). So, is what you are per te.

3.5 includes a criterion for essence, already cited as 3.3 above, which I repeat here: 3.1 The “what it is to be for each thing” is what it is said per se. (b13–14)

(As we shall see, the language of “per se” is firmly rooted in the Organon.22) In line with 3.3, your essence is what you are per te; and in general, a thing, x, owns the essence as of ç, only if x is per se ç. But if for some ç, you are not per te ç, then the essence as of ç is not your essence (and, presumably, not a part of your essence either). By way of illustration in 3.5, Aristotle suggests an unsuccessful statement of essence: (1)

Archimedes is per se musical.

We are yet to be warned (in 3.6 immediately following) that there is more than one meaning to expressions of the form, x is per se y. But adjusting to the appropriate use of “per se” in (1), we find in (1) a would-be statement of essence that is false, because the content of the proposed essence is wrong for the subject given. This evaluation of (1) indicates that the “per se” condition in 3.3 is a necessary condition for a statement of essence; but we will see immediately that the condition is not sufficient, given the different notions of “per se”. (b) Our next passage is 3.6, repeated here: 3.1 (continuing 3.5) Yet not all of this [not all of what a thing is per se is (or is part of ) its essence]; for not per se in the way that pale is to surface [we do not mean “per se” in the way that surface is per se pale], because the for-surface to be is not the for-pale to be. (b16–18)

In 3.6, Aristotle acknowledges that there are various uses of expressions of the form, “x is per se y”, not all of which are intended to identify the content of a thing’s essence. By way of example, we have (2): (2)

The surface is per se pale.

22 The star passage in the Organon is Aristotle’s distinction among different uses of “x is per se y” in An. Po. A4; for this and other references, see the definitions of “x is per se1 y” and “x is per se2 y” later in this Section.

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As we will see shortly, we may incline towards a reading of (2) on which (2) comes out true. Of more immediate relevance, however, if (2) is read as a statement of essence, then (2) comes out false. As Aristotle explains in the last line of 3.6, it is not the case that (3)

The for-surface to be is the for-pale to be.

That is, it is not the case that (3a)

The surface has for its essence, the for-pale to be (the essence as of pale),

since the essence, the for-pale to be (designated by content), has the wrong content for the given subject (it is not “the for-surface to be”—not the essence owned by the surface). As to the alternative reading of “per se” on which (Aristotle thinks) (2) is true:23 it is by now customary to distinguish the two formulae, “x is per se1 y” and “x is per se2 y”; under this convention, explained immediately below, we will say that it is (quite possibly) true that (2a)

The surface is per se2 pale;

but (obviously) false that (2b)

The surface is per se1 pale.

The correct resolution with respect to (2), accordingly, would seem to be that the wrong sense of “per se” has intruded, so that (2) gives us something that the surface is per se2 (as in [2a] above). That is, (2) gives a per se accident of its subject—but not its essence.24 It would be natural at this point for Aristotle to distinguish the two uses of “x is per se y” that are competing for our attention and disrupting the proposed “per se” criterion for essence. He might then be in a position to tell us, for example, that the sense of “per se” on which (2) is true, is not one that yields a counter-example to the per se criterion for essence, once the different uses of “per se” are set before us. Alas, the use of “x is per se y” that is relevant to statements of essence is itself defined in terms of a thing’s essence, and cannot be spelled out independently of the account of essence that is Aristotle’s target in the chapter:

23 Pallor is a per se accident of surface (a surface is per se2 pale), because we cannot fully explicate the quality, pallor, without explaining that it is a property of surfaces (it is in the nature of pallor that it is an accident of surfaces; the antecedent to the pronoun, “se”, on this reading is “pallor” rather than “surface”). For more discussion, see this chapter, nn. 26 and 27, and for some of the complications in Aristotle account, Barnes (1994), 113–14. 24 Definitions of the two relevant uses of “per se” are given in the main text immediately below. Peramatzis (2010) suggests a way of knitting together the two notions of per se into one, but I follow the more conventional account here.

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x is per se1 y if and only if y is in the essence of x (y is en to¯i ti esti, “in the what is it?”, of x).25

At the same time, the competing use of “x is per se y” is also defined in terms of the notion of essence: x is per se2 y (y is a per se accident of x) just in case x [= the subject] is in the essence of y (more fully, “the logos or the onoma of x is included in y, and y cannot be revealed apart from x”).26

Male and female, for example, are per se accidents of animal: each gender is to be defined as the gender of an animal.27 Similarly, odd and even are per se accidents of number; snub and aquiline of nose; and even pale is a per se accident of surface (see this chapter, n. 26). Because the apparatus of per se2 is also defined in terms of a prior notion of essence, it is not open to Aristotle to say that x genuinely has the essence as of ç, just in case both x is per se ç and x is not per se2 ç. (c) In the continuation in 3.7 and 3.8 above, we find what appear to be successive attempts at repairing earlier, failed efforts. We may begin with 3.7, repeated here: 3.7 (continuing 3.6) Nor again the combination of both, namely the for-pale-surface , because the thing itself [= surface]28 is added. (b18)

Recall that Aristotle rejects (2) from 3.6 above, repeated here, (2)

The surface is per se pale,

as an example of the wanted statement of essence. (2) fails as a statement of essence: whether we render (2) as (3) or (more perspicuously) as (3a), both repeated here, the result is false: 25 For this definition, see, for example, An. Po. A4, 73a34–37, A22, 84a13, and Metaphysics D18, 1022a24–9. 26 An. Po. A4, 73a34 ff, b16 ff, 74b5–12, A22, 84a11–17, Physics A3, 186b18–23, and with the expansion indicated, Metaphysics Z5, 1030b23–5. An alternative explanation is in terms of incompatibility ranges: x is a member of some two-member range R of “opposite” properties y and z, where y and z are either one the privation of the other or they are contradictories in the same kind, and necessarily, exactly one member of R belongs to x. On this view, presumably, snub is a member of the range, snub-aquiline, De Caelo A9, 278a29 ff, and for the general account, see An. Po. A4, 73b23–4, 74b5–12. But Aristotle’s use of pallor as a per se accident of surface—not to mention the lack of fit with his explanation cited in the main text—suggests that the view of R as containing exactly two members (as with the examples, odd and even, snub and aquiline, and the rest) is unnecessarily exclusive; as Wedin (1973), n. 9, suggests (following Ross (1949), 519, see also Granger (1981), 120), “status as a per se accident requires only occurrence within an appropriate finite disjunction whose members are jointly exhaustive and each of which in incompatible with all the rest.” Aristotle suggests at An. Po. A4, 73b16 ff that the first account implies the second, but to my knowledge he says nothing more about how the two accounts are related. 27 Male and female are accidents of animal, because (while it is necessary that all animals are either male or female) it is not necessary that all are male, or that all are female; they are per se, because items that are either male or female are limited to the class of animals, so that male and female must each be defined by reference to their proper subject. 28 For the identification, see this chapter, n. 21.

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4

(3)

The for-surface to be is the for-pale to be,

(3a)

The surface has for its essence, the essence as of pale.

Aristotle turns his attention now to extracting a different, perhaps successful, statement of essence from (3), with the suggestion to be found in 3.7, that (4)

The for-surface to be is the for-pale-surface .29

If (4) is to repair (3), then presumably—in line with (3a)–(4) should be read to say (4a)

The surface has for its essence, the essence as of pale surface.30

The repair is no sooner offered than rejected. The proposed repair in (4) founders, apparently because it gives a false statement of essence. The surface does not have as its essence, the essence as of pale surface, for the proposed essence again has the wrong content for the surface. It does not improve the suggestion in (3) that the essence as of pale is the essence of surface, if we suppose that the surface has as its essence, rather, the essence as of pale surface. So why make the suggestion in the first place? This difficulty has been pressed by Woods,31 who argues that, given the notion of essence as what a thing cannot lose, on pain of ceasing to exist, the proposed amendment is pointless. The new essence, the essence as of pale surface, that Aristotle introduces in (4) presumably includes both the essence as of pale and the essence as of surface as constituents. Clearly, a surface can fail to have this compound essence, simply by failing to be pale even while it continues to be a surface. So if the essence as of pale to be is not the essence of surface, then surely the compound essence, the essence as of pale surface, is not the essence of surface either. But there may be a way of making the proposed revision in (4) seem better motivated. Arguably, the revision takes on board a point about accidents and their essences. The idea has already entered the discussion that pale is a per se accident of surface (see (2a) above). But if pale is a per se accident, then its definition must also include the definition of surface. Accordingly, the essence, (simply) the for-pale to be—the essence as of pale—is not the essence of anything. As it stands, it is incomplete, and must be supplemented by a reference to the appropriate subject, namely surface. The result is the compound essence, for pale-surface-to be, a.k.a. the essence as of pale surface. So (4) may plausibly seem an advance on (3), since it at least cites a bona fide essence as the purported essence of surface, even if for the reasons already stated it is not a suitable essence for its proposed owner. Questions about accidents, in particular, per se accidents—whether properly speaking such things can have an essence at all, and if they do have an essence, the nature of

29 30 31

For a closer look at how to understand (4), see the discussion of (4a) and (4b) in Section 4(d) below. For this reading, see Ross (1924) II, 168, and compare the flaw of prosthesis in definition, 3.11 below. Woods (1974–5), 173–4.

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the compound essence that will be theirs—are to the front of Aristotle’s attention later in Zeta 4, and for virtually all of the following chapter, Zeta 5, and for part of Zeta 6 as well. (d) (4)

With his (4), repeated here, The for-surface to be is the for-pale-surface ,

simultaneously suggested and rejected in 3.7, Aristotle introduces some of the difficulties associated with compound essences like the for-pale-surface to be. On a more positive note in 3.8, he sees what may pass, not as an account of the essence of things in general, but as a route to the content of an essence in a given case: 3.8 (continuing 3.7) Therefore, the formula in which the thing will not be present, but which formulates it, this the formula of what it was to be for-each-thing, so that if the for-palesurface to be is the for-smooth-surface to be, then the for-pale and for-smooth to be are the same and one. (b19–22)

The route to an essence comes in steps. First, (4) is to be replaced by (5) (among other differences, note that in [5], “the for-smooth surface ” replaces the simple “the for-surface ” in [4]): (4)

The for-surface to be is the for-pale-surface .

(5)

The for-pale-surface and for-smooth-surface to be are the same and one.

Equivalently, (5) tells us that the essence as of pale surface and the essence as of smooth surface are one and the same. This reading of (5) suggests a new look at how we are to read (4). Nominally, (4) is a correction of (3), and thus to be read as (4a) The surface has as its essence, the essence as of pale surface. But, thanks to the owner/content ambiguity (Section 3), (4) is also open to the reading, (4b) The essence as of surface is the essence as of pale surface. The claim in (4b) opens the door to the new (5) above. We may be inclined to think that the readings, (3a), of (3), and (4a) of (4), suit the context of the preceding 3.6, while the reading, (4b), of (4) suits rather the continuation in 3.7 and, especially, 3.8; if so, then it may be that the owner-content ambiguity in Aristotle’s designations of essence helps make each reading available where it is most needed. (The shift between the two readings of (4) may be helped or, perhaps, disguised by the extreme terseness of 3.7, where the grammatical subject, presumably “the for-surface to be”, is to be supplied from the previous sentence.) How might (5) improve on (4), read as (4b)? The trouble with (4b) begins with the fact that the essence of a thing is also its definition. The connection with definition is all-important (see the conclusion to Zeta 4 and 5, cited in 3.2 above). But Aristotle does not argue for the connection here; he treats it as simply part of the set of “received

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views” he is entitled to draw on in these chapters.32 On the assumption that the statement of a thing’s essence also serves to give its definition, (4b) is subject to a familiar objection. The difficulty is that the term “surface” that appears as definiendum at the left-hand side of (4a) is included in (prosestin, 1029b19) the term “pale surface” in the definiens to the right. That is, (4b) fails a non-circularity condition on definition: (From 3.8 above). The formula in which the thing will not be present, but which formulates it, this the formula of what it was to be for-each-thing. (1029b19–20, and see the references in n. 8)

Thus, a definition cannot be overtly circular—the definiens cannot contain the term being defined, as in (4a). At the same time, a definition may not be covertly circular— the definiens cannot contain a term whose definition itself contains the definiendum (or whose definition contains a term whose definition contains the definiendum . . . and so on). Both types of circularity are expressly prohibited in the Topics: among the different ways in which in a definition we may fail to use terms that are prior: 3.9 Another is if he has used the term defined itself. This passes unobserved when the actual name of the object is not used, e.g., supposing anyone had defined the sun as a star that appears by day. For in bringing in “day”, he brings in the sun. To detect errors of this sort, exchange the word for its definition, e.g. the definition of “day” as “the passage of the sun over the earth”. Clearly, whoever has said “the passage of the sun over the earth” has said “the sun”, so that in bringing in the “day” he has brought in the sun. (Topics Z4, 142a34–b6, cf. Z9, 147b12–25)

But a simple move, also due to the Topics, will take us from (4b) to a group of statements that are free of circularity of the kinds Aristotle criticizes in 3.9. Amend (4b) so as to give (5), and from (5) we obtain the result in (6): (5) The for-pale-surface and for-smooth-surface to be are the same and one, (6)

The for-pale and for-smooth to be are the same and one.

As I read these two, this is just the move from (5a) to (6a): (5a) The essence as of pale surface and the essence as of smooth surface are one and the same, (6a)

The essence as of pale and the essence as of smooth are one and the same.

The inference to (6), as also to (6a), is supported by the rule of subtraction: 3.10 Furthermore, you must note the result of an addition and see whether each added to the same thing fails to produce the same whole; or whether the subtraction of the same thing from each leaves the remainder different. Suppose, for example, someone has stated that a double of a half and a multiple of a half are the same, then, if of a half has been subtracted from each, the remainders ought to signify the same thing: but they do not. (Topics H1, 152b10–15) 32

For the credentials of the connection in the Topics, see this chapter, n. 34.

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Difficulties remain, however, if we are to see (6) as a definition by proper Aristotelian standards. (6) meets Aristotle’s non-circularity condition. But a definition must not be what in the Topics Aristotle calls, “equimembral” (Z11, 148b32–149a7): it must not have the same number of terms on each side of the definition. So (6) violates the rule that a definition should give a logos (a phrase) as definiens in place of an onoma (a single name) as definiendum, or a longer logos in place of a shorter one.33

5 A Second Approach to Essence: the Connection with Definition The discussion of (4) from 3.8 above illustrates how readily Aristotle can move from the topic of essence to that of definition. The connection between the two is one of the two points Aristotle takes to be clear in the summary at the end of Zeta 5 (3.2 above). Although Aristotle does not say so here, the connection follows by definition: x is the definition of y (x is signified by the definiens in a definition of y) = df x is the essence of y.34

So the formula of the essence for a thing will be a suitable definiens in the definition of the thing. In particular, perhaps, the formula of the essence of compound entities of the sort already contemplated in 3.8 above, pale surface, for example, or the pale man (3.11 below), may be a suitable definiens in the definition of the compound: 3.11 But since there also exist compounds by way of the other categories (for there is something underlying for each, for example, to the of-what-sort and to the how-much and to the when and the where and the motion), we must look into whether [i] there is a formula of the essence for each, and whether [ii] there belongs an essence to these, e.g, to the pale man—let the name for this be ‘cloak’. What is the for-cloak to be? (b28) But in fact, it too is not one of the things said per se. Or rather, “not per se” is said in two ways, and the one case of it is by prosthesis (“addition”), the other not. (1029b22–31)

The question whether there exists a formula of the essence for a given compound, as in [i], just is the question whether we have a suitable definiens for the definition of the thing. But there will be no definition—no “formula of the essence”—if (strictly speaking) the compound has no essence in the first place. Accordingly, Aristotle goes on to address the prior question, [ii], and to look for reasons why we should not assign an essence to items like the pale man, or as he prefers to say, to “cloak” (using a single term to conceal the point that there are apparently two essences to deal with here, that of man and also that of pallor). “What is the for-cloak to be?” Aristotle’s response presses further on the constraints governing what things will qualify for having an

33

Topics A5, 101b38–102a5, Z11, 149a1–4. For this definition, see Topics A4, 101b21–22, A5, 101b38, A8, 103b9–10, H3, 153a12–22, H5, 154a31–2, An. Po. B3, 91a1, B10, 93b29, 94a11, Metaphysics D6, 1016a33, 1017a6, D8, 1017b21–2, Z5, 1031a12, H1, 1042a17, and Bonitz Index, 764b45–57. 34

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essence. On the face of it, items such as cloak, a.k.a. pale man, are not “things spoken of per se” (1029b28–29; this is the third use of “per se” from An. Po. A4, at 73b5–9, 3.22 in this chapter, n. 47); as we will see a few lines later in Zeta 4 (3.12 below), compound entities of this kind, with a structure in which “one thing is said of another”, will not properly qualify as having an essence, even if their nature as structured entities is concealed by the artifice of the evidently simple name, “cloak”. At the present point in the chapter, however, Aristotle deflects this line of thought (e¯ to ou kath’ hauto legetai dicho¯s, “or rather, ‘not per se’ is said in two ways”, b29), in favour of two fresh ways of “not being per se” that will defeat a definition and, hence, promise to disqualify a statement of essence for a thing. But the detour is only temporary, since neither of the ways of failing to be per se need apply to a definition of cloak. Thus—the flaw of “addition” (prosthesis)—what is being defined is added to something else in the definiens, as if we were to define pale with a definiens appropriate to pale man. (The notion of prosthesis gets much wider play in connection with the snub in Zeta 5 immediately following; see Chapter 4.) Or—the reverse of addition— something else is included in what we are defining but is omitted in the definiens, as if “cloak” signified pale man, but we define cloak as just pale.35 (It is certainly true that the pale man is pale; but the for-pale to be is not his essence, if this is the correct understanding of the difficult text at 1030a1–2, see Ross (1924) II, ad loc.). Neither of these two ways of “not per se” that will disturb a definition, need count against thinking that cloak can have an essence. So we will need a new start, and a new test for having an essence.

6 Does a Compound of a Substance with an Accident have an Essence?: Essence and the Thisness Test Aristotle’s new start on a test for having an essence involves yet other terms of art, “hoper” and “tode ti”, from the Organon, in combination with the connection between essence and definition. Aristotle retains the device of letting “cloak” be his term for the pale man: 3.12 But is the to be for-cloak any sort of essence at all? Or not? (a3) For, an essence is just-what (a) this (hoper tode ti estin to ti e¯n einai, text as in Bonitz); but whenever one thing is said of another, is not just-what (a) this (ouk estin hoper tode ti), for example, the pale man is not justwhat (a) this, if in fact being (a) this belongs to substances alone (a4–6); so that essence is of as many things whose formula (logos) is a definition (horismos). (1030a2–7)

35

The two kinds of mistake are discussed at Topics Z3, 140a24–32, and b16–26; for the mistake of prosthesis (“addition”, not to be confused with the rule of addition mentioned in 3.10 above); see also E2, 130b25–8, and Z1, 139b15–17. An example of prosthesis already appears in (4a) from 3.7 above; see this chapter, n. 30.

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Aristotle elaborates on the connection with definition in the continuation of 3.12, which I defer to Sections 7 and 8. In 3.12, Aristotle makes a new start on the question, Do accidental compounds have essences? Alternatively, is there such an essence as the essence of cloak (= the essence as of pale man)? In fact, he argues, there is no such essence. The argument in support of this negative verdict, however, is only incidental on the way to a second, positive but restrictive conclusion, that things have an essence just in case their formula (logos) rises to the level of a definition (a6–7). The opening lines of 3.12 feature, first, what appears to be a necessary condition on the things that can have an essence; followed by a general statement about a carefully circumscribed class of cases (this chapter, n. 40) in which the condition is not met; and finally, a single example (that stock character, the pale man, sans cloak) in which the condition is not met: 3.13 (excerpted from 3.12 above). For, [i], an [its?] essence is just-what (a) this (hoper tode ti esti to ti e¯n einai)36 (a3) . . . [ii], whenever one thing is said of another, is not just-what (a) this (ouk estin hoper tode ti) (a3–4) . . . [iii], the pale man is not just-what (a) this . . . (a4–5)

The correct reading of Aristotle’s Greek is hardly beyond dispute, and the interpretation I will give in what follows is correspondingly tentative. The hardest component of 3.13 is surely [i], and I should explain first what I think Aristotle is not saying in [i]. He is not saying that it is a property of an essence, x, that x itself is just-what a this—that x is essentially a this. The property of being a this, on this account, would be a second-order property: a property of this or that first-order property or set of properties that count as a thing’s essence. I have not been able to see that this reading of Aristotle’s Greek gives any traction in understanding his surrounding argument.37

36 As the addition in angle brackets suggests, in English (as I will read the line) we need “is” twice, while Aristotle gives us estin once. Which estin he gives us, and which he omits, I find it impossible to be sure. 37 Suppose we adopt the second-order property account, and read [i] from 3.13 in the main text to say that

[i*] An essence is just-what [= is essentially] a this. On this reading, Aristotle in 3.12 and 3.13 asserts of (Aristotelian) essences what he denies of Platonic forms: 3.14 Ecthesis is not what produces the Third Man Argument, but rather, conceding that essentially a this (to hoper tode ti sugcho¯rein), SE 22, 179a3–4, cf. Metaphysics Zeta 13, 1038b35–1039a3 (= 8.10 below). If we combine [*i] with the reading of [iii], also from 3.13, as [iii'], [iii'] The pale man is not essentially a this, we get the result that the pale man is not an essence. But this is a misfire: we need to show, not that the pale man is not an essence, but that the pale man does not have an essence. In any case, we will also need to know Aristotle’s grounds for asserting [i*]. One explanation is not available in the present context. In his official, “partisan” theory, Aristotle is more than willing to say that Aristotelian form, which he will count as the essence of a thing, is a this. But we must not look for help to this source, on pain of importing assumptions from the “partisan” theory of form and matter into the non-partisan context in Z4. (An extended argument for finding a reference to Aristotelian forms, contrary to the “species of a genus” reading of genous eide¯ at 1030a11–14 in 3.21 below, is to be found in Wedin (2000), 230–47; see also this chapter, n. 49.)

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I am inclined to think, instead, that Aristotle means to assert, not that being a this is a property of an essence, but that it is a lower-level property of the bearers of an essence. The upshot, as I see it, is that in [i] of 3.13 Aristotle is imposing it as a necessary condition on x’s being an essence, that for any y such that x is the essence of y, y is a this. For this reading of Aristotle’s text, see Bonitz (1848–49), 308: “Cuius enim rei esse velimus ti e¯n einai, eam oportere esse tode ti”. In the remaining two components of 3.13, Aristotle will cite two cases in which this condition fails. Altogether, then, we have this trio of claims: [i']

Its essence is just-what a thing is, provided that thing is a this.

That is, to be clear about it, x is the essence of y, only if y is a this.38 Aristotle goes on to suggest a class of cases in which this condition is not satisfied: [ii'] For any (two-part) compound entity, x, such that one part is said of the other, x is not just-what a this—x is not essentially a this. (a3–4) In particular, [iii'] The pale man (= the compound of man and pale) is not just-what a this—not essentially this. (a4–5, see this chapter, n. 37)39 For present purposes—in particular, in a context where his own ontology of form, matter, and form–matter compounds is not up for discussion40—Aristotle assumes that

38 The reading [i'] I am giving to Aristotle’s hoper in [i] from 3.13 above requires more than the usual attention to the syntax of the larger context in which hoper appears. In the reading I am arguing for, we are to think of hoper as in what I take to be its original role, as a relative pronoun, as part of a construction comparable to that of the pseudo-cleft sentence in English; details are in the Appendix to this chapter. 39 I understand Aristotle’s use of hoper in [ii'] and [iii'] in the main text rather differently from how it is understood in [i']. To take the simpler of the two sentences: [iii'] is the negation of a subject + predicate sentence in which, as with the standard use of the expression in the Topics and elsewhere, hoper is functionally a modal adverb, “essentially” (the original syntax from which this use originates is disputed). In this use, commentators typically say, hoper serves to introduce a thing’s essence, or its species, or even its genus. For example,

3.15 The pale is an accident of the man, because he is on the one hand pale, but not just-what pale (ouch hoper leukon). Metaphysics ˆ4, 1007a33. Thus, Archimedes (say) is not hoper pale, for he does not have as his essence, the essence as of pale—he is not essentially pale. Again, 3.16 Snow is not hoper white, on which account the white is not the genus of snow . . . indicates not what snow is (ti estin he¯ kio¯n), but a certain quality (poion ti). Topics D1, 120b23, 27-8. For the family of uses of hoper exhibited here, see also Topics G1, 116a26–7, D2, 122b25–6, 123a2, D4, 124a17–18; An. Po. A39, 49b6–9, B22, 83a25–28; and the citations in Bonitz Index, 533b44–534a23. 40 As throughout Z4, Aristotle stays well away from any mention of his own conception of individual substances as compounds of form and matter; see this chapter, n. 47. So form–matter compounds are not candidates for inclusion as thises and as substances; and not candidates for exclusion on the grounds that they are in their own way composed by way of one thing’s being said of another. For Aristotle’s positive views about the unity of form–matter compounds, see Eta 6.

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items that are structured in the way that accidental compounds are structured, fail to be thises. Indeed, accidental compounds cannot be thises: only substances can be thises (a5–6 from 3.12), and accidental compounds are not substances.41 In accordance with the “black-and-white” view of essence in force in this part of Zeta 4, then, the pale man and its like do not have an essence at all. Aristotle moves next to his second, more general conclusion (ho¯ste, a6), that only those things whose formula (logos) is a definition (horismos) have an essence. His conclusion completes the sequence of thought in 3.12 above; I reproduce the closing lines here: 3.17 (from 3.12 above) . . . so that essence is of as many things whose formula (logos) is a definition (horismos). (1030a2–7)

His argument to this conclusion is elliptical. But it will be evident that (with one unproblematic exception)42 Aristotle explicitly gives us all the assumptions the argument needs. The argument requires us to borrow two assumptions from the earlier part of 3.12: (1) (2)

A

The result, (5), is tantamount to the first of the two conclusions Aristotle registers at the end of Zeta 5 (= 3.2 above).

7 Two Conditions on Definition and Essence: Unity and Primacy The connection between essence and definition which forms part of Aristotle’s official conclusion to Zeta 4 and 5 is well-established as a fundamental feature of his work both inside and outside the Organon. Unsurprisingly, it is also a sub-text in the discussion of essence in Zeta 4 from the very beginning of the chapter. The connection between the two notions centres around the What is it? question (Section 1), which in the philosophical tradition constitutes a request for definition, but which Aristotle uses to

41 Accidental compounds, which I take to be not identical with individual substances, are a part of Accidental Compound Theory (ACT, Chapter 1, n. 3), which is not altogether uncontroversial in the secondary literature. But 3.11 and 3.13 in the main text above leave little doubt that for present purposes the pale man is not a substance. 42 The one assumption he does not state is (3) below in the main text, presumably too obvious to need stating.

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define the essence of a thing.43 His notion of definition, in turn, is defined in terms of that of essence.44 With the topic of definition there comes a requirement about the primacy of the would-be objects of definition. As I have understood Aristotle in Section 6, only a this, that is, only what counts as a substance, can have an essence. In particular, we have already learned (3.12 above) that structured entities, in which one part is said of another— accidental compounds like the pale man, for example—strictly speaking have no essence. Similarly, definition must have something primary as its object, where primacy is reserved for things that “are said not by way of one thing’s being said of another”— for items that display the required degree of unity. Aristotle holds in the Topics that it is a necessary condition on definition that definiendum and definiens signify the same thing (Topics Z11, 149a8–11). But as he points out twice in Metaphysics Zeta 4, considerations about unity indicate that the condition is not sufficient: 3.18 (continuing 3.12 above). But a definition is not whenever a term signifies the same as a formula (logos)—for then all formulae would be definitions: for there will be a term corresponding to any formula whatever, so that even the Iliad will be a definition—but whenever it is of something primary (a10): of this sort are whatever are spoken of not by virtue of one thing’s being said of another. (1030a7–11, cf. b7–10, included in 3.24 below)

The Iliad example appears in connection with definition in An. Po. B7, 92b31–2, and B10, 93b35–7, cf. perhaps B3, 90b16. On the Iliad example again, from Metaphysics H6: 3.19 A definition is a logos that is one not by being bound together (sundesmos), like the Iliad, but by being of one thing. (H6, 1045a12–14, cf. Poetics 20, 1457a28-30)

Aristotle offers two arguments to the same effect in the An. Po. (the second overlaps in an obvious way with 3.18): 3.20 For first, [i], there would be of not-substances (me¯ ousio¯n) and of things that are not: for it is possible to signify also things that are not. Again, [ii], all logoi (“sets of words”) would be definitions: for it would be possible to assign an onoma (“term”, “name”) to any logos 43

According to Aristotle’s definition of the essence of a thing,

x is the essence of y = df x gives a complete answer, in order, to the question, What is y? For this definition, see Topics H3, 153a15–22, An. Po. A22, 82b37–83a1, and especially B13, 97a23–b6; for “complete”, see 96b35–97a6, a25–6, 35–b6; “in order”, Topics Z5, 142b27–29, An. Po. B13, 96b30–5, 97a25, 28–34, Metaphysics B3, 998b5–6, D28, 1024b4–6, Z12, 1037b29–30. 44 According to Aristotle’s definition of the definition of a thing, constructed via the notion of a thing’s essence, x is the definition of y (x is signified by the definiens in a definition of y) = df x is the essence of y; see Section 5, n. 34. This definition captures a notion of (call it) metaphysical definition, construed as a relation between entities; corresponding to a given metaphysical definition there will be a notion of linguistic definition, connecting the linguistic items signified in the metaphysical definition (for more on metaphysical and linguistic definition, see the Appendix to Chapter 10). Aristotle relies on context to identify the relevant notion, and I shall follow his lead.

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you please, so that we would all talk definitions, and the Iliad would be a definition. (An. Po. B7, 92b28–32)

The text of the Iliad is only one by continuity,45 so the fact that we can introduce a name (the title of the poem) that signifies the same set of events as does the entire text does not make the latter the definition of the former.46 On top of the requirement that definiens and definiendum signify the same, then, the (metaphysical) entity that is the object of the (linguistic) definition must also be suitably primary, with the further proviso that it be suitably one. Aristotle says nothing in Zeta 4 about what constitutes a unity in the strict sense required. Instead, he tells us what will defeat unity in a thing, and identifies items of the sort that apparently exhibit the required unity and, hence, are suitably primary. He also adds conciliatory remarks about items that have a unity to a lesser degree. All this is the business of 3.21: 3.21 (continuing 3.18 above) So there will not be an essence for any of the things that are not species of a genus (genous eide¯), but for these alone (for these seem not to be spoken of in virtue of participation and affection (pathos), nor as an accident): (a14) but there will be a formula (logos) of each of the others too what it signifies—if there is an term (onoma) , that this belongs to this, or in place of a simple formula (logos) a more precise one; but there will be no definition (horismos), and no essence (no “what it was to be”). (1030a11–17)47 45 I take it that this is not a piece of literary criticism, commenting about the literary unity of the poem. Instead, as Alan Code has suggested in discussion, Homer’s text exhibits a syntactic unity, which is the result of the various sentence-connectives distributed throughout the work. Aristotle’s fullest account of a sufficiently strong form of unity is in Eta 6, which is not our concern here. 46 Aristotle’s first argument in [i] may also make a point present also in Zeta 4, if his meaning is that only substances can be defined. At issue is the understanding of Aristotle’s “not-substances” (me¯ ousio¯n) in 3.20: if the following “and” is epexegetic, so that me¯ ousio¯n are instead, things that do not exist, then the point is the same as at An. Po. B7, 92b5–8, where Aristotle points out that we can say what a logos or onoma signifies, for example, “goatstag”, but we cannot know what a goatstag is. (This is the reading favoured by Barnes and Philoponus.) But this reading requires an unparalled use of the Greek “ousia”. 47 It is instructive to compare the string of passages, 3.13, 3.18, 3.21, with some lines from the An. Po:

3.22 Again, certain items are not said of some other underlying subject: e.g. [i] what is walking (to badizon, “the walking ”) is walking while being something different, and similarly for what is pale (to leukon, “the pale ”), but [ii] substance and whatever signify a this, are not just-what they are while being something different. Items which are not said of an underlying subject I call things in themselves (per se), and those which are said of an underlying subject I call accidents. A4, 73b5–9. Aristotle contrasts entities of two kinds: things per aliud: the walker, or the walking , the pale , both of them accidental compounds of a underlying (but unidentified) substance with an accident; and things per se: Archimedes, Xenocrates (say), each of whom qualifies as the underlying thing, or the substance, that is doing the walking, or that is pale. (In this account, the class of per se beings is marked off by a condition on predication: “X is or exists in itself if X is Y is never an unnatural predication”, Barnes (1994), 117; but still, I take it, the relevant notion of per se [“per se3”] selects for a given class of entities, not for a notion of predication, as argued in Peramatzis (2010).) Two points emerge in the process of drawing Aristotle’s contrast between the two kinds of entity: first, substances signify a this (whatever the meaning of this dark phrase may be); and substances are just-what they are—they are just-what X for some choice of X— without our having to identify some other entity as the appropriate subject to X. I will suppose that where Archimedes is just-what X, X introduces the essence of Archimedes. That is, in this part of the An. Po. at any

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Aristotle has already argued that compound entities like the pale man do not have an essence. The point is, we now see, that the compound is an accidental one. The compound, Archimedes + pale, for example, exists, only for as long as pallor is an accident of Archimedes. An entity that is primary, by contrast, cannot owe its nature and very existence to accidental relations of this sort. That is, Aristotle says, piling it on, what is primary cannot exist by virtue of participation—or as a pathos—or accidentally. I take it all three of these last characterizations amount to the same thing.48 The suggestion that only genous eide¯ satisfy the definition of what is truly primary is, if anything, yet more controversial. I shall suppose that Aristotle has in mind lowest species of a genus, in line with the idea under discussion in the seventh Aporia in Metaphysics Beta.49 So the option is very much part of the philosophical tradition, even if it is not an option that he will endorse in his own, “partisan” theory.

8 Grades of Being, of Essence, and of Definition In the mood expressed in 3.13 and 3.21, the primacy and unity conditions exclude all other kinds of entity besides species of a genus from having a definition; other entities may have a logos, but they will not have a horismos—a definition proper—3.22. Aristotle immediately goes on to soften this exclusive, “black or white” view of what can have a definition or an essence: 3.23 (continuing 3.21 above) Or is definition, like the what is, “spoken of in many ways”? For, the what is in one way signifies substance and the this, but in another way each of the things predicated: so-much, so-qualified, and whatever else is of that sort. (a21) For, just as the “word” “is” belongs to everything, but not in the same way but to one primarily and to others secondarily (“derivatively,” hepomeno¯s, a22), so too the what is

rate, in contrast to accidental compounds, individual substances are per se items, and they are endowed with essences. In Metaphysics Z4, as we have seen (in Section 6), Aristotle will agree with the negative verdict about accidental compounds. But what he identifies as the hallmarks of substance will no longer attach to individual substances but to general items, or (perhaps) species of a genus, as in 3.21. In the Analytics, there is no talk of the analysis of individual substances as compounds of form and matter, so they are not subject there to qualms about one thing’s being said of another. Those same qualms are again not mentioned in reference to form– matter compounds in Zeta 4, not (presumably) because they are not on Aristotle’s mind, but because form and matter have no place in this part of his discussion, which stays with “received” views; see this chapter, n. 40. 48 The notion of participation is open to a variety of interpretations. The definition at Topics ˜1, 121a11–14, cf. 5, 126a17–20, is exactly what is needed for the relation of a lower species to a higher genus; but Aristotle excludes participation here as a relation between species and genus, in view of the Platonic variety of participation, which Aristotle often regards as an accidental relation. Aristotle again rejects participation as a relation between species and genus at 1037b18. So the two kai’s (kai pathos kai kata sumbebe¯kos, “not . . . as an attribute and accidentally”) are epexegetic. In this note, I follow the interpretation in Ross (1924) II, ac loc.; see also his note in (1924) I, on A9, 991a31. 49 Beta 3, 998b14–999a23, cf. 1, 995b29–31, Topics Z1, 139a29–31, 5, 143a18–19. For the primacy of genous eide¯ in 3.21, see especially Metaphysics B3, 999a14–16; also Z12, 1038a13–33, and PA A4, 644a24–5. In favouring the eidos in Z4, Aristotle is reversing the preference for the genos in Z3, cf. H1, 1042a13–15. A different option in the secondary literature for the identity of genous eide¯ is Aristotelian forms; see Wedin (2000), 230–47.

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without qualification to substance and somehow (“in a limited way,” po¯s) to the rest. For even of a quality we might ask, what it is, so that quality too is one of the what is, but not without qualification, but just as in the case of what is not some say logiko¯s that what is not is, not without qualification, but what is not—just so with quality. One must, then, examine also how one must speak about each thing, but certainly no less than how things are; so now too, since what is said is clear, the essence, too, equally [i] will belong primarily and without qualification (pro¯to¯s kai haplo¯s) to substance, and next in order, “secondarily” (hepomeno¯s) to the others—exactly as does [ii] the what is—not without qualification what it was to be (haplo¯s ti e¯n einai ), but what it was to be for-quality, or for-quantity (poioi e¯ poso¯i ti e¯n einai). (1030a17–32)

In 3.23, Aristotle traces his more liberal attitude towards essence to views that are not present in the Organon: namely, the notion of “core-dependent homonymy”.50 Thus, the being of an item in one of the different non-substance categories is a core-dependent homonym of the being of items in the category of substance with respect to the term “being”. That is to say, there is a core or primary universal, being: namely, substance being, that attaches to substances, and a variety of peripheral universals, being, in the case of items in the different non-substance categories: quality being (the being of the quality of a substance), quantity being (the being of a quantity of a substance), and so on. So, the term “being” evokes the core universal, being, when the term is applied to a substance; and it evokes a different, core-dependent or peripheral universal, being, when the term is applied to an item from one of the non-substance categories.51 Quality-being, for example, is a core-dependent homonym of substance-being with respect to the term “being”. And the way in which the different peripheral items are dependent on the class of substances at the core is a form of ontological dependence in different ways of non-substances on the core substances. The doctrine of core-dependent homonymy as it applies to the different notions of being has an immediate application to essence—to what it is for-a-thing to be. As Aristotle notes, the notion of the different grades of being, primary and secondary, runs pari passu with the notion of differing grades of essence. The result is a theme that runs throughout the remainder of the discussion of essence in this and the following two chapters of Zeta. Thus, according to Aristotle, 3.24 This is plain: what primarily and without qualification is definition and essence, is of the substances. Even so, they are similarly of the other things too, only not primarily. (b7) For it is not

50 On the topic of core-dependent homonymy (what he calls “focal meaning”), Aristotle “is beyond the Organon as a whole”, Owen (1960) 1986, 173. The term “core-dependent homonymy” is from Shields (1999), cf. Lewis (2004), Ward (2008). Core-dependent homonymy is an elaboration of a notion of plain homonymy, which is present in the Organon and explained in Categories 1. For example, the wetland bird and the construction crane that is the topic of the (spurious) Mechanics 18 are homonyms with respect to the term “crane”: each is called a crane, but the accompanying definition is different in the two cases. 51 I assume that core-dependent homonymy is in the first instance a relation among universals with respect to a given term; but as Aristotle observes (a21 in 3.23 in the main text), it will follow that the term in question will apply in different ways, in one case primarily (proto¯s), and in the remaining cases secondarily (hepomeno¯s).

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necessary, if we stipulate this, that a definition of this be whatever term signifies the same as a formula, but a certain kind of formula: and this if it is of one thing . . . in as many ways as one is said; (b10) but one is said like being: being signifies on the one hand some this, and on the other quantity, or some quality. (b12) Accordingly, there will be an account and a definition even of the pale man, but in a different way of the pale too [= pallor] and of the substance [= Archimedes (say)]. (Zeta 4, 1030b4–13)

Similar sentiments appear as Aristotle’s conclusion at the close of the following chapter 5: 3.25 Definition and essence must be spoken of in many ways, so that in one way there is not a definition of anything and essence will not belong to anything except to substance; but in another way there will be. It is plain, then, that [i] definition is the formula of the essence, and [ii] the essence is either of substances alone, or of them chiefly and primarily and simpliciter. (Zeta 5, 1031a9–14, translation by Furth)

The final sentence of 3.25 (repeating 3.2 above) echoes the final sentence of 4.4 below. As before, Aristotle’s first inclination is to bar a variety of items from having an essence. Or—a later concession—they will not have an essence in the full-blooded sense. As we shall see, he will continue to qualify his initial black-and-white view in later chapters of Zeta.

Appendix: Greek Hoper and the PseudoCleft Constructions in English My target is the syntax of the problematic [i] from 3.13 above, repeated here: 3.13 For an [its?] essence is just-what (a) this (hoper tode ti esti to ti e¯n einai). I begin with the simple subject + predicate sentence of English,

(1)

Archimedes is a man,

and the corresponding cleft construction,

(2)

It is a man that Archimedes is.

With (2), in turn, compare the pseudo-cleft sentence, (3), and its “inverted” variant, (4):

(3)

(Just-) what Archimedes is, is a man. [P-CC]

(4)

A man is (just-) what Archimedes is.52 [IP-CC]

52 For the pseudo-cleft construction [P-CC] and its inverted variant [IP-CC], see Higgins (1973). (Only what Higgins calls the specificational reading of (3), as opposed to the predicational reading—e.g., “What Archimedes is, is a property”—seems relevant.)

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In the Greek equivalent of (3) and (4) above, the philosophical use of hoper (“just-what”) trades quietly on the old Socratic What is it? question (Section 1). The relative pronoun, hos, or its neuter, ho, with or without the intensifying enclitic, -per, in contrast to the other relative pronouns, hosos, as much or as many as, and hoios, of what sort, such as, is weighted for those descriptions of a thing that assign it to its kind, rather than classifying it in some incidental way by quantity or quality and the rest (the restrictive force of hoper is in evidence, for example in Categories 5, 3b36–9, and 7, 6a39–b11). So, for example, 200 lbs is how-much Socrates is in weight; but a man is hoper—is just-what—he is. So the use of hoper in Greek counterparts of the pseudo-cleft sentences (3) and (4) selects for what Archimedes is essentially, rather than accidentally (and comments about his weight, complexion, and the rest will not be relevant). We may generalize on the examples featured in (3) and (4) to give the pseudo-cleft sentence,

(5)

(Just-) what a thing is, is its essence, [P-CC]

and the “inverted” form,

(6)

Its essence is (just-) what a thing is. [IP-CC]

We can think of (5) and (6) as schemata which have pseudo-cleft claims like (3) and (4) as their instances. Something like schema (6) appears in An. Po. A22, where (once our predications are regimented into what Aristotle regards as the form suitable for the syllogism), we can distinguish two classes of predication. The class relevant here features substance-predicates, “man” and the like: 3.26 Again, that signify substance signify, of what they are predicated, just-what that thing [= the thing of which it is predicated] or just-what a certain kind of that thing [hoper ekeino e¯ hoper ekeino ti]. (A22, 83a24–5) The reading indicated in square brackets is the reading adopted in LSJ, loc. cit., “Expressions which show the essence [our ‘substance’] show precisely what the thing in question is or precisely of what kind it is (i.e. indicate either its species or its genus)” (their emphasis); the paraphrase in Ross (1949), 574, is similar: “Predicates indicating essence express just what the subject is, or what it is a species of ”. So understood, 3.26 accords closely with schemata (5) and (6) above. Lastly, notice that the pseudo-cleft constructions can serve as a device of emphasis, to highlight either the importance of a given set of attributes to their subject, or the identity of the subject of those attributes:

(3')

What Archimedes is, is a man (not a ghost, not a god . . . ) [P-CC]

(4')

A man is what Archimedes is (he is that very thing, a man) [IP-CC]

(3'')

What Archimedes is, is a man (he’s the man; Affirmed is the horse) [P-CC]

(4'')

A man is what Archimedes is (don’t confuse him with Affirmed, his horse) [IP-CC]

We come now to our target passage [i] from 3.13 above; because word-order in Greek is so much more flexible than in English, the correct translation may be either [i] or its uninverted variant, which I cite first: Just-what a this is an [its?] essence. [P-CC] [i] An [its?] essence is just-what a this . [IP-CC]

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As in (5) and (6) above, I take these two to be schemata, here linking the notions of essence and thisness. As I understand them, the sentences have the syntax of respectively a (regular) pseudocleft and an “inverted” pseudo-cleft sentence, comparable to, and generalizing over, the “regular” and the “inverted” pseudo-cleft constructions in (3'') and (4'') regarding Archimedes in contrast to his horse. As with the intended emphasis on the subject in these last examples, the job of the pseudo-cleft construction [i] and its uninverted variant is to emphasize that it is a this— and not some other kind of entity—that has this or that essence. The result is to place a constraint on the nature of the subjects that qualify as having an essence. For this reading of Aristotle’s text, see again Bonitz, “Cuius enim rei esse velimus ti e¯n einai, eam oportere esse tode ti”, quoted in Section 6.

4 Sameness, Substitution, and Essence (I): Zeta 5, the SE, and “A Nose by Any Other Name” In the opening chapters of Zeta, as we have seen, Aristotle assigns himself the task of identifying the “what-it-is”—that is, finding the definition—of substance (Zeta 1, 1028b7 from 1.1 above, 2, 1028b31–2). In his first discussion of items on the list of “the principle ways in which substance is said” in Zeta 3 (1.4 above), the goal of producing a definition of substance appears to give way to a critique of the subject criterion that was supposed to guide us. In the following chapter Zeta 4, Aristotle moves to the second item on the agenda he set himself in Zeta 3, namely, the received view of substance as essence—or better, the view of the substance of a thing as the essence of that thing. So we will expect him to say how the notion of essence (or the essence of a thing) contributes to the larger project in Zeta of defining substance (the substance of a thing). The early parts of Zeta 4 are taken up by attempts at defining the essence of a thing that prove inconclusive;1 as these attempts proceed, Aristotle appears interested less in producing an explicit definition, and more in exhibiting the connection between essence and other notions in the received philosophical lexicon (see Chapter 3, Section 1). In this same spirit, I take it, Aristotle’s main concern in the remainder of Zeta 4 and in Zeta 5 is with determining what things have an essence, in particular, what level of things have an essence (= conclusion [ii] in 4.2 below). But his interest in these “non-partisan” chapters of Zeta is in the constraints on which things may have a definition or an essence, and not at all in identifying which entities they are that have an essence in his (or even in someone else’s) ontology. By the same token, he has 1 In the summary at the end of Z11, Aristotle himself is noticeably more sanguine about the results of Zeta 4:

4.1. What, then, the essence is, and in which sense it is “itself in respect of itself ”, has been stated generally, for every case. Z11, 1037a21–22. Despite Aristotle’s claim to have told us what essence is, it is worth noting that contrary to the “received” tradition he records in Z3, the connection between the essence of a thing and its substance does not give us a definition of substance; see the cautionary remarks in the introduction to Chapter 7. The definition Aristotle is looking for, of the substance of a thing, or primary substance, must wait until Z17; see Chapter 11.

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no interest in these chapters in introducing his own, partisan notion of form, which for him constitutes the substance and the essence of a thing.2 In setting constraints on what things have an essence in the second half of Zeta 4, Aristotle argues first for an exclusive view of essence and definition: only those things that are suitably primary can have an essence (pro¯tou tinos, Z4, 1030a10), and nothing else can (3.16 above). This said, he goes on almost immediately to find reasons for a more relaxed, inclusive view. To summarize 3.21 above, just as is applies to everything, but to some things primarily and to others secondarily (pro¯tos, hepomeno¯s), so too the what a thing is in one way signifies substance and a this, but in another way each of the things predicated: it applies without qualification (haplo¯s) to substance, but in a way (po¯s and ouk haplo¯s) to everything else.3 The contrast between the inclusive and exclusive views is repeated throughout the remainder of the chapter (see, for example, 3.21 through 3.23 above). Like definition or what a thing is, “essence too belongs without qualification and primarily (pro¯to¯s . . . kai haplo¯s) to substance, and after that to everything else”—except that this is not “essence without qualification” (haplo¯s ti e¯n einai), but “essence-for-a-quality, for-a-quantity”, and so on. And definition for its part requires not just “signifying the same as a formula (logos)”, but signifying the same as a formula of something that is one, in one of the many ways in which one is said. So there will be a definition even of the compound, pale man, and a definition “in another way” of the pale and of substance. Strictly speaking, then, only things that are suitably primary have an essence, but we may allow also for a less strict, secondary notion of essence, in connection with a wider class of entities. This is Aristotle’s summary of the work of the two chapters, Zeta 4 and 5, in the closing sentences of Zeta 5: 4.2 (= 3.25 above) Definition and essence must be spoken of in many ways, so that in one way there is not a definition of anything and essence will not belong to anything except to substance; but in another way there will be. It is plain, then, that [i] definition is the formula of the essence, and [ii] the essence is either of substances alone, or of them chiefly and primarily and simpliciter. (Zeta 5, 1031a9–14, translation by Furth)

The puzzles in Zeta 5 speak directly to these conclusions. The chapter opens with two rounds of puzzles devised around a new set of entities that are per se accidents like the

2 This reticence disappears in the “partisan” portions of the segment, where Aristotle’s “official” doctrine is given: for example, “definition is of the universal and the form”, Z11, 1036a28–29; and “the soul of animals (this being the substance of the living thing) is the substance in respect of the formula, i.e. the form, i.e. the essence of [he means: that is introduced to] a body of a certain sort”, Z10, 1035b14–16. For Aristotelian form as the essence and substance of a thing, see in particular Zeta 17, Chapter 11. 3 The fact that in the end Aristotle argues for an inclusive view does not mean that he is willing to enlarge the class of things that have an essence in the strict sense, or that the exclusive view is not correct as far as it goes; the inclusive view is possible, only because he also allows secondary or derivative ways in which things may have an essence. It is worth asking whether the relaxation he envisions concerns secondary or derivative cases of essence, or of the essence of relation: I argue for the latter in Lewis (1984), 91–118, and Lewis (1995), 529; the former view is developed in Loux (1991), chapter 3.

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snub or snubness.4 In the opening paragraph (4.3 below), Aristotle argues that such entities must be defined by “addition”—snub, for example, cannot be understood without reference to noses—so that either they have no essence or definition or, again, they do so “in a different way”. The set of three puzzles that are our main concern follow at b28ff. (4.4 below). As before, a definition of snub requires reference to the appropriate class of subjects; on this assumption, each puzzle apparently leads to unacceptable consequences of one sort or another, most spectacularly, “babbling” or even babbling to infinity. Aristotle concludes again that it is “absurd” (b34) that snub and the like should have an essence or a definition. More mildly, such cases call for a weakening in the standard ways of having an essence or a definition. By a series of suppressed premisses, he goes on to suppose that similar results hold of every item in a non-substance category, and also for every compound of a non-substance item and a substance. Accordingly, “only substance” can have a definition in the full and proper sense (a1–2, 10–14). The trouble with this account is that two of the three puzzles that supposedly support these conclusions are lifted virtually straight out of the SE, which is Aristotle’s handbook on arguments that “appear to be refutations, but are fallacies instead” (1. 164a20–1); what Aristotle tells us in the SE suggests not only that the puzzles are invalid, but also why they fail.5 But in the Metaphysics he shows no recognition that the puzzles can be defeated, much less that he has the means for defeating them. Faced with this discrepancy, commentators have been hard pressed to find much virtue in the puzzles, much less the hoped-for connection with essence and definition. I hope to find a measure of both virtue and relevance in all three puzzles.

THE PUZZLES OF ESSENCE, AND AN APPARENT DISCREPANCY

1 The Three Puzzles in Zeta 5 As we have seen, Aristotle argues first in Zeta 4 for an exclusive view of essence and definition, so that these belong only to things that are suitably primary; but later in the chapter he finds reasons for a more inclusive view. The puzzles in Zeta 5 extend the argument in favour of these conclusions. The chapter opens with a single puzzle

4

A per se accident like snub is an accident because a given nose may or may not be snub; it is per se in the special sense that the definition of snub includes a selection-restriction to noses as suitable subjects; see Chapter 3, nn. 26 and 27. 5 Both SE 13 and 31 discuss how in general arguments that purport to produce babbling can fail; in both chapters, the second of the puzzles in Metaphysics Z5 (= puzzle [ii] in Section 1), and in 13 a close analogue of puzzle (iii), are apparently on Aristotle’s mind. I discuss Aristotle’s remarks about invalidity in SE 13 and 31 in Sections 7 and 8; the application in detail to the puzzles is given in Section 13.

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concerning per se accidents like the snub or snubness,6 which revives the issue of definition by addition (prosthesis), discussed inconclusively earlier in Zeta 4. Thus, the snub must be defined by “addition” (prosthesis)—by reference to the appropriate class of subjects:7 6 For Aristotle’s notion of per se accidents, see the references in this chapter, n. 4. As his explanation in terms of (what we would call) incompatibility ranges suggests, it is tempting to think that a term introduces a per se accident just in case it is governed by a selection-restriction to its suitable class of subjects. If so, then the class of per se accidents extends well beyond obvious examples like snub. For example, Aristotle discusses the different ways in which “sharp” divides its semantic field—that is, the different selection-restrictions to different classes of subject—in connection with comparability in Physics ˙4, 248b7–10, and in connection with clarity in definition (and avoidance of homonymy) at An. Po. B13, 97b32–9; see also Topics A15, 106a12ff. For the idea that, in the end, all accidents are per se accidents, see this chapter, n. 7 and Section 15. 7 How are we to understand the new class of per se accidents like the snub or snubness? At the beginning of Z5, Aristotle says that his arguments are directed at “things that are not simple but couples” (sundeduasmena, 1030b16, 1031a6). What he means by “couples” is obscure, as is his example, which he refers to variously as “the snub” (to simon, 1030b29, 30) and “snubness” (simote¯s, b17, 19). We are (he says) to distinguish three things: a nose, hollowness, and finally, snubness, which is “spoken of out of these two, a this-in-this” (simote¯s to ek ton ¯ duoin logomenon tode en to¯ide, 1030b17–18). But the property snubness is not obviously a compound of a nose together with hollowness. Again, if the entities Aristotle is concerned with are compounds, it is harder to see the force of the objection that their definition can be only by prosthesis: if what is being defined is already a compound, we cannot object that if the definiens refers to a compound of a subject and a property, the definition is on those grounds alone definition by prosthesis. (This is not to say, however, that the definition of a compound is never by prosthesis: see below.) In other places towards the beginning of Z5, Aristotle clearly has in mind not compounds, but accidents by themselves. The properties he is interested in, he says, are the accidents that are per se to their subject: for example, male, which is per se to animal, or equal, which is per se to quantity. And in the second half of the chapter, he gives the snub (to simon) as an example of a property “which cannot be spoken of without the thing of which it is the pathos per se” (1030b30–1). Towards the end of the chapter, finally, Aristotle seems to suggest that his conclusion that definition must be by prosthesis applies in the first instance to single members of non-substance categories, for example, odd. And if the result holds in these cases, then it holds too for “couples”, for example, odd number (oude, 1031a6). Possibly, then, rather than confusing the two kinds of entity, Aristotle has an argument for transferring his conclusions about the one to the other. If to define a per se accident by itself involves prosthesis, then arguably the definition of any compound involving that accident will also involve prosthesis. For example, let the definiens of “odd” be ‘number containing a middle’—that is, a definition by prosthesis. Then the definiens of “odd number” will be “number number containing a middle” (arithmos arithmos meson echon)—that is, again, a definition by prosthesis, given the additional occurrence of ‘number’ in the definiens. This example is from SE 13, 173b5–11. To move beyond these cases to reach his final conclusion, that only a substance has a definition or an essence in the primary sense, Aristotle apparently relies on the suppressed premiss that any item in a non-substance category has the same logical behaviour as does the per se accident odd or snub. That is, non-substances too must be defined by prosthesis. It is natural to assume that the “focal meaning” account of non-substances plays a crucial role in this part of his thinking. (Aristotle himself says that focal meaning involves prosthesis, if prostithentas kai aphairountas at 1030a33 describes focal meaning and not, as Owen holds, an alternative to it; Owen (1960) 1986, 166, n. 7.) Qualities, quantities, and the rest, are the qualities, quantities, and so forth, of a substance. So their definition too involves prosthesis. According to the argument given, ultimately, all accidents can be seen as per se accidents of substances. A final extension of this idea may threaten trouble. Aristotle insists that only forms can properly be defined, leaving out the matter. At the same time, an animal of a given kind cannot be defined without reference to its parts, that is, to an appropriate matter (Z11, 1036b22–32; see Chapter 7, n. 12). It seems, then, that form itself stands in a relation to its appropriate kind(s) of matter analogous to the relation between a per se accident and its appropriate subject. How, then, are we to include reference to the appropriate kind(s) of matter in the definition of a form? If we are forced to define form too by prosthesis, then we are left with nothing that is definable in the strict sense. This difficulty is discussed briefly in Section 15.

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4.3 There is a puzzle: if we say that an account by prosthesis (“addition”) is not a definition, of which of the things that are not simple but couples (sundeduasmena) can there be definition?; for they can only be explained as by prosthesis . . . so that of any of these things either there is no essence and definition, or, if there is, it is in a different way, just as we have said. (Zeta 5, 1030b14–16, 26–28, following Furth’s translation)

The puzzle hints at an inconsistent triad: if we say that (a) an account that proceeds by prosthesis is not a definition (as Aristotle did say in Zeta 4, 1029b29–1030a2, Chapter 3, Section 5), and given that (b) the account of per se accidents requires prosthesis, then (c) how can the account of a per se accident be a definition? Aristotle concludes by rejecting or qualifying any positive answer to (c): such entities either have no essence or definition or, as before, they do so “in a different way” (allo¯s, 1030b26–28).8 The three puzzles that are our main concern now follow. Between them, the puzzles try out all the options for a suitable definition of snub,9 so that taken together they form a single argument “by exhaustion” to show that snub cannot have an essence or a definition after all—or at least, not in the standard way.10 The three puzzles read as follows: 8 Presumably, then, he must also qualify (a): an account by prosthesis either is not a definition at all, or it is a definition of a different, non-standard kind. Or is prosthesis itself subject to revision?—see Sections 2, 6, and especially 13. The objection to definition by prosthesis is presumably that it violates the condition that in a definition, a definiendum and its definiens must “reveal the same” (Topics H2, 152b36–153a5, cf. A5, 102a7–17, Z4, 142a34–b6 (= 3.9 above), 9, 147b12–25, Metaphysics Z4, 1029b19–20 [legonti auto] from 3.8 above); see Section 11. For a survey of other views, see Bostock (1994), 96–7. 9 When Aristotle lays out the options supposedly available (see this chapter, n. 10), one assumption that constrains his selection is so deeply embedded in his thinking that it seems pointless to challenge it. This is the assumption that the selection-restrictions that govern the use of the term, “snub” (say), should be reflected in the lexicon, rather than in the construction. That is, Aristotle assumes that the selection-restrictions for “snub” will be reflected directly in the definiens supposedly intersubstitutable everywhere for “snub”, rather than their being confined to the rules for the use of the term. This assumption is honoured even in the definition of “snub” as “having the hollowness of a nose” that he ultimately finds acceptable; see Section 13. In the absence of the assumption, however, Aristotle’s puzzles pretty much lose their force. 10 If the argument is by exhaustion, it is worth spelling out the details. A central assumption of the passage is that snub is a per se accident, so that its definition must include a reference to its appropriate subject in the definiens (this chapter, nn. 6 and 9) and the term “snub” must be tied by definition to the larger context, “snub nose”. Argument (i) (see the main text immediately following) calls into question would-be definitions of snub where the definiendum contains the target term along with its larger context:

(ia) snub nose is the same as hollow nose. I assume that (ia) goes proxy for any attempt to define snub in combination with its proper subject. Puzzle (ii) takes up and rejects a proposal for handling snub without a reference to its subject in the definiendum; in this case, the reference to noses in the definiens makes this a case of definition by prosthesis: (iia) snub is the same as hollow nose. In puzzle (iii), Aristotle examines the idea that (iiia) snub is the same as snub nose. If this is meant seriously as an attempt at definition, then it belongs with (iia) as a renewed attempt at defining snub without mention of its subject in the definiendum, and by prothesis thanks to the required reference to noses in the definiens. (iiia) and its aftermath in (iiib) below might also be seen, however, as a response to the suggestion that, if “snub” cannot appear in the definiendum either with or without mention of its proper subject, as arguments (i) and (ii) appear to show, then we should think of “snub” as elliptical for “snub nose”.

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4.4 There is yet another puzzle about them. For (i) (a28) if snub nose and hollow nose are the same, the snub and the hollow will be the same; but if not (ei de me¯, b30), because it is impossible to speak of the snub without the thing of which it is the attribute per se (for the snub is hollowness in nose), (ii) (b32) either to speak of snub nose is not possible, or the same thing will have been said twice, hollow nose nose (for the snub nose will be hollow nose nose), for which reason it is absurd that essence should belong to such things; but (iii) if not (ei de me¯, b35), it will go to infinity: for in snub nose nose yet another will be present. It is clear, therefore, that definition is of substance alone. For if it is also of the other things predicated (kate¯gorio¯n, 1031a2), then it must be by addition (prosthesis) . . . That definition is the account of the essence, and that essence is either of substances alone, or above all and primarily and without qualification, is clear. (1030b28–1031a2, a11–14)

Aristotle argues first in puzzle (i) that (a) snub nose cannot be the same as (a) hollow nose: 4.5 (from 4.4 above) For (i) (a28) if snub nose and hollow nose are the same, the snub and the hollow will be the same; but if not (ei de me¯, b30 [sc. if these two are not the same]), because it is impossible to speak of the snub without the thing of which it is the attribute per se (for the snub is hollowness in nose), either to speak of snub nose is not possible, or . . . (1030b28–32)

Thus, if (ia)

snub nose is the same as hollow nose,

then (taking equals from equals)11 (ib)

snub is the same as hollow.

But (ic)

snub is not the same as hollow

(ei de me, “but if not”, b30). On pain of contradiction, then, (ia) cannot stand—and (since we have failed to identify an appropriate meaning for “snub nose”?) it may be that we cannot use the expression meaningfully at all (b32). Aristotle defends (ic) in the first puzzle on the grounds that snub is a per se accident (while presumably hollow is not)—its definition must include mention of its appropriate subject (b30–2), that is, it can be defined only by prosthesis. Given the failure to define snub in combination with its required subject in (ia), in argument (ii) Aristotle tacitly drops (ia) in favour of a sameness claim about snub by itself, so that we now find prosthesis in the definiens:

The final possibility, that snub is the same as hollow, with no mention of noses in the definiendum and no prosthesis, is set aside in the discussion of (ic) in puzzle (i). The point that the argument is apparently by exhaustion perhaps explains why in Z5, puzzle (i) is added to the two puzzles that are repeated from the SE; see Section 2. Finally, if the three puzzles together comprise an argument by exhaustion, the obvious response is to think that if each attempt at definition fails, then snub cannot be defined at all; for an argument that things are not that simple, see Section 7. 11

For the rule of subtraction, see 3.10 above and Section 10.

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(the) snub is the same as hollow nose.12

So, putting equals for equals on the strength of (iia), we find that (iib)

snub nose is the same as hollow nose nose.

I read Aristotle’s account of how to obtain (iib) in light of the unstated assumption that the discredited (ia) has now been dropped in favour of (iia): 4.6 (continuing 4.5, both from 4.4 above) . . . either to speak of snub nose is not possible, or [sc. if we adopt (iia) in place of (ia), and if in (iib) we reinstate talk of snub nose] the same thing will have been said twice, hollow nose nose (for the snub nose will be hollow nose nose), for which reason it is absurd that essence should belong to such things. (b32–5)

In this way, our tolerance for prosthesis in (iia) has as a consequence (sumbainei, a5) that we must “say the same thing twice”.13 “Saying the same thing twice”, in turn, supposedly undermines (iia), so that on this option too, it is absurd that snub should have an essence or definition in the first place (b34–5). We have seen that any definition of “snub” requires prosthesis, which in turn leads to saying the same thing twice. If we attempt to avoid this result by dropping (iia), Aristotle now argues,14 we must instead say the same thing infinitely many times (4.7 below). Once (iia) has been rejected, the only possibility that remains, apparently, is to suppose that the definiendum, “snub”, is elliptical for “snub nose”:15 thus, (iiia)

(the) snub is the same as snub nose.

It may seem that prosthesis is now no longer an issue: how, strictly, can we be adding “nose” in the definiens, if the definiendum itself already refers to a compound? According to argument (iii), however, given (iiia), we have a recipe for extending the definiendum indefinitely: 4.7 (continuing 4.6, and repeated from 4.4) . . . but (iii) if not (ei de me¯, b35 [sc. if such things after all do have an essence]), it will go to infinity: for in snub nose nose yet another will be present. (b35–1031a1)

Thus, from (iiia), putting equals for equals, we have See Ross (1924) II, 174. For the place of (iia) in the larger “argument by exhaustion”, see this chapter, n. 10. Saying the same thing twice is not equivalent to prosthesis, as commentators often suppose (see, for example, Hare (1979), 168), much less its definition (Frede-Patzig (1988) II, 85), but a special (reiterated) case of it. 14 ei de me¯, b35, “But if not”, “Otherwise”: that is, supposing that we set aside (iia). Aristotle’s account here is elliptical in the extreme: (iiia) in the main text below is supplied in order to produce the regress Aristotle predicts. My interpretation follows the alternative interpretation mentioned in Ross (1924) II, 174; Ross himself takes ei de me¯ to withdraw the suggestion that the relevant items have no essence or definition, and this alternative is incorporated without notice into Furth’s translation: “But if it does . . . ”; which leaves no trace of the negative in Aristotle’s text. For further discussion, with alternative ways of setting up Aristotle’s overall argument in the middle part of the chapter, see Burnyeat et al. (1979), Balme (1987), Frede-Patzig (1988) II, 82–4, Ferejohn (1994), 297–300, and Bostock (1994), 97–8. 15 “the only possibility that remains”: see this chapter, n. 10. 12 13

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snub nose is the same as snub nose nose,

and so on ad infinitum.16 These three puzzles together call into question the idea that there can ever be a definition in the proper sense of a per se accident. On this basis, Aristotle concludes finally that “only substance” can have a definition in the full and proper sense.

2 What Aristotle Knows About Snub in the SE There is a fundamental difficulty with the strategy of Zeta 5 as just described, for elsewhere Aristotle is not only familiar with arguments like those of Zeta 5, but also apparently knows how to defeat two, if not all three, of them,17 on grounds that at first sight have nothing to do with essence or definition. In the SE, Aristotle describes the technique applied in puzzles (ii) and (iii) as “reducing an opponent in the discussion to babbling—that is, to constrain him to repeat himself a number of times” (3. 165b15–17); the technique comes in fifth best, after refutation, exposing a fallacy, leading into paradox, and reducing to grammatical solecism. In SE 13 the technique is used to produce two puzzles, the second an approximation to the puzzle given as (ii) in Metaphysics Zeta 5: 4.8 Thus, e.g., odd is a number containing a middle: but there is an odd number: therefore there is a number-containing-a-middle number. Also, if the snub be a concavity of the nose, and there be a snub nose, there is therefore a concave-nose nose. (SE 13, 173b8–11)18

Earlier in the same chapter, the technique is used to produce a close parallel to (iii): 4.9 If it is all the same to state a term and to state its definition, the double and double of half are the same: if then double be the double of half, it will be the double of half of half. And again, if instead of “double” he were to posit “double of half ”, it will be said three times, double of half of half of half. (SE 13, 173a34–8)

But in the SE, Aristotle apparently knows how to counter the puzzles raised in SE 13. Partly, he is concerned with differences between the meaning of a word (if any) independently of certain special contexts, and its meaning within those contexts.19 Failure

16 Ferejohn (1994), 299–300, shows how to obtain the regress from (ia) and (iia), thus dispensing with the need for (iiia) as an independent assumption, cf. Bostock (1994), 98. But contrary to Ferejohn, I am sceptical that (ia) is still in force at the beginning of argument (iii). For “putting equals for equals”, and an application, see 4.9 below (= 4.12), cf. 4.19 (= 3.10 above). 17 Frede-Patzig, for example, find it astonishing (“erstaunlich”) that Aristotle should reiterate arguments that have been rebutted expressly and on obvious grounds in the SE, but they see no satisfactory solution to the difficulty: Frede-Patzig (1988) II, 85. 18 “an approximation”: in place of the problematic premiss, (the) snub is the same as hollow nose (= [iia] above), Aristotle gives its correction, (the) snub is the same as hollowness of the nose (173b10, cf. 31, 182a4). I take it that this is a slip on his part, contrary to Hare (1979), 173, who takes the argument at face value. 19 “the meaning of a word, if any”: for the sceptical note here, see the last paragraph of this chapter, n. 40.

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to attend to such shifts in meaning, Aristotle says, may cause us to seem to reduce an opponent to babbling, without actually doing so: 4.10 People sometimes appear to produce this result [= babbling], without really producing it, because they do not add the question whether the expression “double”, just by itself, has any meaning or no, and if so, whether it has the same meaning, or a different one; but they draw their conclusion straight away. Still there is the appearance, inasmuch as the word is the same, that it has the same meaning (se¯mainei) as well. (173b12–16, following Pickard-Cambridge)

That is to say, the meaning-shifts undermine the validity of the arguments concerned. Later, in the closing lines of SE 31, Aristotle has different thoughts about how the move to babbling can fail. Not every paraphrase for a term for a per se accident leads to babbling if it mentions the required subject. In particular, in place of premiss (iia), which takes “the snub” to mean “hollow nose” (where “nose” occurs kat’ euthu, “in the nominative case”, Bonitz Index, 296a2), we should prefer the paraphrase, ‘something (for example, an affection) of the nose [genitive case]’: 4.11 Moreover, the expression must not be granted in the nominative case: for it is a falsehood. For the snub is not concave nose but something (e.g. an affection) of a nose; hence, there is no absurdity in supposing that the snub nose is a nose possessing the concavity of a nose. (SE 31, 182a4–5, following Pickard-Cambridge)

This definition, which also appears parenthetically in Metaphysics Z5 at 1030b31–2, promises a way out of all three puzzles. If the way out of the puzzles is real—I will say more about the details later—then there are things Aristotle knows in the SE that he seems not to know in the Metaphysics. He appears to think that his remarks in SE 13 and 31 will disarm the two puzzles of SE 13; by extension, then, he should think that his remarks are effective also against two, if not all three, of the puzzles in Metaphysics Z5. But in the Metaphysics he is silent about the defects of the puzzles. Does he not know that the arguments are bad? And if he does know they are bad, what purpose could possibly be served by repeating them? It is hard to believe that he propounds virtually the same arguments in Zeta 5 with a totally straight face, either unaware of the defects apparently exposed in the parallel arguments in the SE,20 or aware of them but willing simply to brush them to one side.21 20 In fact, Z5 cheerfully recapitulates SE doctrine: with Metaphysics Z5, 1030b31–2, compare SE 31, 182a4. 21 It is especially hard to think that Aristotle would recite the puzzles in Z5 without thought for attempts at resolving them of the kind set out in the SE, given his methodological remarks about the utility of such puzzles in philosophy at Metaphysics B1, 995a24–b4. On the general topic of “dialectical puzzles” (his term), see Irwin (1988), chapter 2, sections 20ff. It is worth saying that our worries about the discrepancy are not allayed by the hypothesis that Aristotle’s discussion in the SE postdates that in Z5 (in the SE, Aristotle “came to see that this argument [= (ii)] is wrong”, Kirwan (1993), 186, my emphasis). The criticisms Aristotle sets out in the SE have the same conceptual or argumentative relevance to the puzzles in Z5, regardless of when either work was actually composed. It is also worth recalling Burnyeat’s warning (cited in Preface, n. 1) that since the works under study were unpublished

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If, as seems likely, the puzzles of Zeta 5 for Aristotle evoke the similar puzzles in the SE, the lack of “fit” between the two texts raise questions about the value in this case of the interaction with one of his own “other” selves. Aristotle is consistent in these chapters of Zeta in arguing for his exclusive and, concessively, inclusive views of essence. These conclusions are present not only in the first part of Zeta 4, which avowedly is conducted logiko¯s—in dialectical terms, perhaps, as Ross suggests22—but also in the last part of the chapter, arguably still inside the scope of the earlier dialectical discussion.23 The same inclusive view is taken for granted in Zeta 6. Aristotle is apparently in dialectical mode again with the puzzles of Zeta 5,24 where he proceeds to the same conclusions as in surrounding chapters. Can we be sure that the resort to the puzzles of Zeta 5 does not compromise his results? His discussion in the chapter is clouded by the fact that two of the puzzles appear on the list of fallacies in the SE, and stand condemned by his own words there. What possible contribution can he think is made by the puzzles of Zeta 5 to the serious business under way elsewhere in Zeta?

HOW TO MAKE ROOM FOR THE PUZZLES IN ZETA

5

If we are to resolve the apparent discrepancies between the Metaphysics and the SE, our best hope lies with the explanations Aristotle gives in the SE for why the puzzles fail. in Aristotle’s lifetime, the opportunity was always before him to bring earlier and later thoughts into line with one another. I also cannot accept the extreme suggestion in Ferejohn 1994 that the SE has nothing of interest to say to the puzzles of Z5. This view makes quick work of the idea of a discrepancy between the SE and Z5, but at the cost of ignoring most of the discussion in the SE (he refers parenthetically [n. 35] to 31, 181b35–182a7, but thinks that it contributes nothing to the solution of the puzzles in Z5). In Ferejohn’s view, the solution to the puzzles of Z5 is yet to come in Z10 and 11, where (after some preliminary discussion of how to mention matter by way of the “bronze”-“brazen” example in Z7) Aristotle “eventually uncovers” the possibility of an appropriate reformulation of the definition of snub by way of a “fused propositional phrase” that refers to the subject only “indirectly” (but if the phrase is fused, is there reference to noses at all?). But while the discussion of snub is undeniably relevant to questions later in Zeta about the role of matter in definition (see this chapter, n. 7 and Section 15), this connection hardly cancels out the importance of the passages in the SE. 22 logiko¯s, 1029b13. Ross 1924 II, 168, takes the (now) contrarian view, that the term logiko¯s “suggests plausibility rather than truth . . . Usually its sense is depreciatory”. Ross takes a dim view in general of Aristotle’s use of dialectic in the chapters on essence; his comment on Z6 is especially harsh: “The reasoning of the chapter is weak, and to an unusual degree verbal and dialectical”; Ross, I, xcix. “Logical” questions are one of three kinds of dialectical propositions and problems distinguished at Topics A14, 105b19 ff; the topic of “logical” argument is discussed in Irwin (1988), chapter 2, nn. 46, 48, 49, and chapter 7, n. 15; see also Chapter 1, nn. 34 and 36. The sense of “logical” in Z4 is a matter of controversy. Ferejohn (1994), for example, argues that that “logical” here is properly opposed to “physical”: thus, the materials for an answer to the puzzles is Z5 are given in the discussion of change in Z7–9, and the final answer, which combines the “logical” and “physical” perspectives, is assembled in Z10 and 11; see this chapter, n. 21. I argue below that Aristotle’s solution to the puzzles is already adequately given in the SE, which is not notably a source of “physical” views. 23 It is sometimes supposed (Ross (1924) II, 168) that the dialectical part of Z4 ends at 1030a27: we must also “say how things are, not just how they are said” (cf. b3–4, “it does not matter in which of the two ways people want to speak”); for a dissenting view, see Woods (1974/75) and Burnyeat (2001). 24 The use of puzzles is a standard part of dialectical procedure; again, see Irwin (1988), chapter 2, section 20ff.

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Understanding his explanations may suggest why the arguments, flawed as they are, may yet have a place in the discussion of essence in the Metaphysics. I begin in Sections 3–6 with some received opinions about his explanations and the sketch of a new suggestion; a closer look at the text of the SE follows in Sections 7–8.

3 The No-Solution Solution The most pessimistic of the reactions to Aristotle’s explanations is that he has no real answer to the puzzles: the switch the SE recommends from nominative to genitive, avoiding duplicate occurrences of the noun, “nose”, in the nominative (Section 2), is ad hoc and no more than verbal. This appears to explain away the seeming discrepancy between the SE and the Metaphysics: Aristotle can repeat the puzzles in Zeta 5, apparently taking them at face value, because the moves to counter them in the SE are bogus.25 A bonus is a clear connection between the puzzles and the wanted conclusions about essence. Aristotle’s overall argument, on this account, is a straightforward reductio: If the snub has an essence or a definition, then either the definiendum is “snub nose” (with wider context included), or it is “snub” by itself. If the definiendum is “snub nose”, the result is a contradiction. But if the definiendum is “snub” by itself, then the definition or essence must be by prosthesis,26 and the result is either babbling or babbling ad infinitum. Given that each of these consequences is unacceptable, it is impossible that the snub should have a definition or an essence at all.

Two things should give us pause, however. If Aristotle puts his faith in this strategy, he is at odds with the suggestion in the SE that two, if not all three, puzzles are invalid. Even if the countermeasures in the SE against the puzzles are bogus, it may still be right that the puzzles are invalid, as the SE suggests.27 Second, if he thinks in Zeta 5 that the puzzles are valid, contrary to the SE, he cannot comfortably hold in the same chapter that the difficulties they lead to there are insuperable.28 Were he to find the difficulties insuperable, he could not simply tolerate defining the snub by prosthesis, and

25 See Bostock (1994), 99. Ferejohn (1994), n. 35, takes a similarly dim view of the recommendations about reformulation in SE 31; but his scepticism is deeper-rooted, since he thinks that the discussion in the SE is essentially irrelevant to the puzzles in Z5; see this chapter, nn. 21 and 22. But for reasons for thinking the move more than simply verbal, see n. 42. 26 See this chapter, n. 10. As before, the possibility that the definiendum is “snub” by itself but the definition is not by prosthesis (“snub is the same as hollow”) is rejected outright when Aristotle sets out the premisses for argument (i). 27 See this chapter, n. 5. 28 So apparently Bostock (1994), 96. According to Bostock, arguments (ii) and (iii) are valid; Aristotle is wrong, however, that the conclusion in each case is unacceptable (Bostock does not explain how this view jibes with Aristotle’s own discussion of acceptable and unacceptable babbling in Topics Z3; see this chapter, n. 42). The problem with argument (i), meanwhile, he thinks is the reverse: the move from (ia) to (ib) is a logical mistake; but Aristotle infers that we should reject the premiss, (ia). See Bostock, 97–9. My own view will be that all three arguments are invalid, and that Aristotle knows it in each case, see Section 7.

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conclude as he wishes to that the definition is non-standard; he must think, not that the definition is non-standard, but that it is flat-out impossible.

4 Accidents and Compounds On a less pessimistic reading, behind the verbal moves in the SE there lies a substantive metaphysical point. It is sometimes suggested that puzzles (ii) and (iii) in the Metaphysics trade on a confusion between a compound and the accident that is just one of its ingredients. The expression, “(the) snub”, can refer either to a compound of a substance with a per se accident, hollow (or snub) nose—that is, a sunduazomenon (1030b16), a “this-in-this”—or to the quality, snubness, by itself.29 We may disambiguate by adding subscripts: “snubc” will designate the compound, while “snubq” will designate the quality, snubness, and can also do duty as an adjective as needed (compare the way that Aristotle’s example “white” in the Categories can function both as a name of the quality, and as an adjective when paronymy fails in the surface-grammar of the language). Once subscripts are suitably distributed, puzzles (ii) and (iii) collapse: (iia*) snubc is the same as hollow nose (iib*) snubq nose is the same as hollow nose nose. (iiia*) snubc is the same as snubq nose. (iiib*) snubq nose is the same as snubq nose nose (and so on ad infinitum). The difference between “snubc” in the premiss of each argument and “snubq” on the left-hand side in each conclusion, invalidates the attempt to put equals for equals in the two conclusions. But the ambiguity between terms for accidents and terms for the corresponding compounds has no role in disarming puzzle (i). Whatever the relevance of this ambiguity to the other puzzles, it cannot tell the whole story about all three puzzles. Worse, nothing has been said about Aristotle’s motivation for introducing this ambiguity into a discussion of the essence and definition of the snub. The puzzles in Zeta 5 are intended to draw attention to features peculiar to terms like “snub”, and to the selection-restrictions that accompany them, that allegedly make the notions of essence and definition non-standard in such cases. But the difficulty, if there is one, of separating terms for accidents and for the corresponding compounds, is not local to

29

See, for example, Ross (1924) II, 174; Ross thinks this is the significance of the switch from nominative to genitive at SE 31, 182a4, cf. perhaps Hare (1979), 173. For the record, on the interpretation I offer below, as on that of Ross, the puzzles depend in part on the potential for ambiguity in connection with the use of terms for per se accidents (and the corresponding potential for failure of the constancy assumption, see Section 7). But the possible ambiguity has more to do with the logic of these terms, in particular, their use in and out of certain special contexts, and the ontology of accidents and compounds is incidental, if it is relevant at all.

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terms for per se accidents. So Aristotle’s argument hits too wide a target, and does not support the special treatment for per se accidents for which he is arguing.30 On the view under discussion, finally, in Zeta 5 Aristotle means to offer the same reductio noted above (Section 3); but the puzzles that are meant to lead to babbling or worse are spoiled by the confusion between compounds and accidents supposedly criticized in the SE. Again, then, Aristotle can think that the puzzles support his conclusions about essence, only if he is willing to turn a blind eye to the criticisms of the puzzles he himself expresses elsewhere.31

5 Contextual Definition Yet a third view of the puzzles takes up a different hint in the SE. In separate chapters of the SE, Aristotle suggests that “snub” has no significance by itself (4.10 above (= 4.13 below); 4.14, 4.15 below). This may explain why in puzzle (i) in Zeta 5 the definiendum in premiss (ia) is not “snub” by itself, but “snub nose”, with larger context attached. Perhaps Aristotle experiments here with the idea of something like contextual definition.32 He may think that snub and the like can be defined—not in the standard way, however, but only contextually. If this is his view, he must also think that the definition in (ia), which arguably provides a contextual definition, survives the difficulties of puzzle (i). Meanwhile, we are to read the remaining two puzzles as successful attacks on what happens if we revert to the standard notion of definition, which takes just “snub” as our definiendum, without any reference to noses. If all three puzzles were to succeed, Aristotle would have to conclude that the snub has no essence or definition. In fact, however, if he is pressing the option of contextual definition, he must think he has reason to doubt puzzle (i). This is the only puzzle that is not in common with the SE but, arguably, it shares a significant innovation with that text. In (i) we suppose that the proper definiendum is “snub nose”, on the grounds, perhaps, set out in the SE that “snub” by itself is not separately significant. On this assumption, arguably, “snub” has only an “accidental” occurrence in the context, “snub nose”,33 and we cannot apply the rule of taking equals from equals within that context in the way that puzzle (i) requires. So the puzzle fails, and Aristotle is free after all to settle for non-standard notions of definition and essence in the case of snub and the rest, rather than no definition or essence at all. But the definition is non-standard, 30

The difficulty that Aristotle’s arguments may indeed hit too wide a target is discussed in Section 15 of the Afterword below. 31 See this chapter, n. 5. 32 The possibility of contextual definition is also raised and dismissed in Ferejohn (1994), 296–7. For the record, the appeal to contextual definition is loose at best: the idea that a purported definiendum is not separately significant is only part of what is meant in the classic contemporary use of the notion in Russell; the syntactic transformations, much less the ideas about logical form, that are central in Russell are not relevant to Aristotle’s discussion. There is a helpful discussion of Russell’s use of contextual definition in Kaplan (1972), 233–4. 33 For “accidental occurrence”, see for example Kaplan (1969) 1971.

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not because it must commit the formal flaw of prosthesis, but because definition here is contextual definition. Aristotle can drop the idea that “snub” must be defined by prosthesis, for he has dropped the idea that it is separately definable in the first place. In fact, however, contextual definition does not suit Aristotle’s project either in Zeta 5 or in the SE. His idea in the SE that terms like “snub” that are tied to a special context have no meaning outside that context,34 seems quite close to the idea of contextual definition; but his more relaxed view that “snub” has one meaning in the relevant context and another out of it fits less well. And in Zeta 5, on the strategy described, we avoid babbling by rejecting prosthesis and, ultimately, the non-contextual view of definition on which prosthesis rests. But far from rejecting definition by prosthesis for snub and the rest, Aristotle says repeatedly that prosthesis is inevitable in their case.35 At the same time, even if he believed that some alternative to definition by prosthesis exists, his argument could use the absurdity of babbling to overturn prosthesis, only if the argument from prosthesis to babbling or worse in puzzles (ii) and (iii) is valid. In the SE, however, as we have seen, he has reason to think that the two puzzles are invalid.

6 Making Room for the Puzzles in Zeta 5: the Issue of Validity Given the verdict suggested by the SE that the puzzles of Zeta 5 are invalid, it is hard to see that any conclusion about essences properly follows. We can find a way to the wanted conclusion about essence, however, if instead of pretending to assume validity (contrary to Aristotle’s own assessment) and inferring the falsity of a premiss, we make validity itself the initial target of the reductio. On the view I will defend, the arguments are not valid as they stand, in line with Aristotle’s own verdict in the SE. More than this, for Aristotle’s purposes in Zeta 5, the interest and the chief virtue of the arguments is precisely that they are invalid. The arguments are invalid—but they should not be, if assumptions that standardly hold about essence and definition also hold in the case of snub and the like. To review: the puzzles in Zeta 5 together apparently form an argument by exhaustion (this chapter, n. 10). If each of the attempts at definition leads to trouble, it is natural to conclude that snub cannot be defined at all. As before, this response to the puzzles is undermined by the invalidity objection: in the SE Aristotle has reason for doubting the validity of two if not all three puzzles. I conclude that ultimately a second-order response is the correct one: Aristotle holds that the first-order argument against definability fails, but for reasons that (again) call into question whether a genuine definition of snub exists. Aristotle’s argument, then, contains two steps of reductio rather than just one:

34 35

See the final paragraph of n. 40, this chapter. Z5, 1030b16, cf. 23–6, 1031a2–5.

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If a thing has a definition or an essence in the standard way, then the relevant statements of definition or essence support application of a certain familiar rule of inference. [For a statement of the rule in question, and an application, see 4.9 above (= 4.12 below), cf. 4.19 below (= 3.10 above).] At the same time, as before, if the snub has an essence or a definition in the standard way, then either the definiendum is “snub nose”, or it is “snub” by itself and the definition is by prosthesis. Of the three possible formulations of the definition that result, one leads to contradiction, the next to babbling, and the last to babbling ad infinitum, by the familiar rule of inference just noted. Given that these results are unacceptable, we conclude, (1), that statements of definition or essence involving “snub” and other terms for per se accidents are not open to applications of the familiar rule of inference, and the inference to babbling and the like is not valid. At the same time, (2), precisely because the familiar rule of inference does not apply in the case of the snub and the rest, these cannot have a definition or an essence in the standard way.

On this account, the move to babbling is countered by questioning whether in the puzzles application of the familiar rule results in a valid argument. In line with the SE, then, Aristotle is not committed to the validity of the puzzles in Zeta 5. But the failure of the puzzles serves his wider destructive purposes in the chapter. The fact that the puzzles are not valid shows that certain conditions that hold in the case of items having an essence or a definition in the standard way, do not apply in the case of the snub. His conclusion is that the snub has a definition or an essence in some non-standard way. But the definition is non-standard, not because it leads to babbling and the rest, but because by ordinary standards it should have these consequences, but in fact does not. At the same time, Aristotle is perfectly serious that snub and the rest must be defined by prosthesis.36 But there is room for adjustment in how exactly reference to the appropriate class of subjects is to be accomplished (see Sections 2 and 13). So there will be some adjustment in how the term, “nose”, should appear in the definiens in the definition of snub. But Aristotle does not find every form of prosthesis unacceptable. In particular, we will be able to reformulate the definition of snub to include a reference to noses in the definiens in such a way that the familiar rule of inference can be applied after all, but without any threat of babbling. The adjustments just noted hold special significance. According to the argument I will attribute to Aristotle (Sections 10 and 11) our normal expectation is that definition will support application of a “familiar rule of inference”, namely a Principle of Substitution. In the case of per se accidents, however, this expectation can fail, and we must check first to see whether reformulation is needed if the definition is to support substitution without babbling or other anomaly in the result. These complications are our signal that the notion of definition in such cases is itself a qualified one. These doubts over the application of a Principle of Substitution invite us to think that the puzzles in the centre of Zeta 5 are invalid, but that Aristotle has strategic reasons

36 See the references in this chapter, n. 35. As already suggested, then, he cannot be committed to an outright ban on definition by prosthesis: the phrasing at 1030b14–15 from 4.3 above—“if we say that an account by prosthesis is not a definition” (my emphasis)—gives him the wiggle room he needs.

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for parading the puzzles there, invalid as they are. To support this interpretation I turn again to the account suggested by the SE of why the puzzles that threaten babbling fail, and to his comments there about what it would take for them to succeed.

BACK TO THE SE

7 Double Trouble Aristotle’s first extended discussion of babbling in the SE gets under way in chapter 13. The following is typical of the arguments he has in mind: 4.12 (= 4.9 above) If it is all the same to state a term and to state its definition, the double and double of half are the same: if then double be the double of half, it will be the double of half of half. And again, if instead of “double”, he were to posit “double of half ”, it will be said three times, double of half of half of half. (SE 13, 173a34–8)

We are to pretend for a moment that “double” is defined as “double of half ”,37 and that the two expressions are everywhere intersubstitutable (“it is all the same to state a term and to state its definition”, a34–5). Then we have this argument: (1) Double is the same as double of half. (2) Double is double of half, only if double is double of half of half [substituting at the place indicated]. As Aristotle notes, the argument can be extended, presumably without limit, but I forego these further developments. Each step in the argument involves a licensing principle based on sameness, which Aristotle formulates, “it is all the same to state a term and to state its definition (logos)”, a34–5. So the principle he has in mind is genuinely a Principle of Substitution, intersubstituting expressions for the same thing, and not a Principle of Identity.38 The use of substitution is subject to an important qualification in the final paragraph of SE 13. Aristotle is commenting on what separates cases where arguments to force babbling work and where they do not: 4.13 (= 4.10 above) People sometimes appear to produce this result [= babbling], without really producing it, because they do not add the question whether the expression “double”, just by itself, has any meaning (se¯mainei ti) or no, and if so, whether it has the same meaning (se¯mainei), or a different one; but they draw their conclusion right away. Still there is the appearance, inasmuch

37 As Dorion (1995), 310, n. 216, points out, this is not a proper definition, since the would-be definiens contains the defiendum; strictly, we have only “une espe`ce de paraphrase et d’e´clarcissement.” 38 For this distinction, see Cartwright (1971). Dorion (1995), 310, n. 216, cites a Principle of Substitution from Plato Laws X, 895e: we “address the same thing” (tauton . . . prosagoreuomen) whether we use a name or the corresponding definition (compare Aristotle’s similarly vague me¯den diapherei, “it is all the same”). At Rhetoric, ˆ6, 1407b25–8, also cited by Dorion, Aristotle says only that a name and a description for the same thing may be exchanged for literary effect. None of these passages is explicit in the way we might like about the crucial point that such substitutions are supposedly truth-preserving.

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as the word is the same, that it has the same meaning (se¯mainei) as well. (173b12–16, following Pickard-Cambridge)

Aristotle does not hold that reduction to babbling is invariably fallacious. But it will be—we will only appear to produce babbling—if a key assumption fails to hold. This is that the relevant term has the same meaning both by itself and in certain special contexts: for example, that “double” by itself has the same meaning as its occurrence in the context, “double of half ”.39 For the inference to babbling in (2) above to go through, we must assume that what (1) tells us about the meaning of “double” “by itself ” applies also to the occurrence of “double” in “double of half ” in the antecedent of (2). Aristotle argues explicitly that this constancy assumption must govern the use of the term “double”, if the sameness statement in (1) is to support substitution for the occurrence of “double” in the antecedent of (2). If, on the contrary, the term functions differently in the two places, then substitution fails and the argument is invalid.40 39 Aristotle notes, however, that in the absence of the explicit assumption, the broad assumption, “same word, same meaning”, in practice can often get us by (the assumption is notorious from Plato Republic IV, 435a5–8). (Aristotle himself has evident reservations about the broad assumption, see for example, SE 1, 165a3–19.) For the reference to meaning here, see this chapter, n. 40. To assume that “double” does, or does not, have the same meaning by itself and in the context, “double of half ”, does not by itself say that “double” (by itself) means, or does not mean, the same as “double of half ”. So constancy or its absence by themselves do not settle the truth or otherwise of the definition in premiss (1) two paragraphs back in the main text. 40 The issue of constancy (on which Dorion (1995), 312, n. 222, also comments) is a primary reason for reservations over a Principle of Substitution in contrast to a Principle of Identity (this chapter, n. 38). To borrow an example from Kaplan (1969) 1971: suppose that

(a)

F. D. R. is the same as President Roosevelt,

so that (b) F. D. R. ran only once, only if President Roosevelt ran only once. The result in the consequent of (b) is not babbling, but historical inaccuracy; and the result is blocked, by noting that “F. D. R.” in (a) names the man (if [a] is true), while it names the television programme in the antecedent of (b) (assuming that it too is true). Alternatively, “F. D. R.” names the programme both times, but (a) is false. In other, more interesting cases, the denotation-shift is systematic. For Frege, famously, it is produced with the move from regular to oblique contexts; since the shift is caused by the change in context and not by any intrinsic feature of the term itself, any denoting term whatever is liable to such shifts. In the cases Aristotle has in mind, by contrast, the shift is rooted in the logic of the term itself and is not (or not solely) a product of certain of the contexts it occupies: according to Aristotle, it is a peculiarity of terms for per se accidents (and also relative terms, this chapter, n. 57) that they are associated by definition with a larger containing expression (“snub nose”, “double of half ”), and their signification shifts with the move into and out of that larger expression. The shifts Frege has in mind are shifts in denotation (his Bedeutung). I use the term “meaning-shift” for Aristotle’s views as a term of convenience, but I shall not try to analyse the various changes in semantic and even syntactic role that occur, or that Aristotle thinks occur, as “snub”, “double”, and the rest move in and out of their associated context. Finally, I am unable to explain Aristotle’s claim, defended in SE 31, that a relative term or a term for a per se accident may have no meaning, shorn of the context that is definitionally associated with it. He attempts to support his point by the use of “ten” by itself and its occurrence in “ten minus one”, or the difference in saying of someone that he is not pale, and that he is pale; he also cites the different occurrences of the relative term, “knowledge”, by itself and in the context, “medical knowledge” (unlike the latter, the former is simply of what is knowable). But I am doubtful that these cases support the weaker point, that a meaning-shift is involved, let alone the stronger claim that the target terms have no meaning outside the wider context.

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8 Saying the Same Thing Again Again 4.14 With regard to those who draw one into repeating the same thing a number of times, it is clear that one must not grant (ou doteon) that predications of relative terms have any meaning in abstraction by themselves, e.g., that “double” is a significant term apart from the whole phrase “double of half ” (ou doteon . . . se¯mainein ti chorizomenas kath’ hautas tas kate¯gorias) merely on the grounds that it figures in it. (31, 181b25–28) 4.15 (some lines after 4.14) The word “double”, one might perhaps say, has not even any meaning at all, any more than has “the” in “the half ”: and even if it has a meaning, yet it has not the same meaning as in the combination. (b32–34) 4.16 (two lines after 4.15) In the case of terms that are predicated of the terms through which they are defined, you should say the same thing, that the term defined is not the same separately (cho¯ris) as it is in the whole phrase. For “concave” has a general meaning (koine¯i men, 181b38, cf. to koinon, b35) which is the same in the case of a snub nose, and of a bandy leg, but when added to either substantive nothing prevents it from differentiating its meaning; in fact, it bears one sense as applied to the nose and another as applied to the leg: for in the former connection it means “snub” and in the latter “bandy-shaped”; i.e., it makes no difference whether you say “a snub nose” or “a concave nose”. (b35–182a3) 4.17 (continuing 4.16, and repeating 4.11 above) Moreover, the expression must not be granted (ou doteon) in the nominative case (kat’ euthu, a3); for it is a falsehood. For the snub is not concave nose but something (e.g., an affection) of a nose: hence, there is no absurdity in supposing that the snub nose is a nose possessing the concavity of a nose. (182a3–5, all four translations following Pickard-Cambridge)

In SE 31, Aristotle visits arguments that induce babbling for a second time. The chapter is structured around two things “we must not grant” (ou doteon, 4.14, 4.17 above). First, we must not suppose, just because the term “double” is part of the significant expression, “double of half ”, that it is therefore separately significant outside that context (ou doteon . . . se¯mainein ti chorizomenas kath’ hautas tas kate¯gorias, 4.14 above). Less radically, we must be willing to consider that it may have a different meaning elsewhere (4.15 above, cf. 4.13 [= 4.10]). Both suggestions are in line with the remarks about constancy in the final paragraph of chapter 13. If we turn, next, to terms for per se accidents, “snub”, for example, again what is revealed is not the same in context and when the term occurs separately. Or, to take a different example, we can give “hollow” a “general” meaning, which it bears independently of context (koine¯i men, 4.16 above, cf. to koinon, b35). But equally, we can give different terms, with different meanings, as the meaning of “hollow”, if we choose occurrences of “hollow” in appropriately different contexts, for example, “hollow [= snub] nose”, “hollow [= bandy] leg” (4.16 above).41 41

I am inclined to think that Aristotle’s discussion has here veered off course, to illustrate the vicissitudes not, as needed, of “snub” (say) in different occurrences, but of “hollow”, where the example is relevant only indirectly to the discussion of per se (so also Dorion (1995), 398, n. 430). The relevance, I take it, is this. Say that “hollow” partially divides its field into “snub” and “bandy”. Then the terms “hollow” divides into are governed by the appropriate selection-restrictions: “snub” has a selection-restriction to noses (a sub-class of the

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But there is a second thing “we must not grant” (ou doteon, 4.17 above). It is false to say that the snub is hollow nose; we must drop the use of the nominative case and move instead to the genitive: snub is this, for example, an affection, of a nose. There is no absurdity in the result, that the snub nose is nose having the hollowness of a nose.42 Quite how this second piece of advice fits with the first is something we shall return to in Sections 11 and 13.

SAMENESS AND SUBSTITUTION

9 The Puzzles, Sameness, and Definition Our rereading of the SE points to a feature of the puzzles that connects them directly with Aristotle’s agenda in Metaphysics Zeta 5. Aristotle means to promote a level of scepticism about definition and essence in the case of per se accidents like snub: either such things have no definition or essence, or at best, non-standard varieties of essence and definition apply to them. What is it about the puzzles that is challenging to his standard notions of essence and definition? The connection has to do with sameness. The connection between the puzzles and sameness is left completely unadvertized in Zeta 5; in SE 13, however, as we have seen (Section 7), Aristotle is clear that a Principle of Substitution, based on sameness, is the key licensing principle in the puzzles considered there. Meanwhile, the relevance of sameness to definition is confirmed

class of things that may be hollow), and “bandy” a selection-restriction to legs. For the point about “hollow”, see Topics A15, 107a36–b5; and for worries about putting facts about the restrictions governing the use of a term in a given context into the lexicon—that is, seeing different meanings for the term in these different contexts—see this chapter, n. 9. For a different view, see Bostock (1994), 99–100, who argues that like “snub”, “concave” (or “hollow”) too is “trapped” in a special application to noses, which does not transfer to its application to other subjects. 42

Our best clue as to why this result is not absurd is discussed in Topics Z3 (the remarks at E2, 130a29ff, cited by Hare (1979), are less helpful). Mere repetition of words by itself need not be absurd (so it cannot be right that the difficulty Aristotle sees is limited to “re´pe´ter me´caniquement les meˆmes mots,” as Dorion (1995), 216, n. 25, cf. 310, n. 215, supposes): the absurdity is rather to predicate the same thing many times of something (Z3, 141a4–6). For example, we know that (a) man is a biped, so that (b) what is the same as man is a biped. But (c) walking biped animal is the same as man, so that (d) walking biped animal is a biped. But nothing absurd follows, since in (d) biped is predicated just once, of walking biped animal; it is not also predicated of walking animal. The ban against reiterated predications also comes up at de Int. 11, 20b31ff. Aristotle is considering the alleged rule that, if each of two things holds of a subject, then both hold of it jointly. The rule breaks down in familar cases: a man may be good, and a cobbler, but it does not follow that he is a good cobbler. A different example involves repetition and, hence, presumably “babbling” in the sense of the SE. If man holds of a subject, and pale holds of him, then pale man holds of him too. It does not follow, however, that since pale holds of him, and pale man holds of him, that pale pale man holds of him as well. These and any subsequent repetitions are blocked, because the one predicable, pale, is contained in the other, pale man, so that they cannot together form a unity. Hence, they cannot be predicated in combination. As a limiting case of containment, presumably, a predicable cannot be combined with itself to form a unity. So Aristotle can object in the SE or in Metaphysics Z5 to saying of something that it is a nose nose, or a hollow nose nose; but not that it is a nose having the hollowness of a nose.

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close by, in the main body of the Topics; once we arrive at definition, the move to essence in the Metaphysics is immediate.43 I take up these two points in the two sections that follow.

10 The Puzzles and Some Principles of Sameness I begin with the licensing principles at work in the puzzles of Zeta 5. In Topics H1, Aristotle sets out a fundamental principle of sameness. Suppose that two things are numerically the same. Then in general, Aristotle says: 4.18 One ought to consider if there is any discrepancy among what is predicated of each in any way whatsoever, and among what these are predicated of. For everything that is predicated of the one must be predicated of the other, and everything the one is predicated of, the other must be predicated of too. (Topics H1, 152b25–29, my emphasis)44

In ordinary contexts we might expect that this principle of sameness goes along with a Principle of Substitution (“putting equals for equals”): two terms for the same thing should be freely intersubstitutable without change of truth-value or other penalty.45 Although Aristotle does not say so in Metaphysics Zeta 5, as noted in Section 1 a Principle of Substitution is at work in puzzles (ii) and (iii) in that chapter.46 Aristotle puts forward a variety of other licensing principles that depend on the general sameness principle already given. In particular, if you take equals from equals, then equals should remain (a parallel rule governs adding equals to equals): 4.19 (= 3.10 above) Furthermore, you must note the result of an addition and see whether each added to the same thing fails to produce the same whole; or whether the subtraction of the same thing from each leaves the remainder different. Suppose, for example, someone has stated that a double of a half and a multiple of a half are the same, then, if of a half has been subtracted from each, the remainders ought to signify the same thing: but they do not . . . (Topics H1, 152b10–15)

43 For Aristotle, the relation, “x is definition of y”, is defined in terms of the relation, “x is the essence of y”, this chapter, nn. 34 and 44. 44 Aristotle also gives a version of the principle with a restriction to accidents, H1, 152a33–37. A variety of related sameness principles are discussed in Lewis (1991), 116–21. 45 Of course, we today have learned that a Principle of Substitution falters in a way that a Principle of Identity in the strict sense does not (see this chapter, n. 38); even so, prima facie the two kinds of principles should be equivalent, and if they are not in certain kinds of case, is there some principled reason why not? A terminological note: I use “Principle of Substitution” (with capital letters) in the strict sense, for a principle governing the intersubstitution of terms for the same thing; but I use “principle of sameness” (without capitals) generically for either a Principle of Substitution or for the different Principles of Sameness (with capitals), regarding the indiscernibility in various respects of things that are the same in one or another of Aristotle’s senses of “same”. One of these latter Principles of Sameness may correspond, with some reservations, to what we count as a Principle of Identity in the strict sense: Chapter 5, n. 2, and Chapter 6, n. 1. 46 For Aristotle’s commitment to a Principle of Substitution, see 4.9 (= 4.12) and the discussion in Section 7; see perhaps 4.19 (= 3.10 above) and this chapter, n. 47. As noted in Section 7, the commitment is clearly signalled in SE 13.

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The rules of addition and subtraction in 4.19 can be derived from the sameness rule in 4.18.47 Suppose that x is the same as y. Then given the general principle of sameness, x minus (plus) z is the same as y minus (plus) z, as required. Although again he does not say so, Aristotle’s puzzle (i) in Metaphysics Zeta 5 utilizes the rule of subtraction; the same rule is applied (but once more not cited) earlier in Zeta 4, and multiple times in Zeta 6.48 On this showing, the entire discussion of essence in Zeta 4–6 fairly bristles with applications (or misapplications) of principles of sameness from the Topics.

11 Sameness and Definition: Substitution and the Extended Sameness Test I have described the connection between the puzzles and sameness; now for the connection between sameness and definition. A prime test of definition for Aristotle, according to the Topics, is whether the appropriate sameness relations hold: 4.20 For in fact, the most energy in connection with definitions is exercised on the question whether the same or different . . . for if we are able to argue that the same, or that different, we shall be well supplied to attack the definitions, by the same line of argument: for if we show that they are not the same, we shall have overturned the definition. (Topics A5, 102a7–14)

This sameness test sets a necessary—but, notice, not a sufficient—condition for definition; any would-be definition in which definiens and definiendum do not name the same thing is immediately disqualified.49 The test can also be extended in a natural way. If the appropriate sameness relations hold, then the obvious principles of sameness should apply. In particular—in the absence of some special reason to the contrary50—sameness should support the application of a Principle of Substitution, as explicitly in 4.9 (= 4.12) above, in line with the fundamental sameness principle set out in 4.18.51 A successful definition, then, requires not only sameness, but also success in the relevant substitutions. If a given sameness statement does not support substitution 47 For purposes of the derivation, I pretend that the rules of addition and subtraction are principles of sameness and involve metaphysical rather than linguistic operations of adding and subtracting; for a metaphysical interpretation of the principles, see Chapter 4, Section 3. But the translation making them out to be overtly linguistic principles, as in the Oxford Translation, so that it is expressions that are being added or subtracted, has an equal chance of being correct (see Lewis (1991), 119); the linguistic formulation is reached from the metaphysical one by the same shift that leads to a Principle of Substitution from a Principle of Identity. 48 Z4, 1029b21–2, Z6, 1031a19–28 (see 5.2 below), cf. 1032a6–10. 49 The condition is necessary but not sufficient, see Topics A5, 102a15–16, cf. H2, 152b36–153a5. Other conditions, beyond sheer sameness, include the requirements in Metaphysics Z4 that a definition be of what is primary, and is a unity of the right kind; and with 4.20, compare the references for “revealing the same,” this chapter, n. 8. I am about to suggest that the argument in Z5 points to the existence of yet another necessary condition in the case of snub and other per se accidents: see two paragraphs below in the main text. 50 See this chapter, n. 45. 51 “in line with the fundamental sameness principle”: as before (this chapter, n. 47), I slur over the distinction between a Principle of Sameness and a Principle of Substitution (see this chapter, n. 38 and the terminological note in n. 45).

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into a given context, however, or if substitution produces anomalous results, then arguably, Aristotle will conclude that the sameness is not standard and that the sameness statement cannot count as a definition in the standard sense.52 This, then, is the relevance of the puzzles in Zeta 5 to the topics of essence and definition. In the Zeta 5 puzzles, the assumption that certain purportedly definitional sameness statements involving snub or snub nose support substitution in the expected way, leads to paradox. So the sameness claims fail the sameness test for definition, or rather, they fail an extended version of the test, which asks whether they support substitution in the standard way. Because they fail the extended sameness test, they cannot provide a definition—at least, not a definition in the standard sense. On this account, Aristotle supposes that anomaly-after-substitution of the kind exemplified, spectacularly, by babbling is a sign of a special kind of defect in the original sameness statement. The end of SE 31 (4.11 [= 4.17] above) suggests a more precise statement of the defect. Even where a sameness statement involving snub is true, it cannot also be definitional, unless it is itself in the appropriate form to support substitution into the problem contexts. This is the place for the notorious shift from nominative, “snub nose”, to genitive, “snubness of a nose”. In the puzzles in Zeta 5, the relevant sameness statements support substitution without anomaly, only after they have been suitably reformulated in the way indicated. Special conditions are required governing any purportedly definitional sameness statement involving snub, both to trigger reformulation of the statement as needed and, when reformulation is required, to specify the form the rewriting must take if the statement is to support substitution without difficulty. Every purportedly definitional sameness statement for snub and items like it is subject to conditions of this kind.53 It does not follow that every definition of snub, however formulated, must fail the extended sameness test. Given the connection 52 It is a nice question (pressed in correspondence by Michael Wedin) how widely Aristotle thinks the extended sameness test applies. I argue in this chapter that he applies it to contexts containing an occurrence of a term for a per se accident (see [iib], [iiib], and [i*] in Section 13), and that he infers from failures of substitution into these contexts that the relevant sameness statement is less-than-standardly definitional. But can we plausibly ascribe to him the contrapositive of this, that where a sameness statement is definitional in the standard sense, it will support substitution into every context whatever? The difficulty is discussed in Section 15. There is evidence that (contrary to modern sensibilities) Aristotle may incline towards an affirmative answer. At SE 24, 179a37–9 (cf. Physics ˆ3, 202b14–16), Aristotle endorses a Principle of Sameness featuring numerical sameness in being in place of (mere) accidental sameness. The implication is that the inference from “I know that Coriscus is Coriscus” to “I know that the masked man is Coriscus” (the Masker Paradox) fails because Coriscus is only accidentally the same as the masked man; had they been the same in being, the inference would have succeeded. A comparable strengthening, but in the antecedent of a Principle of Substitution, is Carnap’s L-equivalence and “intensional isomorphism”. For discussion, see Lewis (1991), chapter 4. 53 For conditions on substitution, which may be syntactic or even semantic in character, see Fine (1989) and Section 17. Notice, however, that the conditions Fine envisions involve the character of the context into which substitution is made, or of the subject-expression of the sentences that precede and result from substitution; his discussion would not be sympathetic to the suggestion that what is at issue is rather the sameness statement on the basis of which substitution is made, or that where reformulation is appropriate, the sameness statement is where it is best carried out.

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between sameness and definition (and between definition and essence), the mere fact that substitution might fail given one formulation of the definition, but not fail given another, suggests that the notions of definition and essence for snub and the rest must be non-standard.54 Vulnerability to the extended sameness test, however, supposedly is not evident in the definition of other kinds of entities.55 So, apparently, there is special reason, local to snub and other per se accidents,56 for thinking that definition and essence for these must be non-standard.

THE ZETA

5

PUZZLES REVISITED, AND A DEFENCE

OF BABBLING

12 The Remaining Strategy The puzzles exploit two kinds of problem context, substitution into which leads to unacceptable consequences: in puzzles (ii) and (iii), contexts of the form, “ . . . nose”, in which the subject is already mentioned—here, the problem will be that there will be too many noses—and in puzzle (i), contexts from which mention of the appropriate subject is subtracted: in this last case, the nose count will be too low. The misuse of the selection-restrictions on “snub”, whether by omission or by unwanted repetition, fastens on a feature distinctive of terms for per se accidents.57 The puzzles revolve also around questions of sameness. In all three puzzles alike, we get questionable results from the attempt to substitute into problem contexts involving snub on the basis of a purportedly definitional sameness claim. We are now in a position to look in detail at how substitution fails in the puzzles and, with the SE as our guide, at the diagnosis and cure Aristotle likely has in mind in each case. A by-product of our account will be a defence of reducing an opponent to babbling as a philosophical tool: despite its disreputable origins, even the threat of fallacy, inducing babbling takes on a new respectability for what it can show about definition and essence.

54

I assume here that we have a way of telling apart cases where we have rival formulations of a single definition, and where there are simply different definitions: for examples of the former, see (ia) and (ia') in Section 13. See also Section 15. 55 I here ignore the complication introduced by Fine (1989), which argues that reformulation conditions standardly govern application of a Principle of Substitution. Aristotle himself seems to hold that substitution is unproblematic, provided that the intersubstituted terms name the same thing in the appropriately strong sense of “same”, even in epistemic and doxastic contexts, ordinarily thought to be less tractable; see this chapter, n. 52 and Section 15. 56 “local to snub and other per se accidents”: see this chapter, n. 57. 57 Relative terms are also included in SE 13 and 31, but I ignore this complication here.

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13 A Nose By Any Other Name: Substitution and Reformulation in the Three Puzzles The role of substitution in puzzle (i) (4.5 above) is obscured by the use of the derived rule of taking equals from equals (the rule of “subtraction”, 4.19 above). In long form, the argument becomes this: (ia) (i*) (ib)

snub nose is the same as hollow nose. snub nose minus nose is the same as hollow nose minus nose (putting equals for equals at the place indicated on the strength of [ia]). snub is the same as hollow (actually performing the subtractions advertized in [i*]).

At the same time, however, (ic)

snub is not the same as hollow.

The role of a Principle of Substitution in the argument is now plain to see. This apart, the crucial feature of the argument is the use of subtraction, highlighted in the “trick” context, “snub nose minus nose”, in (i*), which is specially designed to facilitate deleting the needed reference to noses. Aristotle argues in the SE that “snub” is associated by definition with the context, “ . . . nose”, and that out of that context, its meaning is uncertain,58 or at the least different. The damage comes when we substitute into the trick context, “snub nose minus nose”, to produce (i*). Given (i*), we are can move from an occurrence of “snub” within its associated context in (ia) to one outside that context in (ib), where the term occurs sans noses thanks to the advertized subtractions.59 With the reference to noses gone, the meaning-shifts predicted in the SE come into play, in violation of the constancy requirement.60 We cannot both validly perform substitution and lop off noses together; and if we suppose otherwise and

58

See this chapter, n. 40. It is not obvious that the subtraction advertized in the trick context is consistent with substitution in the way the argument requires. If “snub nose minus nose” in (i*) simplifies to just “snub”, as the inference to (ib) suggests, then arguably the phrase, “snub nose”, does not really occur in (i*)—it is an “orthographic accident”, or just part of a long-winded way of writing the four-letter word, “snub”—and any attempt to substitute for it is doomed from the start. In the main text, I suppose that the phrase, “snub nose”, survives in (i*) long enough to permit substitution, prior to the move to eradicate the reference to noses, and that the use of substitution is undercut instead by the meaning-shifts familiar from the SE; see also this chapter, n. 60. 60 I oversimplify in the main text. The occurrence of “snub nose” in (i*) can mean the same as that in (ia), as constancy requires, only if the constituent term, “snub”, has the same meaning in both places. But what meaning are we to assign to “snub” in its occurrence in (i*)? Let us say that “snub” means S1 in (ia) and S2 in (ib), where S1 6¼ S2 thanks to the meaning-shifts already noted. Which of the meanings S1 and S2 are we to assign to the occurrence of “snub” in (i*)? If it means S1, then it is tied to the larger context, “snub nose”, and it is hard to see how “snub nose minus nose” can simplify to just “snub”, as Aristotle supposes. But if it means S2, then the meaning of “snub” and, hence, the meaning of the larger context, “snub nose”, have changed between (ia) and (i*); if so, then constancy is not satisfied, and the attempt at substitution fails. (In fact, constancy goes doubly unsatisfied: according to SE 31, the signification of “hollow” in the context, “ . . . nose”, in [ia] is also not identical with its signification after subtraction in [ib]; comparable questions arise, then, about the meaning of the substituted phrase, “hollow nose”, in [i*].) 59

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defend the use of substitution in this case, we run into conflict with the true claim denying the sameness of snub and hollow in (ic). Aristotle’s conclusion, I take it, is that substitution cannot go forward in the standard way on the basis of (ia). Two things stand out about (ia). First, in the SE, Aristotle says that “it makes no difference” whether we say “snub nose” or “hollow nose” (182a2–3); from this, it seems to follow that (ia) is true.61 He also insists that “hollow” in the context of “ . . . nose” means the same as “snub”; this suggests that despite the truth of (ia), we cannot reliably move from it to the claim that “hollow” means the same as “snub” independently of context. The problem, then, lies with constancy, and with the applicability of the Principle of Substitution in the given case. Aristotle’s response involves reformulation. If substitution is to work here, the initial sameness claim in (ia) must be rewritten so that the necessary reference to noses survives substitution, even substitution into “trick” contexts of the kind given. The new argument takes this form: (ia')

snub nose is the same as nose having the hollowness of a nose (182a5–6).62

(i*') snub nose minus nose is the same as nose having the hollowness of a nose minus nose. (By substitution on the basis of [ia'].) (ib') (the) snub is the same as having the hollowness of a nose (see 182a4, “the snub is not hollow nose, but something, e.g. a pathos, of a nose”). (Here we perform the subtraction advertized in [i*'].) (ib') (ic)

is not obviously in conflict with the further claim that snub is not the same as hollow.

I turn next to puzzle (ii) (4.6 above). In SE 31, as we have seen (Section 8), Aristotle issues two prohibitions that will prevent babbling. The first repeats his points from SE 13 about constancy; the second adds advice about how to reformulate. The end of 31 indicates that Aristotle is addressing his comments to puzzle (ii): (iia) (the) snub is the same as hollow nose; (iib) snub nose is the same as hollow nose nose; where the conclusion is supposed to follow from the premiss by an application of a Principle of Substitution.

61 Contrary to Hare (1979), 173, then, (ia) is not in itself objectionable (even if it requires reformulation, as we are about to see). To argue that it is by itself objectionable, Hare is forced to imagine that we might refuse to describe a given nose as snub, even though it is concave in some more generic way, as the result of a boxer’s blow, for example. I suspect that he is motivated partly by the mistaken assumption that Aristotle’s subtraction argument from (ia) to (ib) is valid, so that the premiss has to go, see his 172–3. 62 Arguably, this new definition again exhibits prosthesis of a kind, so that it is clear that snub is a pathos of something—but prosthesis here is of a kind to avoid babbling, rather than to introduce it, see Sections 5 and 6 with this chapter, nn. 35, 36, and 42.

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Aristotle’s remarks in SE 13 and 31 suggest that he responds to puzzle (ii) with a dilemma: either the argument is invalid, or its premiss is false; either way, we are free to reject its conclusion. On the first option: as with the examples involving the term, “double”, earlier in 13, and in line with the first prohibition in 31, the argument is valid, only on the assumption that we hold the meaning of “snub” constant. But in puzzle (ii), the target term, “snub” (or in 13, “double”) occurs in the premiss out of its associated context, but within that context in the conclusion at the spot where substitution has been carried out.63 If this difference between the two occurrences forces the usual shift in meaning, constancy fails and the Principle of Substitution cannot be validly applied. To this point, I assume, Aristotle supposes that different meanings are required for the occurrences of “snub” outside its associated context in (iia) and within that context in (iib). To counter this, someone might simply stipulate that “snub” has the same meaning throughout in the puzzle, both in and out of its associated context.64 But (the second limb of the dilemma of the previous paragraph) if the meaning of “snub” in (iia) is adjusted to fit its meaning in (iib), then (iia) is evidently false.65 On this reading, even if the argument is valid, it is not sound, and the problems of babbling are again moot.

63 On one common interpretation (this chapter, n. 29), the occurrence of “snub” on the left-hand side of the premiss is naturally interpreted as a name for the compound, “snubc”, while in the conclusion it should be interpreted as a term for the quality, “snubq”. But this cannot be Aristotle’s main point in Z5; see Section 4. 64 So perhaps SE 31, 173b15–16. On one possible version of this view, the term “(the) snub” out of its associated context is ambiguous between “snubc” and “snubq” (Section 4). One of the readings that result puts different subscripts in (iia) and (iib), so that the inference is fallacious: see (iia*) and (iib*) in Section 4. The other reading gives a version of the argument on which the constancy assumption is satisfied, so that substitution goes through and babbling is apparently back:

(iia**) (the) snubq is the same as hollow hose. (iib**) snubq nose is the same as hollow nose nose. But the premiss (iia**) is false, as Aristotle’s comment at SE 31, 182a3–4, requires. A more fruitful response to the difficulties of the original argument is to reformulate (iia): this is the move Aristotle sets out in the second part of SE 31, see the paragraph immediately following in the main text. 65 According to Aristotle’s second prohibition at SE 31, 182a3–4, “we must not grant the expression in the nominative: for it is false.” I am supposing that this diagnosis assumes that the reading of “(the) snub” in (iia) has been adjusted to fit the reading required for the conclusion (iib), so that constancy is satisfied; but there remains the recommended switch from nominative to genitive, which alters both premiss and conclusion (see [iia***] and [iib***] in the next paragraph in the main text). This eventual reformulation gives a reading on which the argument is sound, but also harmless. Despite the falsity of (iia) as it is currently understood, it would be a mistake to think that the point of this and the other puzzles is simply that the first premiss is in each case false. If the premiss is false, it is no wonder that it fails to support substitution into later premisses of the argument. At best, however, Aristotle sends mixed messages on the status of the first premiss of each argument: while he says that (iia) is outright false, he also seems to assert (ia); see this chapter, n. 61. Again, if the point of the puzzles is just that the opening premiss in each case is false, then presumably each argument is designed as a straightforward reductio; but as we have seen (Sections 4–6), Aristotle’s view that two if not all of the puzzles are invalid makes it hard to sustain this account of them.

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But while simple stipulation will not yield a sound argument, reformulation of the right kind may. Aristotle’s remarks at the end of SE 31 point to a systematic way in which we can reformulate sameness claims like (iia), so that the definiens applies equally to occurrences of a term for a per se accident in as well as out of its associated context. The result in the present case, apparently, is a sameness premiss that is true, and that allows substitution to go through without the meaning-shifts that bring us into conflict with the constancy assumption: (iia***) (the) snub is the same as something (for example, an affection, hollowness) of the nose [genitive] (SE 31, 182a24), (iib***)

snub nose is the same as nose having the hollowness of a nose.

The revised argument is sound, but its conclusion is babble-free.66 Finally, puzzle (iii) (4.7 above). The argument again trades on the ambiguity of “snub”. Without the ambiguity, and if (iiia) is rewritten as Aristotle recommends, we get (iiia')

(the) snub is the same as having the hollowness of a nose,

and the revised argument becomes identical with the new version of argument (ii) in the previous paragraph, with no regress in sight.

14 In Defence of Babbling Puzzle (i) warns us that we can properly apply a Principle of Substitution in the case of terms like “snub” only after if necessary reformulating to adjust for “trick” contexts that otherwise force a meaning-shift that will invalidate substitution. Babbling plays no role in this argument, which focuses instead on the consequences of an undersupply of references to noses. Puzzles (ii) and (iii) again point to the problems of substitution in the presence of the meaning-shifts Aristotle thinks are typically associated with terms for per se accidents.67 Here, the argument goes in the direction of not an undersupply but rather a surplus of noses, and babbling is the result. Babbling indicates that substitution is problematic in the case of terms for per se accidents; for troublesome terms of this kind, we may again need to reformulate the original sameness claim in a way that avoids any meaning-shift. Correctly formulated, the sameness claim can be true, and will not have babbling as a consequence. Perhaps, then, babbling is of use after all in metaphysics. Babbling in a conclusion reached by way of substitution warns us that sameness claims in the case of per se accidents do not invariably support substitution in the expected way. Substitution in their case is subject to qualification. We must first check to see if reformulation is required, to avoid the meaning-shifts threatened by the move from occurrences of the 66 For why this is no longer babbling, despite the dual occurrence of the word “nose” in the right-hand side, see this chapter, nn. 42 and 62. 67 See this chapter, n. 57.

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term in a given special context to occurrences outside that context. Since in these cases the sameness does not reliably support substitution without the qualification about reformulation, the sameness claim cannot express a definition or, at least, not a definition of the standard kind. But if definition is non-standard in such cases, so too is the notion of essence. On this view, there is no discrepancy between Zeta 5 and the SE. Aristotle is aware in Zeta 5 that the arguments in common there with the SE are failures. Their failure, however, suits his wider purposes in the chapter. The failure is further evidence for the breakdown for which he is arguing in certain special cases in the notions of essence and definition, and so further evidence too for the division prominent in chapters 4 through 6 between the strict cases of essence and definition, where the conditions of unity and primacy are met, and other, secondary cases that are subject to more relaxed requirements. At the same time, we can also draw a conclusion about method. For if our account of Zeta 5 is right, there is ample room for puzzles that are the hallmark of dialectic—even dialectic in the manner of the SE—even in the austere regions of Aristotelian metaphysics.

AFTERWORD: RESERVATIONS AND RETRACTIONS

15 Does Aristotle’s Argument Hit Too Wide a Target? In the strategy I attribute to Aristotle, the Zeta 5 puzzles are part of a larger argument for reduced notions of essence and definition in the case of snub and other per se accidents (and, ultimately, in the case of everything except substances, 3.2 and 3.25 above). His argument starts from the selection-restrictions typical of terms for per se accidents like “snub”: only noses can be snub, and so on. Thanks to these restrictions, purportedly definitional sameness claims involving snub typically exhibit prosthesis (“addition”), and they support substitution in the expected way, only subject to special reformulation conditions telling us whether reformulation is needed and, if needed, the form it must take. The fact that sameness statements involving snub and the rest do not support substitution without these kinds of conditions, suggests that those statements cannot also be definitional—or at least, not definitional in the standard way. For similar reasons, either snub has no essence, or it has an essence in some less-than-standard way. Aristotle can think that this argument succeeds, only if he believes that substitution is in general unproblematic—that it is not in the majority of cases subject to conditions of the sort that govern terms for per se accidents. He does himself seem to allow that some widenings of the argument against per se accidents are possible. For Aristotle, every item from some non-substance category—that is, every accident—is defined as the accident it is of an individual substance. So he may well think that the selection-restrictions that accompany “snub”, along with the tell-tale definition by prosthesis, apply to accidents of every sort, per se or otherwise.

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But can he contain the argument to just these two sets of cases? Two arguments suggest that he cannot. Aristotelian forms are the star cases of definable objects for Aristotle. But he is committed to holding that in general his forms are each restricted to a range of suitable matters as their subject. And in the case of the forms of natural objects, arguably there is a single kind of matter suitable to receive the form—a human body with human organs for human form, a canine body for canine form, and so on.68 So if the primary objects for definition themselves can be defined only by prosthesis—by reference to the appropriate matter—and if definition by prosthesis is not definition in the strict sense, is nothing strictly definable at all?69 The good news is that we can find specifications of the matter that are appropriately part of the content of the form, and do not intrinsically involve reference to something other than the form. In defining the form, we are not required to refer to a particular set of material structures; instead, we can give a functional specification in terms of the passive capacities the matter must have to be a suitable matter for that form. These capacities themselves are constitutive of the form. It is then a contingent fact, and not part of the content of the form, that this particular stuff or structure rather than that satisfies the specification given.70 But there is a difficulty. If we favour a definition of form that gives a functional specification of the matter over a definition that mentions particular stuffs or structures, this preference looks suspiciously like reformulation conditions special to the definition of form, along the lines of the special conditions said to govern the definition of per se accidents. On the story told above, the need for reformulation, or the possibility of it, indicates that a definition is less than fully standard. But Aristotle can hardly mean to suggest that form too can have an essence or a definition only in a reduced sense, along the lines reserved for per se accidents and other lesser items in his ontology. Once again, then, his argument apparently hits more than its intended target. A possible response might be that producing the preferred definition requires not reformulation, but replacing an incorrect definition with the correct one (see this 68 On this topic, see Metaphysics Z11, and Chapter 7. Aristotle’s views about the homonymy of matter (Chapter 2, Section 7) point in the same direction. 69 See this chapter, n. 7. Whether the definition of the form should include the definition of the matter is a matter of debate in Z10 and 11, with a negative answer at Z10, 1035a9–23, but the suggestion of a positive answer later in the same chapter at 1035b14–18, pressed harder in Z11 in the debate with Socrates the Younger at 1036b21–32. The point of the present argument is that a form may stand in relations to things other than (and external to) itself, that threaten its suitability as a primary object of definition. We may contrast this objection with the argument Aristotle gives at the end of Z13, that facts about the internal structure of substances (or rather, the seeming lack of it) seem to make substances not a proper object of definition. In Z4, meanwhile, he seems to think that the items that properly have an essence or a definition (identified there as genous eide¯, Chapter 3, Section 7) are indeed structured entities, but subject to an impredicability condition (Wedin (2000), 221–7) restricting the internal relations among their constituents. 70 This is in essence Aristotle’s notion of hypothetical necessity, as I understand it: if there is to be a saw, then it must be made of something capable of this and that performances (here, we put the required functional specification). Aristotle explains that the uniform parts are for the sake of the non-uniform parts, because the various capacities (dunameis) associated with the former are required for the capacities that typify the latter, PA B1, 646b11–27.

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chapter, n. 54). A correct definition of form comes with the appropriate application conditions, specified in purely functional terms; but it does not mention particular physical structures, and it does not lack application conditions altogether. So the correct definition does not have the same ontological commitments as its erroneous counterparts, and they are not different formulations of a single definition, but different definitions entirely. The distinction between different formulations of a single definition and the replacement of an incorrect definition by a correct one, is not ad hoc. Where a definition is incorrect, it can perhaps be saved by reformulation; or it may need to be replaced by a different definition entirely. But the triviality that error is all around us, so that almost any definition can be gotten wrong, does not neutralize the claim that some definitions may require reformulation—but not outright replacement—on systematic grounds peculiar to terms for per se accidents. But there are further reasons for thinking that (once more) Aristotle’s argument hits more than its intended target. As we have seen, the proper objects of definition are forms, so that the definition of a given form should support substitution without the reformulation conditions that apply elsewhere. It follows that the definition is circular in one step. For, suppose that the form ł is by definition çå. Then, putting equals for equals, by definition ł is ł.71 If this objection succeeds, then forms are not properly definable, so that (as before) nothing is. One obvious remedy is to enforce Aristotle’s ban on equimembral definitions (Topics Z11, 148b32–149a7; Chapter 3, Section 4): the definiens should contain more terms than the definiendum. Another is the requirement in Metaphysics Zeta 4 that the definiens “state but not contain” the definiendum (Zeta 4, 1029b19–20, in 3.8 above).72 Either response heads off circularity. And more than plausibly, both conditions hold across-the-board, for all definitions; neither, then, can be interpreted as imposing conditions on substitution peculiar to a select set of cases, in the way that we supposed was the sign of a less-than-standard definition. It may seem that the responses sketched in the previous paragraph do no more than demonstrate why the difficulties cited are genuinely objectionable for Aristotle, rather than tell us how he can plausibly avoid them. But even if the objection in its present form can be kept at bay, it is the symptom of a wider difficulty. I have argued that if an apparently definitional sameness statement supports substitition into a given context only with the appropriate reformulation conditions, then according to Aristotle the statement is not fully definitional after all. It follows that where a sameness statement is fully definitional, it will support substitution into every context with no (special) reformulation conditions attached. On this account, Aristotle may be willing to accept unrestrained substitution, not just into statements of definition, but also into epistemic/ doxastic contexts, and into modal contexts. The evidence here is indirect, but it is not 71 I owe this objection to Gareth Matthews. The objection resurfaces in connection with Z6; see Chapter 6, n. 57. 72 For a suitably charitable interpretation of this requirement, see Wedin (2000), 202–3.

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obvious that he is protected against these larger consequences.73 So the difficulty of unrestrained substitution, while real, may be one Aristotle is oblivious to in connection with other contexts as well.

16 Does the Argument Hit No Target At All? We have considered two objections to the effect that if some definitions are nonstandard, then all are, including definitions of Aristotelian forms. A variation on this objection is that none is less than standard. We argued that because snub is a property exclusively of noses, the very notions of definition and essence are non-standard in the case of snub and the rest; if similar selection-restrictions apply in the case of form, however, then apparently the notions of essence and definition in both cases must be non-standard. But perhaps the argument should go the other way. Evidently, the definition or essence of a form cannot be less than standard; but if as snub goes, so form goes too, and vice versa, then the original argument that snub has a non-standard definition or essence must surely fail. One way it may fail is this.74 The original argument pointed to the possibility that the definition of snub require reformulation. But a given definition may not require reformulation—it may be correct from the start. And in any event, once reformulation has been done, the definition is thereafter correct. Either way, the definition now supports substitution without qualification—without the need for reformulation conditions. So the notions of essence and definition for snub and the rest are standard after all, at least, as far as the present argument has shown. This objection rests on a misconception over the form the rule of substitution takes in the case of snub and the rest, as Aristotle envisions it. Aristotle’s rule for these cases has two clauses, the first requiring us to perform reformulation as needed, the second instructing us to go ahead with substitution in the usual way. Once clause one of the two-clause rule has been enforced, the remainder of the rule is identical with the standard, one-clause rule. The two-clause rule itself, however, is quite different from Aristotle’s one-clause rule, and the fact that they are different, Aristotle thinks, is what entitles him to set apart snub and the rest from the standard cases. A comparison may help: standardly in first-order predicate logic, the rule of Universal Generalization requires us to check for previous occurrences of the instantiating constant. The fact that 73

The evidence I am aware of bears only on a Principle of Sameness, and not one of Substitution. Aristotle appears to think that (contrary to modern sensibilities) a Principle of Sameness holds in epistemic contexts, given a sufficiently strong relation of sameness in the antecedent. At SE 24, 179a37–9 (cf. Physics `3, 202b14–16), he endorses a Principle of Sameness featuring numerical sameness in being in place of (mere) accidental sameness. The implication is that the inference from “I know that Coriscus is Coriscus” to “I know that the masked man is Coriscus” (the Masker Paradox) fails because Coriscus is only accidentally the same as the masked man; had they been the same in being, the inference would have succeeded. If he is willing to accept this result without qualification, it will be no surprise if he is also liable to the difficulties sketched involving substitution into statements of definition and other contexts as well. See this chapter, n. 52. 74 Versions of this objection have been pressed in discussion by Alan Code and Robert Bolton.

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the constant does not occur in any undischarged assumption in a given application of the rule does not mean that the stipulation is not part of the rule after all, or that a oneclause rule holds in the one kind of case, and the more complicated two-clause rule only in the other.

17 Systematic Considerations But is Aristotle right that in the standard case a one-clause Principle of Substitution will do the job? If not, we must once more face the possibility from Section 15 that his argument hits too wide a target. A systematic point, due to Fine (1989), suggests that this result is unavoidable. Fine argues that conditions on substitution of the sort envisioned in the case of terms for per se accidents in fact apply universally: syntactic as well as semantic conditions must be satisfied whenever we attempt to apply the rule of substitution, without exception. Fine cites a variety of cases which are governed by conditions of this kind, and the existence of these cases by itself throws doubt on Aristotle’s claim to have fastened on a feature that is peculiar to terms for per se accidents. If Fine’s more global claims are correct, there are systematic reasons for doubting any version of the piecemeal approach of the sort Aristotle describes, which attempts to discriminate between cases where reformulation conditions are required, and other cases where they are not.

5 Sameness, Substitution, and Essence (II): The SE, and the Pale Man Argument from Zeta 6 In Metaphysics Zeta 6, Aristotle makes what appears to be a fresh run1 at the connection announced in the agenda at the beginning of Zeta 3 between the notion of essence and the definition of substance which is his target in Zeta. In his earlier discussion in Zeta 4–5, one important theme concerned the different grades of being among items in the ontology, and the corresponding idea that, in addition to the “black-and-white” view that essences belong exclusively to those entities that are suitably primary, we might also allow the more inclusive approach that recognizes a lower-level notion of essence in connection with entities in the ontology that are themselves less than first class. In particular, Zeta 5 has given us a series of puzzles to show that per se accidents like snub, and perhaps accidents generally, either have no essence, or do so in a less than first-class way. The concern with levels continues in the arguments of Zeta 6. We can begin with the suggestion in the opening lines of Zeta 6, that it bears on the topic of substance to ask whether a thing and its essence are the same or different: 5.1 Whether each thing and its essence are the same or different, needs to be looked into. For it is somewhat relevant to the study of substance: for (first) (te, a17) each thing is thought to be not other than its own substance, and (second) (kai, a18) its essence is said to be each thing’s substance. (1031a15–18)

Aristotle’s “is thought to be” and “is said to be” (a17, 18), indicate the stoutly “received” character of this argument (the “Basic Argument” of the chapter; see the introduction to Chapter 6). Distinctions in levels will have a role in addressing the question we are directed to in 5.1. It soon turns out that certain things—those that are truly primary substances—are (in some strong sense) the same as—even identical with2—their 1 “A fresh run”: the summary, 3.2 (= 4.2) above, at the end of Z5 suggests that 4 and 5 together form a unit (throughout Zeta, the division into chapters is not by Aristotle); the argument for relevance at the beginning of 6 suggests that he sees himself as embarking there on a new approach to his topic. 2 The brand of sameness Aristotle intends is left unclear at the opening of Z6, but with the help of the Pale Man Arguments at 1031a19–28 to exclude an unwanted weaker notion, he later settles on essential sameness,

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essences. In other, less metaphysically privileged cases, the identity fails. The pale man, for example, is not the same (in the relevant sense) as the essence of the pale man. My interests in this chapter revolve around the arguments Aristotle uses to advance the negative half of his position, that the pale man is not (in the relevant sense) the same as its essence (Sections 2–5). (Later arguments in the chapter will be the subject of Chapter 6.) The Pale Man Argument (1031a19–25), like the second argument he gestures at to replace it (a25–28), draws on the same pool of logical moves from the Topics and the SE that Aristotle puts to use in Zeta 4 and 5.3 In Zeta 5, the fact that the puzzles concerning per se accidents like the snub are invalid by the standards of the SE need not undermine his conclusion, that per se accidents cannot have a definition or an essence in the proper sense.4 Invalidity is also an issue in Zeta 6, where Aristotle confesses openly that the Pale Man Argument and its successor alike are invalid, even though the negative conclusion they were meant to support stands. Is there again a way in which, invalid as they are, those arguments still point to the desired conclusion? Can a positive result arise from the wreckage of these arguments? I will argue that, in contrast to the proceedings in Zeta 5, there is here no happy ending: in Zeta 6, there will be no virtue in invalidity.5 Disagreement over the effectiveness or otherwise of the Pale Man Argument rests on deeper disagreements over fundamental features of Aristotle’s metaphysical theory. In particular, is Aristotle committed to a theory of accidental compounds—a further kind of entity, in addition to individual substances and their accidents? Related issues include sameness and substitution, and the place, if any, of substitution failures and of referential opacity in the Pale Man Argument (Section 6); and the place, if any, of substitution failures and of referential opacity in the broader theory of essence (Sections 7–10). First, however (Section 1), I offer a brief reminder of the metaphysical background.

which he appears to think supports application of a Principle of Substitution, if not a straightforward Principle of Identity; see SE 24, 179a37–9, and Physics ˆ3, 202b4–6. For the distinction between the two Principles, see Chapter 4, nn. 38 and 45, and for the different Sameness Principles in Aristotle, Lewis (1991), 116–21. The second, stronger sameness relation in Z6 holds only between entities that are suitably primary and qualify for an essence in the strict sense. Accordingly, I will suppose that x and y are essentially the same just in case both x is identical with y and x is a primary entity. For opposing views about the nature of the stronger sameness relation, see Dahl (2003) with his (C) in Section 5, Charles (2011), and Chapter 6, n. 57. 3 For Z4, see, for example, the use of the rule of subtraction (3.9 = 4.19 above and 5.2 below) at 1029b21–2 (Chapter 3, Section 4); for subtraction in Z5, see the puzzle at 1030b28–32 (Chapter 4, Sections 1 and 10). 4 The puzzles involving snub in Z5 are built around various attempts to define the snub. In any proper statement of definition, according to Aristotle, definiendum and definiens must name the same thing, in a sense of “same” strong enough to support a Principle of Substitution, if not a Principle of Identity. The fact that the sameness relation featured in the definitions offered in the puzzles is too weak to support the inferences on which the puzzles rest, so that the puzzles are invalid, indicates that the sameness statement is not definitional in the full sense—the very conclusion Aristotle intends; see Chapter 4. 5 This negative assessment is controverted in Dahl (1997) and (1999), who suggests that Aristotle’s arguments commit a fallacy that, when properly diagnosed, does steer us to the conclusion, that the pale man is not the same as the essence of a pale man, which Aristotle wants. I will disagree.

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SOME BACKGROUND IDEAS

1 Aristotle’s Hierarchy of Essences, and “Things that are the Same as Their Essences” In both the “partisan” and “non-partisan” parts of his discussion, Aristotle is more than ready to make room for different grades of being among the items in the ontology. Part of the very idea of being a substance, as we saw in the introduction to Chapter 3, for Aristotle includes a notion of primacy over entities of every other sort, which are not substances. At the same time, the non-substances, which have a lesser grade of being, stand in a relation of ontological dependency on substances, which are primary. And if, as I suppose (this chapter, n. 3), Aristotle’s ontology also includes accidental compounds, these will come in third, behind their two constituents, the individual substance and its various accidents. Along with the different grades of being just noted, Aristotle recognizes more or less robust cases of essence. Things have an essence in the full-blooded way, if they are whatever in your favourite ontology count as primary substances (instead of pushing his own agenda in the chapter, Aristotle uses Platonic forms as examples of entities that are suitably primary): these are the cases in which a thing is essentially the same as, and hence identical with,6 its essence. As it turns out, Aristotle suggests that non-substance accidents—pallor, generosity—are also the same as, and hence identical with, their essences.7 He is firm, however, that accidental compounds are not the same (in the relevant way) as their essences.8 Why essential sameness, even identity, for some things and their essences, but not for others? On the “black and white” view of essence already noted, only entities that are properly one and primary can have an essence. But if an item is primary, and also has an essence, what standing shall we give to that essence? The essence of a thing is also its substance; so surely a thing’s essence must be prior to it. How, then, can the thing itself be primary? The only answer is to suppose that a primary substance and its essence are identical, so that neither is prior to the other. In this way, Aristotle succeeds in “staunching the flow of essences”, or “cutting short the parade of essences”,9 that might otherwise have threatened the primacy of primary substance. In the case of entities that are not primary in the ontology, however, it is perfectly proper to think that they are not the same as their essences. In their case, the chain of explanation continues, and we are to unravel their essence in terms of yet 6

On the brand of sameness relevant here, see this chapter, n. 2. This claim is difficult to reconcile with other things Aristotle says about what qualifies an item to be the same as its essence in the required sense; but I will not take on these difficulties here. For discussion, see Wedin (2000), 264–5, 282–3. 8 For the various ways in which Aristotle restricts the scope of his sameness result, see Chapter 3, n. 5 with the references there, and, especially, Chapter 6. 9 These memorable phrases are borrowed from Wedin (2000), 276, 278. 7

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other essences that are its constituents. Thus, for example, the essence of a pale man is, presumably, composite, cobbled together, I will suggest (Section 11), from the essence of pallor and the essence of man.10 With perhaps these two constituents, or with constituents of the constituents, as needed, we will at the end arrive at terminal essences—entities for which the only possible candidate for their essence is: themselves. Our interest, however, is in cases where identity fails. This non-identity result is the would-be conclusion of the Pale Man Argument that is our main target.

THE PALE MAN ARGUMENT

2 Things that are Not (Essentially) the Same as Their Essences: the Pale Man Argument The target argument reads as follows: 5.2 Now in the case of things said accidentally (to¯n legomeno¯n kata sumbebe¯kos) they [a thing and its essence] would seem to be different, for example, pale man is different from the essence of pale man (“the for pale man to-be”, to leuko¯i anthro¯po¯i einai). (a21) For, if they were the same, so would the essence of man (“the for man to-be”, to anthro¯po¯i einai) and the essence of pale man (to leuko¯i anthro¯po¯i einai) the same; for man and pale man are the same, as they say (a23), so that also the essence of pale man and the essence of man. (a24) Or , it is not necessary that whatever things are accidentally (hosa kata sumbebe¯kos) be the same , for the extremes are not the same in the same way. (1031a19–25)

I begin by setting out the argument as Aristotle gives it (on the usual account, there are premisses missing, but we shall see): I (1) The pale man is the same as the essence of the pale man. A (2) The man is the same as the pale man. A (“So they say,”11 a23). (3) The essence of the man is the same as the essence of the pale man. By “addition” from (2)? In this argument we assume (1) for purposes of reductio. (2) is a commonplace: there are pale men around, and we say of each of them that it is the same as the relevant man. 10

See Chapter 3, n. 6. Aristotle himself is included under the “they”; see, for example, Topics E4, 133b15–21, 31–6, Metaphysics D6, 1015b16–36, D9, 1018a2–3, D29, 1024b30–31, E2, 1026b15–18. At the same time, in a contested text at Z4, 1031b22–28, Aristotle seems momentarily to lose sight of ACT (Chapter 1, n. 3). He explains that his class of “things said per accidens” includes the pale, or the musical, where these signify [i] the accident as well as [ii] that to which pale belongs [or: that which happens to be pale?]—that is, presumably, Archimedes who happens to be pale. Here, Archimedes occupies the spot we had thought reserved for the compound: the pale man. But the pale man reappears in the next line at b27. For discussion, see Lewis (1991), 101, n. 27, and Dahl (1999), n. 29 (but when Aristotle says that its essence is not the same as the man and the pale man, it begs the question against ACT to assume with Dahl that “and” here must be “i.e.”). 11

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The conclusion, (3), we are to suppose, is evidently absurd,12 and so we are to reject the target of the reductio in (1). How is this argument supposed to work? In the Topics, Aristotle states a rule of inference that appears to license the inference from (2) alone to (3): 5.3 (= 3.10 and 4.19 above) Furthermore, you must note the result of an addition and see whether each added to the same thing fails to produce the same whole; or whether the subtraction of the same thing from each leaves the remainder different. Suppose, for example that someone has stated that double of a half and a multiple of a half are the same, then, if of a half has been subtracted from each, the remainders ought to signify the same thing: but they do not. (Topics H1, 152b10–15)

One way of understanding addition is to think of it as a linguistic affair. On the supposition that the man and the pale man are the same, if we add the two terms “the man” and “the pale man”—allegedly, names for the same thing—in turn to the same linguistic context, “the essence of . . . ’ the resulting expressions, “the essence of the man” and “the essence of the pale man”, should themselves name the same thing.13 (But it is not clear, even after significant argument, that they do.) At the same time, given the appropriate metaphysical apparatus, addition may be a metaphysical procedure. In the following expanded version of Argument I, addition is interpreted metaphysically: II

(1) The pale man is the same as the essence of the pale man. A (2) The man is the same as the pale man. A (“as they say”)

From (2), by addition. (3) The essence of man is the same as the essence of the pale man. From (2*), carrying out the addition advertised.

Here, we can think of addition in terms of applying the function, the essence of ( ), in turn to the man and to the pale man as arguments. As with the rule of subtraction (Chapter 4, Section 13), the rule of addition is a special case of “putting sames for sames”, so that what is added to the man in the left-hand side of (2*) is added also to the pale man, by the sameness relation in (2). It is not too soon, however, to worry whether the sameness relation in (2) is strong enough to justify the inference to (2*).

12 To see that (3) must be absurd, reflect that a comparable argument to the Pale Man Argument can be constructed as (say) the Argumentative Man Argument (AMA); from (3) and the counterpart to (3) in the AMA, it apparently follows by transitivity that the essence of the pale man is the same as the essence of the argumentative man. 13 For the linguistic interpretation of Aristotle’s rule, see Lewis (1991), 119–20.

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A related reading of the argument again involves putting sames for sames: III

(1) The pale man is the same as the essence of the pale man. A (2) The man is the same as the pale man. A (“as they say”) (3) The essence of the man is the same as the essence of the pale man. Putting sames for sames, on the basis of (2).

If the man is the same as the pale man, as in (2), then putting sames for sames, the essence of the first should be the same as the essence of the second, as in (3). The fact that instead we go from true to false suggests that the man and the pale man are not the same in the needed sense of “same”. In essence, all three arguments I–III are subject to the same objection: the sense of “same” in (2) (“The man is the same as the pale man”) is too weak to support the needed inference. In Aristotle’s terms, the man and the pale man are only accidentally the same. In all three arguments, meanwhile, the relation in (1) is a different relation, stronger than that in (2) and maybe even of equal strength as our identity (even if it is not exactly that relation). The point, however, is not that there are these two different relations (although Aristotle appears to say that they are), but only that the relation in (2) is not the one required. But there are good reasons against reading Aristotle’s argument as either I, II, or III. He complains that “the extremes are not the same in the same way”, and we have not found extremes in any of the three arguments. (We will see what counts as extremes in later versions of the argument.) Worse, neither I, II, nor III makes any use of premiss (1), expressly present in the argument for purposes of reductio. So none of the three can be the argument Aristotle has in mind. But what addition cannot do, perhaps subtraction (5.3 above) can: IV

(1) The essence of the pale man is the same as the pale man. A By subtraction from (1). (2) The pale man is the same as the man. A (“as they say”) (3) The essence of the pale man is the same as the essence of the man. From (1), (1*), and (2), by symmetry and transitivity of the sameness relation.

But of course, premiss (2), based on “what they say”, involves accidental sameness, which is a weaker and, more importantly, a different, brand of sameness than that in the other lines of the argument. So the problem is that the sense of “same” changes as we makes our way from the first of the extremes, the essence of the pale man, at the left-hand side of (1), to the last, the essence of man, on the right-hand side of (3), as Aristotle himself seems to object. But failure in this argument may be over-determined, for the rule of subtraction may also be under suspicion here. To see how this might be, here is the long way of making the move by subtraction from (1) to (1*) in the argument just given:

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(1) The essence of the pale man is the same as the pale man. A

From (1), by subtraction, and a special case of the rule, to the same things, the same things belong (4.18 above).

From (1**), by the subtraction advertised. (2) The man is the same as the pale man. A (“as they say”) (3) The essence of the pale man is the same as the essence of the man. From (1), (2), and (1*), by the symmetry and transitivity of the sameness relation.

As before, the appeal to transitivity fails, for no single sameness relation prevails throughout the argument. At the same time, the principle that to the same things, the same things belong, which engineers the use of subtraction in the move to (1**), is applied in (1) to a case that features the weaker of the two sameness relations. In one place, then, the argument fails because there are too many sameness relations, and in another, because the sameness relation is the wrong one for the purpose. It is worth noting, finally, that the very process of subtraction in arguments IV and V supposes that the essence of the pale man and the pale man itself are both alike compound entities, from which one constituent can be removed—uncontroversial, perhaps, in the case of the essence, but something that sceptics over ACT will deny in the case of the pale man. So as not to rule out these doubts over ACT from the very start, we should add a further version of the argument, following Ross:14 VI

(1) The pale man is the same as the essence of the pale man. A (2) The man is the same as the pale man. A (“as they say”). From (1) and (2).

An assumption [Patzig]; or by parity with (1) [Ross]; or by subtraction from (1). (3) The essence of the pale man is the same as the essence of the man. From (1*) and (2**).

The two lines, (1*) and (2**), in angle brackets are added to the argument Aristotle gives. The move from (1) and (2) to (2**) highlights the extremes he mentions. The first extreme, the essence of the pale man, at the right-hand side of (1), supposedly is connected to its other term in (1) by the strong sameness relation noted above. But the second extreme, the man, at the left-hand side of (2), is connected to its other term in (2) by the different relation of accidental sameness. If the inference from (1) and (2)

14

The version in Patzig (1979), 45, is similar, but broken down into two distinct syllogisms.

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to (2**) is based on the supposed transitivity of the sameness relation, then the move fails because there is no one sameness relation in all three lines. (This is the “two samenesses” objection.) Alternatively, the argument supposes that what is true of the pale man (that he is the same as the essence of the pale man) is true of the man himself, given the sameness claim in (2), that the man is the same as the pale man. But the sameness in question is accidental sameness, and not a sufficiently strong notion of sameness to support the wanted inference. (This is the “wrong sameness” objection.)

3 So Many Arguments, So Many Ways To Go Wrong Which of these different arguments, I through VI, best fits Aristotle’s description of the fault he finds in the argument he gives? Here again is his comment on the argument: 5.4 (repeated from the second half of 5.3) Or , it is not necessary that whatever things are accidentally (hosa kata sumbebe¯kos) be the same , for the extremes are not the same in the same way. (1031a24–5)

By “it is not necessary that . . . ” I take him to mean that the conclusion, that “whatever is accidentally is the same ”, does not follow from its premisses. And his reason, apparently, is that “the extremes are not the same in the same way”. The comment that there are two notions of sameness at work in the argument, perhaps suggests that the argument fails because of shifts from the one kind of sameness to the other. So the fallacy is that of equivocation on the sense of “same”. Alternatively, the difficulty may be that, of the two kinds of sameness, the argument reasons from the wrong kind: the mistake is the fallacy of accident—the mistake of supposing that to things that are (merely) accidentally the same, all the same things belong.15 IV, fleshed out as V, and Ross’s VI plausibly fit either or both of the fallacies described. Why inquire further? A possible motive lies with the very fallacies that Aristotle admits to in the Pale Man Argument (as also in the second argument he gestures at to replace it)—even while the negative conclusion they were intended to support still stands. Is that negative conclusion left altogether unsupported by the arguments he has offered, or is there a way in which, invalid as they are, those arguments still point to the desired conclusion? Dahl has argued that the failure of the Pale Man Argument, properly diagnosed, points us in the direction of the conclusion, that things like the pale man are not the same as their essences, that Aristotle wants. To understand how, even in failure, the

15

The supposed principle is given at Topics E4, 133b17–21, and H1, 152a33–7, b25–9; see Lewis (1991), chapter 4, section 1. Under pressure from the modal and epistemic paradoxes (SE 6, 168a34–b10, 24, 179a26–b7), the principle is corrected, with a stronger sameness relation in the antecedent, at SE 24, 179a37–9, and Physics ˆ3, 202b14–16.

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argument in the end supports the conclusion it was designed to prove, we must first settle on how the argument fails. The key to the failure of the Pale Man Argument, in Dahl’s reconstruction, is the part played by contexts that are referentially opaque, in which applications of a Principle of Substitution, or “putting equals for equals”, must fail. The upshot will be an account of how this diagnosis, in the end, leads us to see that the conclusion of the argument is correct—even if the argument itself is invalid. These are our topics in Sections 4 and 5.

REFERENTIAL OPACITY AND THE PALE MAN ARGUMENT

4 Referential Opacity, and the Fallacy of Accident I discuss Dahl’s first version of the argument (it is superficially similar to Ross’s VI above): VII

(Dahl’s IA): (1) The pale man is the same in (number and) substance as his essence, the essence of the pale man.16 A (2) The man is accidentally the same as the pale man. A

“Putting equals for equals” in (1), by (2).

A (by parity with [1]). (5) The essence of the man and the essence of the pale man are the same in (number and) substance. From (3) and (4).

I make two preliminary comments on this argument. First, we could have said that (4) is not by parity with (1), but by “taking equals from equals”—that is, by subtraction— from (1), as in IV above; but this would require, what Dahl denies, that like the essence of the pale man, the pale man too is a compound entity, from which one constituent can be removed (Section 2). So we leave (4) as an independent assumption. Second, this version of the argument, unlike Aristotle’s, flags the two kinds of sameness; so in this rendering at any rate, the argument will not commit the fallacy of equivocation— for example, by an appeal to transitivity in moving from premisses (1) and (2) to (3)— despite Aristotle’s fears in 5.4 above.

16 With some hesitation, in this premiss and throughout VII I have replaced Dahl’s indefinite article (“A pale man is the same . . . as his essence, the essence of a pale man”) with the definite article. As Dahl himself says, Aristotle has in mind a particular pale man: I take this to mean, a given particular pale man. And in any case, the attempts at substitution in the course of the argument require definite rather than indefinite singular terms.

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There remains the question of where instead we are to find the fallacy in his argument that Aristotle warns us of. An obvious point at which to apply pressure is the nature of the sameness relation in (2), which seems too weak to legitimate the move to (3) (see Section 2 and especially n. 15). Dahl will have things to say about the sameness claim in (2), which he interprets in light of his view that VII fails because the expression “ . . . is the same in (number and) substance as its essence” is referentially opaque. As we shall see shortly (in Section 5), his views on these points are part and parcel of his rejection of ACT. First, as to referential opacity: Dahl identifies two contexts he considers opaque; they show up from the very beginning in the first premiss of Argument VII, at the places indicated: (1) The pale man is the same in (number and) substance as his essence, the essence of the pale man.17 Meanwhile, second, the sameness claim in (2) from VII apparently gives us the point only that the expressions, “the man” and “the pale man”, are co-referential, but not that they are synonymous. Importantly, it is not part of Dahl’s view that man and the pale man are accidentally the same, but not strictly identical: this would be to concede the truth of ACT, which he does not wish to do. Instead, the two are identical, and the problem lies with the different expressions that refer to them. The expressions are co-referential—they refer to the identical thing—but not synonymous; given, then, the further claim that the context in (1) in which we are attempting to exchange the one expression for the other is referentially opaque, the inference to (3) is fallacious. Accordingly, the Pale Man Argument, rendered as VII, is subject to what Dahl calls the “linguistic version” of what Aristotle describes as the fallacy of accident. How are we to evaluate this account of Aristotle’s argument? The classic example of the fallacy of accident is in the SE: Coriscus happens to be (or “is accidentally the same as”) the one approaching, it may be, or the masked man; I know Coriscus; I do not know the one approaching, or the masked man; so I both know and do not know the same thing (Coriscus, or the one approaching, or the masked man). According to Aristotle, the licensing principle required to get us to the last step—that to things that are (merely) accidentally the same, all the same things belong—is not valid. What Dahl calls the linguistic version of the fallacy of accident is a Principle of Substitution, to the effect that we can freely intersubstitute names for the same thing, without change in

According to Dahl (1997), 256, “The essence of a pale man (a man who is accidentally a pale man) that counts as his essence is the essence of a pale man”. The emphasis is his, and indicates two places at which he finds referential opacity. The two contexts are referentially opaque, he explains, because of the “accidentally” and the “essence of ” (see this chapter, n. 27), and also because the same expression is required in both places. (This last point, however, seems more a question of pronominal cross-reference in the phase “his essence”: = the essence of the man?, or the essence of the pale man?, where these may be distinct essences, even though given Dahl’s rejection of ACT, the man and the pale man are identical; Section 5.) 17

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truth-value.18 Contrary to the Principle of Substitution, the fact that the singular terms, “Coriscus” and “the one approaching”, or “the masked man”, name the same thing in a given context of utterance, is not enough to license the inference on display in the SE. Substitution fails in the context “I know . . . ”, which is referentially opaque at the position indicated. Difficulties involving referential opacity, according to Dahl, also afflict the Pale Man Argument, rendered as VII above. But the argument is not simply bad—a failed attempt at reductio—and of no value in supporting the desired negative conclusion, that the pale man cannot be the same in the relevant way as its essence. On the contrary, reflection on how the argument fails, in particular, on how the referentially opaque contexts at various points undercut the inferential moves the argument tries to make, will help us see why, despite everything, its negative conclusion must be true. If this is correct, then this particular bad argument does do some philosophical good. But how does the diagnosis of referential opacity support the desired negative conclusion?

5 From the Fallacy of Accident to the Non-Sameness Result: the Supporting Argument Dahl offers an argument, based (he suggests) on an understanding of the missteps in the original Pale Man Argument, that shares its conclusion with the original failed Argument. In this Supporting Argument (as I will call it), two assumptions underpin everything else. First, the “No ACT” Assumption: (A) The pale man is not an accidental compound of the man with his accident, pallor, but just a man who happens to be pale. All things being equal, then, the expression “the pale man” gets the Russellian (referential) reading—it picks out the one and only thing that happens to be pale. Second, we have an assumption about essence: (B) The pale man, a.k.a. the man who happens to be pale, has “what it is to be a pale man”—the composite essence—as his essence. So we must tune out any reading of Aristotle that suggests that the essence, “what it is to be a man” (the essence as of man), is the only essence the pale man has or deserves. We will also need a different account of the stronger sameness relation at work in the Pale Man Argument: not essential sameness, which I have taken to approximate our identity,19 but the relation of sameness in substance, to be understood as follows:

18 For the Principle of Substitution, see Chapter 4, nn. 38 and 46. I discuss the relation between the Fallacy of Accident and the “linguistic” Principle of Substitution Dahl puts in its place in Section 5. 19 See this chapter, n. 2.

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(C) x is the same in substance as its essence if and only if x and its essence have the same essence. For example, Archimedes is the same in substance as his essence, namely what it is to be a man, since they share the same essence: each Is a rational animal;20 but it does not follow that they are identical. The Supporting Argument will claim that, given assumptions (A) and (B), the condition in (C) for sameness in substance between the pale man and his essence is not met. “What it is to be a pale man” includes being pale: by hypothesis in (B), it is the composite essence of the man who happens to be pale. Because the essence is composite, its definition will make reference in one way or another both to man and to pallor. But by assumption (A), the man in question only happens to be pale—being pale is not part of his essence. So the pale man and the composite essence do not have the same essence and, by definition (C) above, they are not the same in substance. And if we adjust for the new account of sameness, this is just the Pale Man result Aristotle has been arguing for. Setting aside for the moment any other doubts we might have over the Supporting Argument, what bearing do the Supporting Argument and the fallacy of accident in the original Pale Man Argument have on each other, as Dahl suggests they do? The connection between the two is hardly a simple one. In the first place, the fallacy of accident must be reinterpreted as the fallacy of intersubstituting co-referential terms in an opaque context. But the second fallacy is not trivially the linguistic counterpart of the first. The fallacy of accident traces inferential failures to the wrong kind of sameness: accidental sameness is too weak a kind of sameness to allow us to suppose that to things that are the same in this sense, all the same things belong. A Principle of Substitution, meanwhile, is prone to fail because the expressions we attempt to substitute stand in the wrong relation to each other: they are co-referential, but not (perhaps) synonymous. And a failure of substitution is to be traced to the referential opacity of the context in which substitution is attempted. Given ACT, an argument can succumb to the fallacy of accident without falling foul of a principle of substitution. For, if ACT is true, Archimedes and Archimedes + pale are accidentally the same, but not identical, so that the names “Archimedes” and “Archimedes + pale” do not name the identical thing. So an argument may commit the fallacy of accident; but in the presence of ACT, the relevant names name different things, and the question of substitution failures in a referentially opaque context simply does not arise. So we need not just reflection on the fallacy of accident, but also the “No ACT” assumption, if we are to be steered towards Aristotle’s non-sameness result through the topic of referential opacity in the way Dahl suggests. I have suggested that in the presence of ACT, cases of referential opacity drop away. At the same time, if we rule against ACT, as in (A), claims of referential opacity are all 20 Actually, rational animal is the essence of Archimedes’ essence, but only the essence* of Archimedes himself; see Chapter 3, n. 11. The distinction invites reservations about cross-level cases of sameness in substance; as already noted, to say that Archimedes and his essence have the same essence elides an important difference between the two cases.

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but a certainty. In particular, a claim of referential opacity allows us to blunt an obvious objection to the Supporting Argument. This is the objection. In assumption (B) of the Supporting Argument, we assume that the pale man—that is, in a world without ACT, the man who happens to be pale—has the composite essence, “what it is to be a pale man”. But, surely, in a world without ACT exactly one thing is the (contextually given) pale man, and that thing is identical with Archimedes (say); if so, they should have exactly the same essence. That is, if Archimedes has the plain vanilla essence, “what it is to be a man”, so should the man who happens to be pale, since Archimedes is that pale man. If Archimedes and the man who happens to be pale, a.k.a. the pale man, are identical, how is it that they have different essences, as the Supporting Argument requires? This objection to the Supporting Argument is the backbone of Aristotle’s original Pale Man Argument: as that Argument says, “man and pale man are the same, as they say, so that also the essence of pale man and the essence of man ” (a22–4, cf. [2] and [5] in Argument VII). So if we understand the mistake that undermines this move in the original Argument, then we will also have the needed countermeasures against the objection to the Supporting Argument. And if this is correct, then getting straight on how the original Argument goes wrong positions us in some way for reaching its conclusion by alternative means. So what is the appropriate response to the objection? The partisan of ACT will say that “what it is to be a man” and “what it is to be a pale man” are different essences, because the man and the pale man—Archimedes and Archimedes + pale (say)—are themselves non-identical. Dahl, on the other hand, will solve the riddle by appealing to referential opacity. The expression ‘ . . . has the essence, E’ is referentially opaque at subject-position: accordingly, even if Archimedes is the pale man in question, it is no contradiction to suppose that Archimedes has the essence “what it is to be a man”, but not the essence “what it is to be a pale man”, while conversely, the pale man has the second essence but not the first. On the story so far, if we adopt the “No ACT” rule in (A), we can replace the Aristotelian diagnosis21 of the failure of the Pale Man argument in terms of the “fallacy of accident” with a diagnosis of referential opacity. The appeal to referential opacity in turn allows us to blunt the objection, derived from the Pale Man Argument, to giving the pale man one essence (the composite essence, “what it is to be a pale man”) and the man in question another. A finding of referential opacity does not mandate that the pale man, and the man, get different essences, but it removes a sizeable objection to supposing that they do. And given the now untroubled agreement that the man who happens to be pale has the composite essence “what it is to be a pale man”, it follows by definition that the man who happens to be pale and his essence cannot be the same in substance—the very result the Pale Man Argument was intended to 21 I say “Aristotelian” rather than “Aristotle’s”, since Aristotle does not mention the fallacy of accident in Z6, although he does discuss it, for example, in the SE; see this chapter, n. 15.

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produce (if we assume with [C] that the sameness relation is sameness in substance, and not essential sameness as I have understood it, this chapter, n. 2). Even in failure, then, supposedly, with the help of the Supporting Argument, the Pale Man Argument achieves its goal. I am really not clear whether or not it is plausible that Aristotle himself intended us to follow this line of reasoning from the Pale Man Argument and his comments on its failure, to the new Supporting Argument that achieves the goals the original Argument failed to reach. Beyond doubts on this score, there are larger consequences of injecting referential opacity into Aristotle’s discussion of essence in the way sketched. Consider, for example, the question: What does the composite essence, “what it is to be a pale man”, belong to? If we think that Aristotle’s ontology does not include accidental compounds, then whatever the composite essence “what it is to be a pale man” does belong to, it will not belong to an accidental compound, the man + pale. At the same time, it does not belong to the man, Archimedes (say), if for no other reason, because he is only accidentally pale; and properly speaking, pace (B) above, not even to the pale man, if this is just Archimedes all over again. Instead, if I read Dahl right, it belongs to Archimedes (say), under the description, “pale man.” This gives us our next topic.

REFERENTIAL OPACITY AND THE THEORY OF ESSENCE

6 “Under a Description” As I understand Dahl’s reconstruction of the Pale Man argument, it is under the description “a pale man” that Archimedes (say) is the same in (number and) substance as the essence of a pale man.22 On a view of this kind, we are not committed to compound entities of the form, the man + pale, but only to compound descriptions, “the pale man” and the rest, and to the corresponding compound essences, the essence as of pale man, and the like. But there are no compound entities that these compound essences are the essences of. More generally, if the expression “the essence of the so-and-so” is referentially opaque in the position noted—as we are currently understanding this, if things have essences only under a description23—then strictly speaking, there is no entity—not just no pale man, but no entity whatsoever—that any essence is straightforwardly the essence of. 22 For the connection between “under a description” and Aristotle’s own jargon, see Anscombe (1979), 219, quoted by Cohen (2008). See also the remarks on qua-clauses in Lewis (1991), 207–10, and Freeland in Judson (1991). 23 As others have already pointed out (White (1972), 60), Aristotle does not draw the relevant scope distinctions needed for a formal distinction between de re and de dicto modal statements. It does not follow that we should deny him a doctrine of de re essentialism. For one argument that Aristotle is committed to such a doctrine, see Matthews (1990), 256–7. Another argument is this. In the Categories, Aristotle tells us that man is said of Archimedes, so that (in the jargon of Code and Grice) Archimedes Is a man—with no hint that this

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Archimedes under the description “man”, for example, will have an essence; but Archimedes himself will not. The view that a thing has an essence only under a given description, tells us that for Aristotle, there are no de re ascriptions of essences to things. On the contrary, on this showing, Aristotelian essentialism follows the pattern of Quine’s bicycling mathematician, who under the description “bicyclist” is essentially bipedal, and under the description “mathematician” essentially capable of solving quadratic equations (say)— but there is no place for the idea that he himself, not under any description, is essentially the one, or essentially the other, or indeed, essentially anything. All the metaphysical modalities are de dicto, and at best necessary truths, or analytic truths, or the like. Contrary to these claims, I will argue, there are seldom, if ever, grounds for finding opacity in Aristotle’s talk about essence.

7 Ownership versus Content Again As we have seen (Chapter 3, Section 3), Aristotle has two means for specifying an essence (ignoring for the moment a third, hybrid of the two): by way of its owner, and by way of its content. In Aristotle’s “what it is to be for-each-thing”, or “the for-each-thing to be”, both of which occur frequently, the demonstrative pronoun gives no guide as to content. The same, I suspect, is true where an essence is specified by means of a proper name: the essence, “what it is for-Socrates to be”, most likely is not an individual essence, Socrateity, but the general essence as of man.24 In these cases, how the owner of the essence is specified is no guide to the content of the essence. We may also specify an essence in a way that takes notice of its content. But it is not easy in a given case to tell whether the essence is specified via its owner—“what it is for (the) [or this] man to be”—or via its content, “what it is to be (a) man” (= the essence as of man), and often, the best hypothesis may be that Aristotle specifies an essence by way of ownership and content combined. In his (abbreviated) “the for-man to be”, for example, the owner is this man here, and the content of the essence in question is the (unarticulated) notion, man.25 Meanwhile, the ambiguities and uncertainties of the abbreviated expressions of essence are put to rest in a fully expanded designation, “what it is for man to be man”,26 where owner and content are both identified in turn. In the case of “to be for (a given) man”, perhaps, Aristotle’s term specifies simultaneously owner and content of the essence: its owner Is (a) man, and the kind, man, is the starting point for a full explication of its content. But if a specification of essence does holds true of Archimedes only under a description. But the kind, man, suitably unpacked, will yield Archimedes’ essence. So the connection is de re, and not relative to a description. Metaphysics D18, 1022a26–7, Z6, 1032a8; see Ross (1924) I, xcv, n. 1. For more on “the for-man to be”, see Chapter 3, n. 19, and for “the for-Socrates to be”, Chapter 3, Section 3. 26 See Chapter 3, n. 18. 24 25

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double duty in this way, then a change in how we specify the owner of the essence can disrupt the specification of its content. For example, if Archimedes is the man in question, replacing the term “man” by the name “Archimedes” in (i), (i)

“to be for (a? the?) man”,

yields the essence-designation, (ii), (ii)

“to be for Archimedes”,

which (I will suppose) gives no guide as to content; and if the man is also a musician, the designator, (iii), (iii)

“to be for (a? the?) musician”,

may seem to direct us to the wrong content altogether. In such cases we start with a context that, plausibly, directs us to content and owner alike; but switching designators brings about a shift in the containing context, so that it addresses the owner of the essence with, in (ii) no specification, or in (iii) a potentially misleading specification, of its content. These shifts attest to the disruption that switching designators can bring, but are they are a symptom of referential opacity? In fact, the shifts among (i), (ii), and (iii), attest above all to the ambiguity of designations of essence of the form “what it is for-X to be”, where the position occupied by the variable can contain either a name for the owner of the essence, or a designation of its content. So any evaluation of the moves among (i), (ii), and (iii), will require us first to disambiguate the entire context, to become (iv)

“what it is for-X [the owner] to be ç [the content]”.

There are now two positions inside a designation of essence at which to look for referential opacity.27 What, first, of the position devoted to giving the content of the essence? How does substitution fare in these cases? For example, we may imagine that all and only men are capable of laughter (to borrow Aristotle’s example). Still, we would not think that what it is to be a man (the essence as of man) is the same as what it is to be a laugher (the essence as of a laugher). Kinds are not sets, and while the set of men and the set of laughers are one and the same, man and the laugher are not the same kind. (Indeed, man is a kind but the laugher is not: it is a proprium, and unlike a kind it does not indicate the essence of a thing, Topics A5.) So even if man and the laugher are exemplified by exactly the same things, they are not identical. And if they are not identical, we cannot intersubstitute terms for the two, and require that the result name the same essence. This is a failure of identity, however, and in no way goes to show that the expression “what it is to be (a) man” is referentially opaque at the position indicated. 27 Assigning ownership to the first position and content to the second, as in (iv) above, is I suspect a friendly amendment to Dahl’s (1) (this chapter, Section 4, with n. 17), where what he alleges as opacity in the first position indicated will attach to the ascription of ownership, and in the second position to the assignment of content.

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But there is the prospect of a different sort of substitution: in expressions specifying an essence via its content, can we without penalty intersubstitute names for the identical essence? I take it to be fundamental to Aristotle’s theory of definition and essence that we can. For Aristotle, definition is the account of essence; and its job is to articulate out the concept being defined into its definitionally significant parts, where the result yields an identity between the original concept and its fully-articulated self. Again, Aristotle’s rules of addition and subtraction (5.3 above) depend on a principle of substitution (Chapter 4, Section 10). Equally, Aristotle emphasizes in the Topics that identity is a test for definition (“argument about definitions is mostly concerned with sameness and difference”, A5, 102a7–17, cf. Topics H2). So we should expect a general pattern in which the specification of an essence by way of its content will survive substitution among more or less refined names for the same content.28 We come, second, to ownership. Of course, if we fail to find referential opacity in connection with content, this will not be sufficient for denying it elsewhere. Nonetheless, I see no reason to think that our ascriptions of essence-ownership are referentially opaque, or that Aristotelian essences cannot make de re contact with their owners, rather than merely with things under a given description (Section 6). Indeed, whether in an ontology without ACT, or (even) in one with ACT in the appropriately Extended version, it will still hold that Archimedes has such-and-such an essence, just in case the greatest mathematician of antiquity has that very same essence.29 On this view, the argument against ACT is lost—no real loss, in my book—and also lost is the ability to show that some good comes from the bad argument, the Pale Man Argument, that Aristotle advances in favour of his non-sameness result. This milk is well and truly spilt; and as I see it, Aristotle acknowledges that the arguments are bad, and then simply moves on. It remains to test my account against answers to the questions still outstanding about the composite essence, “what it is to be (a) pale man”. What account can we give of its content? And given an essence with this content, who or what is its owner?

28 Aristotle himself warns us that intersubstitution of names for things that are accidentally the same is not invariably unproblematic; see the modal paradox at SE 6, 168a34–b10, and the epistemic paradox (“The Masked Man”) at SE 24, 179a26–b7, reviewed briefly in Section 4. In response, at SE 24, 179a37–39, cf. Physics ˆ 3, 202b14–16, he introduces a stronger principle, based on a relation of sameness in being which, for all he tells us, he thinks is impervious to counter-example. 29 On the Russellian account, we have (i) a has essence E, while (ii) for some x, x alone is ç and x = a (in ordinary English, “a is identical with the ç”), so that (iii) for some x, x alone is ç and x has essence E (in ordinary English, “The ç has essence E”). On standard ACT, the comparable inference fails. Thus, suppose that (iv) a is accidentally the same as a + ç, while (v) E belongs to a. We cannot conclude on the basis of (iv) and (v) that (vi) E belongs to a + ç, because the relation of accidental sameness is not strong enough to support the inference (this chapter, n. 28). But the inference is trivial in Extended ACT (Chapter 2, n. 28): as before, we suppose that (vii) a is accidentally the same as a + ç, while at the same time, (viii) E belongs to a. It follows harmlessly in Extended ACT that (ix) E belongs* to a + ç; indeed, (ix) is equivalent by definition (D4) of the accident*-of relation (Lewis (1991), 110) to the conjunction of (viii) and the claim, obtainable from (vii), that (ix) ç belongs to a. There is more on the different logical moves on display in these three arguments in Lewis (1991), 108–28.

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8 Composite Essences and Their Owners The case of a composite essence presents an obvious problem. We know that Archimedes is essentially a man, and is essentially such and such a kind of animal. We also know that Archimedes Has pallor, and that pallor Is a colour of a certain kind; but Archimedes himself is not essentially pale, and he is not essentially a colour of a certain kind. No single thing both Is essentially a man and Is such-and-such a kind of animal, and simultaneously Is pale and Is a colour of such-and-such a sort. Archimedes Is a man; his pallor Is a colour; but if we run the two facts together, we get the conjunction of two facts, about two things. There is, it seems, no one essence here of any one single thing. Aristotle himself admits to especial difficulty in talking about the essence of the pale man: 5.5 (from 3.11 above) But since there are also compounds with the other categories (kata tas allas kate¯gorias suntheta) (for there is something that underlies each, for example, quality and quantity and the when and the where and motion), we must consider whether there is an account of “the what it is to be” for each of these, and whether there belongs to these too “the what it is to be”, for example, to pale man. Let this [= pale man] have the name, cloak. What is “the for-cloak to be”? But to be sure this too is not one of the things said in virtue of itself . . . (Zeta 4, 1029b22–27)

In this passage, pale man is Aristotle’s example of a “compound with the other categories”, equipped with its own “underlying subject”, so it is plausibly an accidental compound. He stipulates towards the end of the passage that “cloak” designate the compound in question; and his last sentence sets up the idea that accidental compounds are not candidates for having an essence in the first-class sense. At the end of the chapter he allows a lower-class way in which accidental compounds do have an essence (1030b10–13, from 3.24 above [= 5.7 below], cf. 3.25). But he is otherwise of no help in the chapter in answering his own question: What is “the for-cloak to be”? But why does Aristotle hide behind the “cloak” manoeuvre in the first place? Recall that a first step in giving a full account of a thing’s essence is to find the lowest kind under which the thing falls: in the case of Archimedes, for example, Archimedes Is (a) man, so that Archimedes’s essence is “to be for (a) man”. But in the case of accidental compounds, the very designator “(the) pale man”, for example, suggests that there is no single genuine kind under which the thing falls. If, as in ACT, the pale man is a cross-categorial hybrid—a compound of items from different categories—then how is it proper to say that the pale man Is anything at all? Indeed, later in Metaphysics Aristotle devotes chapter Iota 9 to arguing that there is no kind, pale man, any more than male or female makes for a difference in kind, and casts a sceptical eye on the “cloak” manoeuvre: 5.6 Nor is there a differentia with respect to species between the pale man and the dark man, even if a single name is assigned . (I9, 1058b3–5)

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So the point of the “cloak” manoeuvre is to supply a “dummy” kind-term, so that the question whether accidental compounds have an essence is not ruled out from the start.30 But the fact that there is no single, unified essence need not, in Aristotle’s scheme of things, show that there is no essence at all. On the contrary, he may well think that the conjunction of two “first-class” essences will itself be an essence, albeit in some suitably second-class way. Suppose, then, that “what it is to be a pale man” is an essence in this second-class way. Can there be some concrete particular, the pale man, that owns this essence? The particular in question cannot be Archimedes, nor can it be the pale man, if (the Russellian reading) this is just Archimedes all over again—his essence is just “what it is to be (a) man”. And there is no entity, Archimedes, under the description, “the pale man”. There is, of course, the phasal entity, Archimedes for the time that he is pale; or the modal segment of Archimedes, Archimedes in the worlds in which he is pale. But there is considerably more Aristotelian warrant for thinking that we are dealing instead with the accidental compound, Archimedes + pale. Suppose, then, that Aristotle’s ontology includes accidental compounds, like Archimedes + pale. Then one set of modal facts is anchored in the parent substance, Archimedes—he is essentially a man—and the other in the accident half of the compound—pallor is essentially a colour. But because Archimedes + pale is itself a compound, the two halves of the compound essence each have something to latch on to, so that the conjunction of entities in the essence fits the conjunction of entities in the accidental compound.

9 Conclusion I began (Section 1) by noting Aristotle’s doctrine of the grades of being and the different notions of essence and definition that go with the items of different grades. With the items that are assigned the top grade of being—the (primary) substances—are associated the top notions of definition and essence. Entities of lesser grade—those, it turns out, that have a lesser degree of unity—will have an essence in a corresponding lower-grade way. “This much is plain”, says Aristotle: 5.7 (= 3.24 above) . . . what primarily and without qualification is definition and essence, is of the substances. Even so, they are similarly of the other things too, only not primarily. (b7) For it is not necessary, if we stipulate this, that a definition of this be whatever term signifies the same as a

30 Notice that the “cloak” manoeuvre seems to rule out an account of the essence of the pale man that might tempt us today. Aristotle appears to worry that if the pale man is a compound of items from different categories, it is hard to see how the pale man Is anything at all. Suppose, however, we set aside ACT, and return instead to the Russellian reading of “the pale man”, adjusting for the relative scopes of the definite description and of the question-word: What? Giving the definite description wide scope, we may be asking, of the x such that x is uniquely pale and a man, What Is x? (Answer: he is a man.) But while this avoids our difficulties over Izzing, it does not take us to where we need—it is not a route to the required composite essence.

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formula, but a certain kind of formula: and this if it is of one thing . . . in as many ways as one is said; (b10) but one is said like being: being signifies on the one hand some this, and on the other quantity, or some quality. (b12) Accordingly, there will be an account and a definition even of the pale man, but in a different way of the pale too [= pallor] and of the substance [= Archimedes (say)]. (Zeta 4, 1030b4–13)

Archimedes + pale, then, has a lesser degree of unity than its two constituents, Archimedes and pallor, have separately. Similarly, the composite essence “what it is to be (a) pale man” is put together out of “what it is to be pale” and “what it is to be (a) man”, and it has a lesser degree of unity than either of its constituents by themselves. But it has exactly the right degree of unity to be partnered with its owner, the accidental compound, Archimedes + pale. Aristotle opens the discussion of essence in Zeta 6 by citing received views about the sameness of things with their essence and with their substance (5.1 above, repeated here): 5.1 Whether each thing and its essence are the same or different, needs to be looked into. For it is somewhat relevant to the study of substance: for (first) (te, a17) each thing is thought to be not other than its own substance, and (second) (kai, a18) its essence is said to be each thing’s substance. (1031a15–18)

One sign that these lines rest on the philosophical tradition, innocent to this point of any corrections or refinements we may think they need, is the absence of a distinction between different varieties of sameness (see this chapter, n. 2), and between the different cases in which the different relations are appropriate. To repair these deficiencies, Aristotle is anxious to distinguish the relation of essential sameness that holds between a thing that is suitably primary—one of the “things spoken of in virtue of themselves”—and its essence, from the lesser relation between one of the “things spoken of per accidens”—as I see it, an accidental compound like the pale man—and its composite essence. He begins with arguments which he himself admits are unsuccessful, purporting to show that the pale man and its essence are not essentially the same and so not identical. Immediately after, the arguments turn positive. Aristotle looks to a fresh set of entities, which he argues are indeed the same as their essence. The wrong kind of sameness no longer intervenes, and he expresses no reservations of the kind attached to the Pale Man argument and its immediate successor earlier in the chapter. Things that are suitably primary—Platonic forms, for example—will be essentially the same as and, hence (as I understand it), identical with their essences. As the engagement with Plato shows, this and the arguments that follow still stop short of “partisan” Aristotelian doctrine—but the quality of the arguments is not subject to criticism by Aristotle. These arguments are the subject of Chapter 6.

6 Plato as Friend: Is There Room for Plato in an Aristotelian Theory of Essence? It is not obvious why Aristotle should have chosen as his illustration of the identity of a kath’ hauto term with its essence a class of kath’ hauto terms which he does not believe in, the Ideas. The reason doubtless is that the argument in a29–b11 conveys a covert criticism of the ideal theory. Ross (1924) II, 177, on 1031a29 It is unfortunate that he has thus improved the occasion by a fling at the Platonic theory, but his own view, that terms kath’ hauta are identical with their essences, appears clearly enough. Ross (1924) I, xcix The reasoning of the chapter is weak, and to an unusual degree verbal and dialectical. Its meaning is rendered difficult to seize by the fact[s] that . . . the argument for the identity of “self-dependent terms” with their essence is conducted with reference to one particular kind of supposed self-dependent terms, the Platonic forms. Ross (1924) I, xcix

In Metaphysics Zeta 4 and 5, as we have seen, Aristotle’s discussion of how the notion of essence contributes to the project of defining substance (or the substance of a thing), is concerned largely with determining (in a suitably ontology-neutral way) what things have an essence, in particular, what level of things have an essence. In both chapters, Aristotle presses an exclusive notion of essence, belonging only to those things that are suitably primary, even while he allows that other, more relaxed cases also exist. The interest in levels persists in Zeta 6. The main thrust of the chapter is to argue in favour of a broadly structural point about essences: for a certain privileged class of

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entities—primary substances, which are “said in virtue of themselves”—each thing is essentially the same as—that is, I shall suppose, it is identical with—its essence.1 We can perhaps see this identity as a condition on what properly is to count as an essence, or as the essence of something, in the strict sense2 (equally, it will be a condition on what things strictly speaking are to count as having an essence). At a certain level we reach a set of entities that are fundamental, so that to the question, What is the essence of this item?, the only possible answer is: itself. But the identity result that is the main topic of the chapter will not hold for the wrong cases of essence, at the wrong level (Chapter 5). It remains to show that the result does hold for what he will say are the primary cases. The distinction between primary and secondary is a recurring feature of Aristotle’s own metaphysical theory. But there is clear precedent for the distinction in Plato, and the distinction is central to the discussion of essence in Zeta 6, which remains at the “non-partisan” level, with Plato as the representative of the received tradition. As Aristotle thinks of the philosophical tradition, there exist fundamental cases of essence, which form a metaphysical and definitional base on which other, reduced cases are built.3 The distinction between primary and secondary is reflected in the very sequence of the arguments that pass under review in the first half of Zeta 6. Aristotle sketches an initial sameness argument in the opening lines of the chapter (the Basic Argument, 1031a15–18), and appends a brief excursus. The Basic Argument itself is preliminary, even dialectical, and for this reason, it can be vague about two key issues. In these lines, nothing is said to clarify either the scope of the sameness thesis, or the variety of sameness involved: 6.1 (= 5.1 above). Whether each thing and its essence are the same or different, needs to be looked into. For it is somewhat relevant to the study of substance: for (first) (te, a17) each thing is thought to be not other than its own substance, and (second) (kai, a18) its essence is said to be each thing’s substance. (1031a15–18)

The Basic Argument in 6.1 reports how various received opinions point in the direction of some sameness conclusion or other. The Argument is innocent of the distinction between primary and secondary cases of essence, and of the distinction between different kinds of sameness Aristotle will introduce later in the chapter; instead, as I see it, the Basic Argument is studiously vague as to the needed details.

1 It bears repeating that the variety of sameness Aristotle intends is left unclear at the opening of Z6, but in the wake of the Pale Man arguments at 1031a19–28, where an unwanted, weaker notion is excluded, he comes to settle on essential sameness; this I take it is equivalent to our relation of identity with a restriction to primary entities; see Chapter 5, n. 2. As before, for an opposing view see Dahl (2003), Charles (2010), and this chapter, n. 57. 2 See Wedin (2000), Chapter VII. 3 The substance-of relation, the definition-of relation, and the essence-of relation are all three subject to variation in degree; see Lewis (1984). For how the notion of essence is articulated within Aristotle’s own ontology, see Loux (1991), chapter 7, and Lewis (1995) 1999, 529.

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The excursus that follows (1031a19–28, 5.1 above) is the Pale Man Argument that is the subject of Chapter 5; as we saw, the Argument takes up the question whether and in what way an accidental compound, the pale man, may be the same as its essence. Since the pale man is not a primary entity in Aristotle’s (perhaps in anyone’s) ontology, the argument contributes usefully to paring away the items that have an essence in only a reduced sense, and are not identical with their essence. There follows the Elaborated Argument (a28ff.), where Aristotle fixes on a class of items that, in their owner, Plato’s, ontology, do count as primary and, in consequence, (a) genuinely enjoy an essence in the primary sense, and (b) are duly identical with their essences. For us, the main interest will be in what appears to be the “arm’s length” strategy Aristotle uses in arguing for these last conclusions. The Elaborated Argument is indirect, in the obvious sense that it proceeds by reductio of the opposing view, that certain primary substances, which are “said in virtue of themselves”, are non-identical with their essence.4 But the argument is also indirect, or perhaps oblique, in a way that has challenged some of Aristotle’s commentators. For in the Elaborated Argument, as elsewhere in Zeta, he proceeds on the basis of the views of others, even while arguing for conclusions that are central to his own, Aristotelian project. Aristotle frames his argument, not propria persona, but speaking on behalf of the Platonist, for whom the things “said in virtue of themselves” will be Platonic forms. Must not this resort to Platonism, however temporary, restrict or otherwise undercut Aristotle’s arguments? On perhaps the least optimistic appraisal, Aristotle’s arguments are impure, and rest essentially on Platonic assumptions that he himself does not accept.5 But if he does not accept one or more assumptions needed for his arguments, how can the arguments increase his confidence in their conclusion? Alternatively, Aristotle may have some other, ulterior motive—perhaps a covert criticism of Plato, as Ross and others suggest.6 If his arguments have Plato as a target, 4 Strictly, the opposing view is that x and its essence are “not essentially the same”: if the two are not essentially the same, but they are both primary, it follows (if the equivalence in Chapter 5, n. 2 is correct) that they are non-identical. (At the same time, if as Aristotle’s reductio suggests, it results in the end that x and its essence are identical, the restriction to primary entities ensures that they are also essentially the same.) 5 Notes on Zeta; see Section 2. 6 According to Ross (1924) II, 177, Aristotle has in mind the “covert criticism” of Plato that because the Platonic form is neither a particular good thing nor the essence of good, and because insuperable difficulties arise if we “separate” the form from the essence of good, we should make do with essences and stop believing in forms. Against this, however, Aristotle may well think that the essence of particular good things makes the Platonic form superfluous; but he has in mind here the different point that even granting that the form of good exists, it, the form, cannot in turn have some distinct entity as its essence. That is, he is concerned with whether (and on what terms) the form itself can have an essence, not whether there exists an essence of particular good things. The second option tried out in Bostock (1994), 107–8, follows Ross. Bostock says explicitly that Aristotle is concerned with the essence of all good things, and not (as appears at first sight) with the essence of the form, cf. this chapter, n. 21. Finally, it is not clear whether, in Ross’s view, the very same argument that establishes Aristotle’s sameness result also refutes the separation of (Platonic) form and essence and promotes the case of essences over that of (Platonic) forms. It may well be that the criticism Ross envisions is only incidental to the argument Aristotle gives: if so, the criticism has the same status as the objections Aristotle himself levels against Plato at b15–18, which do not even pretend to be simultaneously a proof of the sameness result.

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and if the Platonic assumptions Aristotle himself does not accept are discharged at the end, then his arguments start impure but end with purity regained. But the path to purity is not easy. One problem is technical. On some accounts, apparently, the very views of Plato Aristotle means to criticize are essential to the argument for his, Aristotle’s, own conclusion: but if some Platonic assumptions remain undischarged, then the argument for sameness is impure after all.7 At the same time, it is not clear that criticism is in Aristotle’s mind at all, at least not for the duration of his arguments for identity. Aristotle seems to say that his identity result holds whether or not (Platonic) forms exist, but all the more if they do:8 but how, if Plato is a target, can Aristotle in the same breath claim him as an ally? Recent commentators have been kinder to Aristotle. In this gentler vein, I shall argue that his arguments are pure, and essentially contain no assumptions that Aristotle himself cannot accept. On this view, as we shall see, the reference to Platonic forms is not essential to his arguments.9 Nor, in these arguments at least, does he have any polemical point in mind. On the contrary, Aristotle co-opts Plato in the passage in the way he co-opts other philosophers elsewhere, with a view to establishing broad metaphysical principles that hold across ontologies. In the search for “big tent” principles that are ontologically neutral in this way, he can appeal for support not just to Plato, but to Democritus, for example (Metaphysics Eta 2), to Anaxagoras (the treatment of nous in De Anima ˆ4), or as I argue in other chapters, in Zeta itself to one of his own other selves in the Categories, for example (Zeta 1 and, somewhat differently, Zeta 3, where the Physics is also relevant), or in the De Sophisticis Elenchis (Zeta 5), or in the Analytics (Zeta 17)—all places where he stops well short of the partisan views towards which he is tending in Zeta. In this non-partisan spirit, as I hope to show, there is room even for Plato in an Aristotelian theory of essence.

7 It is not ruled out on logical grounds that one and the same reductio argument should simultaneously refute Plato and establish Aristotle’s desired conclusion about the relation of a thing to its essence: if the target Platonic assumption is (an instance of) the negation of the desired sameness result, and if everything else goes right, the desired result can be obtained by negating the target Platonic assumption, with no special Platonic assumptions remaining. In practice, however, not all the special Platonic assumptions are discharged, and the argument remains impure: see the discussion of Cherniss (1944) in Section 2. A different attempt at purity regained, in connection with the argument involving “severance” at b3ff., appears in Frede and Patzig (1988) II; see this chapter, n. 38. 8 So, perhaps, 1031b14–15; see Section 7. 9 Compare, for example, the third option tried out in Bostock (1994), 108: Aristotle hopes that his argument “will establish that, where X is a fundamental substance as specified, then X and the essence of X must be identical, whatever the fundamental substances turn out to be” (his emphasis). What place is left for Plato, if this last view is correct? Plato can be included, consistently with the requirements for purity, in the way nicely summarized by Burnyeat (2001), 27: “ . . . the argument will serve his purpose provided that the only feature of the Forms used to derive the conclusion is that, by hypothesis, they are primary things which are in their own right what they are said to be. The conclusion then stands whatever the baseline of one’s ontology may be.” On some readings, including Burnyeat’s, this is much what Aristotle himself says at 1031b14–15 (included in 6.8 below), but the translation and interpretation of the passage is under dispute; see Section 7. Other advocates of purity include Dancy (1975), 100, Wedin (2000), and Lewis (2003). The “big tent” view advocated here has its ancestry in Code’s “general metaphysics”, Code (1997).

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PURITY IN THE ENGAGEMENT WITH PLATO

1 The Basic Argument for Sameness Plato—more exactly, a Platonic ontology, since Plato himself is nowhere mentioned by name—makes its official appearance in the discussion of essence midway through Zeta 6; but Plato’s influence is at work throughout the segment on essence, if (as I suspect) he is the author of the assumption that governs the segment, that the substance of a thing is its essence:10 x is the substance of y if and only if x is the essence of y. The Governing Assumption in Zeta 4–6

The Governing Assumption is one of the four received opinions reported in Zeta 3 that shape Zeta’s inquiry into substance (1.4 above): it is this assumption that motivated the inquiry into essence in the first place (see also Zeta 4, 1029b1–3, = 3.1 above). The assumption is deeply entrenched in Aristotle’s own metaphysical theory: in addition to its reappearance at the beginning of Zeta 6 (1031a18) and twice again in the same chapter, it reappears three or four times more elsewhere in Zeta–Eta.11 Burnyeat is at pains to note that Aristotle does not straightforwardly assert the Governing Assumption in Zeta 6.12 His point that “the idea remains an unasserted hypothesis” in the chapter, however, may be misplaced: in ordinary-language contexts, “If P, then Q”, can often be a compressed form of Modus Ponens: “If P, then Q; and P; therefore, Q.”13 My own view is that Aristotle will think the Governing Assumption acceptable in any metaphysical theory that recognizes the notions of the essence and the substance of a thing. So put the Assumption on the “big tent” side of the ledger— consistent with its being part of the discussion that is conducted within a framework of received views, rather than in Aristotle’s own partisan terms.

10 On the question of Platonic authorship, see Metaphysics M5, 1080a1, cf. A6, 988a8–11, 7, 988b4–5. At M5, 1079b15–17, Aristotle says that (contrary to Plato?) Plato’s forms cannot be the substances of sensibles. And some of the arguments in Z14 take Plato to task on the related idea that certain forms are the substance of other forms (“the form man is not accidentally composed of animal”, 1039b7–9, 9–10, 12–13, 15–16, = 9.8, 9.9, and 9.10 below); he suggests at the end of the chapter that similar arguments apply to the relation between (Platonic) forms and sensibles. 11 See also the apparent attribution to Plato at Z6, 1031b2–3 (included in 6.2 below), and yet a third appearance later in Z6 at b31–2. The assumption is also stated explicitly in Z10 and 13, in H1, and perhaps also in Z7: Z10, 1035b14–16, Z13, 1038b14–15 (from 8.7 below), Z7, 1032b1–2, see also the unqualified assertion in H1, 1042a17. 12 Burnyeat (2001), 26; see also Frede and Patzig (1988) II, 88, who add that perhaps the Platonic antecedents of the idea make any proof of it superfluous. Presumably, then, on the Frede–Patzig view, Aristotle endorses the Assumption, while Burnyeat holds that he abstains with respect to it. But it is hard to see how Aristotle can hold the Assumption at arm’s length in Z6, or anywhere else in the segment on essence (unless—which I doubt—for purposes of reductio), given his statement of his agenda for the bulk of Zeta at the beginning of Z3 (1.4 above). 13 Here I appropriate a point made in a different connection by Gareth Matthews (the point is also recognized in LSJ s.v. ei, BVI, and eiper, II).

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The Governing Assumption is a premiss in the Basic Argument, sketched at the very beginning of Zeta 6, which Aristotle suggests may or may not point to the sameness in some sense of a thing with its essence. This is 6.1 above, repeated here: 6.1 Whether each thing and its essence are the same or different, needs to be looked into. For it is somewhat relevant to the study of substance: for (first) (te, a17) each thing is thought to be not other than its own substance, and (second) (kai, a18) its essence is said to be each thing’s substance.

That is to say: if as people commonly suppose, (i), each thing is the same as its substance, and if as they also think, (ii), a thing’s substance is also its essence (the Governing Assumption), then on the opinions of record at any rate, it follows that (iii) each thing and its essence are the same. The argument as a whole constitutes Aristotle’s Basic Argument for the sameness in some sense of a thing with its essence. As we shall see, however, there is work to be done before the conclusion can be stated in a form that Aristotle will find acceptable. His primary goal in the chapter is to establish the identity in certain cases of a thing with its essence. While he has reasons of theory for maintaining a sameness result in this more refined form, these interests emerge at best indirectly, and only in the second half of his discussion.14 Instead, at the beginning of the chapter, as 6.1 above shows, he is anxious to justify inclusion of the topic at this point in Zeta, by pointing to its connection even in its rough and ready form with the larger inquiry into substance.15 One point above all stands out in the Basic Argument. The argument is clearly non-partisan: both the Governing Assumption, (ii), and the opening premiss, (i), are cited anonymously, as “received opinion”, and not as fact that Aristotle himself is ready 14 See Bostock (1994), 112–13, and especially Loux (1991), chapter 3. I have in mind Aristotle’s desire to avoid an infinite regress, together with the reasons he gives elsewhere for finding a regress objectionable: if an essence is infinitely long, then it will have no cognitive value, An. Po. I.22, 82b37–83a1, cf. 84a25–26; see also Metaphysics Æ2, 994b16–18 with Alexander in Met. 160.30–161.1. On Aristotle’s antipathy in general to infinite regresses, see also Kung (1981), 255, with nn. 48 and 49. 15 These efforts to highlight the connection with substance are noteworthy, in view of indications that Z6 is, in origin at least, “semi-detached” from the surrounding discussion in Z4–5 and its continuation in Z10 (supposing with the current orthodoxy that Z.7–9 are themselves an addition); see Burnyeat (2001), 26. Ironically, Aristotle’s very efforts in the Basic Argument to secure relevance for his question about sameness have been thought to make the question itself pointless. According to the redundancy objection, given (i) and (ii) above in the main text as premisses, it appears to follow trivially that each thing and its essence are the same. How can this conclusion, so easily obtained, require the kind of inquiry Aristotle proposes in his first sentence and carries out in exquisite detail in the remainder of the chapter? Pelletier (1979), 289, suggests that we can avoid pointlessness, if in contrast to the contemporary notion of identity, the relation of sameness that Aristotle thinks holds between a thing and its essence is not transitive: on this view, the remainder of the chapter has point, only because the opening argument is invalid. A less drastic response to the redundancy objection is that Aristotle quotes the premisses of the Basic Argument as received opinion, not fact: the conclusion to the argument is not assured, until the premisses are on a more solid footing. More than this, both premiss (i), that each thing is the same as its substance, and the conclusion, (iii), that each thing and its essence are the same, are provisional in nature (see two paragraphs below in the main text); formulating each in a form Aristotle will find acceptable, I take it, is part of the point of the Elaboration of the Argument conducted in Plato’s name at a28–b3 (6.2 below).

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to endorse. Later in the chapter, in what amounts to an elaboration of the Basic Argument that he puts into Plato’s mouth at a28ff., Aristotle comes closer to naming names. But (I will argue) he does more than offer an argument that Plato might find acceptable. The later, elaborated argument will be one that, in essentials, he and Plato can both accept in support of the conclusion, subject now to the needed refinements, that each thing is not other than its essence. Accordingly, the basis of the Basic Argument in received views leaves room for the thought that the Argument is also, in a certain way, provisional. In order to find an argument that Aristotle and his ally of the moment, Plato, will find acceptable, the opening premiss, (i), and the conclusion, (iii), alike must be restricted to entities that are suitably primary. At the same time, the opening claim about substance and sameness in (i), where the variety of sameness is left vague, can be firmed up into an identity claim: Where x is the substance of y and y is a primary substance, x = y.16 The Identity Premiss Similar transformations apply to the conclusion, (iii), which is sharpened to become the principal conclusion of the chapter, that in the case of primary substances at least, a thing is identical with its essence: Where x is the essence of y and y is a primary substance,17 x = y. The Identity Result In the later Elaboration of the Basic Argument, Aristotle argues in favour of the Identity Result for the case where the primary substances in question are Platonic forms; on certain reasonable assumptions, including (again) the Governing Assumption, that a thing’s substance is also its essence, it transpires that Platonic forms are indeed identical with their essences. Aristotle makes common cause with the Platonist in part, I suspect, because he sees Plato as one of the authorities for the Governing Assumption. More than this, however, I suggest, he thinks he also has Plato’s support for the opening premiss, (i), that each (primary) thing is not other than its substance—if Plato is not to be enlisted as one of the sponsors of the Basic Argument as a whole.18 16 For the use of identity here and in the Identity Result immediately following in the main text, see this chapter, n. 1. 17 The stipulation that y be suitably primary is not present in the Basic Argument, which is preliminary to the more detailed work later in the chapter, where Aristotle will want to differentiate the primary cases in which the Identity Result holds from other cases in which it does not. But the needed restriction is signposted almost immediately with his “on the one hand” (men) at 1031a19, answered at a28 (“on the other hand”, de), where primary cases are introduced. Notably, Aristotle does not in this chapter explain what in his own “official” theory will count as a primary substance. (For speculation about the reason for his reticence, see the comments towards the end of Section 2.) 18 Burnyeat (2001), 26, thinks the precedent for (i) is in the Organon at An. Po. A21, 83a24–32. I do not know if he would agree in finding Plato to be a common ancestor for the Organon passage and for Metaphysics Z6 alike.

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Here is an informal sketch of how the shared ideas underlying the Identity Premiss will go (Aristotle supplies the materials for a more formal defence of the Premiss in the Elaborated Argument; Section 2). We start with the class of things “said in virtue of themselves”—items that can be defined and explained without reference to some distinct entity. Among these, in turn, are included the primary substances, which have no nature or substance prior to them. For Plato and Aristotle alike, this is part of what it means for something to be a primary substance. How, then, can there be a substance of a primary substance? In general, if one thing is the substance of some distinct second thing, the first must be prior to the second, in at least the sense of “prior” already before us. So there can be the substance of a primary substance, only if the original substance and the substance of that substance are identical, so that neither is prior to the other. For a more formal look at these ideas we must turn to the details of the text in the middle of Zeta 6. As we shall see, the overt engagement with Plato in this part of the chapter constitutes a much more elaborate argument in support of the Identity Thesis, in place of the Basic Argument with which the chapter began. Aristotle’s Elaborated Argument, and the support lent to it by Plato’s theory of forms, is our next topic.

2 Plato and the Elaboration of the Basic Argument Aristotle initiates the alliance with Plato in the following terms: 6.2 But in the case of things said in virtue of themselves, is it necessary that they are the same , (a29) for example, if there are certain substances than which there are no other substances or natures prior, of the kind that some say the forms (ideas) are? (a31) For if the good itself and the for-good to be (to agatho¯i einai) will be different, and animal and the for-animal , and the for-being and being ,19 (b1) (first) (te) there will be other substances and natures and forms (ideas) in addition to the ones recognized [sc. in Plato’s theory], and (second) (kai) these will be prior and more substances [Jaeger’s text], if essence is substance. (1031a28–b3)

We are to suppose that there exists a class of entities described as “substances than which there are no other substances or natures prior”—primary substances, for short—and that examples of these include Plato’s forms. Primary substances, in turn, are examples of “things said in virtue of themselves”. Aristotle does not say which the primary substances are in his own ontology: at this stage, he borrows his examples from Plato.20 19 For the “itself ” (a marker for Platonic forms) supplied twice over in angle brackets at a32, see Ross (1924) II, 177. 20 Aristotle sidesteps the question whether things other than primary substances are “said in virtue of themselves”: so of the entities said to be per se at ˜7, 1017a22–3, he does not here explain that individual substances (which in the Metaphysics in contrast to the Categories are not primary substances) are not subject to the identity result of Z6 (see Lewis (1984) and this chapter, n. 57); accidents, however, which also are per se entities according to ˜7, apparently are identical with their essences, 1031b22–28. He also ignores the possibility that there exist primary substances other than Plato’s forms, namely his own (Aristotelian) forms. I say more on

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Now for the details of the argument. Let G be the Platonic form of the good, and suppose that G is essentially good: reproducing Aristotle’s term for the essence in question, (1)

The for-good to be (to agatho¯i einai) is the essence of G.21

A

Aristotle’s argument takes aim at the view that, contrary to the Platonic version of the Identity Result, (2)

G 6¼ the for-good to be.22

A

Against the targeted view, he sets down first a fundamental assumption about substance: (3) For each substance in a certain class of substances (in fact, the “primary” substances), there is no substance or nature prior to that substance. (a29) A Next comes an assumption central to the Platonic theory of forms, along with a consequence: (4)

Platonic forms are primary substances of the kind mentioned in (3). (a29–31) A

In particular, (5) There is no substance or nature (a29–31), and no Platonic form (b1–2), which is prior to and more of a substance than G. From (3) and (4). Aristotle also tacitly helps himself to an assumption featuring the relation, “x is the substance of y”, together with notions of priority and of the degrees of substance that (presumably) he and Plato will share: (6) x is the substance of y and y 6¼ x, only if x is prior to y and more of a substance than y. A In particular, (7) The for-good to be is the substance of G and G 6¼ the for-good to be, only if the for-good to be is prior to and more of a substance than G. A final assumption connects the essence-of and substance-of relations in the familiar way: the benefits of favouring Plato’s forms while avoiding reference to (Aristotelian) form and matter at the end of this section. 21 Surprisingly, Aristotle does not explicitly state (1), although what I take to be its denial (= [15] in Section 4) appears later at 1031b5–6. It is likely that Aristotle’s term for the essence in question serves as an implicit assertion of (1): “the for-good to be” [to agatho¯i einai] may convey simultaneously the ownership of the essence [“what it is for the good to be ”], as well as its content [“what it is to be good”]. (For more on the ownership-content distinction in this context, see Chapter 3, Section 3.) As to ownership, my (1) runs counter to Bostock (1994), 108, who argues that the essence in question is the essence of—that is, belonging to—a good thing—that is, any good thing, see this chapter, n. 6—rather than the essence that belongs to G itself. 22 See this chapter, n. 4.

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(8) x is the essence of y if and only if x is the substance of y. (1031b2–3, cf. a18, b31–2) The Governing Assumption

As we have seen, the Governing Assumption appears in Zeta 3 as one of the received opinions that shape Zeta’s inquiry into substance.23 We can now proceed against the targeted view (2), that G 6¼ the for-good to be. First, given (1) and (8), we have (9)

The for-good to be is the substance of G.

Given (9) and the non-identity in (2) together with the priority principle, (7), it follows that (10) There is some substance or nature or Platonic form [in fact, the for-good to be] that is prior to G and more of a substance than G. (b1–3) (5) and (10) are the two halves of a contradiction: (11) There both is and is not a substance or nature or Platonic form that is prior to G and more of a substance than G. By reductio on (2), then, (12)

The for-good to be = G,

as required.24 On the present account, Aristotle co-opts Plato in support of his own Identity Result, by relying on a cluster of assumptions most or all of which are thoroughly at home in a Platonic theory of forms. But why should the non-Platonist care, given that the desired Result rests even in part on assumptions that are local to Plato’s theory? Assumption (6), about priority and the degrees of substance, is not at issue here; it formalizes views about what it means for a thing to be a substance, or for one thing to be the substance of another, and it is at least as much part of Aristotle’s theory as it is of Plato’s.25 Aristotle and Plato can also agree to the underlying assumption, (3), that a primary substance has nothing prior to it. From (3) together with the introduction of Platonic forms in (4), Aristotle derives the Platonic thesis, (5), that there is no substance or nature prior to a Platonic form, or more a substance than a Platonic form is. But Aristotle can plausibly argue that (5) holds mutatis mutandis in any ontology that 23

Z3, 1028b33–6 (1.4 above), cf. Z4, 1029b1–3 (3.1 above); see also the opening paragraph of Section 1 and this chapter, n. 11. 24 Again, see this chapter, n. 4. 25 See Section 1. Arguably, both assumptions are applications of a general causal principle (“A cause is equal to or greater than its effect”) that Aristotle and Plato alike accept without question. (For the application to Plato, imagine that Plato will think that his Forms are the primary substances, and that the sensibles that depend on them are substances to a lesser degree.) The causal principle is discussed in Lloyd (1976).

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includes a class of primary substances, which are “said in virtue of themselves”, however the various ontologies may differ in other respects. In this sense, the reference to Platonic forms in (1) and (4) is inessential to the argument. In principle, Aristotle is free to replace both with assumptions instantiating to his own choice for entities that are suitably primary, or even with assumptions that do not instantiate to any particular set of entities at all.26 The one remaining assumption is (8), which is the lead assumption of the entire segment. It follows that Plato is present in the argument in only a very weak sense. The premiss-set to the argument, as it stands, includes assumptions that mention Platonic forms and that are, strictly, unacceptable to Aristotle on that account. But the use of Plato’s forms is not essential to the argument, and the reference to Plato comes down to (what is here) the triviality that while Aristotle and Plato agree over the identity of things that are suitably primary with their essences, they disagree over the existence or otherwise of Platonic forms. On this story, the engagement with Plato is pure, and stops well this side of compromise. But purity is not Aristotle’s only option. It is not beyond credibility, for example, that he should quote Plato approvingly for a conclusion that can be reached only on the basis of assumptions Aristotle himself rejects: such a use of Plato would be impure. An interpretation of this sort appears in Notes on Zeta, where the assumption that essence is substance—on the view I have been pressing, yet another statement of the Governing Assumption, that “its essence is said to be each thing’s substance”, from the beginning of the chapter (6.1 above)—is taken to be a statement of Platonic separation.27 On this reading, according to Notes, “[T]he argument uses Platonic machinery to extract a conclusion the Platonist will have to accept if he once says that Form and essence are distinct.” Notably, however, this account lacks an explanation of what about the argument recommends its conclusion to Aristotle, given the (on his terms) wildly Platonic slant of its assumptions.28 Yet a third kind of account attempts to meet the difficulties of impurity by supposing that while the argument apparently begins in impurity, this is only as a means to purity regained at the end. On a view of this sort, the assumptions essential to the initial steps of the argument include an assumption that Aristotle rejects, but is present there only because it is the target of a reductio argument, and will eventually be discharged.29 An account of the argument along these lines appears in Cherniss (1944), 334–6. Cherniss holds that the argument is simultaneously an attack on Platonic separation and 26

With this conclusion, compare the quotation from Burnyeat (2001), this chapter, n. 9. Notes on Zeta, on 1031a31–b3. The notetaker on this occasion is identified as Burnyeat: the later views of Burnyeat by himself on issues of purity in Burnyeat (2001) are quite different. 28 “Arguing from false premisses” is discussed without enthusiasm by Aristotle in the Topics E11: it is identified as a fourth kind of fallacious argument at 162b11–15. 29 For the record, this cannot be the view of Notes (cited in the previous paragraph in the main text), for they deny that the argument is intended as a reductio of Plato’s views; in our terms, then, their account is straightforwardly impure. 27

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a proof of the identity of a thing with its essence. According to the argument as he reconstructs it, if (a) a thing and its essence are not identical, and if (b) essence is substance, then (c) there exists a set of forms prior to the Platonic forms generally recognized. Since Plato must find this result unacceptable, he must (if Cherniss is right) both reject separation and embrace Aristotle’s identity thesis. This account is troubled on at least two scores. First, it requires an unlikely gloss on (b), identical to that found in Notes two paragraphs back: by “essence is substance”, according to Cherniss, Aristotle means that an essence is a separate substance; more fully, it is itself a form and separate from what it is the essence of, in the way that the usual run of Platonic forms supposedly are both the essence of and separate from the things that fall under them. But there is no explicit reference to Platonic separation in this part of the text.30 At the same time, as before, it is hard to see a covert reference to separation in the claim that essence is substance, which is more naturally taken as one of the assumptions that guide the argument of Zeta.31 It is also hard to see how on Cherniss’s account the argument achieves its twin goals of refuting separation while establishing identity. Since on Cherniss’s view Aristotle’s intentions are hostile, Aristotle will use the falsity of the conclusion (c) to reject the assumption (b) that forms are separate. Suppose we grant Aristotle this anti-Platonic point, so that (b) goes. How can he simultaneously reject (a) in order to obtain the positive conclusion he wants, that forms are identical with the things they are the essence of? We can reduce only one assumption to absurdity at a time, and without an argument that the failure of separation implies identity, the Identity Result must remain moot. As predicted, then, if the argument serves Aristotle’s alleged anti-Platonic purposes, it is difficult to see how it also gives him the desired Identity Result.32 Of the three options we have surveyed—purity, impurity, and purity regained— purity remains the most attractive. Even granting purity in the engagement with Plato, however, the question remains: why the engagement with Plato at all? In part, the reasons are ones of strategy. In later parts of Zeta, Aristotle undertakes a major revision in the metaphysical theory of individuals and their kinds found in the Categories (Chapters 1 and 8). By keeping his questions about essence within the confines of Plato’s ontology, Aristotle spares himself the need to sort through here the complications that separate not just Plato but also his own views in the Categories from the new theory distinctive of the partisan portions of Metaphysics Zeta.33 In addition to simplicity, the use of Plato also gives Aristotle the advantage of drama. For Aristotle, I have argued (in Section 2), the Identity Result flows directly from what Even the subsequent talk of taking a thing and its essence “apart from” each other—supposing we were to think this a reference to Platonic separation—is introduced only as part of the set of arguments that follow at b3–11 (6.3 below). But any connection between b3–11 and Platonic separation is contested in Section 3. 31 See this chapter, nn. 11 and 12 with the associated main text. 32 For another attempt at purity regained, see the interpretation Frede and Patzig (1988) II, 96–7, give of the arguments in connection with separation at b3–11; see this chapter, n. 38. 33 See this chapter, n. 20. 30

“SEVERANCE”

AND ITS CONSEQUENCES:

1031 B 3–11

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it means to be a primary substance, independently of partisan questions of which entities fill the role of primary substance in a given ontology. The use of Plato conveniently dramatizes the fact that the case in favour of the sameness thesis is not “loaded” by the presence of distinctively Aristotelian assumptions; on the contrary, it does not sink the case for the thesis even when the argument on its behalf is couched in Platonic terms. In itself, the Identity Result is a “big tent” principle that stands independently of its application to Aristotle’s choice for primary substances, and independently of his own, “partisan”, conclusion that Aristotelian forms are identical with their essences.34 Once this initial round of arguments in favour of his Identity Result is done, in the lines immediately following Aristotle apparently drops discussion of the identity or otherwise of things that are suitably primary with their essence. He turns instead to a discussion of the consequences of the two being “severed” one from another, in particular, the consequences of the supposed “severance” of Platonic forms and their essences. The relevance severance and its consequences have to Aristotle’s larger theme is not immediately apparent: severance and its place in the wider argument are our topic in Sections 3 and 4.

“ S E V E R A N C E ”:

HOW PLATONIC SEPARATION

IS NOT A TARGET

3 “Severance” and Its Consequences: 1031b3–11 In the next stretch of argument, Aristotle launches abruptly into a discussion of the consequences of the assumption that the Platonic form and its essence, G and the for-good to be, are “severed from” one another: 6.3 And, on the one hand,35 if they are severed from one another, then of the ones [= Plato’s forms] there will not be knowledge, and the others [= the essences] will not be beings (by “severed”, I mean if neither the for-good to be belongs to the good itself (me¯te to¯i agatho¯i auto¯i huparchei to einai agatho¯i), nor does to be good to it [ = the essence of good]); (b6) for (first) (te) there is knowledge of each thing whenever we know its essence, (b7) and (second) (kai) the same holds equally of the good and of the others, so that if not even the for-good to be is good, then neither is the for-being a being, nor the for-one one: (b9) in the same way, either all the essences are, or none is, so that if not even the for-being being, neither any of the others. (b11) Again, that to which for-good to be36 does not belong is not good. (1031b3–11)

34 One further bonus of purity is surely friendship: Plato and Aristotle see amicably eye to eye on the issues currently before them. But Aristotle can also view Plato as a philosophical foe in the hunt for substance: one signal place in which the relationship between the two is tested is the account of substance and universals in Z13, see Chapter Eight below. 35 men, b3. There is no corresponding de (no “other hand”). 36 Following Ross (1924) II, 178.

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Aristotle is silent about the source of the Severance Assumption, and about why it merits discussion here. But he does explain what he takes it to mean: [i] “neither the for-good to be belongs to the good itself ” (b5, cf. 11), [ii] “nor does to be good to it [= the essence]” (b6, 8). That is, we will suppose, (15)

The for-good to be is not the essence of G; and

(16)

The for-good to be is not good.37 The Severance Assumption

The two-piece Severance Assumption, composed as it is of (15) and (16) together, is problematic in a variety of ways. In the first place, the consequences to which the Assumption is said to lead at b6–7 and b7–10 are presumably altogether unacceptable. Inevitably, interpreters have been led to suspect controversy with Plato. If severance is the same as (or at least a close counterpart of) Platonic separation, and if the effect of the arguments is to overturn Platonic separation, then the alliance with Plato struck in previous lines is now abruptly shattered. The distancing from Plato is more violent than in the argument explicitly directed against the theory of forms later at b15–18, where Aristotle prepares for conflict with Plato by saying that the identity result for which he has been arguing—arguing, as we have seen, with Plato’s help—holds if Platonic forms exist, but also even if they do not (b11–15). At the same time, if Platonic separation is both the initial assumption and the ultimate target of the arguments, there need be no worries over Purity—for the distinctively Platonic assumption at the head of the argument is to be discharged by reductio at argument’s end. If the Severance Assumption does invoke the Platonic theory of separation between forms and sensibles, then the conclusion that Platonic forms will not be known will seem reminiscent of the argument in the first half of Plato’s Parmenides that if forms are separate from sensibles, they cannot be known by us. Is Aristotle constructing, at the level of Platonic forms and their essences, a counterpart to Plato’s argument concerning sensibles and the forms that (arguably) are their essences?38

The reading of [ii] as (16) is guaranteed by the parallel passage at b8. The first clause, [i], is more difficult to decipher; one constraint on how it is read is that it supply a suitable assumption for the argument at b6–7 that G is therefore unknowable. I see three possible translations. (a). Bostock translates, “being for a good thing does not belong to goodness-itself ”: that is, he explains, the essence is not identical with the (Platonic) form, but neither does the form have an essence as a constituent (in the way, perhaps, that an Aristotelian form–matter compound will do). On this reading of [i], on the assumption that to know a thing is to know its essence, where either the thing is identical with its essence or, more weakly, has its essence as a constituent, it follows from [i] that G is unknowable. (b). “G is not essentially good” or, as in the main text, (c), “the forgood to be is not the essence of G” (for the reading of huparchei here, see Z13, 1038b10 (included in 8.7 below) and Chapter 8, n. 20); on either reading, presumably, G has no essence at all, so that if to know a thing is to know its essence, G is unknowable, b6–7. 38 On the account offered by Frede and Patzig (1988) II, 96–7, Aristotle’s assumption that a form is “severed” from its essence is the basis for an argument on behalf of his own conception of essence, and simultaneously part of an attack on “certain Platonists”, if not on Plato himself. We are to assume a version of Platonism on which 37

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161

It tells against these suggestions that when Aristotle explains what he means by “severed” at b4–6, his explanation seems quite distant from Platonic separation. Aristotle’s (15) and (16) appear in the argument by stipulation: these together are just what he means by “severing a form from its essence”. But if the conjunction of (15) and (16) tells us how we should understand Aristotle’s Severance Assumption, the question arises, what justifies his adopting the Assumption, so understood, in the first place? And what support does the Assumption offer for the Identity Result for which he is arguing? I will argue that Severance has a place in the discussion because, taken together with a fundamental principle from a framework that arguably Plato and Aristotle have in common, it forms the basis of a fresh round of reductio arguments in favour of the identity of a Platonic form with its essence. The negations of each of the two components of Severance, together with the fundamental principle, combine to make again the case for the identity of a thing and its essence. In this way, Severance is present in the argument strictly for purposes of reductio: both parts of Severance are admitted into the discussion solely in order to be ejected from it. I describe the details of this strategy in Section 4.

4 A Fresh Argument for Identity: Severance and a Principle From the Theory of Izzing and Having The Severance Assumption introduces a fresh round of reductio arguments as part of a larger argument designed once more to support the identity of a Platonic form (i) (Platonic) forms are the essence of the relevant sensibles. Suppose, next, contrary to what Frede and Patzig take to be Aristotle’s true view, that (ii) In general, things are separate from their essences (the sense of ‘separate’ here is given at b4–6), so that, by (i) and (ii), (iii) Platonic forms are separate from the relevant sensibles. By parity with (iii) or, perhaps, by instantiation from (ii), we have (iv) The essence of a (Platonic) form will itself be separate from that (Platonic) form. Given the various absurdities that follow from (iv), we must deny the premiss, (iii), on which (iv) rests. That is, (v) (Platonic) forms are not separate from the sensible of which they are the essence. More generally, contrary to (ii), (vi) In general, things are not separate from their essences. In this argument, Aristotle is imagined arguing the absurdity of separating things from their essences for the special case of (Platonic) forms and their essences. But if no special Platonic assumptions remain when he moves from the special case to the general conclusion (unless they are concealed in the different arguments to absurdity), the argumentative strategy is a successful example of purity regained. Unfortunately, the route to purity is again illusory. In the first place, we cannot reject (iii) without rejecting one or other of the assumptions on which (iii) rests. As before, however, we are not entitled to reject both at once. But if (ii) is the assumption to go, we are left with (i)—the assumption that Platonic forms are the essences of the sensibles that fall under them. Alternatively, we can eliminate (i), and the attendant commitment to Platonism—but no conclusion now follows to force the rejection of (ii) and the separation of things from their essences. There is also a difficulty regarding the correct disposal of (ii). If (ii) is false, then it is not the case that things in general are separate from their essences. But the desired conclusion, (vi), puts the negative in a different place, giving it narrow scope with respect to the universal quantifier. So (vi) is not in any case a proper conclusion to the argument.

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with its essence. A key component of the argument is a principle set out by Alan Code, which, arguably, is part of the theory of Izzing and Having:39 (17)

X = Y $ X Is Y and Y Is X.

Code regards (17) as a definition, and part of an “ontological framework common to Plato and Aristotle”.40 Thanks to this common background, even if the reference to Platonic forms is uncongenial to Aristotle, the argument will be pure, and will not essentially depend on Platonic assumptions Aristotle rejects. The argument goes as follows. Plausibly, we can instantiate from (17) to G and the for-good to be in the ontology of Platonic forms and their essences: (18) The for-good to be = G $ the for-good to be Is G [= the for-good to be is good] & G Is the for-good to be [= the for-good to be is the essence of G]. (18) suggests how the two components, (15) and (16), of the Severance Assumption, repeated here, may have purchase on the identity or otherwise of a form and its essence: (15)

The for-good to be is not the essence of G,

(16)

The for-good to be is not good.

Thus, if Aristotle can show that the negative claim in (16) is false, this will give the first conjunct on the right-hand side of (18), (Unneg-16) The for-good to be is good. And if he can show that (15) is false, this will give the second conjunct: (Unneg-15) The for-good to be is the essence of G. Given this two-fold assault on Severance, we can now use (18) to give the desired Identity Result, that G = the for-good to be.

39 Code (1980); see D4 in his (1986), 414. In the theory of “Izzing and Having” Plato and Aristotle alike recognize two basic modes of predication, one (roughly) connecting a subject essentially to what is predicated of it, the other connecting them accidentally: for example (two cases Plato and Aristotle agree over), Man Is (an) animal and Socrates Has generosity; or (in Aristotle’s book but hardly Plato’s) Socrates Is (a) man, and Man Has grammar. (In these four cases—but not, perhaps, universally, see this chapter, n. 43—Izzing and Having are the converses of the said-of and in relations respectively from Aristotle’s Categories.) Other basic claims in the theory that will command assent from Plato and Aristotle alike, for all the differences between their two positions, are noted in this chapter, n. 44, and for the full theory, see Code (1980). 40 While Code views (17) as a definition, it is not hard to see how one might argue in support of (17). Going from left to right, we suppose that Izzing is reflexive. Then if X = Y, and given that X Is X, we know that X Is Y and that Y Is X. Going from right to left: the structure of an Aristotelian genus-species tree inclines us to think that Izzing will be asymmetric: for example, man Is an animal but not vice versa. But this and similar examples are preserved if we think that the relation is antisymmetric: that is, that X Is Y and Y Is X, only if X = Y.

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On this account, the reductio arguments against Severance in (15) and (16), together with principle (17) from the theory of Izzing and Having, are the main components in a fresh argument in favour of the Identity Result reached in earlier lines. This may be the point at which to counter two kinds of objections to the key principle, (17). First, (17) has the apparent analogue in set-theory, 8x8y (x = y $ x  y & y  x): does the parallel require us to adopt an extensional view of Aristotle’s kinds or Plato’s forms—that is, to think that they have the identity conditions of sets? In a word, no. Each of two kinds Is the other, by (17), just in case they are identical; and from the identity, it follows trivially that they are coextensive. But this last entailment does not hold in the opposite direction. From the fact that the two kinds are coextensive, nothing follows: not that they are identical, nor that each Is the other. On the contrary, all and only men are capable of grammar (say); but it is not the case either that man Is grammatical or that the grammatical Is (a) man, much less that the two kinds, man and the capable of grammar, are identical. Instead, man Has the capacity for grammar, and in general, for Aristotle, propria are coextensive with, but not essential to, their subjects.41 So sameness of extension is not enough for identity; it must also be the case that each of two kinds Is the other, if we are to conclude that they are identical. It is not clear that a similar remedy is open to Plato if, as on some accounts, in his theory Platonic forms are exclusively Izzers, and only sensibles Have their predicables. Plato will need some device to avoid saying that where two forms, man and capable of grammar (say), are co-extensive, each also Is the other. He may even have to accept help from Aristotle, and allow that Having can also be a form–form relation, if he is simultaneously to accept (17) in his theory, and to avoid an extensional view of Platonic forms. For present purposes I will assume that Plato has the needed device to hand. A second objection sets (17) against a fundamental doctrine from the Categories, along with what seems an obvious point signalling Izzing as the converse of Aristotle’s said-of relation: (17) X = Y $ X Is Y and Y Is X. (a) Socrates (a Categories-style primary substance) is not said of Socrates (Categories 5, 3a36–37, apo.. te¯s pro¯te¯s cate¯gorias oudemia esti kate¯goria). (b) X Is Y $ Y is said of X. From these three premisses, it follows immediately that (c) Socrates 6¼ Socrates.42 Given the fundamental doctrine in (a) and the seemingly obvious point about converses in (b), it seems that (17) must be false. There are independent reasons, however, for laying the blame instead at the feet of the seemingly obvious point in 41 42

Categories 2, 3, Topics A5, 102a18–22. This argument is based on a comment in discussion by Paolo Crivelli.

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(b). Thus, as before, assume the truth of (a) and (b), and add a third claim, (d), from Metaphysics ˜18: 6.4 . . . that which is per se (kath’ hauto) too necessarily is said in many ways: in one, what it is to be is per se to each thing, for example Callias is per se Callias and what it is to be for-Callias. (˜18, 1022a25–7)

The result is an inconsistent triad: (a) Socrates (a Categories-style primary substance) is not said of Socrates. (b) X Is Y $ Y is said of X. (d) Socrates Is Socrates. Given the textual credentials of (a) and (d), we should abandon the claim about converses in (b) and thereby retain our faith in (17).43 I conclude that Plato and Aristotle can overcome the objections to (17). At the same time, (17) works correctly for the cases of interest in Zeta 6. For Plato, contrary to (15) and (16), the for-good to be Is G,44 and G Is the for-good to be; by (17), accordingly, G = the for-good to be, as required. It remains to follow the details of Aristotle’s attack on the two components, (15) and (16), of Severance. These arguments are our next topic.

GOODBYE TO SEVERANCE, AND IN DEFENCE OF UNIFORMITY

5 The Applications of Uniformity: Fallacy, or True Platonic Doctrine? Aristotle sees two negative and uncongenial consequences of (15) and (16): (Platonic) forms will not be objects of knowledge, contrary to the Platonic view that forms above 43 The textual evidence for (d), cited in 6.4, suggests that Izzing is reflexive; it also speaks against restricting the field of the relation to universals. For any X, therefore, whether X = man (say), or X = Socrates, X Is X. But the said-of relation is non-reflexive: where X is said of Y, X = Y only if X is a universal. The upshot is that the proposed biconditional, (b), is false; only the conditional in the right-to-left direction can be true since—what is not the case with Izzing—entities in the domain of the said-of relation must be universals. As to the cases in which a thing is said of itself—I owe the point to audience members in Los Angeles—it may be objected that where X is said of Y, Y is a subject or hupokeimenon to X, and it is hard to think that X = Y so that X is hupokeimenon to itself. To this, I answer that where X is said of Y, and X and Y are both universals, as stipulated, we must find some individual substance, s, such that s is hupokeimenon to both X and Y. Harmlessly, then, X is said of X, and there exists some individual substance, s, such that s is hupokeimenon to X and s 6¼ X; see Chapter 8, n. 44. 44 Plausibly, Izzing is reflexive (this chapter, nn. 40 and 43), so that the Aristotelian kind, man, Is (a) man; and in any theory that recognizes Platonic forms, the Platonic form, G, Is good. But if G Is good, and has the for-good to be as its essence, then by general principles about essences, the for-good to be will be the cause of G’s being good (see, perhaps, Z17, 1041a28, from 11.6 below); and by certain general causal principles Plato and Aristotle share (this chapter, n. 25), the for-good to be Is therefore itself good.

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all, or even forms alone, are the objects of knowledge; and no essence will exist. First (b6–7),45 if (15) is true, and if we know each thing when we know its essence, then G and Platonic forms generally will be unknowable.46 In the remainder of the passage (b7–11), Aristotle uses the second assumption, (16), to reach the complementary result, that no essence exists.47 The chief point of controversy concerns this last argument, from (16), (16)

The for-good to be is not good,

to the conclusion that essences do not exist. Aristotle argues, first, that if the essence of good is not good, then (by a principle of uniformity) for any X, the essence of X is not (an) X; and second, that if the essence of being is not a being, then (by uniformity again) no essence exists. Of the two would-be applications of uniformity featured in this stretch of argument, the second has been viewed with scepticism by Aristotle’s critics; unexpectedly, I will argue, Aristotle can reasonably call upon Plato as an ally against the charge of fallacy. I begin by repeating the relevant part of Aristotle’s text: 6.5 (repeating selectively from 6.3 above) . . . if they are severed from one another, then . . . the others [= the essences] will not be beings . . . (b6) for . . . the same holds equally (homoio¯s echei) of the good and of the others, so that if not even the for-good to be is good, then neither is the forbeing to be a being, nor the for-one to be one; (b9) in the same way (homoio¯s), either all the essences are, or none is, so that if not even the for-being to be being, neither any of the others. (1031b3–11)

The argument rests on applications of different versions of a uniformity principle, which Aristotle states in undifferentiated form: “the same holds equally of the good and of the others” (b7–8). First (b6), if the for-good to be is not good, as (16) asserts, then in general, for any form, X, the for-X to be is not (an) X, in particular, the for-Being to be is not (a) Being. But, second (b9, taking up the conclusion of the first installment 45 Following Ross, I will suppose that the two results are proved separately: Ross (1924) II, 177; see also Bostock (1994), 109, and this chapter, n. 47. 46 This first argument is incomplete as it stands; but perhaps we are to supply the thought that if the forgood to be is not the essence of G, as (15) asserts, then G can have no essence at all; if then to know G is to know its essence, and if G has no essence, then G cannot be known. There is a different account in Bostock (1994), 109–10. See also Frede and Patzig (1988) II, 95, who take not (15) by itself but the entire assumption that a Platonic form and its essence are “taken apart” from each other (as I see it, the conjunction of [15] and [16]) to be the premiss of the argument. 47 On the “two argument” view adopted in the main text, Aristotle proves the same result, that essences do not exist, twice over, first (and elliptically) en route to the conclusion that forms cannot be known (this chapter, n. 46), and then for a second time, apparently independently, for its own sake. Alternatively, he gives just a single argument: after warning us first of the connection between knowing a thing and its essence, he goes on to argue for the one conclusion, that no essence exists; from this, there follows almost immediately, given the advertized connection between knowledge and essence, the second conclusion, that no form can be known (so, perhaps, Notes on Zeta, on b3–4). On this second view, which sees only one argument, with two intertwined conclusions, Aristotle uses assumption (16) to reach both conclusions, and (15) is put to work only in the one-line argument that follows at b11 (Section 6).

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of argument, but with a fresh application of uniformity), if the for-Being to be is not (a) Being, then in general, for every form, X, the for-X to be is not (a) Being. That is, absurdly, no essence of a Platonic form exists. An initial objection to Aristotle’s reductio argument, due to Bonitz and echoed in Bostock, questions the second application of uniformity, which purports to show that if the for-Being to be is not (a) Being, then for any form, X, the for-X to be is not (a) Being.48 If Aristotle intended uniformity to work in the same way here as in the first part of the argument, then as Bonitz complains, he would be entitled to conclude, as before, only that for every form, X, the for-X to be is not (an) X. It may seem that Bonitz’s objection is groundless because, as Ross suggests, he has simply failed to recognize two different applications of uniformity. Lest this response seem too easy, we might press Bonitz’s objection a step further. Someone might argue that, while the first kind of uniformity is privileged, what Aristotle takes to be a second kind of uniformity is a fallacy. In contemporary predicate logic, we know that by the rule of Universal Introduction (UI), along with the appropriate restrictions, from My horse’s head is the head of my horse, we can validly infer, (8x) (x’s head is the head of x): take anything you like, its head is the head of it. It does not follow, however, that by UI, (8x) (x’s head is the head of my horse) —take anything you like, its head is the head of my horse. (On the contrary, take anything you like, its head is its own, and only my horse’s head is the head of my horse.) As an application of UI, the move I am objecting to is certifiably fallacious, because it violates the restriction that the “instantiating constant”, “my horse”, in the premiss may not appear in the universally quantified conclusion. The logic is the same in the target case in Aristotle. To The for-Being to be is not (a) Being, we can apply the rule of UI to conclude that for any form, X, the for-X to be is not (an) X, along the lines of the first application of uniformity. But the application of UI to produce the second purported conclusion, for any form, X, the for-X to be is not (a) Being,

48

Bonitz (1848–49) II, 317–18, cf. Bostock (1994), 110.

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is fallacious, for the same reason as before: the instantiating constant, “Being”, in the premiss may not also appear in the conclusion. So perhaps Bonitz is right: only the first, but not the second, is a legitimate consequence of Aristotle’s uniformity principle. In fact, however, Bonitz is not right. On the account just given, uniformity is assimilated to the logical rule of Universal Introduction. But uniformity is not a matter of logic alone. Rather, it is the application of an “all or nothing” principle, to the effect that with respect to a given domain of entities and a given property, F, either everything in the domain has F, or nothing does: ð8xÞFxvð8xÞ˜Fx This “all or nothing” principle has different consequences, depending on what property we take F to be. Two choices are relevant here: (19)

‘Fx’ = ‘the for-x to be is (an) x’.

(20)

‘Fx’ = ‘the for-x to be is (a) Being’.

The argument of 6.5 now falls into place. Suppose, first, that the for-good to be is not good, as in the target claim, (16), and that the “all or nothing” uniformity principle is understood in line with (19), (Uniformity-1) Either for every form, X, the for-X to be is an X, or for no form, X, the for-X to be is (an) X. Given (16), that the for-good to be is not good, the first disjunct of Uniformity-1 must be false; by Disjunctive Syllogism (DS), then, no form, X, is such that the for-X to be is (an) X. In particular, the for-Being to be is not a being. This gives the result of the first half of Aristotle’s reductio. At the same time, the “all or nothing” principle may also be applied with (20) as our choice for ‘Fx’, (Uniformity-2) Either for every form, X, the for-X to be is (a) Being, or for no form, X, the for-X to be is (a) Being. We begin with the conclusion to the first leg of the argument, that the for-Being to be is not (a) Being. On this assumption, the first disjunct of Uniformity-2 must be false, so that by DS again no form, X, is such that the for-X to be is (a) Being. This gives the conclusion to Aristotle’s reductio.49 Given that this result is absurd, and if the two Uniformities 1 and 2 are sound, we are in a position to deny the initial assumption (16), that the for-good to be is not good, as required. 49 With the different choices that are open here, we can compare an example from Aristotle’s ethics and theology. If the virtuous man imitates God, and God thinks only himself, should we conclude that (a) the virtuous man only thinks himself? or (b) that the virtuous man thinks only God? (Answer: how do you define imitation? Is it with respect to the property, thinking oneself, or the property, thinking God?) The “all or nothing” claims in this part of Z6 can be compared with the similar Uniformity assumption at Z13, 1038b12–13 (included in 8.7 below), for which see Code (1978), 70, and Lewis (1991), 313, 344.

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Both applications of uniformity in this two-part argument are defensible. But the defence is not merely that these are different applications of uniformity. There is the further point—which Ross does not mention—that the two applications of uniformity are not a matter simply of logic. If they had been, Bonitz would be right. In fact, however, they rest on the propriety or otherwise of the relevant “all or nothing” principle, which is a matter not of logic but of the content of each principle. Arguably, the relevant principles will hold across ontologies, and will govern whatever counts as a primary substance in Plato’s and in Aristotle’s ontology alike. In fact, Plato and Aristotle can agree over stronger principles of uniformity, which drop the second, negative disjunct in (Uniformity-1) and (Uniformity-2). Plato, for example, can reasonably claim that for any form, X, its essence is an X: this is a candidate for a “categorial” or “formal” property that belongs necessarily to all forms, in virtue of their status as forms.50 Again, for any Platonic form, X, its essence is a being: this, again, is arguably a categorial property of all forms across the board. These two claims take to be true for every form what in the two halves of Aristotle’s reductio is assumed to be false for G and for Being. To avoid an inconsistent premiss-set in the two halves of his argument, Aristotle limits himself to weaker versions of uniformity: namely, the disjunctive (Uniformity-1) and (Uniformity-2). Similar considerations apply to the primary substances in Aristotle’s ontology. Whether with Zeta 4 we think that the primary substances are the genous eide¯ (the lowest species of the different genera),51 or (as in the official theory) that they are Aristotelian forms, it seems that for any primary substance, X, its essence both Is (an) X, and Is (a) Being.52 As before, arguably, it is a categorial feature of primary substances across the board that each has the properties noted. This is enough to support the essentially weaker disjunctive principles, (Uniformity-1) and (Uniformity-2). With one notable exception, these different Platonic and Aristotelian ideas essentially involve the notions of primary substances and their essences, and only incidentally engage the details of their authors’ differing ontologies. One exception to purity, however, stands out (I owe the point to Alan Code). Both applications of uniformity presuppose the existence of a Platonic form of being—to be faulted not for its status as a Platonic form, but because, for Aristotle, there is no widest genus, being. Aristotle’s argument, then, is at best conditional in form. Beyond this one concession to Plato, no other assumptions are essential to the use of uniformity that Plato would embrace but 50 Recall here that Platonic forms are causes, and that “the cause is equal to or greater than its effect” (Lloyd (1976)), see this chapter, n. 25. My appeal to “formal” or “categorial” properties rests on their use in a different context in Keyt (1971). 51 See B1, 995b29–31, 3, 998b14–999a23; for the choice of genous eide¯ in Z4, see especially 999a14–16; also H1, 1042a13–15 and PA A4, 644a24–5. In favouring the eidos here, note that Aristotle is dropping the candidacy of the genos in Z3, see Chapter 1, nn. 18 and 54 (and for the debate between the two options, see again the passages cited from Beta). 52 If X is a primary substance, then by the Identity Result of Z6, X = the essence of X. But it is a theorem of the theory of Izzing and Having that X Is X; accordingly, the essence of X Is X, as required. Similarly, the primary substance, X, is a being, so that the essence of X too is a being, by the Identity Result noted.

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which Aristotle would reject. Once we allow Plato’s widest genus, Being, the appeals to uniformity are not idiosyncratic to Plato, but unsuitable for anyone else or (merely) unsuitable within Aristotle’s own theory. Not only, then, are the arguments not bad, as Bonitz thought; but also, as before, the use of assumptions Aristotle shares with Plato conveniently dramatizes the point that his conclusion is—as close as may be—a “big tent” view, which applies across ontologies.

6 Fallacy Again, or More True Doctrine? Our passage ends with a one-line argument to supplement the argument just given: 6.4 Again, that to which the essence of good does not belong [ho¯i me¯ huparchei agatho¯i einai] is not good. (b11)

An important first step in seeing the point of the argument is to resist reading Aristotle’s sentence as a universal generalization: for every x such that the essence of good does not belong to x, x is not good.53 As Ross suggests, Aristotle has a particular case in mind: we are to suppose that the for-good to be does not belong to the Platonic form, G,54 so that it, G, is not good. So the argument has as its premiss our old friend, (15): (15)

The for-good to be is not the essence of G.

It follows, Aristotle suggests, that (21)

G is not good.

On this reading, the argument has the appearance of a fresh reductio: its point, presumably, is to discredit the non-identity theorist’s (15) (to this point, targeted only by the argument from knowledge at 1031b6–7) by showing that it leads to (21). But two problems remain. On what grounds should we find (21) unacceptable? At the same time, second, like its immediate predecessor the argument seems vulnerable on purely logical grounds. We can discuss this second objection first. The effect of (15) is that G is not essentially good. But, Frede and Patzig complain, it is a fallacy to suppose that if a thing is not essentially good, then it is not good at all: it may be accidentally good.55 So

53 See Bostock’s gloss (using the contrapositive), “the essence of a good thing belongs to everything that is good” Bostock (1994), 110, my emphasis. This reading may explain why Bostock finds the argument oddly motivated. 54 See Ross (1924) II, 178, and 169 on Z4, 1030a1–2. On the preferred reading, the negation me¯ (in contrast to ou) is conditional rather than general in force; or if it is general, it is still restricted to (Platonic) forms. 55 Frede and Patzig (1988) II, 97–8. Frede and Patzig say that Aristotle certainly rejects the inference; they also say that the argument rests on the earlier assumption that a Platonic form and its essence are to be “taken apart”, and also calls that assumption into question. But they do not explain how the assumption is called into question, given what they take to be Aristotle’s view that the inference is invalid.

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the inference to (21) is apparently an instance of an invalid argument-schema, and even if (21) is unacceptable it is hard to see how that fact can be used to undermine (15). As before, however (Section 5), not every instance of an invalid argument-schema is itself invalid. This is why the restriction to Plato’s forms is important, for there are grounds in Plato’s theory for finding the move from (15) to (21) compelling. For Plato, arguably, at least in a large range of cases, whatever is true of a Platonic form is essentially true of it: in the theory of Izzing and Having, a form Is whatever it is (within that range of cases). Hence, if the for-good to be does not belong to G, that is, if G is not essentially good, then Plato can legitimately infer in (21) that G is not good at all. Arguably, for Aristotle too, properties of primary substances of the kind on display in (15), if they hold of their subject at all, do so essentially, and the inference to (21) is again without blame. But, next, is (21) unacceptable, as required? For Plato and Aristotle alike, uneasiness about (21) rests on a deeper-seated aversion to the premiss, (15). As before (Section 4, and n. 44 ), in the shared theory of Izzing and Having, Plato’s claim that the Good Is good, or that Man Is (a) man, made within a Platonic ontology of (Platonic) forms, has a direct counterpart in an Aristotelian ontology of kinds and (Aristotelian) form—independently of the more parochial assumptions that separate a Platonic and an Aristotelian ontology. So Aristotle’s reductio holds good: both philosophers have as good a reason for rejecting (21) as they do for rejecting the premiss, (15). In the body of theory that Plato and Aristotle share, both lines get swept away together. With the dispatch of (15) (this section), and the dispatch of its partner, (16) (Section 5), Aristotle has shown that both components of the Severance Assumption are false. It remains to recapitulate the relevance of Aristotle’s arguments against (15) and (16) to his larger aims in Zeta 6. Now that (15) and (16) are defeated, his argument from Severance in 6.3 (Section 4) is complete. Aristotle is free to apply the principle (17) from the theory of Izzing and Having, in conjunction with the defeat of the two halves of Severance, in a second, major proof of the Identity Result that is his main concern in the chapter.

7 Aristotle on How Plato’s Forms are Inessential to His Argument In the lines at 1031b11–15 (6.8 below), Aristotle appears to sum up the net profit (or loss) from his involvement with Plato. But his conclusion is obscured by various issues of translation and interpretation. Dogmatically, I give my translation first, then append Burnyeat’s version of the second half of the passage that begins at b14: 6.8 It is necessary therefore that the good and the essence of good be one, and the beautiful and the essence of beauty, and whatever is said not per aliud, but per se and primary: (b14) and this would be sufficiently established, even if [Platonic] forms do not exist, but all the more perhaps if there are [Platonic] forms. (1031b11–15)

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. . . (b14) It is enough if they are this [sc. primary things which are in their own right what they are said to be], even if they are not eide¯, and perhaps all the more so if they are eide¯ [or . . . even if there are no eide¯, and perhaps all the more so if there are eide¯]. (b14–15; Burnyeat (2001), 27)

(i) Burnyeat’s translation of and gloss on b14, kai gar touto hikanon an huparche¯i, follows the standard account: “It is enough”—that is, we get the desired Identity Result—“if (an = ean) they are this” or, perhaps, “if this condition is met” [= the condition from b13–14 that the items in question be suitably primary]. The back-reference seems sufficiently awkward to make tempting the reading huparchoi in Ab and in Alexander for huparche¯i (on this reading, an 6¼ ean): the meaning would then be, “This would be sufficiently established, whether or not Plato’s e¯ide exist”, where the “this” refers back to the Identity Result mentioned in the previous lines. (ii) By “eide¯ ” I suppose that Aristotle means Platonic forms. Burnyeat wonders whether Aristotle’s word here means, (a) “Platonic forms” (a shift from his use of the Greek, “idea”, everywhere else in the surrounding text), or (b) “species” (in line with the earlier “genous eide¯” in Z4), or finally, (c) “Aristotelian forms”. In favour of (c), and against (a), is what Burnyeat describes as otherwise the mystery of why Aristotle would think that his Identity Result holds more firmly in the case of Plato’s forms than for his own primary substances.56 But (iii) if we adopt my reading under (i) above (finding a reference to Plato’s forms, as in [iia] above), Aristotle is not saying that the Identity Result holds in any case for primary substances, but even more firmly for Platonic forms; rather, the Result is adequately established whether Plato’s forms exist or not—but more firmly, if Platonic forms do exist. The alliance with Plato in Zeta 6, then, comes to this. Aristotle’s arguments in the chapter, couched as they are in terms of Platonic forms, offer one further supporting case for the desired Identity Result—and this is still support, even if in fact Plato is wrong in thinking that Platonic forms exist.57 56 Burnyeat (2001), 27. It is telling that Ross (1924) II, 178, dismisses this as a contemptuous aside on Aristotle’s part. 57 I append here more detailed comments on two recent contributions to the secondary literature on Z6. I am thoroughly in agreement with one main theme of Dahl (2003)—that the various inferences in the target passage 6.2 should be “appropriately generalizable”—insofar as this means validating them in Aristotle’s own theory as well as in Plato’s. This puts us both on the side of purity in our approach to Z6. Beyond this lies disagreement. I am not sympathetic to extending the project of “appropriate generalization” so that the sameness result of Z6, suitably understood, applies to the composite material substance and what counts as its essence (strictly, suitably asterisked to show that this is a different relation, with different logical properties, its essence*; Chapter 3, n. 11). According to Dahl, if the sameness result includes this further case, then the sameness relation in question must be sameness in substance or formula, but not also numerical sameness. That is, the relation does not imply identity, as I suppose. But if the sameness result is restricted, as I think, and does not apply to the compound material substance and its essence, then the sameness relation can be correspondingly more stringent, and can imply identity. Is it right that the conclusion of Aristotle’s Elaborated Argument applies also to the compound material substance and its essence, so that use of the weaker sameness relation is triggered, as Dahl supposes? Although the compound material substance is a substance, it is not a primary substance, and it does have a substance prior to it: namely, its constituent substantial form, which also is its essence*. So the compound material substance apparently is disqualified out of hand for the Elaborated Argument, which Aristotle expressly

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restricts to entities that are primary. Dahl is well aware of the difficulty (his 164), and attempts to counter it by pointing out that (a) the substantial form is itself dependent on its parent compound material substance. He adds that (b) the various passages in Zeta that apparently make form primary substance can be interpreted differently, and that anyway (c) what goes elsewhere in Zeta need not hold for this chapter. I do not think that (c) can bear much weight: for all the fluidity in Aristotle’s thought in Zeta, we should not want to encourage a Protagorean interpretive stance, where a new Aristotle presents himself in each chapter. And Dahl is not above bringing in the results of Z17, for example, and the notion of a thing’s essence as the cause of its being, in order to supply assumptions to make his version of the Elaborated Argument go. I am also not in sympathy with (b): think of Z16, for example, on why an individual substance cannot be a primary definable; see Chapter 10. At the same time, with respect to (a), Aristotle does not discuss how the existence conditions for a given form introduce a dependency on compound material substances. It bears noting, however, that a given substantial form is not (existentially) dependent on a given compound material substance, but requires only that there be some compound material substance or other in which the form is enmattered. On the other hand, a given compound material substance is (essentially) dependent on a given substantial form—without that very form, the substance could not exist. So the dependency in the two directions is not of equal strength. At the same time, I also do not agree that the weaker sameness result, with its attendant hospitality to the compound material substance, is required, as Dahl claims it is, if we are to have an acceptable account of Aristotle’s discussion of severance at b3–11 (Sections 3 and 4). There is no such requirement, if the argument using (17) in Section 4 succeeds. Finally, a fresh attack on the view that the variety of sameness at work in the Elaborated Argument entails identity has been launched in Charles (2011). On the identity reading, Aristotle means to establish that Plato’s primary entities—which here go proxy for whatever entities are primary in a given ontology—are identical with their essences. Success here, however, may bring a heavy price. Like its (linguistic) definition, the essence of a given primary entity is composed of parts, and these parts will be in some sense prior to the essence to which they belong; by the Identity Result, then, these parts will be prior also to the entity that was supposedly primary. Among the different remedies that might be set in place to meet this objection, Charles suggests (with Dahl (2003)) that essential sameness between a primary entity and its essence does not after all require that they be identical. But is it clear that essential sameness is sufficiently weak so that the unwanted inference does not go through? In particular, the relation must not be that of “being one and indistinguishable in being”. SE 24, 179a37, cf. Phys. ˆ3, 202b14–16, which would appear to license this and other troublesome inferences; see Chapter 4, Section 15, n. 73. Be this as it may, Aristotle suggests elsewhere that the thing defined— equally, then, the entity of which the essence is being given—will have parts that correspond exactly to the parts in the definition (Metaphysics Z10, 1034b20–22): so the puzzle remains, independently of the exigencies of Z6. At the same time, the proposed solution itself appears to be open to the fresh difficulty that there may now exist a multiplicity of essences associated with a single given Platonic form—multiple essences of the Good (say)—so that the Form of the Good can have an essence, and that essence have an essence, and so on, for all we know, ad infinitum (see 1031b28–1032a2, leading to the regress argument at a2–4). These essences for the one Form will all be essentially the same and so, presumably, indistinguishable in content—but they will remain numerically distinct. At this point, I see no definitive answer to these problems.

7 Substance as Essence: The Shift to “Partisan” Mode in Zeta 10 and 11 As we saw in earlier chapters, the discussion of essence in Zeta 4 begins with the attempt in “non-partisan” terms—in terms, perhaps, of what informed people, Aristotle among them, have already said on the topic—to establish what it is for one thing to be the essence of another. From here, one might expect that with an account—even a definition—in hand, Aristotle will go on in the “partisan” portion of the segment, beginning some fifteen lines into Zeta 10 at 1035a1, to apply the definition within his own ontology of form and matter. On this line of thought he will first identify the items in his own “partisan” theory that satisfy his definition and, hence, count as the essences of things. He will then be in a position to use the received view at the head of the segment, that the essence of a thing is its substance (and hence, perhaps, primary substance), to solve the Application Problem and identify the entities that in his theory count as primary substances. In fact, however, things go rather differently. In the first place, the attempt to define the essence of a thing apparently ends in failure. What we might be tempted to see as an attempt at definition in the opening paragraphs of Zeta 4, starting from the idea that a thing’s essence is what it is per se, founders on the failure to isolate the wanted sense of “x is per se y”. Instead, the discussion is turned into a question about the scope of the notion of essence: what things can properly be said to have an essence? Aristotle will not in these early chapters answer this question in the terms of his own, partisan ontology of matter and form. Instead, we are given various constraints on whatever items will qualify as having an essence. In this spirit, we are told that a thing has an essence if (and only if ) it has a definition in the strict sense; and it has a definition in the strict sense if (and only if ) it is suitably primary and if it is not “said by way of one thing’s being said of another” (the connection between essence and definition is highlighted as one of the main conclusions to the two chapters Zeta 4 and 5, 3.23 above).1 In light of these constraints, Aristotle identifies a familiar candidate from the philosophical tradition, the “species of a genus” or genous eide¯ (3.21 and Chapter 3,

1 The connection with definition does not give the definition of essence; rather, Aristotle defines definition in terms of essence, and essence in terms of the what is it? of a thing, Chapter 3, nn. 43 and 44.

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n. 49), as alone having an essence in the primary sense. At the same time, he also endorses a more relaxed view: in addition to the primary case of essence, we find secondary cases, so that individual substances, their accidents, even compounds of an individual substance with its accidents, can have an essence. These conclusions are pressed further in Zeta 5. Zeta 6 then takes up the identity of things that are suitably primary with their essence. Zeta 4’s distinction between primary and secondary cases of the essence-of relation is central to separating cases where the identity result holds from cases where it does not. Aristotle does not in Zeta 4–6 produce a definition of essence (this chapter, n. 1). We should also be cautious about how much the discussion of essence contributes to Aristotle’s goal of defining substance. We know from Zeta 17 that an item—in fact, an Aristotelian form—counts as (primary) substance, or the substance of a thing, just in case it is also the essence of the thing in question (11.6, 11.9 above); but this indicates only that the notions of essence and (primary) substance are coextensive, and falls well short of defining substance, as in Zeta 17 Aristotle succeeds in doing. To this extent, then, the “received” tradition that sees the notion of a thing’s essence as the definition of substance (1.4, 3.1, above) overreaches. The tradition is correct, to the extent that the essence is substance, as Aristotle again says in the retrospective in Eta 1 (1042a17, Chapter 12, Section 1). But the connection between the two, while close, does not by itself amount to a definition of (primary) substance. As to the definition of essence, meanwhile, as the summary two paragraphs above suggests, in lieu of a full-fledged definition Aristotle in Zeta 4–6 situates the notion within a circle of closely related ideas, definition, for example, and the What is it? question and its elaboration in terms of what a thing is per se. He also exhibits an interest in which items they are that have an essence or a definition in the primary sense. This too contributes to our understanding of the circle of ideas within which the notion of essence has its place. Given the connection between essence and substance, a contribution to the Application Problem for the notion of essence will also contribute to solving that problem for the target notion of substance. But the promise of a solution to the Application Problem in either case can seem surprising. Why should Aristotle (or we) attend to the Application Problem for the notions of essence and of substance, when the question of how the actual definitions for each notion should go is as yet unresolved? In the comparable situation in Physics B1, after all, Aristotle brings forward form and matter as the two candidates for the nature of a thing, only after a definition a thing’s nature as an internal principle of behaviour for the thing is already before us.2 All the more urgency, then, to the question, how does the discussion of essence in the five chapters of this segment of Zeta contribute to Aristotle’s goal of producing

2

See Chapter 2, n. 10.

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a definition of (primary) substance? Perhaps we can understand Aristotle’s reasoning as follows. He sketches in Zeta 10 two puzzles, framed in “non-partisan” terms, that he goes on to show are handled with equal success in the larger, “partisan” theory in which (Aristotelian) forms are recognized as the primary substances. Zeta 11 then follows up the puzzles of 10 with a third, framed from the start in the distinctively Aristotelian framework of form and matter; the result will be to help confirm the place of (Aristotelian) form as primary among the different choices for substance, form, matter, and form–matter compound. The success of Aristotelian forms in responding to the puzzles in these two chapters hints that we already know the answer to the Application Problem, well in advance of a definition of (primary) substance. And if we already have a good idea of what in Aristotle’s theory will count as primary substance, even before we have arrived at the required definition, it becomes plausibly a constraint on the—as yet unstated—definition that the definition be satisfied by the candidate of choice. Aristotle’s discussion in Zeta 17 (Chapter 11) confirms that the definition of (primary) substance presented there delivers the solution to the Application Problem already favoured in these earlier chapters. I will return to these points in the conclusion at the end of this chapter. In Section 1 immediately following, meanwhile, I take up the puzzles that recommend (Aristotelian) form as the choice for primary substance.

1 Zeta 10 and the Transition to “Partisan” Mode By the end of Zeta 4, as also at the end of Zeta 5, Aristotle routinely pairs his conclusions about the essence of a given thing with their counterpart for the definition of the thing (3.25 above; cf. 3.2 and 3.24). When the segment resumes in Zeta 10 after the intrusive chapters 7–9 he quietly shelves the topic of essence almost entirely until the summary at the end of Zeta 11 (it reappears only fitfully at Zeta 10, 1035b16, 32, 1036a1, 18), and his topic is all but exclusively definition. Aristotle initiates the transition from “received views” to his own, “in-house” theory of form and matter in Zeta 10 and 11, with the intention above all of seeing how well his partisan theory handles puzzles for definition for which the tradition has at best only provisional solutions. As so often in Aristotle, accordingly, we have the promise of progress when we come to grips with a good puzzle (aporeitai, 1034b22). In the event, the beginning of Zeta 10 gives us two puzzles,3 both starting from the thought that a definition has parts (the point is familiar from the Topics and the de Interpretatione), and that to the parts of a definition there correspond parts of the thing (see also Physics A1, 184a26–b13): 7.1 Since [a] the definition (horismos) is a formula (logos), and [b] every formula has parts, and [c] as the formula is to the thing, so the part of the formula is to the part of the thing—the aporia

3

Two puzzles, not just one, this chapter, n. 6.

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comes up right away (aporeitai e¯de¯, b22): must the formula of the parts be present in the formula of the whole, or not? In some cases they are seen to be present, but in others not . . . (b28) Then again: suppose the parts are prior to the whole, and the acute angle is part of the right angle, and the finger is part of the animal; then the acute would be prior to the right angle and the finger to the man. But the latter seem to be prior . . . 1034b20–24, 28–30, following Furth’s translation.

The presence of puzzles at the very beginning of the chapter, stated in neutral terms as these are, suggests that the “non-partisan” approach in force at the end of Zeta 6 continues into the body of Zeta 10. In the Organon, the fact that a definition uncovers the parts of the thing being defined above all raises the question of the unity of definition, and Aristotle repeatedly notes the concern in the present segment of Zeta. But any solution to the problem of the unity of definition is deferred—in part, to Zeta 12, but in its fullest form to Eta 6. Instead, in Zeta 10 Aristotle has two other puzzles on his mind that come up “right away”, given the points about definition and parts presented in non-partisan terms in the opening lines of the chapter in 7.1. Where one thing is a part of another, (i), must the formula of the part be included in the formula of the whole? On a first look, different cases pull us in different directions (“yes” to the constituent letters of the syllable, “no” to the segments in the circle). A second puzzle, (ii), is about priority. Where, again, one thing is a part of another, must the part be prior to the whole? On a first look again, in some cases (the man and his finger, the right angle and the acute) the whole is prior to the part, contrary to what we ordinarily might expect. The different results in each case are rationalized by a clarification about what we take to be a part of what. The clarification involves different notions of substance, and the part–whole relations among the different kinds of substance. The restriction to substances presumably reflects the result of Zeta 4, that substances are the primary definables (3.2, 3.24, and 3.25 above). More important, by “substance” Aristotle now has in mind his own notion of substance. At long last, we are allowed to return to the different levels of substance in Aristotle’s own partisan theory—form, matter, and form–matter compound, last mentioned (ignoring the intrusive Zeta 7–9) in the “partisan” portions of Zeta 3—so that the various part–whole relations are explained in terms of relations among these three kinds of substance: 7.2 Now, then: if there is matter and there is form and there is what is out of these, and if the matter and the form and what is out of them are substance, then in a way even the matter is called part of something, and in another way it is not, but rather those things out of which the formula of the form . (1035a1–4, after Furth’s translation.)

The different notions of substance outlined in 7.2 give two cases of part–whole relations between substances of one sort or another, and one case where no such relation holds:

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I The matter is a part of something (sc. it is a part of one kind of substance, namely the compound material substance). II The matter is not a part of the form (“in another way it is not”, 7.2 above, sc. it is not a part of a second kind of substance, namely form). III (Only) the parts corresponding to the parts in the formula of a form count as parts of the form. Aristotle moves immediately to examples: 7.3 (the immediate continuation of 7.2) For example, of concavity, flesh is not a part (this [flesh] being the matter upon which it [concavity] comes to be), but of snubness it is a part; then again (a6), of the composite statue, the bronze is a part, but of statue said as form (tou d’ ho¯s eidous legomenou andriantos), it is not—for the form and the thing as having form is called the so-and-so (hekaston) [e.g. statue], but the material is never called per se. (1035a4–9, translation following Ross (1924) II, 196, and Furth)

In keeping with I and II, then, the bronze is a part of the composite statue, but it is not part of the statue taken as form (a6–7); the divergent results reflect not just the different notions of substance, but also that different things—both the composite statue and its form—answer to the term “statue”. Meanwhile, result III applies to Aristotle’s forms the general correspondences noted at the beginning of Zeta 10 in 7.1 above, between parts of the formula that constitutes the linguistic definition of a thing, and the parts of the thing being defined. The form will have parts, corresponding to the different parts in the linguistic definition of the form. Now that these examples of parts and wholes are in place, under what circumstances will the definition of the whole contain the definition of the parts? (III) gives a clear set of cases where the definition of the part will be included in the definition of the whole: with respect to substance in the sense of form, the definition of the form will include the definition of its (formal) parts. The formula of the syllable, for example, will include that of the letters (a10–11). In another set of cases, (II), the form does not have the matter on which it supervenes as a part, and the definition of the form does not include the definition of the matter. For example, the formula of the circle will not contain that of its segments, or of the half-circle: these latter are parts only in the way that the matter on which the form supervenes is a part—that is, I suppose, they are the matter half of the form–matter compound (a9–10, 12). Similarly, these token letters inscribed in the wax (a14–16) are merely perceptible matter, and they are parts of the composite syllable but not of the form: so the definition of the form will not include their definition. Lastly, (I), we come to substance in the sense of compound material substance: the matter is part of the compound material substance, and insofar as the compound substance is a suitable object of definition,4 Aristotle seems to allow that the definition

4 Properly, the compound material substance cannot be defined, for reasons Aristotle sets out in Z10, 1036a2–9 (included in 7.11 below), and Z11, 1039b31–1040a5 (= 10.1 below); see Chapter 10, Section 1.

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of matter may be included in the definition of the whole. Strictly speaking, however, matter and its parts cannot be defined at all.5 Similarly, with respect to question (ii) and the issue of priority: as Aristotle explains (1035b3ff.), the parts into which a thing divides as matter are posterior to the thing (some lines later, as we shall see, Aristotle notes an exception in the bodily parts of an animal that are simultaneous with the whole, b25–7). But the parts of the form are prior (all of them, or some) to the compound material substance, and apparently (1036a22 in the summary at the end of Zeta 10) prior also to the form itself.6 In this way, Aristotle’s initial questions about parts and wholes and about priority and posteriority are answered by saying how those questions play out in the “official” theory of form and matter. But while his answers expressly require that there be different kinds of substances—form, matter, and form–matter compound—his account at this point nowhere appeals to any ranking among these three, or to the thought that of the three, form counts as primary substance. Instead, Zeta 10 fits rather differently into its larger context in Zeta. If Aristotle is to have a formal, partisan theory that can properly replace the informal theory rooted in the philosophical tradition, he must be able to show that the new theory can address questions that come up in the old. And where we are inclined to accept one set of answers when we think in “non-partisan” mode, we must be able to find similarly satisfying answers in the new context of the partisan, Aristotelian theory. So it is with our two sets of questions about parts and wholes: as we have already seen, the relationships amongst entities in the partisan theory support, even rationalize, the answers we were inclined to give in the context of the old, “received” set of views. It is easy to see Aristotle as arguing that anything that can be done within the philosophical tradition, he can do as well, if not better, with the resources of his own “official” theory. So much the better, then, for the official theory! Accordingly, the transition from “received” mode to partisan is both principled and also well under way in Zeta 10. Aristotle’s discussion to this point has been required to navigate the difficulty that the same term can apply both to the form and to the compound material substance:

The trouble is to be traced largely to a thing’s constituent matter, which has the capacity for being and for not being (sc. for constituting a thing of the relevant kind?), Z15, 1039b27–30, and itself resists definition. For Aristotle’s ambivalence over defining the compound material substance, see for example the summary at the end of Z11, 1037a26–30. 5 The concession that a thing’s matter may be included in the definition of the thing occurs in a disputed text, defended by Ross ad loc., at 1035a23. The concession is apparently contradicted in the summary at the end of Z11 at 1037a27, but it accords with his familiar claim in Physics B2, 193b31–194a7, cf. Metaphysics E1, 1025b28–1026a6, and (even) Z11, 1036b22–32, that “nature is said like snub”, so that the definition of a natural substance will best include its matter as well as its form. For discussion, see, for example, Frede (1990), Devereux (2011), and Code (2011), and this chapter, nn. 11 and 12. 6 According to Burnyeat (2001), 39, this is “a solution to the problem of the chapter” [= my (i) above] “in clearer terms”, but it seems more plausibly the solution to (ii), which is a different, if related, puzzle. For the difficulties in the idea that the parts of a form are prior to the form itself, see n. 57 in Chapter 6.

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7.4 (excerpted from 7.3 above) . . . for the form and the thing as having form are called the soand-so (hekaston) [e.g. statue]. (1035a7–8) 7.5 . . . for circle is said homonymously, circle said without qualification [= the form], together with the particular , because there is no name peculiar to the particular . (1035b1–3) 7.6 . . . But only the parts of the form are parts of the definition, and the definition is of the universal: for, the for-circle to be and circle and for-soul to be and soul are the same. But for the composite already, for example, this circle and one of the particulars, whether perceptible or intelligible . . . (1036a1–3)

Summarizing results at the end of the chapter, Aristotle warns that the question whether right angle or circle or animal are prior to their parts, or vice versa, cannot be answered without the proper qualifications. He turns for help to a result from the discussion of essence in Zeta 6. It may be that (even) animal is the same as soul, or that circle the same as for-circle to be, or right angle as for-right-angle to be. These identities fix one use of the terms, “animal”, “right angle”, and the like: “the right angle without matter”—the form—is posterior to its parts, but prior to the parts “in the particular” [in the compound material right angle] (while we get different answers for the bronze right angle and its parts). But if the identities above fail, so that animal for example is not the same as soul, then by “animal” we mean something different—the living animal, not its soul—and different answers apply. Aristotle returns to the dual use of substance-terms like ‘animal’ and ‘circle’ in H3, where the two uses are explained in terms of core-dependent homonymy. We take the form as the core entity, while the matter-form compound belongs on the periphery and owes its nature as a substance to the entity at the core. We distinguish form or actuality from the compound material substance, thanks to the fact that only form satisfies the identity condition from Zeta 6:7 7.7 For soul and to be for-soul are the same, but to be for-man and man are not the same, unless soul too is to be called man: so “in a way yes, and in another, no” [sc. certain results hold only for the form or actuality, and not for the compound substance]. (H3, 1043b2–4, following Furth)

Thus, if we insert the name for a form into the formula, “x is identical with x’s essence”, the result should be a truth: for example, soul is identical with its essence. But if we insert the substance-term “man” into the formula, then the result will be true if “man” denotes the substance in the sense of actuality or form—that is, if by “man” we mean soul; but if we mean the compound material substance, the result will be false.

7 Aristotle argues in Z6 that the identity between a thing and its essence succeeds in some cases, but in others fails. Properly, we should allow for three cases: (i) essences for which the identity condition succeeds; (ii) “lesser-grade” cases of essence for which the condition fails; (iii) items which are not essences at all. Strictly, the fact that “man” is not an appropriate substituend for “ ‘x” in “x is identical with x’s essence” indicates only that the referent of “man”—here understood to be a given compound material substance— does not fall into (i). In fact, as we know, it falls into (iii).

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In this way, if not only the identity of a thing with its essence but also the scope of the identity thesis are settled in Zeta 6, then an ambiguity that stands at the heart of the study of sensible substance is readily resolved. On this account, in H3, Aristotle uses the conclusion in Zeta 6, that in certain cases a thing is identical with its essence, to help disambiguate our different substance-terms. Curiously, in Zeta 6, Aristotle also uses the identity conclusion to resolve an ambiguity—but not the ambiguity of substance-terms noted in Zeta 10 and H3, but that of “the pale” to denote alternatively the accident, pallor, or the subject of the accident (identified here as “the man and the pale man”).8 The essence of the pathos is the same as the pathos—but not the same as the man and the pale man. The ambiguity discussed in Zeta 10 and in H3 has no place in Zeta 6, where Aristotle is interested in the general structure any theory of essence must take; until this general story is done, he will avoid reference to form and matter, and withhold details of how the items in his own ontology fit into the structure he is putting in place. Still in thoroughly partisan mode, Aristotle attends to two other items of business in Zeta 10. First comes a review of the place of soul in the living animal (1035b14ff.), apparently summarizing the views in the de Anima. The soul of an animal is the substance of the “ensouled”—of the animal whose soul it is. That is, the soul of the animal is the substance in respect of the formula, that is, the form, that is, the essence of a certain sort of body. Aristotle adds a gloss on “certain sort of body”: properly speaking, each part of the living animal is functionally defined,9 in terms of its capacity to perform a certain kind of work within the economy of the living animal, tied up here with its ability to perceive. Aristotle’s remarks here are not obviously consistent with his earlier suggestion that the matter of a thing is to be kept firmly out of the definition of the form. If, as he says, a form is the essence of a certain sort of body, are we after all to make reference to the matter when we come to define the form? As his gloss suggests, Aristotle may think that the definition will include different capacities required of the different parts of the living body, if the parts are to perform their role within the economy of the living animal—without its having to specify the actual stuffs or structures that will support the expected work (Chapter 4, Section 15). The idea that the soul is the essence of a certain sort of body also requires comment. The essence of a thing, which is also its form, stands in different relations to the thing itself, and to its matter. Aristotle typically speaks of the relation of the form to the relevant matter: the form is predicated of the matter, and the result is a given compound material substance. Within the finished substance, it is thanks to the active powers associated with the form that the matter of the thing fully realizes its potential for constituting a thing of the relevant kind. So the form is properly the essence of the 8

For more discussion of this disputed text, see Chapter 5, n. 11. This is Aristotle’s notion of biological part, in particular, this or that non-uniform part, or organ: the organ of touch, the organ of sight, and the rest. 9

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finished compound material substance. But because it governs the matter that is a functioning part of the whole substance, the form is also (in this qualified sense) the essence “of a certain sort of body”—that is, of the matter in its fully worked-up state. At the same time, because the body of an animal is truly a living body only when it is fully in the grip of the form or soul, the living body and its living parts will not be prior to the living animal, 1035b23–25.10 Still other crucial parts, the heart, it may be, or the head—depending, I think Aristotle means, on your favourite biological theory—these are neither prior nor posterior to the whole, but exist simultaneously with the living animal itself, b25–27. Finally, on one important point, the shift to discussion in Aristotle’s own, “partisan” terms enables a striking innovation. The innovation has to do with how, on the new, partisan theory, we are to accommodate kinds, man, animal, and the rest, including the lowest kinds or genous eide¯ familiar from Zeta 4 (3.14 above). Far from being primary entities, as Zeta 4 imagines in the case of lowest species, or from rating as secondary substances, as in the Categories, kinds are now not even substances at all. Notably, the downgrading Aristotle has in mind can be achieved only within the new partisan theory of form and matter. In the partisan theory, individual substances, Archimedes, for example, are compounds of forms and matter; correspondingly, the kind, man, under which Archimedes falls, is itself a compound of “this form and this matter, taken universally” (8.6 and 8.17 below). I return to this new construal of kinds, and to the distance it puts between Aristotelian kinds and the conception of universals Aristotle finds in Plato’s theory of forms, in Chapter 8, Section 17, below.

2 A Partisan Question in Zeta 11 In Zeta 11, Aristotle continues to be occupied with the topic of definition. In contrast to Zeta 10, however, in Zeta 11 he is concerned from the start with in-house issues in In the text, Aristotle inclines both ways on the priority of the matter to the thing. With respect to “the parts into which the composite divides as matter”, b21–2, Aristotle tells us that “these are in one way prior to the compound but in another way not—for cannot even exist separated”, b22–3. He goes on to cite a severed (“dead”) finger as an example of what will not exist apart from its living owner. Aristotle apparently recognizes two kinds of case. In the simplest cases, a bronze sphere (say), the matter is the stuff or structure from which the sphere is made, and which persists in the product and can continue to exist after the sphere is hammered out of shape. Such cases conform directly to the pattern set out in the Physics (“By matter, I mean that primary underlying thing in each case, out of which as a constituent [enuparchontos] and not by virtue of an accident something comes to be”, Physics B9, 192a31–2); it also fits the idea, repeated in Metaphysics Z10, that a thing “divides” into its matter, which presumably survives even when the thing does not. But in other cases—the so-called homonymy of matter (Chapter 3, Section 7)—the matter of a thing is “trapped” by the substantial form of the thing: no hand, or finger, or eye that deserves the name exists before the animal comes to life, or after the animal dies (or the organ is removed). In the first set of cases, which conform to the Physics paradigm, the matter exists prior to the compound; but in the second, it clearly does not. Aristotle is far from consistent about the division of cases, however: he cheerfully contemplates dividing the man into bones and sinews and flesh in the role of matter, without worrying that homonymy may now apply, 1035a18–20, cf. 33, in the very chapter where worries about homonymy surface, b23–5. The homonymy of matter is a topic of ongoing discussion: for a recent entry, see, for example, Frey (2007). 10

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his own theory of form and matter. He begins (the opening words of the chapter) with yet another puzzle—a follow-up on its two predecessors in Zeta 10 (7.1 above), now framed in terms of form and matter: 7.8 We may also reasonably wonder (aporeitai de eikoto¯s, 1036a26, cf. b21–2) which sorts are parts of the form and which sorts are not, but the thing taken together. And yet if this is not clear, we will not be able to define each thing; for definition is of the universal, i.e., of the form; so if it is not clear which sorts of things among the parts are as matter, and which not, the definition of the thing too will not be clear. (Zeta 11, 1036a27–31)

Aristotle is straightforward that he has a single purpose in raising these questions: he means to preserve the integrity of definition, for “definition is of the universal and the form”, and if we do not know where form ends and matter begins, we will not be able to define. Where, then, are we to draw the boundary between form and matter in different cases? We may be tempted to include too much as form—to treat what is in fact matter as though it were part of the form. The difficulty is with items like men, where the form appears in a single kind of matter. Aristotle offers the thought-experiment, “Suppose all circles were made of bronze—would we then (mistakenly) think that bronze should somehow be included in the definition of circle?” In the circumstances imagined, we might want to put the bronze on the side of form; as things are, however, there are also wooden circles, and we are able to draw the line where it belongs, here and (perhaps) in the single-matter cases as well.11 But we must not over-correct, and include too little in the form, putting too much on the side of matter. Some Platonists, for example, try to make Two do duty as the form of the line: but the content of the Form here is unduly weakened, and puts us on the road to the conclusion that all differences lie on the side of matter, so that in the end, there is only a single (Platonic) Form for everything! Plato and the Pythagoreans are both liable to this result: 7.9 It then follows both that there is a single form of many things whose form is evidently different (just this conclusion followed for the Pythagoreans also), and it becomes possible to make one “thing-by-itself ” [= a single Platonic form] the form of all things, and the others not forms; however, in this way all things will be one. (1036b17–20, following Furth’s translation)

11 Aristotle’s thought-experiment is sometimes taken to encourage us to conclude that, although in fact all men share a single kind of matter, it is possible that they should not all do so. There arise here issues of the compositional plasticity of mental or psychological properties, and related questions concerning whether Aristotle is open to a functionalist account of soul or (in today’s terms) mind. I will not enter into the controversies over these issues here. As before, however (this chapter, nn. 5 and 12), we are faced with the question of whether definition should include a reference to matter, and if so, how.

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Various related points come up in the course of the discussion. For example, the earlier comparison between men and circles should not obscure the difference that circles can exist without bronze, but a man cannot exist without his parts in the appropriate state, i.e., without the various living structures that constitute his matter. Here, Aristotle may be worrying that we cannot be said to have defined a form fully, until we have somehow succeeded in specifying the appropriate kind(s) of matter.12 Another parenthetical note has to do with specifying the appropriate kind(s) of matter. Intelligible matter is not a source of sensible parts in the thing, but it is matter nonetheless, so that its parts have no place in the definition of the whole. That is: the form of circle supervenes on the semicircle as (intelligible) matter, so that the semicircle does not correspond to any part of the formula of the form of circle. By Rule II, then (Section 2), the semicircle cannot be a part of the form, and the definition of the form does not include the definition of the semicircle. Finally—but Aristotle says nothing about the relevance of the remarks—it is also clear that soul is primary substance, and the body is matter; and the kind, man, or animal, is the compound of these two, “taken universally” (see Section 1). Meanwhile, Socrates or Coriscus are compounds of this body and this soul (except that “Coriscus” can also pick out just the soul); so that “as is the universal, so the particular” (from 8.17 below)—i.e. (presumably) each is in its own way a compound. We are also reminded that there may be other kinds of matter (presumably, Aristotle has in mind the intelligible matter of mathematical entities), and other kinds of substances, numbers, perhaps, or unmoved movers, beyond perceptible substances. These remarks include the point that soul is primary substance (but not expressly that form plays this role); but even this limited remark, on the face of it, is only part of a broader reminder that, in different ontologies—Aristotle’s own, that of a mathematizing Platonist, and so on—similar decisions about what goes into a definition, and what stays out, will need to be made. The chapter closes with the topic of definition that has dominated both Zeta 10 and 11, to note that the question of the unity of definition is still outstanding.

3 On How Aristotle Manages the Shift from the Tradition to the Partisan Point of View (i): The Full-Expansion Condition on Definition, and the Drive to Form as Primary Substance? As the survey in Section 2 shows, even in the partisan portions of the discussion of substance as essence in Zeta 10 and 11, the point that in Aristotle’s own theory, form is 12

For the difficulties in squaring this worry with the strictures against including the matter in the definition of the form, see Section 1 and this chapter, nn. 5 and 11. Aristotle quotes Socrates the Younger as among the Platonists on the side of suppressing from its definition reference to the matter appropriate to a given kind of animal; for an engaging account of how the debate between Aristotle and Socrates might go, see Devereux (2011).

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primary substance, is made at best indirectly. It is not presented as the conclusion to any argument, let alone a conclusion that flows from the initial, “received” view governing the segment (3.1 above), that the substance of a thing is its essence. In the absence of an explicit argument for the place of (Aristotelian) form as primary substance, might we find in Zeta 10 and 11 the raw materials for such an argument? A possible source is the so-called full-expansion condition on definition that enters the discussion in Zeta 10: 7.10 (from 7.1 above) The puzzle comes up right away, whether the formula of the parts must be present in the formula of the whole, or not? In some cases they [sc. the formulae of the parts] are seen to be present, but in other cases not. (1034b22–24)

Formalize this as the requirement that, in the affirmative cases, The definition of a thing should contain the definitions of all the thing’s parts, except those that are definitional primitives. The Full-Expansion Condition13

We may suppose that this is a condition on the best kinds of definition—those that have a primary definable as their object. On this understanding, the Full-Expansion Condition allows that the best kinds of definition may contain definitional primitives but otherwise no parts that resist definition (as matter, for example, is said to do). The Condition would have no content, however, without the work on the different parts of substance and the different cases of substance and their parts, definable or otherwise, in the puzzles in Zeta 10 (7.2 and 7.3 above); and no content without the help we have been given in the puzzle that opens Zeta 11 (7.8 in Section 2) about where to draw the boundary between form and matter. These earlier results allow us to be clearer about definition in general, and about how to implement the FullExpansion Condition in particular. Given the connection between definition and the notion of primary substance, we can now use the Condition to identify which items in the “official” Aristotelian ontology can be reckoned the primary substances. We might think of Aristotle as having in mind an argument along the following lines: (1) (2) (3) (4) (5)

A thing is a primary substance (the substance of a thing) if and only if it is a primary definable. A thing is a primary definable if and only if it satisfies the Full-Expansion Condition. Among the different kinds of substance—form, matter, and compound material substance—only form satisfies the Full-Expansion Condition. (Only) form is a primary definable. From (2) and (3) (Only) form is a primary substance. From (1) and (4)

13

For the Full-Expansion Condition, see Code (1985), 199.

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Premiss (1) of this argument is one of the major conclusions of the earlier, “nonpartisan” discussion of the segment (3.24 = 5.7 above). And while (2) is not explicitly given, it seems to supply the natural motivation for including the Full-Expansion Condition in the discussion in the first place. The final steps, (4) and (5), are both inferred from previous lines in the argument. Meanwhile, the main force of the argument comes from premiss (3), as to how the different kinds of substance fare with respect to the full-expansion condition. The groundwork for (3), already done in Zeta 10 (Section 1), is reviewed in a passage later in Zeta 10: 7.11 A part, then, can be a part either of the form (by form I mean the essence), or of the composite “out of” the form and the matter, or of the matter itself. (b33) But only the parts of the form are parts of the formula, and the formula is of the universal: for the to-be for circle and circle, and the to-be for soul and soul, are the same. (1036a2) But when we get to the composite, e.g. this circle, i.e. one of the particular ones, whether perceptible or intelligible—by “intelligible” I mean e.g. mathematical ones, by “perceptible” e.g. brazen or wooden ones—of these there is no definition, they are known by thinking or perceiving, but when they depart from this completedness it is not clear whether they are or are not; but they are always formulated or known through the universal formula. (a8) But matter, in respect of itself, is unknowable. (1035b31–1036a9, following Furth’s translation)

Thus, the parts of the form alone (monon, 1035b34)—and, in fact, all of its parts, we assume—are parts of the definition (see case III in Section 1 above). But (case I above) a compound substance (a2ff.) contains parts—whether perceptible or intelligible matter—that are impervious to definition. So the compound substance cannot satisfy the Full-Expansion Condition, and is not (properly) definable: in each case, it is spoken of or known (only) through the universal formula, which omits mention of the matter of the thing altogether. Finally, (case II), the third kind of substance, namely matter, “in respect of itself ”, is simply unknowable (a8–9). In the optimal case, that of form, the definition of the whole contains the definition of all its parts, save the definitional primitives. In the intermediate case, that of the compound material substance, some parts (the form and its parts) are definable, but other parts (the matter) are not. And in the worst case—namely, the matter—neither the matter nor any of its parts are definable. On this story, the primary definable—and so also the primary substance—is that item all of whose parts (save the definitional primitives) get defined in the definition of the whole. Providing only that we know where to draw the line between form and matter—between those parts that are definable and those that are not—our work is apparently done. It may seem that this argument bypasses the essence criterion for substance altogether. In fact, however, it connects with the essence criterion for substance indirectly, via the equivalent notion of definition. We can think of premiss (1) in the argument given as a consequence of the received view with which the segment began, that the essence of a thing is its substance (3.1 above), in combination with one of Aristotle’s two main conclusions to the “non-partisan” discussion in Zeta 4 through 5,

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that a thing is an essence (the essence of another), just in case it is a primary definable ([i] in 3.2 above). The result is, in effect, a deductive argument from the received view governing the segment, that the essence of a thing is its substance, to the conclusion that (Aristotelian) form is primary substance.

4 On How to Manage the Shift from the Tradition to the Partisan Point of View (ii): The Full-Expansion Condition on Definition, and an Isomorphism Between Theories? For all the authenticity of its individual components, Aristotle does not actually assemble the argument just described. As before, while he assumes in Zeta 10 and 11 that form is primary substance,14 he nowhere in these chapters offers this as the conclusion of this or of any other argument. At the same time, much of the material just cited can be arranged quite differently, with a different conclusion, and relevant quite differently to Aristotle’s general project. In Zeta 4 and 5 we found grounds for distinguishing different grades of cases of essence. Only things that are suitably primary have an essence and a definition in the full sense. Arguably, Zeta 10 now contributes the following line of thought: (1) The definitions of some things include the definitions of their parts (save only the definitional primitives)—here, we will say that the Full-Expansion Condition is satisfied—but the definitions of other things do not. (2) The disparity just noted is explained if we suppose that there are different grades of definition, where a thing is a primary definable just in case it satisfies the Full-Expansion Condition. (1) and (2) express ideas about definition and the grades of definition that do not go beyond the non-partisan terms of Zeta 4–6. In particular, they share the idea that a primary definable will be a structured entity, with definable parts which (presumably) are subject to the unity condition that they “not be said by way of one thing’s being predicated of another” (Zeta 4, 1030a11–14, from 3.21 above). (But Aristotle gives no more detail in Zeta 11 as to how this unity is to be achieved than he does in Zeta 4.) Can the points about definition and the Full=Expansion Condition recorded in (1) and (2) be reproduced in the official theory? A fundamental assumption in the “official” theory concerns what it will count as the primary definables: (3) In the “official” theory of Aristotelian form, matter, and compound material substance, forms are the primary substances and thereby the primary definables.

14

Z10, 1035b14–16, and (with emphasis on the “primary”) 11, 1037a5, 28–9.

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It remains to refer to earlier work in Zeta 10 and 11 to show how Aristotelian form fits with the Full-Expansion Condition: (4) The Full-Expansion Condition is satisfied in the “official” theory of form and matter precisely when a form is being defined, and nowhere else. (1035b33–1036a1, from 7.11 above) The result in this case is a desirable isomorphism between the received and official theories: (5) Only those things in the official theory that are suitably primary satisfy the FullExpansion Condition, and so have a definition in the full sense. In this argument, if it is his, Aristotle assumes—not argues for—the point that (Aristotelian) forms are the primary substances, and shows that they are able to do the work required of them, where the work they are required to do is described first in “non-partisan” terms that are independent of the theory of form and matter. In particular, the distinction between primary and secondary cases of essence and of definition in an ontology where genous eide¯ are the primary substances (Zeta 4–5), is replicated in Aristotle’s own theory, where (Aristotelian) forms are both the primary substances and also the primary definables.

5 Some Conclusions The quite different account of Aristotle’s intentions in Zeta 10 in the last paragraph of the preceding Section suggests an attractive moral. On this picture, Aristotle is not focused on the Application Problem—on saying which items they are in his ontology that satisfy the definition of (primary) substance—and, at this point, not obviously on the more important and as yet unresolved question of how the actual definition should run. Rather, his aim in Zeta 10 and 11 alike is an holistic one, to bolster the general outlines of his own, partisan theory. To this end, a main concern in the segment on essence is to show how various fundamental features of the received views that are his starting point are properly reproduced in the “official” theory that supersedes them.15 Given his choice in his own theory of (Aristotelian) form as primary substance, Aristotle wishes to show that the properties of form and the relations between form and other elements in his theory duly reflect “received” expectations as to the properties of primary substance and the relations between it and other elements in the theory or theories being replaced. The segment on substance and essence is devoted at least in part to meeting this requirement. I have argued in the previous paragraph that the concluding chapters of the segment on essence support the role of form as primary substance. But the primacy of (Aristo15 For more on the project of “mapping” features of the old, or “received”, theory onto those of the new, partisan Aristotelian theory, see the remarks in Chapter 1, Section 8.

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telian) form is only intermediate on the road to the ultimate conclusion of Zeta. The success of (Aristotelian) forms in the role of primary substance gives Aristotle significant leverage on his larger goal of defining (primary) substance. If he already has strong reason to press the primacy of his forms, then it can be a constraint on the pending definition of (primary) substance, that it yield the required result, that form is primary substance. In this way, the segment on essence suggests that, on a sound conception of essence (and of the allied topic of definition), form is primary substance; this result in turn becomes an element in support of the successful definition of primary substance presented at last in Zeta 17. Now, Aristotle will say in Zeta 17 that the substance of a thing (and so primary substance) is properly defined as the cause of being for that thing. If he has good reason for thinking this definition correctly produces the result that his forms are the primary substances, and if his definition is best among its rivals for explaining this result—and it is surely preferable to the rival definitions that in one way or another have collapsed in the body of Zeta—then we have the materials for an abductive argument in support of the definition in the manner described above in Chapter 2, Section 11. On this account, the strategy I attribute to Aristotle takes the following form: If the Zeta 17 definition of (primary) substance as the cause of being for individual substances is correct, then form is primary substance. (We have antecedent reason in light of the segment on essence for thinking that) form is primary substance.

Therefore, probably: The Zeta 17 definition of (primary) substance as the cause of being for individual substances is correct.

This will not be mistaken for a deductively valid argument. But it is still support, if of a different kind, which Aristotle can put to use in the final chapter of Zeta.

PART FOUR

Substance as Universal

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8 Substance and Universals (I): Plato as Foe: Setting the Stage in Zeta 13 There need not be any forms, or some one item apart from the many, in order for there to be demonstrations. It must, however, be true to say that one thing holds of many. For there will be no universals if this is not the case; and if there are no universals, there will be no middle terms, and hence no demonstrations. There must, however, be something—one identical item—which holds of several cases non-homonymously. An. Po. A11, 77a5-9, Barnes’ translation

In the account of Aristotle’s ultimate objective in the segment on substance and essence (Part Three), I suppose that Aristotle accepts the received view that the substance of a thing is its essence: essence and the related notion of definition genuinely have a place in the new, “partisan” theory of substance. Neither notion rises to the level of a definition of substance, but each has in the new theory a role that mirrors in certain ways the role it has in the “received” theories with which Aristotle began. In the case of substance and universals, however, as earlier with substances and subjects, it is not obvious that the “received” view at the head of the segment even correctly characterizes the notion of substance, let alone successfully defines it. In Zeta 13, Aristotle will be occupied, not with how to make the transition from old theories to new, but with the prior question of whether the received view can so much as survive in the new theory. As we shall see, Aristotle pursues two main lines of attack, and both will be of use in setting up the discussion in the remaining chapters of the segment. Accordingly, the segment is overwhelmingly negative in force. But apart from a veiled reference to Plato (tisin, in 8.5 below), Aristotle lays out the different arguments of Zeta 13 without identifying their target. In truth, views that are vulnerable can be found in Plato’s dialogues, as in Aristotle’s own work; but equally, other views in both philosophers are exempt from—in Aristotle’s case, even fashioned so as to avoid?—the criticisms offered. Plato is all but named as a target at the beginning of the following Zeta 14, on the basis Aristotle tells us (9.2 below) of views expressed in 13, and he is repeatedly Aristotle’s target also in the concluding chapters 15 and 16 of the segment. The present Chapter 8 is the first of four to feature Aristotle’s treatment of universals as (in his view, uncertain) candidates for substances. I take up a further round of

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criticisms in Zeta 14 in Chapter 9, and in Chapter 10 we will look for signs of more positive views in the final two chapters, Zeta 15 and 16, of the segment. (As we shall see, the search will be largely in vain.) The arguments in Zeta 13 focus on a particular treatment of substance kinds— universals like man, horse, and the rest.1 Aristotle’s quarrel here is with two features of an account of kinds, summarized in the concluding lines of the segment at the end of Zeta 16: 8.1 Accordingly, (i), that none of the things said universally is substance and, (ii), that no substance is out of substances, is clear. (Z16, 1041a3–5)

The bare summary in 8.1 is, to say the least, elliptical. I will argue below that Aristotle’s conclusions address certain accounts of how higher kinds are universal to lower kinds, and how kinds are universal to concrete particulars2 (contrary to the views under attack, nothing can be simultaneously universal to and the substance of the same things); and of how a species can be a structured entity that has its genus as (in some sense) its part. Plato’s species- and genus-forms are especially vulnerable to this latter criticism, and Aristotle’s complaints on this score spill over into Zeta 14, which is in the nature of an appendix to 13. Aristotle’s discussion in Zeta 13 proceeds at the level of “received” views, so that his criticisms do not draw on his own “in-house” theory of (Aristotelian) form and matter. Even so, I stray occasionally into partisan territory in Sections 1–14 and in the Appendix, to ask how Aristotle’s developed theory of form and matter hold up under his fire. By contrast, in Sections 15 and following I turn to Aristotle’s own notion of kinds—much diminished in stature as compared to their status in the Organon and elsewhere—and their place in his “official” theory of form and matter: the discussion in these later sections, then, is occupied entirely with partisan concerns. I begin with the outlines of Zeta 13, where as 8.1 suggests, we will find two themes about universals intertwined.

1 The Programme of Zeta 13 Zeta 13 marks the second time Aristotle returns (palin epaneltho¯men, 1038b1) to the project of defining substance. At the beginning of the chapter he revisits and revises the Zeta 3 list of notions thought to be constitutive of substance, and selects his next topic: 1 The temptation to identify Plato as Aristotle’s target in 13 may seem selective, given his view in the Categories that substance-kinds—animal, man, and the like—are both universals and also substances (see also Metaphysics B1, 995b29–31, 3, 998b14–999a23, and H1, 1042a13–15). Notably, Aristotle has already in Z10 and 11 (7.4 above and Z11, 1037a6–7) retreated on the status of kinds, saying that for him, kinds are not substances of any grade (presumably, also, they will not be the substance of anything); see Sections 2 and 15–17. 2 As I understand Aristotle, his relation, “x is universal to y” includes both where a thing is a member of a kind and where one kind is included in another. For a similar remark concerning his said-of relation in the Categories, see Lewis (1991), 73–4.

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8.2 Since our inquiry is about substance, let us go back again. Just as the subject and (kai) the essence and (kai) what is out of these (to ek touto¯n) are said to be substance, so too (kai) is the universal. (Zeta 13, 1038b1–3, translation following Burnyeat)3

The view of substance as a universal, in one formulation or another, is at the centre of the discussion in all four chapters, 13–16, that make up this segment of Zeta. In the body of chapter 13, as we have seen, his discussion of universals is organized around two related conclusions, both negative. In the present section I set out the main points under each heading in his chapter. Aristotle states his first conclusion up front, before the main business of the chapter gets under way: 8.3 For it seems impossible that any whatsoever of the things said universally should be substance. (1038b8)

His first and second conclusions are flagged together in the recapitulation in the final lines of Z16 (= 8.1 above, repeated here): 8.1 Accordingly, (i), that none of the things said universally is substance and, (ii), that no substance is out of substances, is clear.

Ostensibly, each of Aristotle’s two conclusions introduces a restriction on the class of substances: no universal can be a substance (apparently in contradiction of the hypothesis in 8.2 with which the segment began); and no part of a substance can be a substance. What do these two restrictions amount to? How, if at all, is the one relevant to the other? How do they advance the project of defining substance? In particular, is the conflict with the opening hypothesis of the segment irresoluble? Aristotle withholds one obvious source of help, since in the present context at least, he appears indifferent to how in his own ontology the two claims might be either sustained or held at bay. For all the obliqueness of his exposition, we can be confident that Aristotle sees himself as presenting a systematic line of thinking in these chapters. The placement of the two summaries 8.2 and 8.1 above, at the beginning and at the very end of the Aristotle takes us back for a second time (back for the first time at Z4, 1029b1–3, 3.1 above; see Chapter 1, n. 42) to the agenda he set in Z3; as Burnyeat (2001), n. 89, points out, it is not a return to the topic of substance—with the suggestion that (ignoring the excursus in Z12) Z10 and 11 have no bearing on that topic (so Frede-Patzig (1988) II, 241–2). As to Aristotle’s agenda: he has discussed substance as subject in Z3, and substance as essence in Z4–6 and 10–11. “What is out of these”: the compound material substance appears in the “partisan” portions of Z3, and its status as a subject is noted there (1029a23, from 2.15 above) and in the retrospective in H1, 1042a29–31. It cannot claim to be primary substance, for it comes in second between the other members, form and matter, of the familiar Aristotelian trio (1029a30–32). The summary at the beginning of Z13 too strays briefly into partisan Aristotelian territory (to ek touto¯n, b3; he¯ hule¯ te¯i entelcheiai, b6), before settling back into the discussion of received views. Discussion of the universal in Z13 takes up the last surviving option for the definition of substance (the genus and the universal, listed separately among the original four in the Z3 agenda, are reduced to just the universal; Chapter 1, n. 18). Finally, a philological note: in the series of three kai’s (“and”) in the Greek, I read the third, not the first, as responding to the initial ho¯sper (“just as”); pace Gill (2001), n. 6 (following a suggestion by David Sedley), I see nothing in the Greek to favour the second reading over the first, and as Gill acknowledges, the first gives the better sense. 3

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segment, by itself suggests that he thinks of the intervening material—the remainder of Zeta 13 through to the penultimate line of 16—as a unified, coherent whole. I will depart from the order of Aristotle’s discussion in 13, and take up each conclusion separately in Sections 2–9 and 10–14 of the present chapter. I hope to show not only that the two conclusions shape the argument of Zeta 13 in a natural way (this will be the business of the present chapter), but also (in later chapters) that they order the remainder of the segment in Zeta 14, 15, and 16. First of all, however, it will be worth laying out how I take Zeta 13 to be organized. No Substance is a Universal (1038b8–23, 34–1039a3). After the introduction, the main discussion of the chapter begins with two longer, and related, arguments in support of his first negative conclusion, that no substance is a universal: 1038b8–15 (= 8.7 in Section 3): the Primary Argument. 1038b16–23 (= 8.8 in Section 7): a Reprise of the Primary Argument.

Interposed between these two, and not directly related to either, comes a two-line argument for the same conclusion, based on the idea that a universal is predicated of a subject, while familiarly (this chapter, n. 37), a substance is not: 1038b15–16 (= 8.9 in Section 8): on substance and predication.

Finally, following some lines devoted to his second conclusion (1038b23–30, reviewed immediately below), and an intermediate summary of results (8.14 below), Aristotle returns briefly to his first conclusion in the middle of the chapter: 1038b34–1039a3 (= 8.10 in #9 below): on universals and the this-such distinction.

No Substance Has (Actual) Substances As Parts (1038b23–34, 1039a3–23). In the remaining parts of the chapter, Aristotle is concerned largely with the second negative conclusion, that no substance has (actual) substances as its parts. His arguments pro and con—that yes, a substance has parts that after all are (actual) substances; and that no, the parts of a substance are not themselves (actual) substances—are arranged into a dilemma that forms one side of a larger dilemma. Aristotle’s dilemma within a dilemma can be diagrammed as follows:

the parts are substances a1

substances have parts

substances have no parts

A1

B1

the parts are not substances a2

indefinability!

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Thus (the larger dilemma), either (A1) substance is composite or (B1) it is not.

Suppose, now, with (A1), that substance is composite—for example, that the species, man, is a substance, and has the genus, animal, as a part. Then (the smaller dilemma) we have two possibilities: either (a1) man has (actual) substances as its parts, so that the genus animal is itself a substance, or (a2) its parts are not substances.

The failure of the two parts, (a1) and (a2), of A1 supposedly leads to the indefinability result that is said to follow from B1. Thus, against one arm, (a1), of A1, Aristotle argues that 1038b29–30, 30–34, 1039a3–14: substance cannot be composed of (actual) substances (Sections 10 and 13);

and against the second arm, (a2), that 1038b23–29: substance cannot be composed of universals, which are non-substances (Section 10).4

The failure of (a1) and (a2) together (supposedly) marks 1039a14–23: the completion of Aristotle’s “dilemma-within-a-dilemma” (Section 14).

Thus, if (a1) and (a2) both fail, then (A1) fails; it follows, apparently, that (B1) substance must be incomposite (1039a14–18). And if it is incomposite, there follows the crowning absurdity, that substance cannot be defined. But, famously, “if anything can be defined, substance can!” (1039a19–21). All of Zeta 13 that is not taken up with arguing for the first conclusion, that no universal is a substance, is structured around the dilemma featuring (a1) and (a2) and its larger containing dilemma, (A1) and (B1). In the argument against (a1), we find Aristotle’s second negative conclusion, that no substance has (actual) substances as its parts. The unity of the chapter is strengthened by the interdependence of the two conclusions that form its backbone. As we shall see, the two conclusions exhibit a common hostility to a Platonic theory of universals, which on Aristotle’s view violates both conclusions, and which emerges as his explicit target in Zeta 14 and passim in the remaining chapters, 15 and 16, of the segment. In Section 2 I sketch the general outline of Aristotle’s anti-Platonism implicit in Zeta 13 and to the fore in 14 through 16, and the details are taken up in following sections and in later chapters.

4 If the conclusion that “no substance is a universal” is sustained, then the choices, substance or universal, will be mutually exclusive. Aristotle silently assumes that the two options are also exhaustive.

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2 The Platonic View of Universals in Zeta 13–16 As in earlier chapters, Aristotle’s chief concern is with received opinions on the topic of substance. But while Aristotle is vehement in rejecting the received views connecting substances and universals—and most often seems to reject them outright, without qualification—the precise forms of the views he means to contest are not altogether clear. On occasion, his negative conclusions are importantly qualified, and target a specific way of linking the notions of substance and universal. At the same time, his later remarks suggest that some acceptable way of connecting the two notions is after all available.5 But Zeta 13 itself stays determinedly at the level of received views, and Aristotle suppresses details as to his own positive account of substances and universals. So, if we wish to glean the details of the views that meet his approval, we must be all the more careful about the exact form of the view that he means to reject. I argue that his arguments proceed on two fronts: he objects to a particular account of what universals are universal to—the view that they are universal to the very things of which they are the substance; and he objects to a particular account of the internal structure of certain universals (of the species man, for example). As already noted, the author or authors of the views under attack in Zeta 13 are left anonymous (certain views in Plato are an obvious target, but Aristotle’s own views elsewhere are not immune); while Aristotle makes the application to Plato clear in the next chapter, 14, so far as Zeta 13 is concerned it may be best to think that his interest is more in establishing the line of attack and the principles that underlie it, while he leaves the business of identifying suitable targets for later chapters. Now for some details. In Zeta 3 (1.4 above, repeated here), Aristotle cited the received view that one thing is the substance of another just in case the first is a universal: 1.4 Substance is said, if not in more ways, at least chiefly in four: that is, the essence and the universal and the genus seem to be the substance of each thing, and fourth of these, the subject.

This formulation is at least partially relational (“ . . . the substance of each thing”), but in its first formulation in Zeta 13 the view is non-relational through and through: 8.4 A thing is a (primary) substance if and only if it is a universal. (1038b2–3, cf. 9–10)

We come to this view, Aristotle seems to suggest, thanks to an idea due to Plato:

5 The epigraph to this chapter indicates the importance Aristotle places on having a theory of universals, free of the burdens of Platonism. Plausibly, he also sees a connection between the notions of universal and substance in Metaphysics Z16, where he appears to hold that a thing is a (primary) definable, only if it is in some way both a substance and a universal (Chapter 10, Sections 2–3 and Appendix). If this is right, the discussion in Z13–16 forces a revision in rather than the outright abandonment of the received view that substances can be universals (see Compatibility A and B in the Appendix to this chapter). Revision rather than rejection of the received view of substance as a universal can be compared with the similar need for revision in the view of substance as a subject discussed in Z3.

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8.5 The universal, too, is thought in some quarters [dokei tisin: the reference, I assume, is to the Platonists6] to be most of all a cause [“the truest cause”, Ross], and the universal to be a principle. (1038b6–8)

Aristotle may think that Plato sees a connection with substance thanks to the following argument: (1) x is universal to y and z (y 6¼ z) if and only if x is the cause par excellence of y and of z.7 (We know that a universal is, by definition, what is universal to many, and in [1] I assume the case in which the many are two in number.) (2)

x is the cause par excellence of y if and only if x is the substance of y.

Hence, (3)

x is universal to y and z (y 6¼ z) if and only if x is the substance of y and of z.8

That is to say, a universal is universal to the very things of which it is the substance. In contrast to Aristotle’s statement in 8.5 of Plato’s causal idea, (1) is explicitly relational. (2) is one version of the later idea that substance is “a principle and a cause of some kind” (arche¯ kai aitia tis, Zeta 17, 1041a9–10)—an idea cited in Zeta 13 as (presumably) Plato’s reason for promoting the role of universals,9 but which Aristotle greets as the basis for yet another “new start” at the beginning of Zeta 17.10 Finally, the 6

For the restriction to Plato as target, see this chapter, n. 1. For Plato’s view of universals as causes, see also ¸1, 1069a26–28. As I read Zeta, the reference to universals as causes is made solely to explain the Platonic ancestry of the idea: Aristotle makes no use in Z13 or in the other segments of Zeta of the causal ingredient in the notion of substance he is attempting to define, prior to the shift to the causal perspective of the An. Po. in Z17. Passage 8.5 carries the suggestion (“the universal, too”) that earlier candidates, the essence and the subject, also have causal force, but again nothing is made of this idea until Z17 and the retrospective in H1 (Chapter 12). For the contrary view, that Plato’s causal idea permeates the discussion in Z13, see Bolton (1995) 1996 (but we cannot support the causal reading of Z13, as Bolton attempts to, by simply replacing Aristotle’s “substance of ” systematically through the chapter by “cause of ”). 7 “the cause par excellence”: I take this to mean not “bracketing other causes”, but rather, “bracketing lesser varieties of cause”. So we must not press too hard on the definite article, given that more than one Platonic form may be universal to a thing and be among its causes par excellence; the (Platonic) forms, man and animal, for example, are both universal to Socrates and included among his causes. Note that there is trouble to come from the result, by (1) and (2), that man and animal both count as the substance of Socrates (on this, see later in Z13 at 1038b29–30, and Section 10). Finally, yet another caution: Plato typically thinks of a Platonic form as a “one-over-many”—that is, one form is universal to its many participants—but for convenience I consider the case in which an entity is universal to two things. (It would perhaps be more elegant to think of a Platonic form as universal to a (non-empty) set, which may then have either one or as many more members as we please, but I forego that complication here.) 8 The L to R direction of (3) seems essential to the strategy Aristotle sets in motion with the original list of received views in Z3. This direction of (3) is plausible, only if we assume a tacit restriction to substanceuniversals—to the kinds to which individual substances belong, but not their properties or accidents. With this restriction in place, (1), (2), and (3) can safely be written as biconditionals. 9 See this chapter, n. 6. 10 Z17, 1041a6–10 (see 10.1 below), where Aristotle’s inspiration seems to be more his own “other” self in the An. Po. rather than Plato. The statement at the beginning of Z17 is necessarily a good deal more cagey

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conclusion (3) is a relational version of the lead idea in 8.4 above.11 Aristotle’s response (8.1 and 8.3 above) to (3) is also best put in relational form: x is universal to y and z (y 6¼ z), only if x is not the substance of y and not the substance of z. Mutual Exclusivity Like the connection between universals and causes, the view of substance as a universal, or as universal to the very things of which it is the substance, can be also traced to Plato (if pressed, the Aristotle of the Categories and elsewhere may also seem a source for this second view).12 Indeed, Aristotle expressly says (1038b17) that this construction of the relation between substance and universal is modelled after that between substance and essence discussed in Zeta 4 and on,13 which (I have argued) is also due to Plato. More exactly, the idea in its relational guise as (3) expresses a conception of universals in which there hold results of the following two kinds: (i) The species, man, is both the substance of and universal to its instances, Socrates, Callias, and the rest. (In particular, the Platonic species-form, man, is both the substance of and universal to its participants, Socrates, Callias, and the rest.) (ii) The genus, animal, is both the substance of and universal to the different species, man, tiger, and so on. (In particular, the Platonic genus-form, animal, is both the substance of and universal to the different species-forms, man, tiger, and the like.) A primary aim of Zeta 13—16, as I see it, is to oppose any theory of universals with these features, both of which are in direct violation of Mutual Exclusivity above.14 On the interpretation I am suggesting, Aristotle means to address a further point on which Plato seems to be particularly vulnerable. As Aristotle represents him in Zeta 14, Plato holds that a species-form is constructed out of genus- and differentia-forms—man

than in (2), given the reworking Aristotle proposes in that later chapter of both cause and effect (on my account: the form is the cause thanks to which the matter is (constitutes) a thing of a given kind). Aristotle also connects the cause of a thing with its essence, Z17, 1041a28. For details, see Chapter 11. 11

In Z13, there are signs of the lead idea in both relational and non-relational form. Aristotle most often rejects a connection between substances and universals without qualification, in the non-relational form exhibited in 8.5: see this chapter, n. 18. As it stands, the second argument of the chapter, at b15–16, seems also to require a non-relational conclusion; see again n. 18. But there is also evidence of a relational version of Aristotle’s negative conclusion, rebutting the relational claim (3) in the main text: see 1038b30–2 (= 8.13 below), “If man and such things as are said in that way are substances, nothing in the logos”—that is, nothing in the logos of man and the rest (not animal, for example, which is universal to man and the other species of animal)—“will be the substance of anything”—it will not be the substance of any of the species. See also Z16, 1040b18–19. Importantly, it is the relational version (3) that is under attack in the main argument of the chapter at b9–15; see Lewis (1991), 313–14. 12 For Aristotle as target, see this chapter, n. 1. But the Aristotle of the Categories would have to accept use of the notion of the substance of a thing, which he has reason there to avoid, Introduction, n. 1. 13 See Section 7, and Chapter 1, Section 5; and for the connection with Plato, Chapter 5, Section 1. 14 The details of his critique of Plato’s theory and, especially, any assessment of its success or failure, is reserved for Sections 4–6 and 8.

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out of animal and two-footed (say). Since forms are all equally forms and, hence, all equally substances, it follows, to Aristotle’s disapproval, that a substance (the speciesform) has (actual) substances (the genus- and differentia-forms) as its parts:15 (iii) The genus-form, animal (itself a substance), is a constituent in the different species-forms, man, tiger, and the rest (themselves also substances). Aristotle’s arguments against (iii) take up the entirety of Zeta 14 (9.2 below), where the Platonists are evidently his target in all but name. Aristotle combines his conclusions in the summary 8.1 above, repeated here, with which he concludes the segment on substance as universal: 8.1 It is clear both that none of the things said universally is a substance, and that no substance is out of substances.

If Plato can be held accountable for all of (i) through (iii) above, then he will be in violation of both prohibitions in Aristotle’s 8.1. Despite the bluntness of his statement in 8.1, however, Aristotle may not reject outright the idea that (some) substances are universals. Instead, he means to cut down to size a certain conception of universals like man and the rest that are the kinds under which individual substances fall. We are not to think that these are themselves substances, or the substance of the items that fall under them. It remains to be seen whether there exist other entities—Aristotelian forms, perhaps—that are both universals and substances, but in a way that escapes the critique in Zeta 13. In Zeta 13 the argument for Mutual Exclusivity above readily includes Plato among its targets, but the philosophical weight of Mutual Exclusivity extends beyond controversy with Plato. It is tempting to see Exclusivity as an extension of the argument of Zeta 3, where Aristotle’s own Categories is a target. An essential component in the argument of Zeta 3 is the assumption that the items predicated of a subject are accidental to that subject, so that the subject is independent of them all (a24 from 2.15, and Chapter 2, Section 3). But how can a thing’s kind be independent of that very thing? If Archimedes falls under the kind, man, how can it simultaneously be true that his being is independent of that kind? On the independence assumption,16 if a kind is universal to a set of items, then it cannot be the substance of any of them, exactly as Mutual Exclusivity requires. This problem exists unaddressed in the Categories and, I suspect, it helps motivate the removal of kinds from the status of substances of any stripe, already on the books in Zeta 10 and 11: 8.6 Man and horse and the things that in this way to particulars, but universally, are not substance but a kind of compound of this form and this matter, taken universally. (Zeta 10, 1035b27–30) 15 According to Aristotle, Plato assumes that all forms whatsoever—genus-, differentia-, and species-forms alike—are all equally forms and, hence, all equally substances; see Z14, 9.2, 9.3, and 9.5, below. 16 See Chapter 2, Section 3.

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(See also this chapter, n. 1 and Section 15.) Once the kinds of the Categories are removed from the discussion, there remains as Aristotle’s target Plato, for whom kinds are full-fledged substances. Man and the rest, then, are not substances, as Plato thought (and as Aristotle once thought), and they are not the substance of the individuals, Archimedes and the like, they are universal to. And to move up a level, Aristotle will also question the status of the genus, animal (say); and he will also hold that animal is not simultaneously the substance of and universal to the different species, man, tiger, and the rest. In the background, meanwhile—but hardly explicit in the text—there may be a distinctively Aristotelian notion of universals. These will be part of Aristotle’s “in-house” theory of form and matter, which is not his business in Zeta 13. In the Appendix to this chapter I discuss ways in which Mutual Exclusivity leaves open the possibility of different versions of a compatibilist attitude towards the concepts of substance and of universal. The different versions of Compatibility may leave room for a flourishing Aristotelian notion of universals and their relation to substance in terms of the “official” theory of form and matter, details of which are largely suppressed in Zeta. In the end, the flexibility that I attribute to Aristotle over what seems at first the unqualified prohibition that no universal is a substance, may extend also to his views regarding the parts of a substance. The blanket prohibition, “no substance substances”, can perhaps be scaled back, to insist simply that no substance can have two (or more) actual substances as its parts. This modulated version of Aristotle’s view will not help Plato or Plato’s account of how (Platonic) forms can have other (Platonic) forms as their constituents; but it prepares the ground for an elegant solution to the related problem Aristotle sees of the “unity of substance”. As so often in Zeta, however, the details of the solution do not appear in Zeta itself.17 In Sections 3–9 I take up Aristotle’s first major conclusion, that no universal is a substance. I turn first to the Primary Argument, with which the argument of Zeta 13 begins.

17 The problem of unity—intractable for Platonic forms, as Aristotle sees it—arises also in the case of concrete particulars, which Aristotle sees as compounds of form and matter. How is it that the compound material substance can be a unity, if it has both form and matter as constituents—each of them, according to Physics B and Metaphysics ˜, apparently rival candidates for the nature of the thing? Aristotle’s solution is articulated most fully in Eta 6, where the problem of unity arises first in application to Plato’s forms and the thought that a Platonic species-form is a structured entity with given genus- and differentia-forms as its constituents; Aristotle does not say in this chapter whether there exist other kinds of structured entity in addition to compound material substances—Aristotelian kinds, for example, which certainly have a structure (7.4 above, = 8.6 below), or even Aristotelian forms or essences. There are earlier hints of Aristotle’s modulated view about the parts of a substance in the discussion of Democritus in Z13, 1039a7–11, and of lines (a5–7) and numbers (a11–14), Section 13. The modulated view may also be relevant to the closing dilemma of Z13, Section 14. Finally, Aristotle’s promissory note in the last line of Z13 (“what is meant will be clearer on the basis of what follows”, 1039a22–3) points forward to H6 but also, I take it, implies a backwards reference to the body of Z13 itself, where his solution is present only implicitly. For further discussion of the unity of substance in H6, see Charles (1994), Loux (1994), Lewis (1995) 1996, and Koslicki (2007) and (2008).

Z E TA

“NO

13, 1038 B 8–15:

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UNIVERSAL IS A SUBSTANCE”

3 Zeta 13, 1038b8–15: The Primary Argument Work in Zeta 13 begins in earnest at 1038b8, where Aristotle argues for the negative conclusion (i), that “none of the things said universally is substance” from 8.1 above, which, together with the point about the parts of a substance, he sees as the main result of this segment of Zeta. The argument runs as follows: 8.7 (b8) It appears to be impossible that any of the things said universally is a substance. (b9) For first of all, the substance of each thing is the one peculiar to each (he¯ idios hekasto¯i), which does not belong to (huparchei) another, while the universal common; (b11) for that is said to be universal which by nature belongs to many. (b12) Of what, then, will this be the substance? For either of all, or of none, but it cannot be of all; (b13) but if it will be of one, that one will actually be the rest; (b14) for those things of which the substance is one and the essence is one, themselves too are one. (1038b8–15)

As at the beginning and at the very end of the segment (8.1 and 8.2 above), Aristotle’s official conclusion, repeated at b8–9, deals with a non-relational notion of substance tout court. In the event, however, the relational notion of the substance of a thing enters immediately in the first lines of the proof itself at b10, and reappears repeatedly throughout, so that what he has actually proved involves the relational notion.18 In what follows, I will be interested not only in the form Aristotle’s conclusion takes, but also in the assumptions he needs in order to obtain his conclusion. The argument of 8.7 proceeds indirectly. Suppose that (4)

x is universal to y and z, where y 6¼ z,

and that (5)

x is the substance of y,

(“but if it will be of one”, b13 in 8.7 above). Now “. . . that is said to be universal which by nature belongs to many. Of what, then, will this be the

18 With the non-relational form of Aristotle’s conclusion at b8–9 in 8.7, compare b35 and Z16, 1040b21–3 and 1041a3–4, and the summary in H1, 1042a21–2. As it stands, the second argument of the chapter, at b15–16, seems also to require a non-relational conclusion: see 8.9 in Section 8. The non-relational line of thought exhibited in this argument also appears in B6, 1003a7–12, I2, 1053b16–18, K2, 1060b21, and M10, 1087a2. The (non-relational) claim that “no universal is a substance” is explicitly directed against Plato as a target at B6, 1003a9–12, and M9, 1086a32–b13, cf. SE 22, 178b36–179a10. See further, Lewis (1991), 309–21. For a relational version of the conclusion, see Z13, 1038b30–2, from 8.13 below, also quoted in this chapter, n. 11.

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substance? For either of all, or of none” (b11–13 from 8.7, my emphasis). Aristotle has a certain kind of uniformity assumption in mind: (6) Where x is universal to y and z, x is the substance of y just in case it is the substance of z. Uniformity19 Given our previous assumptions, it follows that (7)

x is the substance of z.

But “those things of which the substance is one and the essence is one, themselves too are one” (b14–15 from 8.7, my emphasis). That is, (8)

Where x is the substance of both y and z, y = z.

Partial Functionality20,21

In light of Partial Functionality in (8), and given (5) and (7), we have

19 For Uniformity, see Ross (1924) II, 210, “there is no reason why it should be the substance of one any more than of the others”, cf. Code (1978), 70, and Lewis (1991), 344. So Aristotle’s “either of all or of none” (b13) is not a logical howler. 20 For the sentiment expressed at b14–15, compare also b10, “the substance of each thing the one peculiar to each (he¯ idios hekasto¯i), which does not belong to (huparchei) another”. The interpretation of b10 requires some care. On one reading, what Aristotle is telling us is:

x is the substance of y, only if for any z, x is predicated of z only if z = y. Alternatively, he means that x is the substance of y, only if for any z, x is the substance of z only if z = y (Here, Aristotle’s huparchei (“belongs to”) is taken as merely a place-holder for “is the substance of ”). The first interpretation, pressed in discussion by Mario Mignucci, immediately rules out that the substance of a thing can be a universal—that it can be universal to anything—since it is predicable of exactly one thing: namely, that of which it is the substance, while a universal by definition is predicable of many. This reading of b10–11 requires the strong version of Aristotle’s conclusion, that no substance is a universal of any kind. But if the lines are read this way, then the argument requires just two premisses, rather than the more elaborate argument Aristotle in fact gives. The reading of b10–11 also collides with Aristotle’s remark at b15, to the effect (apparently) that “substance means what is not predicated of a subject”—not predicated of exactly one thing, apparently, but of nothing whatever! Both in this later passage at b15, and in the Primary Argument itself, I prefer the more nuanced reading, that nothing is both universal to and the substance of the very same thing(s), which is the conclusion to the argument that has the second reading of b10–11 as a premiss. On this second interpretation, b10–11 amount to no more than a restatement of Partial Functionality. In support of this reading, note the feminine gender, he¯ idios hekasto¯i, which indicates that Aristotle has in mind the substance (ousia, fem.) that is peculiar to each thing and which does not belong to another (sc. other than that to which it is peculiar). This second reading is also adopted in Code (1978), 67–8. 21 Partial Functionality follows easily from the Identity Premiss from Chapter 6, Section 1; see the Identity Result argued for in 6.2. Thus, on the assumption that y and z are both primary substances, if x is the substance of y, then by the Identity Premiss, x = y, and if x is the substance of z, then x = z; accordingly, y = z, as Partial Functionality requires; see Section 4. See also Zeta 16, 1040b17 (10.4 below), and the comparable principle for essence, Topics Z4, 141a35, and for definition, Z5, 142b35, 14, 151a33–34, b16–17.

Z E TA

(9)

13, 1038 B 8–15:

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y = z,

contrary to our initial assumption, (4). By reductio on (5), then, (10)

x is not the substance of y,

and by Conditional Proof, (11) Where x is universal to y and z and y 6¼ z, it is not the case that x is the substance of y. More generally, either by a fresh application of Uniformity in (6), or by a variation on the larger argument (4) through (11), (12) x is universal to y and z (y 6¼ z), only if x is not the substance either of y or of z. Mutual Exclusivity (4), (5), (6), and (8) are initial assumptions in the argument; (5) is the target of reductio, and (4) is absorbed by Conditional Proof into the antecedent of (11), so that in the end only Uniformity and Partial Functionality in (6) and (8) remain as undischarged assumptions. And as predicted, in place of the announced conclusion, that no universal is a substance, what Aristotle’s argument actually establishes is the relational claim, that if an entity is universal to many things, then it is not the substance of any of them. If, as we can easily imagine,22 Aristotle’s arguments in the Primary Argument can take in one or another version of Platonism as their target, then Mutual Exclusivity will govern not only the relation between a Platonic genus-form and its various species-forms but also, dropping a level, the relation between a Platonic form and the individuals that fall under it (cf. Zeta 14, 1039b16–19 for the move from one level to the other). Thus, if the Platonic genus form, animal, is universal to both man and tiger, then it can be the substance of neither. Similarly, if the Platonic form, man, is universal to the individual men, we must not think that man is the substance of the individual men (not even, perhaps, that it is a substance at all). The importance of the two assumptions, Partial Functionality and Uniformity, extends well beyond the Primary Argument. In Zeta 13 itself, both assumptions play a central role in the reprise of the Primary Argument a few lines later at b16–23 (8.8 in Section 7). Again, Partial Functionality is surely what gives punch to Aristotle’s later comment that if animal is the substance of Socrates, then it will be the substance of two

22 For the application of the argument to Aristotelian kinds in the Categories, and the larger philosophical point of Mutual Exclusivity, see Section 2.

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things (b29–30, 8.11 in Section 10). Partial Functionality crops up again in the outlying chapters of the segment, (perhaps) twice in Zeta 14, and once in Zeta 16.23 There is also a connection between Partial Functionality and the discussion of essence in Zeta 6 (Chapter 6). In Zeta 6, Aristotle strikes up an alliance with Plato. In that chapter, Plato is friend not foe, and is used as mouthpiece in the Elaborated Argument for the Identity Result, which Aristotle endorses, that each (primary) thing is the same as its essence. As I will argue, the Identity Result (or its close cousin), which works to Plato’s advantage in Zeta 6, commits him directly to Partial Functionality. But Partial Functionality, in company with Uniformity, can be made to count against Plato in Zeta 13. How can this be? Does the problem lie with Uniformity? Is Plato mistaken about what his own assumptions commit him to? Or do Aristotle’s criticisms of Plato misfire? These questions provide our topic in the following two sections.

4 Does Aristotle Play Fair with Plato in the Primary Argument?: The Primary Argument and the Argument of Zeta 6 Aristotle’s discussion in Zeta 13 rules against different theories of universals without singling out the author or authors of the views under attack. As we have seen, suitable targets exist in Aristotle’s own work elsewhere, as also in Plato. We may also wonder how Aristotle’s official theory of form and matter bears up under the criticism, even though in this part of Zeta only “received” views, and not Aristotle’s official theory, are a proper topic for discussion. I will reserve the impact of Zeta 13 on Aristotle’s official theory for later discussion (Section 6). And I will assume that Aristotle has already disavowed his own views about kinds that might seem to be under threat (8.6 and Section 2). But it will be useful to see how effective Aristotle’s discussion in Zeta 13 is, if we insert Plato as its target. To assess the fairness or otherwise of Aristotle’s criticisms, I begin with a closer look at what I take to be the background of the Primary Argument in the discussion of essence in Zeta 6.24 As we have seen (Chapter 6), the alliance between Aristotle and Plato in Zeta 6 reflects the fact that the discussion of essence at this point proceeds in a way that is neutral between their competing ontologies. If we want actually to apply the Identity Result of Zeta 6, that each primary thing is the same as its essence, we must first consult the details of our favourite ontology and find what counts as primary substance there; only then can we know exactly which items they are that we say are the same as their essences.

23

Zeta 14, 1036b9–11, and speculatively at b14–16 (see 9.9 and 9.10, with Chapter 9, nn. 2, 8, and 9); Zeta 16, 1040b16–18 (10.4 below with (12) and n. 15, Chapter 9, Section 5). 24 The resources of the discussion of essence are deeply implicated in the opening account of substance and universals in Z13; see Section 7.

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On this showing, since Platonic forms are what count as primary in Plato’s ontology, they should be the same as, even identical with, their essence, as Aristotle concludes in Zeta 6. But the entire segment on essence is ruled by the Governing Assumption, that the notions of essence and substance are equivalent (Chapter 6, Section 1); accordingly, each Platonic form should also be the same as its substance. This conclusion instantiates to Plato’s theory the Identity Premiss of the Basic Argument in Zeta 6, that each (primary) thing is the same as its substance, which I suggested had Plato’s as well as Aristotle’s approval (Chapter 6, Section 1). Accordingly, Plato should still be friend, not foe, in Zeta 13. As we have just seen, Plato and Aristotle alike accept the premiss of the Basic Argument in Zeta 6, that Where x is the substance of y and y is a primary substance, x = y. The Identity Premiss Given their joint commitment to the Identity Premiss, Plato and Aristotle have the same reason for accepting Partial Functionality: Where x is the substance of both y and z, y = z.

Partial Functionality

Thus, suppose that x is the substance of y (and that y is a primary substance), so that by the Identity Premiss, x = y. If x is also the substance of z (and if z is a primary substance), then by the Identity Premiss again x = z, so that by symmetry and transitivity, y = z, as required. At the same time, Plato has no obvious reason to resist Uniformity: Where x is universal to y and z, x is the substance of y just in case it is the substance of z. Uniformity These last two principles are the sole undischarged assumptions in the Primary Argument (Section 3). If both hold good for the Platonic theory of forms, Plato ought to endorse the Primary Argument. How is it that he ends up as potentially its target?

5 The Limits of the Primary Argument The Primary Argument is designed to show that Where x is universal to y and to z (y 6¼ z), x is not the substance either of y or of z. Mutual Exclusivity One difficulty is that this result hinges on principles like Partial Functionality, which (as we have just seen in Section 4) is tied up with the Identity theses of Zeta 6 (Chapter 6), so that the variables range over primary substances, including (if you are a Platonist) Platonic forms. On the current interpretation, however (Sections 2 and 3), Mutual Exclusivity can be used against Plato, to argue that that the Platonic form, man, cannot be simultaneously universal to Socrates and Callias, and the substance of both of them.

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Here, the values of y and z in Mutual Exclusivity are particulars—sensibles, not Platonic forms—and the application of Mutual Exclusivity is not legitimate. This problem is a symptom of a wider difficulty. First, some background. A theme in Zeta is that a variety of key metaphysical relations apply at different levels. For example, one thing has another as its essence in the primary sense, only if the first thing is a primary substance: for these cases, the thing and its essence are essentially the same, even identical. But Aristotle is explicit that lesser items in the ontology have an essence in a secondary or derivative way, and these are not the same as their essence. In these secondary cases, say that one thing is the essence* of another.25 We can make the point if we stray temporarily from the critique of Plato in (relatively) non-doctrinaire terms, to the terms of Aristotle’s own “partisan” theory. In the official Metaphysics theory, Socrates is not a primary substance. He is a compound of form, ł, and matter, m—write this, Socrates = m + ł—where ł is the essence* of Socrates, and manifestly, Socrates 6¼ ł. (Meanwhile, ł is the essence (no asterisk) of itself—of ł!—see Chapter 6.) Similar differences between primary and secondary apply to the relation, “x is the substance of y”. In the primary case of the relation, the terms of the relation must be primary substances, and each thing is the same as, even identical with, its substance. To stray once more into “partisan” mode: in the case of Socrates’ form, ł, ł is the substance of ł. But there are also secondary cases of the relation, so that ł is the substance* of Socrates himself, that is, of m + ł, and clearly, ł and m + ł are not the same. Apply this now to the result of the Primary Argument. The official conclusion, Mutual Exclusivity, of the argument features the unstarred substance-of relation; but this relation cannot hold between the Platonic form man and any particular man, Socrates or Callias (say), since these last are not primary substances. Suppose now that Aristotle means to apply his argument at this lower level, to the relations between individual substances and the relevant Platonic forms, as suggested in (i) in Section 2. If this assumption is correct, Aristotle seems simply to take for granted that a suitable version of Exclusivity can be found at the level of the secondary “starred” relation: Where x is universal to y and to z and y 6¼ z, x is not the substance* either of y or of z. Mutual Exclusivity* Thus, let x be man, and y and z be Socrates and Callias. Then if Mutual Exclusivity* holds, man is universal to Socrates and Callias, but not the substance* of either of them, contrary to what we are to think is Plato’s theory of forms.

For secondary, “starred” cases of the essence of relation, see the second half of Z4, 1030a17–b13 and Chapter 3, n. 11, and for the failure of the identity result in these cases as compared to its success in the primary cases, see the opening arguments of Z6 (Chapters 5 and 6). For similarly reduced, “starred” cases of the substance of and definition of relations, see Lewis (1984), n. 14, and passim. 25

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There is no support for making Mutual Exclusivity* the conclusion of the Primary Argument as it stands. But is there some plausible variation on the Primary Argument that can be forced on Plato, and can lead to Mutual Exclusivity*? Do the assumptions, Uniformity and Partial Functionality, of the Primary Argument have starred counterparts governing the *substance of* relation, that will give Mutual Exclusivity* as conclusion? The quick answer is that there is no starred counterpart to Partial Functionality that Plato can plausibly be made to accept: Where x is the substance* of both y and z, y = z.

Partial Functionality*

Partial Functionality* seems altogether out of the question. For example, the Platonic form, man, is the substance* of Socrates, and it is the substance* of Callias—but the two men are hardly identical. Recall that (unstarred) Partial Functionality springs from the (similarly unstarred) Identity Premiss above. Along with the rejection of Partial Functionality*, Plato and Aristotle alike will also reject the Identity Premiss*, Where x is the substance* of y—man of Socrates [say]—x is identical with y, The Identity Premiss* where the restriction that y be a primary substance has been dropped. The case of Uniformity is more complicated. It may be that there is a starred version of Uniformity that Plato must accept.26 But this will not be enough to make Plato a plausible target for Aristotle’s argument. Without starred versions of both assumptions, 26

As a first attempt, we might suppose that:

Where x is universal to y and z (y 6¼ z), x is the substance* of y just in case it is the substance* of z. Uniformity* For example, animal is universal to Socrates and Callias, and it is the substance* of them both. But this is not the full story. Recsall that animal is universal too to the various species that fall under it, man, tiger, and the rest. If we are allowed to say that animal is universal to man and to Socrates, and if animal is the substance* of Socrates, is it also the substance* of man? Most likely not. If man is a Platonic form, on a par with all the others (this chapter, n. 15), then it is a primary substance and it has a substance in the full sense: if animal is the substance of man at all, it will be the unstarred substance of man, and the substance* relation is not appropriate here. So we are not entitled to press Uniformity* against Plato. Perhaps, however, we need to split the universal-to relation into starred and unstarred cases, as we have already done for the substance-of relation. This will give us a new version of Uniformity: Where x is universal* to y and z (where y 6¼ z, and x is a Platonic form but y and z are individuals), x is the substance* of y just in case it is the substance* of z. Uniformity** Here, “x” ranges over Platonic forms, as before, but “y” and “z” range over sensibles. Uniformity** appears to fit Aristotle’s anti-Platonic purposes far better. For Plato, arguably, man is universal* to both Socrates and Callias; and it is the substance* of both of them. Given Uniformity**, and if he has Partial Functionality* in his armory as well, Aristotle can confront Plato with the unwelcome result (using all starred relations), that Where x is universal* to y and z (where y 6¼ z, and x is a Platonic form but y and z are individuals), x is not the substance* either of y or of z. Mutual Exclusivity** Unhappily, as we have seen, Aristotle is not entitled to assume Partial Functionality* on Plato’s behalf. So the double-starred version of Mutual Exclusivity is, properly speaking, beyond his reach as well.

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Uniformity and Partial Functionality alike, and in the absence of some other suitable argument waiting in the wings, there is no fair way of adapting the Primary Argument so as to construct difficulties for Plato. In a second set of cases, however, involving just Platonic forms, Aristotle’s critique stands a greater chance of success against Plato. Consider the relations between the Platonic genus-form, animal, and the two species-forms, man and tiger. We need to ask if in the case of these three, the unstarred assumptions, Partial Functionality and Uniformity, are satisfied, so that (by the Primary Argument) Mutual Exclusivity holds for this new case. Let us assume that animal is universal to man and tiger. Can Plato be forced to admit that animal is the substance (unstarred) either of both, or of neither, as (unstarred) Uniformity requires? Or can he insist on a starred version of Uniformity, so that man and tiger alike have, or do not have, animal as their substance*? Most likely the substance* relation is not appropriate in this case, if (as Aristotle emphasizes, 9.3 and 9.4 below) all three forms are equally forms and, hence, equally (primary) substances.27 At the same time, plausibly, Plato can be forced to concede on our original, unstarred Uniformity, so that on his theory, animal is universal to and the substance (unstarred) of both man and tiger.28 Can he still escape Aristotle’s argument by rejecting Partial Functionality? I suspect not. Partial Functionality follows from the Identity Premiss, that where x is the substance (unstarred) of y, x = y; and this in turn seems to hold in virtue of what it means to say of a primary substance that it has a substance, by reasoning we have supposed is at work in Zeta 6 (Chapter 6, Section 1). Two results follow immediately—both of them equally unpalatable to Plato. If animal is universal to man and tiger, then by Mutual Exclusivity it can be the substance of neither. At the same time, if animal is after all the substance of man and tiger, then the two species-forms are identical, by Partial Functionality. (And by the Identity Premiss, finally, it will follow both that man is identical with animal, and that tiger is identical with animal, so that again the two species-forms are identical.) To this point, I have argued that certain of Aristotle’s arguments cannot fairly have Plato as their target, on pain of blurring the distinction between starred and unstarred versions of the needed assumptions. But we must not think that his arguments are immune to objection on other grounds. For example, as Aristotle acknowledges, not only the genus, animal, but also the differentia, two-footed (say), contribute to the substance of the species-form, man. This thought invites a distinction between the incomplete and the full substance-of relations. Thus, Plato is in a position to respond that, given the different but complementary roles that the differentia- and the genus-forms play in the composition of the species-form, the genus-form, animal, for example, can

“all three equally forms”: see this chapter, n. 15. For animal as the substance (unstarred) of man, see 1039b8–9 with this chapter, n. 47. 28 Here I continue to set aside an objection based on the distinction between the partial and the full substance-of relations, see two paragraphs below in the main text. 27

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be only the incomplete but not the full substance of man, and only the incomplete substance of tiger, and so on. Since Partial Functionality should be understood to require that where x is the full (and not just the incomplete) substance of both y and z, y = z, Partial Functionality will not apply here, and the argument to a version of Mutual Exclusivity cannot go forward. Against this, Aristotle might think that there is no sense to the idea of an unstarred substance-of relation that is not a full substance-of relation. So if animal is the unstarred substance of man, as it apparently must be, it will also be the full substance of man.29 The move from “unstarred substance of ” to “full substance of ” may seem little more than an equivocation. But Aristotle may have an argument to back up this move. The point here concerns how Plato’s theory can accommodate the constitution of a species-form out of genus- and differentia-forms. On Plato’s terms, animal, two-footed, and man are all equally forms and, hence, all equally substances (this chapter, n. 15); accordingly, there is no ready account of how the first two jointly constitute the third. The rallying-cry of Zeta 13–16, “No substance is composed of substances”, speaks squarely against what Aristotle sees as Plato’s failure to address the problem of unity. Plato’s views leave him no way of seeing animal as anything less than the full substance of man. Similarly, two-footed will also be the full substance of man, so that man, which is a full-fledged substance, is composed of two similarly full-fledged substances.30 Yet a different objection to Aristotle’s arguments—the “own goal” or “friendly fire” objection—is to the effect that if his arguments work at all, they work as well against his own theory of (Aristotelian) forms as they do against a Platonic theory. To evaluate these objections, we will need to move beyond the relatively neutral framework within which Aristotle conducts his critique of Plato in Zeta 13, and address details in his own official metaphysical theory. For this reason, we will look at these objections separately in Section 6 immediately following, and return to our main theme in Section 7.

6 An Ad Hominem Objection to Aristotle: the Problem of Friendly Fire In this section we move away again briefly from seeing Plato as a target in Zeta 13 to consider the impact of Aristotle’s arguments on his own official metaphysical theory. If those arguments represent a trap for Plato, will that trap work as well—if it works at

29 Much this view appears in Topics Z1, 139a29–31, where Aristotle records the received opinion that of the elements in a definition, “the genus above all signifies the substance (ousia) of the item being defined”, cf. Z5, 142b27–9, 143a18–19. The pros and cons of such a view are also debated in Metaphysics B3, 998b14–999a23. I am indebted to Daniel Devereux for reminding me of these passages. 30 This result is the target of Aristotle’s arguments in H6, 1045a14–20 (“if the form, man, is two things, animal and two-footed, how is it that an individual man too is not two things—a member of two competing kinds—rather than just one?”). Meanwhile, for discussion of a related objection, see the comments in Matthews (2003).

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all—against his own theory of Aristotelian forms? Thus, (i), if Aristotelian forms are universals, we must suppose that one and the same form, ł, is found both in Socrates and in Callias; but if ł is also the substance of them both, then apparently, ł is both universal to and the substance of the very same things, contrary to Mutual Exclusivity, which was Aristotle’s conclusion in the Primary Argument. Again, (ii), ł is both the substance of Socrates and the substance of Callias, while evidently Socrates 6¼ Callias, contrary to Partial Functionality. Danger also threatens from the Identity Premiss, which seems to suggest that, (iii), if ł is the substance of Callias, then absurdly, ł = Callias. With respect to (ii): ł is the substance [unstarred] of itself—this is the Identity Premiss (Chapter 6, Section 1), which is harmless; meanwhile, ł is the substance* of Socrates and the substance* of Callias—but for the starred relation, no identity holds. Similarly, the Identity Premiss features the unstarred substance of relation, and so has no application to the case envisioned in (iii). As for (i): ł is predicated neither of itself, nor of Socrates or Callias, but of their matter (2.3, 2.4, and 2.5, and the introduction to Chapter 2); so ł is not predicated of or universal to the very things of which it is the substance or the substance*, and there is no violation of Mutual Exclusivity. Even if he does not have to worry about the problem of friendly fire, however, Aristotle’s critique, applied to a Platonic theory of universals, to this point is at best a qualified success.31 Zeta 13 contains still further arguments to which Plato’s theory of universals may be vulnerable, but again, perhaps, with varying degrees of success; we will discuss examples later in this chapter. First, however, I turn to the follow-up to the Primary Argument, where some main themes from the Primary Argument reemerge.

7 Zeta 13, 1038b16–23: A Reprise of the Primary Argument In what turns out to be a reprise of the Primary Argument (8.7, Section 3), it becomes clear that the Primary Argument is designed to bring out the difficulties in linking the notions of substance and universal in the way that substances and essences are linked in the segment on essence in Zeta 4 and following. In 8.8 below, Aristotle contrasts this earlier approach with what he suggests is a quite different proposal for how universals might be substances:32 31

In arguing in this section that certain of Aristotle’s arguments against Plato are undercut by the distinction between starred and unstarred versions of the needed assumptions, I do not mean to suggest that Aristotle’s criticisms are otherwise immune to objection. See in particular the distinction between the full substance of and the partial substance of relations; this chapter, n. 28. 32 For a very different reading of the lines that follow, see Gill (2001). On the view I am proposing, the reprise at b18–23 of the Primary Argument applies against a proposed revision (b16–18) in the view targeted in the Primary Argument. Gill suggests that the revision of the view under attack in the Primary Argument is

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8.8 (b16) But is the universal not capable in the way that the essence , (b17) but is present in it [= the essence], for example, animal is present in man and in horse?33 (b18) Then clearly, , there will be a logos of it [= of animal]. (b19) But, , it makes no difference even if there is not a logos of all of the things in the substance [“the substance”: man or horse, in Aristotle's example]34; (b20) for it [= animal] will nonetheless be the substance of something—as man of the man it is present in—(b22) so that we will get the same result again; for it will be the substance of that in which it belongs and is peculiar to (en ho¯i ho¯s idion huparchei, Ross’s text). (1038b16–23)

As Aristotle notes (“the same result again”, b22), this argument ends up being a reprise of the Primary Argument with which he began. The initial idea is to find a way in which the universal can be substance distinct from the way in which essence is substance. Aristotle’s final conclusion will be that the new way for a universal to be substance is open to the same objections set out in the earlier Argument. Unsurprisingly, the new argument will rest in part on assumptions familiar from before: on Partial Functionality, restated here at b22–3, and also on Uniformity (which Aristotle does not repeat here). What is the old way—out of favour for the new case of universals—in which essence is substance (b17)? In the segment on essence, Aristotle imposes the Governing Assumption (due, I suppose, to Plato, Chapter 6, Section 1) that one thing is the essence of another just in case the first is the substance of the second. The Governing Assumption is in force for the two species, man and horse, in 8.8: man and horse are essences (b17–18); they are substances (b18–20, see this chapter, n. 33). The initial idea, targeted in the Primary Argument, is that a comparable equivalence exists between the notions of substance and universal: that one thing is universal to another just in case the first is the substance of the second. Given the failure of this idea thanks to the Primary Argument, can we find some alternative way of making universals substances? Aristotle’s suggestion requires that that we define a new notion of substance. With respect to the genus, animal, for example, (i) Animal is a “substance” just in case for some y, y is a substance [no scare quotes] and animal is contained in y.

due to Plato, and occupies lines b16–19 (lines 18–19 here are part of the revised view, as Bolton (1995) 1996, 272, also supposes, and do not initiate criticism of it); meanwhile, the lines b19–23 do not continue an earlier criticism of the proposed revision but constitute a second, positive reply on Plato’s part. The fact that Aristotle appears to add to an existing line of criticism at b23 (so that the lines leading up to b23 will be negative rather than positive in tone) is met by emendation (eti de, “furthermore”, becomes esti de, “but”). My account in the main text follows that in Ross (1924) II, 210. 33 Note the assumption at b18 that man and horse are essences (that is, the essences of particular men and of particular horses). Aristotle also supposes that they are substances; see b20. 34 See this chapter, n. 33.

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Along with this goes a revised notion of universal: (ii) Animal is universal to the species, man and horse, just in case (and only because) animal is contained in both man and horse. We are to assume that the two species, man and horse, are bona fide substances (no scare-quotes), and that the genus, animal, is contained in both. Since animal is contained in one or more things that are genuine substances, it qualifies as a “substance”, by (i) above. At the same time, since animal is contained in the two species, it is universal to them both, by (ii). For better or worse, then, (iii) Animal is a “substance” just in case it is a universal: it is (perhaps) the “substance” of man and animal, and simultaneously universal to them both. What is new here is the proposal that the universal is not a substance directly or in its own right (“in the way that essence is substance”, b17), but indirectly or “by courtesy”, in virtue of being contained in something else that is properly a substance. The move to this new, weakened notion of “substance” may seem to immunize this new suggestion against Mutual Exclusivity, which applies to full-fledged substances, without scare-quotes. Aristotle’s counter-argument takes on the idea of the species, man (say), as a structured entity that has the genus, animal, as a part. The argument has the form of a dilemma. Either all the parts of the definable, man, are themselves definable, or they are not. If both alternatives fail, the attempt to find a new way in which the universal can be a substance is itself a failure. Aristotle’s first alternative, following Ross, points to an infinite regress. We are to suppose that animal is contained in man, so that because man is a substance, animal itself is a “substance”. Is this enough to make animal definable? If so, and if animal is to be defined in the way that man was defined, by distinguishing a genus part from its other constituents, which is itself a “substance” and so definable, we are well on the way to an infinite regress. Such a result is unacceptable, because it requires that the definition of the initial definable, man, be infinitely long, which Aristotle thinks is impossible.35 Suppose instead, however, that not every part of the definable, man, is itself definable, in particular, suppose that its genus part, animal, is not definable. Even with this concession, “it makes no difference”—the initial proposal is still unacceptable. For if animal is a substance—even a “substance”—Aristotle assumes that we cannot avoid one crucial assumption about it: “it will still be the substance of something” (b20–1). This repeats a move from the earlier argument at b9–15

35 Cf. the regress argument at Z6; and for Aristotle’s antipathy towards an infinite regress of essences, see Chapter 6, n. 14. The correct approach to the “full expansion” of a definition is taken up in Z10.

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(“if it is the substance of one”, b13 in 8.7 above). For example, let us suppose that it is the substance of man. The remainder of the argument too repeats much the same material as before. First, recall the assumption of Partial Functionality, invoked in the Primary Argument: x is the substance of y and x is the substance of z, only if y = z. By Partial Functionality, if animal is the substance of something, it will be uniquely the substance of that thing: “it will be the substance of that in which it belongs and is peculiar to” (b22–3). Evidently, however,36 this condition cannot be satisfied on the view under scrutiny. According to the Uniformity Assumption, also at work in the Primary Argument, x is universal to y and to z, only if x is the substance of y just in case it is the substance of z. But by assumption, we have it both that animal is the substance of man, and that animal is universal to man and to horse. By Uniformity, then, animal is the substance of both man and horse, and it cannot be peculiarly the substance of any one thing. It follows that by being contained in a substance, the universal is not after all a substance in any usefully novel way, and the suggestion is liable to exactly the difficulties set out in the earlier argument. It is worth noting that, if we take seriously the suggestion under scrutiny in the Reprise Argument, we are already willing to contemplate the possibility that the parts of a substance are themselves substances. More properly, they are “substances” (in scare-quotes). If we ignore the niceties the scare-quotes represent, we are already poised to consider the thesis contested in Aristotle’s second negative conclusion, that no substance may have substances as its parts. Unsurprisingly, then, the arguments immediately following in the text, beginning at 1038a23, take up the question of a substance and its parts. I will not here follow Aristotle’s order; instead, in Sections 8–9 I finish discussion of the first main conclusion of the chapter, before turning to its second main conclusion in Sections 10–14. Our immediate order of business is to pick up the second argument of the chapter, nominally on the difference between substances and universals, which occupies the two lines between the Primary Argument and its Reprise that have been our subject in these last few sections.

8 Zeta 13, 1038b15–16: On Substance and Predication Despite its announced conclusion, in the end the first argument of the chapter argues for a relational claim (Section 3). In the two-line argument that is its immediate successor, the implied conclusion appears more stubbornly non-relational: 8.9 Again, substance is said to be what is not predicated of a subject, but the universal in every case is said of some subject. (b15–16) 36

Following Schwegler (1847) IV, 115–16.

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That is to say: (13)

No substance is predicated of a subject.37

(14)

Every universal is predicated of a subject.

Hence (the obvious but unstated conclusion, which is both negative and non-relational), (15)

No universal is a substance. See 1038b8 (= 8.2 above).

But of course universals are universal to something; and—what is not true of all substances whatsoever—entities that are primary substances are also the substance of something. So it is not hard to find a relational version of the argument with premisses that Aristotle holds to be true, and that yield as a conclusion the relational claim that is his actual conclusion in the Primary Argument of the chapter: (13') One thing is the substance of another, only if the first is not predicated of the second. (14') A thing is universal to a number of things, only if it is predicated of all of them. Hence, (15') A thing is universal to a number of things, only if it is not the substance of any of them. Cf. Mutual Exclusivity, Section 2. As before, a variety of views may be under threat from the present argument, whether in relational or non-relational form. How well does the argument fare, in either form, against its potential targets? I begin with the non-relational version, (13)–(15), of the argument, and with how Aristotle himself might evaluate the argument. Let us begin with views due to Aristotle that fall outside the framework of the “partisan” theory of the Metaphysics. The ontology 37 (13) harks back to the unpacking in 2.2 of the received opinion 2.1 motivating the segment at Z3 (Chapter 2; see also 2.9 from ˜8, 1017b10–14, cf. 23–4, and—with a restriction to primary substances— Categories 2, 1b3–6, 5, 2a11–14, 3a8–9). The opinion in the form cited in Z3 is abandoned there, under pressure in part from Aristotle’s own “partisan” point of view; see Chapter 2, n. 16, and in the present section. More generally, premiss (13) raises the question whether the criteria governing the first two segments of Zeta, that substance is a universal and that it is a (basic) subject, are incompatible, so that the two segments pull in opposite directions. The definition of a (basic) subject in Z3 requires that everything else be predicated of a (basic) subject, while it is itself not predicated of anything else (this second clause follows from the first on the assumption that there are no predication cycles); but if a basic subject—that is, on the hypothesis at work in Z3, a (primary) substance—cannot be predicated of anything else, how can it be a universal? The conflict will be especially troubling if we assume that the different characterizations of substance offered in the Z 3 agenda (1.4 above) form a unified conception, only if they converge on a single item in the ontology. Two ways seem open to avoid conflict. It may be that the definition of subject in Z3 must be replaced with another that is more suitable in application to substance. Alternatively, even if the conflict is unresolved, the different conceptions of substance can be distributed among the different elements in the causal account of substance offered in Z17. I defer details of the convergence and distributive options to Chapter 11.

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of Aristotle’s Categories is one of individuals, their kinds, and their accidents, and here it is a hallmark of primary substances that they are not predicated of any subject. Against this background, the argument is sound. Aristotle can agree with the first premiss, that no primary substance is predicated of a subject (primary substances are neither said of nor in a subject); and he can agree with the conclusion, that no universal is a primary substance.38 Now Plato’s theory of forms is clearly in violation of this conclusion. But it is not clear that Plato should be bothered by this, since Plato would outright deny the first premiss, on the grounds that Platonic forms are primary substances, and are (metaphysically) predicated of sensibles. To this point, then, the argument settles nothing; it simply highlights differences between the rival Platonic and Aristotelian Categories theories. Certainly, the argument gives Aristotle no independent leverage against Plato. But there is more to the story. In the end—to turn away briefly from the “nonpartisan” views under discussion in Zeta 1339—like Plato, Aristotle himself comes to think that the first premiss, (13), is false. In the “official” theory of the Metaphysics, Aristotle takes a very different view of universals from that on offer in the Categories—in particular, a different view of what is universal to what. In this new context he will deny both the first premiss and the conclusion, (15), of the argument. He denies (13), because he now holds that Aristotelian forms are (primary) substances, but that they are predicated of matter. He denies (15), because Aristotelian forms are not only primary substances, but also (by virtue of their relation to matter) universals.40 On the non-relational reading of the argument, then, one Aristotle (the Aristotle of the Categories) holds that the argument is sound—but for this Aristotle, the result is harmless. Meanwhile, a second Aristotle, along with Plato, holds that it is unsound, with a false first premiss and false conclusion. As a piece of polemic, then—whether we take Plato or the first or the second Aristotle as its target—the argument is, to say the least, inconclusive. Next, the relational version, (13')—(15'), of the argument. As far as the first premiss (13') goes, on the relational reading, Plato would divide the question between the primary and the starred substance-of relations.

These points rest on the Categories conception of universals that are kinds, and which “exist through their instances” and, hence, cannot be primary. The disagreement with Plato over this point is clear, see the paragraph immediately following in the main text. 39 I insert here a reminder (see Chapter 1, nn. 21 and 34) that “non-partisan” in this context means only that Aristotle withholds the views distinctive of his own theory—but not that there is no contention to be found in passages I label “non-partisan” in this sense. On the contrary, there is an abundance of contention, just none of it conducted from a platform of full-blown Aristotelian theory. 40 This, at any rate, is the version of the story in Lewis (1985a) and (1991); variants of the story in Code (1986) and Driscoll (1981) deny that Aristotle’s forms are universals, on the grounds that bona fide universals require countable particulars as subjects. For scepticism on this point, see Lewis (1991), chapter 6, section 2. Again, on the “functional property” account of matter (Lewis (2008), section 8), the familiar stuffs and structures of the natural world can count as matter; on this view, multiple stuffs or structures that each count as matter can serve as subject to a single form, which will then be universal to them all. But for reservations about the notion of predication (and, hence, universal) in such cases and, in particular, the distance from issues of statement predication; see Lewis (2011) and Sections 16–19. 38

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(a) As to the primary substance-of relation, we may test (13') against the relation between a Platonic form and itself: arguably, each Platonic form is the substance (unstarred) uniquely of itself—here we remember the Identity Premiss presented on Plato’s behalf in Zeta 6 (Chapter 6). At the same time, each form Is itself, so that each form is predicated of itself.41 On this understanding, Plato can cheerfully dismiss (13'), and it has no traction in the remainder of the argument. At the same time, as we have already seen (in Sections 2 and 5), Aristotle may want to press on Plato the view that the genus-form, animal (say), is also the substance (unstarred) of each of the different species-forms, man, tiger, and the rest. At the same time, of course, it is predicated of each of them and so universal to them all. On this view, (13') is again straightforwardly false for Plato, and he has no reason to adopt the conclusion, (15'). Consider next, (b), the secondary, starred substance-of relation. On this reading, premiss (13') is once more false. Thus, each (Platonic) form is both the substance* of and predicated of a variety of sensibles: the first premiss is false for these cases too, and the rest of the argument is again moot. In contrast to this—stepping away again from Aristotle’s “non-doctrinaire” approach in Zeta 13, and across to the details of his “in-house” theory of form and matter—Aristotle and Plato will diverge over the starred case. Contrary to Plato, for Aristotle the starred version of premiss (13') is true. Thus, Socrates = the compound m1 + ł, and ł is the substance* of Socrates, but ł is predicated not of Socrates but of his matter, m1. The remainder of the argument then goes through without problem, and its conclusion is yet another statement of Mutual Exclusivity. The form, ł, is universal to, and (metaphysically) predicated of, the matter, m1, of Socrates, the matter, m2, of Callias (m1 6¼ m2) and so on; but ł is not the substance* of either m1 or m2. Acceptance of the key premiss, (13') and the rest, however, is a question only of how things work out in Aristotle’s ontology. Nothing about the decision here rests on “big tent” principles that should appeal to other philosophers to the same degree that they do to Aristotle. Since Aristotle’s position on the premisses is theory-specific, as opposed to theory-neutral, he cannot find in the eventual conclusion, (15'), an independent, nonquestion-begging lever to use against Plato. As noted, the argument just discussed is sandwiched between the Primary Argument at 1038b9–15 and its Reprise at b16–23. There follow at b23–29 and b29–30 two arguments on the second topic of interest to Aristotle in these chapters (= [ii] from 8.1 above), about how a substance can have parts. I have already suggested (in Section 7) that the transition to this second main theme of the chapter is aided by the thesis that Aristotle rebuts in the Reprise Argument, that a substance may have “substances” (in scare-quotes) as its parts. In the two arguments immediately following the Reprise Argument, Aristotle will argue both pro and con—first, that the parts of a substance 41 For the pedigree of this claim, see Chapter 6, Section 5. Thus, if (as Aristotle takes Plato to hold) a Platonic form, X, is identical with its essence, E(X), and if E(X) Is X, it follows that X Is X. The starred–unstarred distinction is explained in Section 5.

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cannot not be substances (without scare quotes); and next, that they cannot be substances either. (The case con—that a substance’s parts cannot themselves be (actual) substances—is argued again twice over later in the chapter.) The two arguments are followed immediately at b30–34 by a summary in which, arguably, Aristotle has both conclusions (i) and (ii) from 8.1 above in view (Section 12). On the view of how Zeta 13 is organized that I offered at the beginning of this chapter, the two arguments and the Summary at b23–34 come out of order. So I defer discussion of them to Sections 10–11, and proceed here to the argument that immediately follows them, which returns unequivocally to the topic of Aristotle’s first conclusion, (i), from 8.1.

9 Zeta 13, 1038b34–1039a3: Universals and the This–Such Distinction After some intervening material, as we have seen, Aristotle reverts at b34 to his first conclusion, (i) in 8.1 above, in its non-relational form, that no universal is a substance. On top of the reasons already given for this conclusion, he now tells us, there is the further point that no universal signifies a this, but a such. (Otherwise we face a variety of difficulties, in particular—in an explicit, if passing, reference to Plato—the Third Man Argument.) Translations of the passage differ, and I give my preferred version in full: 8.10 It is plain both (te) to those looking at it from these , that none of the things belonging universally is a substance, and because (kai hoti)42 none of the things predicated in common signifies a this, but a such (a1–2). Otherwise, among many other results, there is especially the Third Man. (1038b34–1039a3)

Aristotle means to add to the arguments retailed in earlier parts of the chapter, gesturing at a1–2 at an argument that he sets out in full elsewhere (B6, 1003a7–9). On the face of it, the argument he has in mind is this: (a)

A substance signifies a this (but it does not signify a such).

(b)

No universal signifies a this (it signifies instead a such).43 a1–2.

Hence, (c)

No universal is a substance.

It may be, however, that the argument in 8.10, as filled out in (a)–(c) above, can be adapted to produce a relational version of the conclusion, (c). To this end, suppose that premiss (b), that no universal is a this, can be qualified to say that nothing universal kai hoti: “and because”, with most translators, not “and that” (Gill (2001), 238, cf. 246): Aristotle is giving not a new conclusion, but a new reason for an old conclusion. The same construction appears at Z6, 1031b18–20. 43 Aristotle’s reference at the end of 8.10 to the Third Man Argument, I take it, is no more than a footnote to support premiss, (b), that contrary to Plato, no universal is a this, see also Categories 5, 3b10–21, SE 22, 178b36–179a10, Metaphysics B6, 1003a7–12. 42

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to a this can itself be a this. This qualified thesis requires two assumptions. First, uncontroversially, a universal is (metaphysically) predicated of the things it is universal to. Second, less obviously, (metaphysical) predication can tolerate only a mix of thises and suches as its arguments. That is: One thing is predicated of another, only if exactly one of the two is a this, and exactly one a such.44 The This–Such Assumption With the modifications indicated, we get this argument: (a)

A substance signifies a this (and not a such).

(b') If x is a universal and x is predicated of y, and if y is a substance and, hence (by [a]), a this, then (by the This-Such Assumption) x is not a this but a such. Accordingly, (c') If x is a universal and x is predicated of y, and if y is a substance, then x is not a substance. That is, nothing universal to a substance is itself a substance. A fortiori, then, (c'') If x is a universal and x is predicated of y, and if y is a substance, then x is not the substance of y. If the conclusion of the argument Aristotle gestures at in 8.10 is fairly as represented by (c''), then his conclusion is a restricted version of our old friend, Mutual Exclusivity: Where x is universal to y and to z (y 6¼ z), x is not the substance either of y or of z.

I say “restricted” because of the added provision in the antecedent that the item, y, to which x is universal is itself a substance (Mutual Exclusivity, on the other hand, places no restrictions on the status of the entities the universal, x, is universal to). The restricted conclusion in (c'') is well-adapted, if we think of the argument as including the Platonic theory of forms among its targets.45 If the species-forms, man and tiger, are substances, and the genus-form, animal, is universal to these, then by (c'), animal itself cannot be a substance. A fortiori, by (c'') it may not be the substance of either of them. Again, if the form, man, is universal to the individual men, we must not think both that the individual men are substances, and that man too is a substance or is the substance of the individual men. We have just seen that if man and tiger are substances, and animal is universal to these, then animal itself may not be a substance or (presumably) the substance of either of them. But Plato will also hold that animal is a part of both man and tiger. On the 44 The condition on predication is satisfied by the core relations of predication in Categories 5, but, harmlessly, not the defined cases; see Chapter 6, n. 43, and for the core/defined cases of predication, see Lewis (1991), 73–8. 45 Does (c'') have purchase against the different levels of secondary substance in the Categories? Aristotle does not say in the Categories that animal (say) is the substance of man or of tiger (see Introduction, n. 1); and in any event, his view in the Metaphysics is that none of the three counts as a substance of any grade (8.6 above).

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present showing, then, if man (say) is a substance, its part, animal, cannot be a substance, and cannot be the substance of man, tiger and the rest. In this way, Aristotle’s first negative conclusion, (i) from 8.1 above, that no universal can be a substance, overlaps at the level of forms in Plato’s theory with his second negative conclusion, (ii), that no substance may have (actual) substances as its parts: the genusform, animal (say), may not both be a part of the species-form, man, and simultaneously be a substance, or simultaneously the substance of the species-form. Without announcing the shift from the one conclusion to the other, Aristotle mixes in with his discussion of the first conclusion arguments that bear on the second. This new set of arguments is our topic in Sections 10–14.

“NO

SUBSTANCE CAN HAVE ACTUAL SUBSTANCE

AS ITS PARTS”

10 Zeta 13, 1038b23–29, 29–30: A Substance and Its Parts In the Reprise Argument towards the beginning of Zeta 13, as we have seen (in Section 7), Aristotle considers the proposal that a genus can be a “substance” by being part of something that is a substance in the full sense. So the initial topic of the chapter concerning substances and universals, quite early points to Aristotle’s second topic, concerning a substance and its parts. Aristotle is headed for the second of the conclusions he summarizes in the closing lines of chapter 16 (= 8.1 above, repeated here): 8.1 Accordingly, (i), that none of the things said universally is substance and, (ii), that no substance is out of substances, is clear (my emphasis).

At 1038b23, Aristotle turns without formal notice to this second item on his agenda: Are the parts of a substance themselves substances? As we shall see, he suggests that difficulties await both a positive and a negative answer to this question (a positive answer takes up option [a1] in Aristotle’s “dilemma within a dilemma”, Section 1, while the negative answer adopts option [a2]). Aristotle begins by rejecting a negative answer, that a substance is composed of nonsubstances (= [a2] above). If a substance were composed of non-substances, then impossibly non-substance and quality would be prior to substance. But (along the lines of the warning in Zeta 1) substance is prior to non-substance both in definition and in time and in coming-to-be.46

46 Z1, 1028a31–b2, cf. 13, 1038b26–9. But the different kinds of priority do not line up exactly in the two passages, unless we accept Lord’s emendation gno¯sei for genesei at 1038b28.

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Aristotle follows up this argument with another, which I take it addresses the unhappy consequences of the alternative hypothesis, that a substance can after all have substances as its parts ([a1] above). He tells us, baldly, that 8.11 Again, there will be a substance [= the genus, animal?] present in Socrates, so that it [= the genus, animal?] will be the substance of two things. (b29–30)

To provide the stage-setting Aristotle himself omits: we are to suppose (for the sake of reductio), (i), that the species, man, is a substance and has the genus, animal, as a part and that, like man, animal too is a substance. Suppose further that, (ii), the substance, animal, is also the substance of the species, man, of which it is a part (Aristotle defends the application of this assumption to Plato’s forms in the next chapter, Zeta 14).47 Assume also that, (iii), the species, man, is present in Socrates, so that plausibly, not only is man a substance, but also, (iv), man is the substance of Socrates. By transitivity of the presence-in relation, (v), the genus, animal, too is present in Socrates, so that plausibly (by prior reasoning) animal is not only a substance, but also, (vi), the substance of Socrates. It follows, says Aristotle, that, (vii), animal is the substance of two things—of both man and Socrates. Different reasons come to mind for finding the “substance of two things” result absurd, as Aristotle plainly means us to do. One source of difficulty, Aristotle may think, is Partial Functionality. If animal is the substance of both man and Socrates, then by Partial Functionality, absurdly, man and Socrates will be identical. At the same time, there is the threat of conflict with Mutual Exclusivity. Let us grant that animal is universal to man and to Socrates. Suppose now that substances can have substances as parts: for example, that man has animal as a part, and that man and animal are both substances. Suppose also that because it is a part of man, animal is thereby the substance of man, as well as of Socrates. Then we are committed to thinking that animal can be the substance of the very things, man and Socrates, it is universal to. In this way, by violating the one rule, that no substance can have substances as its parts, we seem obliged to violate the other as well, that nothing is universal to and the substance of the very same things. But are things really that easy? In the case Aristotle puts before us, with asterisks added as needed, animal is the substance of man but only the substance* of Socrates. If we allow the use of asterisks in our theory, Partial Functionality (which has no asterisks) cannot correctly apply, and the objection from Partial Functionality fails. What, next, of Mutual Exclusivity? In the example, animal is universal to both man and to Socrates. Contrary to Mutual Exclusivity, animal is also the substance of man: here, apparently, Aristotle scores a hit. But—supposing, again, that we allow the use of asterisks—the fact that man is also the substance* of Socrates is irrelevant to Mutual Exclusivity. The upshot is that while a genuine difficulty can be found, the comment that animal “is the

47

“for man is not accidentally ‘out of ’ animal”, Z14, 1039b8–9, 9.8 below.

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substance of two things”—where Socrates is one of the two in question—may not suitably pinpoint the problem. In particular, if we see Plato as a target of Aristotle’s argument, and if Plato would insist that a Platonic form is (merely) the substance* of the relevant individuals, Aristotle’s record of success against Plato continues to be mixed.

11 The Problem of Friendly Fire Again As with the Primary Argument (see Section 5), the objection also arises that, absent the distinction between the substance-of and the substance*-of relations, if Aristotle’s argument apply to anyone, they also apply to himself. For on his own theory, it seems, the form, ł, will be both the substance of itself and also the substance of Socrates (say), and hence, presumably, the substance of two things.48 As before, it is not Aristotle’s purpose here to address the “fit” between different elements in his discussion of “received” views with his own official theory of substance, so that considerations with regard to Aristotelian form are not to the fore. In defence of the official theory, however, in that theory, ł is the substance of ł (but not of Socrates), and it is the substance* of Socrates (but not of ł); so neither substance relation is such that ł stands unambiguously in that relation both to Socrates and to itself. At the same time, Aristotle can run into difficulties in expressing his position, since he has no separate terms, either for the generic substance of relation, or for the substance of and the substance* of relations that are its subrelations. The embarrassment that results is put before us in a passage from Zeta 16: 8.12 . . . the substance belongs to [huparchei, = “is the substance of ”]49 nothing but itself and what has it, of which it is the substance. (1040b23–4)

Gill takes this to be a source of major difficulty for Aristotle’s own substantial form: how can Aristotle’s observation apply to substantial form, and at the same time, form satisfy the Partial Functionality requirement, that substance be proper to only one thing? And how can 8.12 be squared with the idea that substance is predicated of one thing but the substance of another, along the lines of Mutual Exclusivity?50 As I read 8.12, the final relative clause gives the antecedent of a conditional, for which the remaining (and earlier) part of the sentence serves as consequent:

48

See Gill (2001), 248–9, 253–4. Aristotle’s statement in 8.12 is more than usually obscure. In place of the preferred rendering given in the text, Aristotle could be understood to mean that 49

x is the substance of y if and only if x is predicated of itself and otherwise of y but of nothing else. The huparchein at Z13, 1038b9–11, from 8.7 offers the same set of choices, see this chapter, n. 20. 50 Gill (2001), 253; 252.

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if x is the substance of y, then x is the substance only of y and of itself, x—but of nothing else. So understood, Aristotle’s statement in 8.12 leaves open the possibility that y = x. (On this reading, in “to nothing but itself and what has it” in 8.12, the “and” [kai] is epexegetic: x is the substance of y, only if x = y, i.e. [kai] x is the substance of itself, x.) But if x and y are not identical, then the different substance of relations come into play and, I suggest, we have a case of philosophical syllepsis. That is, x is the substance (unstarred) of the one thing, namely itself, x, but the substance* of the other(s), y and the rest. So Aristotle is not required to admit counter-examples to Partial Functionality or to Mutual Exclusivity into his own theory after all.

12 Some General Results, 1038b30–34 Midway through Zeta 13, Aristotle offers a summary of his results to that point. The summary explicitly states one instance of the first of his two main conclusions in the segment, and hints at his second conclusion, while adding a reference to the alternative proposal (that a substance may have a “substance” as its parts) considered in the Reprise Argument: 8.13 (b30) In general, it follows (holo¯s . . . sumbainei) that if man and such things as are said in that way are substances, (b31) nothing in logos [= animal (say)?] (i) is the substance of anything [= of man and the rest?], or (ii) exists apart from them, or (iii) in something else: (b33) I mean, that, for example, there is no animal over and above (para) the particular [= man, tiger, and the other lowest kinds]; nor anything else of the things in logos. (1038b30–34)

Aristotle writes, “if man and the like are substances”: this is his own view in the Categories; and it is also Plato’s. In Metaphysics Zeta 10 and 11, as we have seen (this chapter, n. 1 and Section 2, cf. Sections 15 and 17), he sets the idea firmly to one side. But suppose with Plato that man and the rest are substances after all. Then, contrary to what Plato will think, the genus, animal (say), which appears in the definition of man, tiger, and the rest, (i) cannot be their substance, and (ii) it cannot exist “apart” from man and the other species-forms—it is not a substance tout court. As these conclusions are written, they apply to any ontology of genus, species, and differentia in which items of all three kinds are taken to be substances. In particular, the conclusions have bite when directed at the status of genus-forms in Plato’s ontology (the last clause of 8.13 leaves room also for differentia-forms). Strikingly, Aristotle states his conclusion in both non-relational and relational form: if man and the rest are substances, then the genus, animal, is not a substance ([ii] above); and it is not the substance of any of the lowest kinds ([i] above)—it is not the substance of the same thing(s) it is universal to. This is just Mutual Exclusivity, which is

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the conclusion to the Primary Argument, and one of the two principal conclusions in Zeta 13–16. Aristotle also reminds us (b31) that animal is included in the logos of man, tiger, and the rest. Since to the parts of the linguistic definition of a thing there correspond real parts of the thing itself (Z10, 1034b20–22, 7.1 above), we have the further assumption that the genus is a part of its various species.51 From this and from result (ii) above, that animal is not a substance, it follows that the parts of a substance are not themselves (actual) substances. This is Aristotle’s other main conclusion in these chapters (8.1 above). Meanwhile, (iii), animal is not “in something else”—that is, I suppose, although it is a constituent in the species, man, it is not for that reason a substance (this is the suggestion put under scrutiny in the Reprise of the Primary Argument, Section 7). In the recapitulation at b33ff, finally, Aristotle has in mind the version of his conclusion stated in (ii): the genus does not exist “over and above” its various species. Even if (what Aristotle denies) the latter are full-fledged substances, the former assuredly is not. More generally, nothing in the definition of man—not the genus, but presumably, not even the differentiae—is a substance.

13 Lines, Numbers, and Democritean Atoms: 1039a3–14 In the passage that follows his summary, Aristotle returns to the question: Can a substance be composed of substances as its parts?52 So far, he has found reason for rejecting both negative and positive answers (Section 10). He now apparently finds grounds in favour of a qualified negative answer, while also leaving the door open to a positive answer, given the right qualifications. No substance can be composed of substances existing in actuality, and what is two in actuality cannot be one in actuality: they will be one only if they are potentially two (1039a3–6). (The emphasis on actuality and potentiality here is significant, in light of the role the two notions play in the eventual solution of the problem of the unity of substance in H6.) Aristotle makes three applications of the qualified negative view: to lines (a5–7), to Democritus’s atoms (a7–11), and to numbers (a11–14). Aristotle is explicit that the unity of substance is a controlling factor in these different cases. If a substance is a unity, it cannot be composed of substances existing in it in actuality (a7–8). Just so, you cannot get one atom out of two (one actual atom out of two actual ones), or two out of one, as (Aristotle notes) Democritus rightly says of the items that count as substances in 51

The assumption is applied explicitly to the Platonic theory of forms in Z14; see Chapter 9. eti de kai ho¯de de¯lon (1039a3; “Again, it will be clear in this way too”): in context, we are given new reasons for an old conclusion, pace Furth’s translation; but not for the generalization of the conclusion in the lines immediately preceding, pace Frede-Patzig ad loc., Burnyeat, 49, n. 101. 52

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his ontology. Similarly, if numbers are combinations of monads, “as some say”, a monad cannot be present in actuality in the number two (say), or two will not be a unity (ouch hen estai he¯ duas, 1039a13). The range of applications of Aristotle’s negative thesis on display in these lines is extraordinary by any measure. What clearer sign could there be of Aristotle’s intention to find metaphysical principles that are not bound to his own or to any single ontology? Plato in earlier lines, now Democritus, mathematicians and geometers—all must recognize in their theories a version of the general principle Aristotle is arguing for, that if, as we suppose, a substance must be a unity, no substance may have (actual) substances as its parts. Notably, however, the discussion leaves open the possibility that a substance may, with no threat to its unity, be composed of substances that are not both actual substances. (The possibility is noted explicitly at a5–6: “but if they are potentially two”.) The fact that this different option remains open is especially relevant to the dilemma with which the chapter closes, where again, I will argue, the issue of the unity of substance is very much on Aristotle’s mind.

14 The Closing Dilemma of Zeta 13: More on the Structure of Universals, 1039a14–23 Aristotle ends the chapter by pressing further questions about the parts of a substance. As we have seen (in Section 1), earlier portions of the discussion are arranged around a dilemma: on the assumption that a substance does have parts, are those parts non-substances (the first horn, [a1]), or are they (actual) substances (the second horn, [a2])? Both options, it seems, are unacceptable: summing up his negative results at the end of the chapter, Aristotle suggests that the parts of a substance can be neither universals (apparently eliminating the first horn, [a1]; see this chapter, n. 4) nor actual substances (apparently dispatching the second, [a2], as well). He notes a remarkable consequence: 8.14 But the result contains a puzzle. For if no substance can be of universals, since signifies a such but not a this, and if no substance can be a composite out of substances-in-actuality, then all substance would have to be incomposite, so that there will not even be a definition of any substance. (a19) Against this, however, it is thought by everyone and has been said long since, that definition is either of substance alone, or most of all; but now not even of it. So there will be definition of nothing; or in one way there will be, and in another not. But what is being said will be clearer from what comes later. (1039a14–23)

In 8.14 the earlier dilemma (a1)–(a2) about the status of the parts of a substance is now folded into a larger dilemma: either a substance has parts (A1) or it does not (B1); and if every available attempt at saying how it can have parts has failed, as the smaller dilemma seems to show, then Aristotle’s larger dilemma seems to require that every substance is

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incomposite. But, as Aristotle goes on to say (1039a19), this result too is hard to accept, for it follows that no substance can have a definition,53 and—given the accredited view that definition is chiefly if not exclusively of substance—if substances cannot be defined, nothing can. Or—a better result, which Aristotle promises to explain later—despite everything we have seen so far, there will be a definition in one way, in another way, not. It is something of a jolt to find at chapter’s end that possibly all definition is under threat. The conventional wisdom is that the result of the two dilemmas is a teaser for some later solution, perhaps in H6 (so Ross ad loc.), that may lift the threat. My own view will be that while Aristotle leaves last word on the topic to H6, Zeta 13 itself already contains a hint of how to escape his smaller dilemma (see the paragraph immediately following). But the immediate relevance of the smaller dilemma to its context in 13 is the possibility it offers of controversy with Plato. As to how Aristotle will escape the threat to definition his dilemmas pose (while leaving Plato on the hook, as it were): suppose, as Aristotle surely holds, that substance can be defined, so that it is composite after all. One way or another, then, the (smaller) dilemma that seems to show otherwise must go. The smaller dilemma offers two possibilities: either the parts of a substance are universals (see M10, 1086b37–1087a4), which are not substances and signify not a this, but a such;54 or they are actual substances. So it appears that this is a case of false dilemma. Aristotle has hinted earlier in the chapter at a qualified version of the prohibition that the parts of a substance cannot be themselves substances: no one substance can be composed of two actual substances. This qualification leaves open the possibility (which Aristotle can accommodate but, he will suggest, Plato cannot) that a substance be composed of one actual substance and one less-than-actual substance.55 If the claim of the contained dilemma, (a1)–(a2), that the parts of a substance can be neither universals nor two actual substances does not exhaust the available options, it hardly follows that every substance is incomposite, much less that they cannot be defined. How, finally, are we to understand Aristotle’s comment in the penultimate sentence of 8.14, that (on the correct view) in one way there will be definition, but in another way not? We are familiar from the discussion of “received” views in Zeta 4 and 5 with 53 Why, if every substance is incomposite, does it follow that no substance can be defined? Aristotle takes for granted the familiar view that a thing is a (primary) definable, only if it is composed of parts (Chapter 7, Section 1, and 7.1 above). If we assume that only (primary) substances are (primary) definables, as Z4 and 5 suggest, we have the compound condition on (primary) definables, that a thing is a (primary) definable, only if it is both a (primary) substance and composed of parts. If a primary substance has no parts, and so is not a primary definable, then perhaps it cannot be defined at all. 54 This is the option under attack at 1038b23–29 (Section 10): the parts of a substance are “not substances or a this, but quality (to poion)”, where “quality” here corresponds to “not a this but a such” at 1039a15–16 in 8.14. 55 Aristotle’s example is of a line that contains two potential lines as segments; on my reading, the italicized feature is not essential to every case. On the general topic, see further Pellegrin (1990), 43–4, Lewis (1995) 1996, 63 with n. 75. Aristotle directly acknowledges the disagreement with Plato over the parts of a substance in chapter 14 immediately following; his views about how the problem is resolved are given in H6; see this chapter, n. 58.

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the idea that some things are definable in the strict sense, and others in a less than strict sense, or not at all. And later in the “partisan” discussion in Zeta 15, Aristotle instantiates this earlier point to his preferred “partisan” ontology, in which form can strictly be defined, but the compound material substance cannot.56 But I doubt this is the moral Aristotle intends us to draw here. In themselves, both points are relatively tame. They also offer no hint as to how to “break” the dilemma. On a stronger reading, I suggest, Aristotle has an eye to polemics: the dilemma is live for Plato, but on his own theory it is harmless. Definition works out differently for the different entities that answer to the label, “primary substance”, in his theory, and in Plato’s. According to Plato, all forms are equally “separate”—they are all equally primary substances.57 At the same time, some forms are composed out of others—the species-form, man (say), out of the genus- and differentia-forms, animal and two-footed. The structure of species-forms in this theory should make them ripe for the method of definition by division; but how are we to show that the item to be defined, man (say), is one thing and not two, both animal and two-footed? Aristotle’s own view, by contrast, requires us to subordinate one constituent of what is being defined to the other. The subtlety that a substance cannot be composed of two actual substances shuts out Plato, but it leaves room for the Aristotelian idea that one constituent in the thing to be defined is its actuality and an actual substance, while the other is only a potential substance. The two approaches to definition, then, are Plato’s and Aristotle’s own. The two divide, not over definition as such, but over the nature of the objects to be defined—in particular, the status of the parts of a substance. For Plato—absurdly, as Aristotle sees it—we are to think that two actual substances can make up one actual substance. So structured, Aristotle thinks, the object of definition cannot exhibit the required unity. For Aristotle, on the other hand, an actual substance is composed of one actual substance and one potential substance, and the problem of unity can be solved.58

INDIVIDUALS AND THEIR KINDS: ARISTOTLE’S ALTERNATIVE TO PLATO

15 A Closer Look at Kinds The critique of a theory of substance kinds in Zeta 13, surveyed in Sections 1–14, extends a line of criticism active in the Organon and elsewhere. In these other texts, we 56

The use in Z15 of the point from Z4 and 5 is not a violation of Non-Linearity; see Chapter 10, n. 6. See Section 2 with n. 15, and Chapter 9. For the unity requirement for the object of definition, see Z4, 1030b7–13, and Z12 and especially H6; see this chapter, n. 17. Aristotle indicates that Plato has no solution to the problem of unity, and suggests how it can be solved for form-matter compounds and by implication even for Aristotelian kinds. The extension of his solution to the true primary definables, namely, Aristotelian forms, is less clear. 57 58

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are told that kinds are secondary rather than primary substances, and that unlike primary substances, they are not thises (this chapter, n. 43). In Metaphysics Zeta 10 and 11, kinds are demoted even further: they are not substances of any stripe, but rather “compounds of this form and this matter taken universally” (8.6 above). Plato’s forms receive even less friendly treatment: they are teratismata, “twitterings”, An. Po. A22, 83a32–35. In Zeta 13 too, universals are not substances (the non-relational claim); or, new in Zeta 13, nothing is universal to the very things of which it is the substance (the relational claim summarized in Mutual Exclusivity, Section 2). Nominally, as we have seen (in Section 2), this last, relational formulation exempts Aristotle from the attack to which Plato is vulnerable. But the reprieve remains nominal, in the absence of some explanation of how, if at all, the relational formulation comports with Aristotle’s larger metaphysical theory, and of how the formulation and the larger theory improve on the theories they are intended to replace. In this and subsequent sections, accordingly, I move away from the studiedly non-doctrinaire cast of Aristotle’s discussion, reviewed in Sections 1–14, to consider the partisan details of Aristotle’s own theory of kinds. Aristotle’s views on these larger issues are distributed over a variety of texts, from the relatively simple account in the Categories, to the more complex views on offer or, more often, implicit in different chapters of Metaphysics Zeta. In the theory of kinds in the Categories, Aristotle will say that man is said of Archimedes, or that Archimedes Is (a) man, where the said-of relation, equivalently, the relation of Izzing, is intended to mark the stronger relation between Archimedes and his kinds, in contrast to the relation between Archimedes and his various accidents: generosity (say) is in Archimedes, or Archimedes Has generosity.59 These views constitute a change over the picture Aristotle finds in Plato, in which sensible individuals can only Have their various predicables, and no provision is made for any stronger relation between Archimedes and what Aristotle recognizes as his kinds. Instead, for Plato, privileged position is reserved for Platonic forms, on the grounds that all and only Platonic forms are Izzers. Aristotle’s view in the Categories that Archimedes is both an Izzer and a Haver—that he Is various of his predicables, and Has others—is an important part of what allows the shift to the view that, contrary to Plato, individual substances now count as primary. In the story developed in the Categories, Aristotle holds that the kind, man, counts as a secondary substance—“secondary” because it depends for its own existence on the existence of individual men, Archimedes and the rest. At the same time—although Aristotle does not say this—Archimedes and the others are in turn essentially dependent on their kinds. So different relations of dependency hold in opposite directions between Archimedes and the kind, man, and the case for the primacy of the former over the latter is under threat (Introduction, n. 1). The work needed to counter the

59

For the theory of Izzing and Having, see n. 5 and associated main text in Chapter 1.

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threat is under way in Physics A and B, with the introduction of form and matter, where these complement and even to a significant degree supersede the theory of kinds. The notions of form and matter are front and centre in the partisan portions of Metaphysics Zeta, where Aristotle recalibrates which items in the ontology he will count as primary: (Aristotelian) form is the substance and cause of being of the various things that exhibit it (Zeta 17, Chapter 11), so that the form of a thing, not the thing itself, much less the kind, is primary substance. On this view, one and the same (general) form appears in many different structures—the living bodies—that count as the matter of this or that individual man, and it is the substance (strictly, the substance*, see Section 2) of each of those different individuals.60 But the form is predicated of and, hence, universal to, something else—namely, the different structures that are the matter of the various individuals. As we shall see, this bare outline is consistent with rather different views of the larger theory of which they are a part.

16 Individual and Kinds, and How the Form is Predicated of the Matter: (i) An Account of Statement Predication According to one popular view in the recent literature, Aristotle changes his mind on an important point in semantic theory. The story begins in the Categories, where Aristotle’s views on predication centre around sentences of two basic kinds, illustrated by (16) and (17): (16)

Archimedes is a man.

(17)

Archimedes is brave.

Each of these is given a certain level of analysis in the Categories (Chapter 1, Section 1). First, they involve one of two basic relations, in order, the said-of and in relations, or their converses, the relations of Izzing and Having. Add to this the device of paronymy (Categories 1, 1a12–15) to convert the adjective “brave” in (17) into nominal form, as Aristotle’s theory of predicate-reference requires. Then we can link (16) and (17) to sentences in the idiom of Izzing and Having: (18)

Archimedes is a man if and only if Archimedes Is (a) man.

(19)

Archimedes is brave if and only if Archimedes Has bravery.

On the story I have in mind, significant complications set in the Metaphysics. The analysis along the lines of (19) of sentences ascribing an accident to its subject remains unchanged. But a significant amount of reworking apparently takes place in the analysis of sentences like (16), assigning an individual to its kind. On this new account, Aristotle

60 The view that Aristotelian forms are general items does not command universal acceptance; see this chapter, n. 64.

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drops the separate appeal to Izzing in (18), in favour of a second application of Having: not only, as already in (19), for the relation of a substance to its accidents; but also—this is the innovation—for the relation between the matter of a thing and its form. So (18) will be reworked, to become, (20) Archimedes is a man if and only if Archimedes’ matter, m, Has the form, ł, of a man.61 A two-part scheme of this kind is apparently in effect in Zeta 3, on substances and subjects. Aristotle identifies two classes of subject: on the one hand, the compound material substance, which Has its accidents, and in the other, matter which Has the relevant form (2.3 above). Similarly in Zeta 13 and again in Theta 7, we are told that there are two kinds of subject: an individual this, a substance, a man (say), is subject for its accidents, musical, for example, or pale or walking; or the subject is “substance in the sense of matter”, and what is predicated is a given form or a this (2.4 and 2.5, with chapter 2, n. 4). In both kinds of case, on the story I have in mind, the same relation of Having relates the subject entity and the entity that is (metaphysically) predicated of it. The star texts for views of this sort, however, are supposedly Zeta 17 and Eta 2. In Zeta 17, Aristotle is making a new start on the study of substance, based now on the conception of substance as a cause—or better, the substance of a thing as its cause (Chapter 11). Here, the first point to be clear on is that our Why? questions, designed to elicit a thing’s cause, must always ask: Why does one thing belong to another? Thus, if we ask, Why is Archimedes a man?—part of our answer will be, he is a man thanks to the form that is the cause of his being or, better, the cause of his being a man. But we must also find a role for some second item: namely (Aristotle thinks) the appropriate matter as subject for the form in question. In every such case, then, 8.15 It is clear that our question is, Why is the matter some definite thing (ti)?, for example, Why are these things a house? Because there belongs what it was for-house to be. Why is this— or why is this body, in this state—a man? As a result, what is being sought is the cause of the matter—that is, the form—thanks to which the matter is something; and this will be the substance of the thing. (1041b5–9)

A similar story has been found in Eta 2. Here, Aristotle finds an antecedent to Aristotelian forms in Democritus’ three differentiae, although there must be many more kinds of forms (kinds of differentiae) than Democritus ever imagined: one fresh differentia, or combination of differentiae, for each distinct kind of thing. For each different kind, and for each form or set of differentiae that corresponds to it, Aristotle thinks, we have a different use of is:

61 Aristotle’s account runs in terms of individual cases—Why are these [= these bricks and timbers] a house? in Z17, for example—and I follow his lead in letting “m” and “ł” in (20) and elsewhere serve as individual constants.

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8.16 It is clear that “is” too is spoken of in many ways. (b26) For a threshold is because it is situated thus, and being for a threshold signifies its being situated thus, and for ice to be that it (auto) has been solidified thus. (b28) Of certain things the being will be defined by all such things, by virtue of these having been mixed, and these blended, and these having been bound, these by being rarified, and these by utilizing the other differentia, as with hand or foot . . . (1043a5) in the case of substance what is predicated of the matter is the actuality itself [= the relevant form]. (1042b25–31, 1043a5–6)

Accordingly, as these lines are often read,62 when we spell out these different uses we find that the kind-term itself disappears in favour of a relation of predication between form and matter. For example, that something is a threshold, or is ice, is to be understood as saying that a certain form (lying thus or being solidified thus) is (metaphysically) predicated of a thing’s matter (1043a5–6). The result is a certain convergence of views in the secondary literature on the topic of individuals and their kinds. Thus, an object is a thing of some determinate species if and only if the associated form can be truly predicated of the parcel of matter constituting that object . . . [A] substance’s belonging to a kind is not a brute fact. It is something that requires explanation, and the explanation is provided by pointing to the fact that the associated substance-form is truly predicated of the parcel of matter that makes up the substance. (Loux (1979), 18, 19)

Again, in the Metaphysics Aristotle supposes that kinds or species exist but are not basic in his ontology; instead, they stand in a derived relation of (metaphysical) predication to individual substances, where belonging by an individual in a kind is now to be understood in terms of a core relation of (metaphysical) predication between the appropriate form and the appropriate matter. (Lewis (1991), 149)63

On the kind of account before us, Aristotle’s theory in the Categories and the more elaborate theory of the Metaphysics accord very different treatments to sentences assigning an individual to its kind. For example, we have the rival accounts (18) and (20) above, repeated here:

62 A certain amount of manipulation is needed to get this reading to come out right. Thus, in the lines up to b28 it is apparently the threshold or the ice that is the subject, while at 1043a5–6 the matter is the subject. On the story under review in this section, the first set of choices is to be regarded as a solecism on Aristotle’s part, while the second passage represents Aristotle’s considered account. (Alternatively, on this same account, the use of auto at b27, which on the present story we might expect to introduce the matter, but which seems instead to refer to the compound substance, can be compared to the use of to pragma at ¸10, 1075b35, to refer to the matter.) For more discussion, see Lewis (2011), and for the text at 1042b26–8, this chapter, nn. 67 and 68. 63 The details of this view are set out in Lewis (1985a) and (1991), cf. Loux (1979) and (1991), chapters 4 and 5 (nicely summarized at his 147–8), and the closely related accounts in Code (1978) and Driscoll (1981). For other accounts in the same vein, see, for example, Anscombe in Anscombe and Geach (1961), 53–4, and Hamlyn (1961), 124–5. Similarly, Furth (1985), 127–8, and (1988), 250–7, sees Aristotle as engaged in a “pattern of eliminative analysis”, or “contextual elimination” (his emphasis), designed to “explain away” “substantial” or “pseudo-substantial” terms in favour of reference to a matter and a form.

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Archimedes is a man if and only if Archimedes Is (a) man.

(20) Archimedes is a man if and only if Archimedes’ matter, m, Has the form, ł, of a man. This new account of membership by a thing in its kind hardly signals the complete disappearance of kinds from Aristotle’s ontology. But in keeping with the demotion of kinds from their status as secondary substance in the Categories (8.6 above), “the relation of predication between an individual and its kind is . . . a derived notion constructed out of other, basic components of the theory” (Lewis (1991), 154). The result is what appears to be a fresh Aristotelian analysis of what it is for an individual to belong to its kind.

17 Individuals and Kinds, and How the Form is Predicated of the Matter: (ii) The Metaphysical Analysis of Kinds The account in the previous section lies squarely on the side of semantics, and gestures towards the analysis of (as we might put it) the proposition expressed by a sentence that assigns Archimedes to his kind. An alternative account lies equally firmly on the side of metaphysics; in more modern dress, it deals with the analysis of the propositional function that we might point to in the analysis of sentences of this sort. We can begin with a fresh look at Aristotle’s more austere view of kinds like man and animal, and all such entities that in the same way are epi to¯n kath’ hekasta—that apply to individuals. Contrary to the Categories, man and other kinds are not substances at all, but rather “compounds of a sort of this form and this matter, taken universally”, 8.6 above, repeated here: 8.6 Man and horse and the things that in this way to particulars, but universally, are not substance but a kind of compound of this form and this matter, taken universally. (Zeta 10, 1035b27–30)

On this analysis, I will suppose, the structure of Aristotle’s kinds replicates that of the particular form–matter compounds to which they apply: 8.17 If simply this soul and this body [ = the compound of these two], then as the universal, so the particular. (Zeta 11, 1037a9–10)

Now, on most accounts, Aristotle’s forms are universals,64 while the stuffs and structures that comprise a given matter decidedly are not. If so, then one constituent, the form, is already a universal, and we need generalize over only the matter. So, I take it,

64 For the contrary view that finds a doctrine of individual forms in Aristotle, see, for example, FredePatzig (1988) I, 39 and 52, II, 256–7, and Irwin (1988), chapter 12.

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(21) (The compound of this matter and this form) taken universally = the compound of (this matter, taken universally) and this form —if the right-hand side of (21) is not what Aristotle intended all along. In (21), Aristotle’s, “taken universally”, in connection with the matter, generalizes over the different stuffs or structures that count as matter in different cases: whatever thing, x, we choose, it will be the matter of that thing, x, that takes on the form that typifies the kind we started with. Accordingly, for Archimedes to be a man is for his matter to take on the relevant form; for Xenocrates, his matter; and so on. These last claims need not commit Aristotle to taking matter and form as the primary ingredients in the proposition expressed by the sentence, “Archimedes is (a) man”. Rather, they suggest only that the attribute of being a man is a complex one, such that for x to be a man is for x’s matter to take on the form of a man. This is an analysis of just one constituent in the proposition expressed by the sentence in question. Similar points emerge from Zeta 17. Aristotle asks, What is (a) man? or What is (a) house?, and suggests the question should be understood as asking, Why is it that these are this? Thus, for No. 10 Downing Street, its being a house comes down to the matter of No. 10 being such that the form of a house belongs to it. And for No. 9, its being a house amounts to the matter of No. 9 taking on the same form. On the account offered in Section 16, claims of this kind were understood along the lines of (20) above, repeated here: (20) Archimedes is a man if and only if Archimedes’ matter, m, Has the form, ł, of a man. Similarly, then, (22) No. 10 Downing Street is a house if and only if No. 10 Downing Street’s matter, m, Has the form, ł, of a house. But it is at least as plausible that, as in Zeta 10, Aristotle is concerned only with analysing the attribute of being a house: as before, the attribute is analysed in terms of matter and form, the form being held constant, while the matter varies with the identity of the house in question. So we will be asking about the nature and structure of the kind, house, that is just one of the constituents in the proposition expressed by the right-hand side of (22). To isolate the contribution to the proposition made by the term “house”, we first subtract any contribution that is due to No. 10 Downing Street. To do this, we replace the occurrence of “No. 10 Downing Street” by a variable, and then bind the variable with a lambda-operator: (23) ºx. For some m such that m is the matter of x and for some ł such that ł is the form of a man, m Has ł.

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That is, the property of being a house amounts to the property of having a matter, m, and of there being a form, ł, of a house such that m Has ł.65 This, more or less, is the account of the kinds, man, horse, and the rest, that Aristotle gives in Metaphysics Z10 (8.6 above). Finally, a passage from Eta 2. In Eta 2, Aristotle argues that we can explain what it is for a thing of a given kind to be—that is, what it is for it to be of that given kind66—in terms of form, or its counterpart in the case of beings that are not properly substances. Thus, for example, 8.18 (excerpted from 8.16 above) A threshold is because it is situated thus, and to be [“to be for a threshold”?67] signifies for it (auto, b27) to be situated thus; and to be ice [“to be for ice”?68] its being solidified thus. (1042b26–8)

It is not immediately obvious whether Aristotle is defining instances of the schema, “a is k”; or defining the attribute, being a k, for different classes of subject entity. That is, is Aristotle occupied with statement predication, and the analysis of sentences like ‘This [the solid material in the lake] is ice’? As his mention of definition elsewhere in Eta 2 suggests, and as I now prefer to think, the issue is rather predicate-reference, in particular, the analysis of kind-terms in predicate position.

18 An Injection of Theory In the previous two sections I have contrasted two treatments of sentences assigning an individual to its kinds. On the relatively simple view Aristotle offers in the Categories, we are to analyse the sentence (16), (16)

Archimedes is a man,

in terms of a relation of Izzing holding between the subject-entity, Archimedes, and the kind, man, as in (18) above: (18)

Archimedes is a man if and only if Archimedes Is (a) man.

In the theory of expression for (16), accordingly, we will say that (24) The sentence, “Archimedes is a man”, expresses the quasi-propositional entity,69 Archimedes’ Being a man. 65 This approach is labeled the NPC account in King (2002), dealing as it does with the “nature” or internal structure of one or more of the “constituents” of the “proposition” expressed. 66 I assume throughout that for a thing to be in the sense intended is for it to be a k. 67 Reading to oudo¯i einai, with Jaeger, following Alexander and Bonitz. 68 Reading to krustallo¯i einai with Jaeger et al., in place of the mss, to krustallon einai. 69 In de Int. 1, 16a3–9, Aristotle talks of sentences as thought as “likenesses of things”, pragmata; for the attempt to adapt his pragmata to the role of the “quasi-propositional” or “structured truth-bearing entities” required in a propositionalist account of Aristotle’s theory of predication, see Lewis (2011), section 2 and nn. 16 and 20, following Crivelli (2004). A list of examples of the relevant structured entities (Aristotle’s

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Outside the Categories, however, as we have seen, it is often thought that Aristotle replaces the account in terms of the unanalysed notion of Izzing, with an analysis that makes a fresh application of the notion of Having, now relating a thing’s matter with the relevant form, as in (20) above: (20) Archimedes is a man if and only if Archimedes’ matter, m, Has the form, ł, of a man. One ready way of thinking about the analysis in (20) in our contemporary terms comes from the “form as function” view. We are to think of Aristotelian form as, in important respects, comparable to a Fregean function.70 For Frege, the predicate in a simple singular predication denotes a function which takes the entity denoted by the subject of the sentence as argument, and returns a truth-value as value of the function for that argument. In Aristotle’s case we can imagine that the “form as function” view plays a role in the theory of expression for sentences assigning an individual to its kind. Suppose that for Aristotle, Aristotelian form acts like a function, returning a proposition (or quasi-propositional entity) as value for a given matter as argument: (25) The result of applying the form, ł, to the matter, m, of Archimedes is the quasi-propositional entity, Archimedes’ matter, m, Having the form, ł, of a man. In light of (25), the new theory of expression for sentence (16) will say that (26) The sentence “Archimedes is a man” expresses the quasi-propositional entity, Archimedes’ matter, m, Having the form, ł, of a man, that results from applying the form, ł, to the matter, m, as argument. The “form as function” view as implemented in (26) is intended to indicate how form and matter together provide the truth-bearer and, with some adjustment, the truthmaker for sentences like (16) that assign an individual to its kind.71 It hardly needs saying that the comparison with Frege should not be pressed too hard. All that we need from the talk of functions and the rest can survive in the requirement that “[A]pplication of a predicate’s denotation to a singular term’s denotation uniquely determines the truth or falsity of a sentence that consists of such a predication.”72 For Aristotle too, then, all that the “function” interpretation of

pragmata)—which must have a dual role as truth-bearers and as truth-makers—appears at Categories 10, 12b5–16, especially 15–16 (see Ackrill (1963), ad loc., 110); see also Metaphysics ˜29 and ¨10, and the discussion in Crivelli (2004) and in Lewis (2011). In (Lewis 2011) the possibility of a sententialist rather than a propositionalist readings of Aristotle’s theory of (statement) predication is also noted. 70 The comparison goes back at least as far as Lukasiewitz (1953), followed by Kung (1981), Loux (1984) and (1991), 132–35, and Lewis (1985) and (1991). As noted in the following paragraph in the main text, there are obvious limits to the comparison; see Loux (1991), 132–3. 71 For the quasi-propositional structured entity (less formally, the state of affairs) that appears in (25) and (26), see this chapter, n. 69. 72 Burge (2007), 597, his emphasis.

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Aristotelian form strictly requires is that introduction of a given form into a given matter uniquely determine the result. It is on precisely this last point that the application of the “form as function” view to the analysis of statement predication runs into trouble. For Aristotle is firmly committed to the view that the application of a given form to a given matter will return an individual substance as value. This is just the familiar analysis of individual substances as compounds of form and matter, formulated here in terms of the comparison of Aristotelian forms with Fregean functions. But now, alas, a given Aristotelian form is cast in two roles, where only one is allowed. Functions in general are required to be onevalued: that is, for a given argument, a given function must return a single value. So the operation of applying the form or function, ł, to a given matter, m, as argument, cannot return both a compound material substance, Archimedes (say), and the quasipropositional structured entity, Archimedes’ matter Having the form of a man, as in the account imagined so far on Aristotle’s behalf: (25) The result of applying the form, ł, to the matter, m, of Archimedes is the quasi-propositional structured entity, Archimedes’ matter, m, Having the form, c, of a man. (27) The result of applying ł to m is the compound material substance, m + ł (= Archimedes, let us say). If, as it seems, Aristotle is committed to a view that broadly aligns forms with Fregean functions, even in the relaxed way envisioned, then either (25) or (27) must go.73 I will assume that Aristotle is committed to the essential intuitions underlying what today we might think of as the “form as function” view in the account of the unity of substance in Eta 6 (this chapter, n. 17 and Section 19): so (27) stays. At the same time, it seems, the account of sentences like “Archimedes is (a) man” in (20) in Section 16 and formalized in (25) and (26), never did have the textual support envisioned on its behalf. So the “form as function” view plays no role in the account of statement predication in the way envisioned in (25) and (26).

19 Some Pluses and Minuses There are both gains and losses, if we adopt the sceptical account of Section 18. On the plus side, predicating a form of matter will return a form–matter compound as value:

73 In addition to the “one-value” objection in the main text, there is the further difficulty—I owe the point to Kit Fine—that the compound material substance returned as value for the function given the matter, m, as argument in (25) is a factive entity, while the quasi-propositional entity returned in (25) is not. For clarity in the present paragraph in the main text, I talk as though Aristotle’s forms are to be taken squarely as (Fregean) functions. For the needed reservations about this way of talking, see Section 18 with n. 70.

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(27) The result of applying ł to m is the form–matter compound, m + ł (= Archimedes, let us say).74 The idea that form is predicated of matter, allied to the “function” view of form, and understood as in (27), gives an account of the unity of the resulting compound material substance that fits well with Aristotle’s other views about unity. For Aristotle, the unity of a thing is a matter of degree, varying with the nature of the thing in question. Among form–matter compounds, a natural substance, Archimedes (say), has a high degree of unity. Artifacts have a lesser degree of unity—the wood that makes up my table might as well have been made into a bookcase—while accidental compounds, Archimedes standing, Archimedes seated, have hardly any unity to speak of: Archimedes seated is, after all, an accidental compound, and is dissolved with a simple change in position on Archimedes’ part. These cases of unity are marginal, and there will be no “function” view of accidents, comparable to the “function” view of forms, to explain the composition of an accidental compound from an individual substance and its accident. The “function” interpretation of form, in the version Aristotle develops in Eta 6, does a good job of explaining unity where explanation is needed, in the case of form–matter compounds that are natural substances. But side by side with saying that form is predicated of matter—as I am understanding him, in the construction of form–matter compounds—Aristotle will also say that accidents are predicated of their subject, where I suppose a different notion of predication is involved. This is now statement predication, and it has nothing to do with the “function” view associated with Aristotelian forms and their relation to matter. The result is a certain amount of untidiness. At ¨7, 1049a18–36, for example, partially excerpted in 2.5 above, Aristotle seems to juxtapose (i) predicating accidents of compound material substances, as when we produce the sentence “Archimedes is pale”, and (ii) predicating form of matter so as to produce form–matter compounds at various levels. (A similar juxtaposition of views appears in Zeta 3.) So Aristotle’s remarks under (i) are relevant to the account of sentences like (17) above, (17)

Archimedes is brave;

but his remarks under (ii) have no application to the analysis of sentences like (16): (16)

Archimedes is a man,

and instead, are concerned solely with the constitution of form–matter compounds. 74

One more piece of work for form in the construction of Aristotelian kinds is relevant here:

The form, ł, of a man takes the matter, m, “taken universally”, of the individual substance, a, into the universal compound, (m + ł) “taken universally” (= the kind, man). For this formulation, see (21) in Section 17. To separate the use of the “form as function” interpretation here from that in (27) in the main text, note that the argument for the function in this case is “this matter, taken universally,” and not just “this matter” tout court.

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I say that it is untidy to see predicating accidents of an individual substance as a contribution to the account of statement predication (with perhaps a quasi-propositional entity as value), while predicating form of matter produces a result of a quite different kind—a form–matter compound. But then, the logic of substances and their accidents is quite different from the logic that governs the relation of matter and form, and the untidiness, if such it is, is here to stay.75 Finally, a note about universals. Along with the shift in the notion of predication from statement predication (as accidents are predicated of their subject) to the operation of constructing compounds of matter and form, we will have to recognize a similar shift in the notion of a universal. The more familiar conception is tied to statement predication: as before, the universal, generosity, is predicated of the many individuals who are generous; or the universal, man, of the many men. But on the new account, there will also be a conception of universal which, like the relevant notion of predication, is tied not to statement predication, but rather to the appearance of one and the same form in the composition of different form–matter compounds: in the way that the form or soul of man is (metaphysically) predicated of Archimedes’ matter and also of Xenocrates’ (but not, as Aristotle tells it, of Archimedes or of Xenocrates himself ). The way in which a single form is universal to different stuffs or structures introduces a new notion of universal quite distinct from that associated with statement predication. 75 Some remarks may be in order here about the curious history that underlies the supposed untidiness. In the early chapters of the Categories, Aristotle is concerned above all with a notion of linguistic predication, and with the correlative notion of metaphysical predication at the level of the truth-makers of the linguistic predications; he is concerned too with drawing out various metaphysical consequences of the resultant theory. In the theory Aristotle describes, we say what it takes for the sentence “Archimedes is standing” to be true in terms of a relation of metaphysical predication, Having, if you will, relating Archimedes and the property of standing. And when Archimedes sits, a fresh contrary, being seated, is (metaphysically) predicated of him, so that the linguistic predication “Archimedes is sitting” is now true. Against this background, Aristotle comments at the end of Categories 5 that it is distinctive of substance that it is receptive of contraries: this is surely the beginnings of an account of change, as a thing persists over time through a succession of accidents that are metaphysically predicated of it. The connection with the predication of accidents persists when in Physics A7 Aristotle takes up the topic of change in general: not just accidental change, but also substantial change, in which an individual substance comes to be or ceases to exist. If in accidental change, an individual substance exchanges one contrary for another, in line with the account of metaphysical predication of accidents in the Categories, then plausibly, in substantial change too some lower-level subject, which Aristotle goes on to identify with matter, is itself subject to various contraries—now a privation, now the associated form—that cycle through it. This account of substantial change, in turn, leads directly into an account of the metaphysical structure of individual substances: an individual substance is to be analysed as a compound of form and matter, in which the matter is subject to the form or, equivalently, the form is (metaphysically) predicated of the matter. In this story (sketched also in Chapter 2, Section 1), the relation of metaphysical predication between form and matter remains, after any reference to subject-predicate truth and the theory of linguistic predication is long gone. Similarly, in different chapters of the Metaphysics too, Aristotle can think without any sense of incongruity in terms of (i) a relation of metaphysical predication between a substance and its accidents, supporting a theory of subject-predicate truth at the top of his scheme, side by side with (ii) a compound-making relation of metaphysical relation, between different levels of matter and different levels of form at the bottom half of the scheme, which makes available an account of substantial change, but where no immediate connection with linguistic predication of any kind is in evidence.

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To be clear about it: Aristotle’s views allow for the existence of the kind, man, now in its reduced state as a compound of this form and this matter taken universally, which is not a substance of any sort (not even a secondary substance, as in the Categories). The kind, man, is straightforwardly universal to its various instances, Archimedes and the rest; and Aristotle can comfortably say of it that it is a universal but not a substance—in particular, it is not the substance of the different individuals of which it is predicated, as he thinks Plato will want to say. At the same time, there is a story in which (not the kind, but) Aristotelian form is predicated of different stuffs or structures that count as matter in different cases; but it is not the substance of any of these. This last story has a place in the account of the structure of the kind as a universal compound of form and matter. It has a place too in the account of the composition of different members of the same kind out of different cases of matter and the same single form. But it is not a contribution to the account of statement predication.

Appendix: Mutual Exclusivity and Some Versions of Compatibility As we have seen, a major conclusion of Zeta 13–16 is the prohibition that no universal is a substance; this prohibition in its relational version can be formulated as Mutual Exclusivity, which I repeat here: x is universal to y and z (y 6¼ z), just in case x is not the substance of y and not the substance of z. Mutual Exclusivity I suggest in Chapter 8, Section 2, that Aristotle’s embrace of Mutual Exclusivity leaves room for a distinctively Aristotelian notion of universals and their relation to the notion of substance. Two versions of Compatibility indicate how the notions of substance and of universals can be linked in terms of the “official” theory of form and matter, consistently with the hard line Aristotle appears to take in his Mutual Exclusivity. Details of Aristotle’s positive view are largely the product of speculative reconstruction of the kind I have tried largely to avoid in this volume, and are correspondingly controversial. Here, however, I set any scruples aside, and sketch briefly the bare bones of the position I take to be his. We suppose that Archimedes and Xenocrates (say) belong to the same kind, man. Aristotle will explain this by saying that each is a form–matter compound: in fact, a compound of (what I take to be) the same general form, ł, that typifies their kind, and the different structures, m1 and m2, that are their respective matters, so that Archimedes = m1 + ł, and Xenocrates = m2 + ł.

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Even this much is to an extent controversial, since not all would agree that forms are universals.76 But there is more material for controversy to come. In the first place, I will suppose, an entity may be universal to one set of things, and the substance of some entity distinct from all of these: For some x, y, z (y and z non-identical with each other and with x), x is universal to y and z, and x is the substance [unstarred] of x. Compatibility A Thus, let x be the form, ł, and y and z the distinct matters, m1 and m2, of Archimedes and Xenocrates. We have this result: ł is (metaphysically) predicated of m1 and m2 and, hence, is universal to them;77 but at the same time, ł is the substance (unstarred) (not of either of them, but) of itself, ł. At the same time, ł is also in a secondary way the substance* of Archimedes and the substance* of Xenocrates. This gives a fresh version of Compatibility, in which an entity may be universal to a given set of things, and simultaneously stand in some weaker substance of relation to some other set of things: x is universal to y and z (y 6¼ z), and for some u, v (u and v distinct from each other and from y and z), x is the substance* of u and of v. Compatibility B As before, let x be the form, ł, and y and z the distinct matters, m1 and m2, of Archimedes and Xenocrates. Then we say that ł is universal to m1 and m2, and it is the substance* not of m1 and m2 (and not of itself ), but of Archimedes and Xenocrates. The two versions of Compatibility leave room for a distinctively Aristotelian notion of universals and their relation to the notion of substance, in terms of the “official” theory of form and matter, which is largely suppressed in Zeta. Notice that the form ł is not in any way the substance of the matter, m1, or the matter, m2. So Aristotelian form is in full compliance with the principle of Mutual Exclusivity that Aristotle brings to bear against the Platonic theory of forms.

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See this chapter, n. 64. As noted in Section 19, the notion of universal here, as with the underlying notion of predication, requires some care. As I see it, the connection with statement predication is pretty much lost, and we are left only with the point that a single form is at one and the same time present to many different cases of matter. 77

9 Substance and Universals (II): Plato on Genus, Species, and Differentia In the remaining chapters, 14–16, of Zeta devoted to the topic of substance and universals, Aristotle puts to work some of the principles that give life to the largely critical remarks of the opening chapter, 13, of the segment. In chapter 14, which is our target here, he develops further the second of the two main conclusions of the segment (8.1, repeated here): 8.1 Accordingly, (i), that none of the things said universally is substance and, (ii), that no substance is out of substances, is clear. (my emphasis)

In Zeta 14, conclusion (ii) now has Plato all but in name as its target. Aristotle’s arguments in these three chapters make repeated use of the principle, Partial Functionality, which is a near-immediate consequence of the Identity Premiss from Zeta 6: Where x is the substance of y and y is a primary substance, x = y. The Identity Premiss Where x is the substance of both y and z, y = z.

Partial Functionality1

The Identity Premiss is central to the Plato-friendly discussion in Zeta 6, where Aristotle offers a proof of the closely related principle asserting the identity of primary substances with their essences, where his examples of primary substances are Plato’s forms (Chapter 6, Section 1, and 6.2 above). In the later segment on universals, less friendly to Plato, the related principle, Partial Functionality, is twice turned against Plato in Zeta 13 (8.7 and 8.8 above). On top of its role in Zeta 13, Partial Functionality is a key player in Zeta 14 in argument (b2), which forms part of the dilemma Aristotle presses against Plato (9.8 below). More speculatively, because Aristotle’s exposition is so succinct, the Identity Thesis

1

The Identity Premiss is a worked-up version of a received opinion from the opening lines of Zeta 6 (1031a17–18 from 6.1 above). Partial Functionality follows from the Identity Premiss, with the proviso that “y” and “z” in Partial Functionality range over primary substances, as the Identity Premiss requires; see Chapter 8, n. 21.

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and Partial Functionality may both have a place in the argument of (b3) (9.10 below).2 Partial Functionality also plays a role in the argument against Plato at Zeta 16 (10.4 below). As we have seen, Zeta 13 is largely critical in tone, but silent about the identity of the target or targets of Aristotle’s criticisms. Zeta 14 is now entirely critical, and has Plato as its sole target, with a battery of criticisms that focus exclusively on the Platonic theory of universals. In particular, Aristotle takes as his target Plato’s assumption that a species-form is to be analysed into genus- and differentia-forms as its parts. Aristotle sets Plato’s analysis against the larger assumptions that a Platonist will bring to his conception of forms: in particular, the Platonist’s view that species-, genus-, and differentia-forms are all three equally substances, and each “a this and separate”, contrary to his, Aristotle’s own rule, that no substance has actual substances as its parts. Aristotle’s arguments are structured around a dilemma that lays out the different unpalatable options that face the Platonist regarding the logical relations among forms of these different orders. Aristotle ends Zeta 14 by remarking that the criticisms he has levelled against Plato’s views of (Platonic) form–form relations can be reproduced at the level of relations between sensibles and Platonic forms: 9.1 Further, in the case of perceptible things all these consequences follow and ones even more absurd. If, then, it’s impossible for it to be like this, it’s clear that there cannot be forms of these [ = of perceptibles] in the way that some people say. (1039b16–19, following Furth’s translation)

Should we think of Plato as rising up in protest against this treatment of his theory? One of the more fascinating aspects of Zeta 14 is its kinship in method and even content with the sustained attack by Plato himself on certain versions of a theory of forms in the Parmenides. For all its surface dissimilarities with the published work of Plato, Aristotle’s book Zeta is a creature of context, and in some ways the product as much of collaboration with Plato as of criticism of him.

1 The Assumptions that Make Plato Vulnerable Aristotle is explicit in the very first sentence of the chapter both about the connection with the arguments of Zeta 13, and about the nature of his target: 9.2 It is clear from these very points [the contents of Zeta 13] the consequences especially (kai) for those who say that the forms (ideas) are separate substances, and simultaneously make the species (eidos, = species-form) out of the genus and the differentiae. (Z14, 1039a24–6)

2 The appeal to Partial Functionality in (b2) and (b3) is muted, but I think still recognizable; see Sections 4 and 5. For the comparable principles for essence and for definition, see Chapter 8, n. 21.

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Especially important to Aristotle is that Plato’s assumptions about his forms hold across the board—for all forms equally, to Aristotle’s dismay, regardless of their status in certain cases as constituents in some larger structured universal, as (on Plato’s theory) genus- and differentia-forms are constituents in the relevant speciesform. Aristotle points explicitly to the uniformity assumption Plato imposes on his forms: 9.3 If then there exists a certain man himself by himself [= a Platonic form, man] a this and separate, it is necessary that what it is out of too, for example, animal and two-footed, signify a this and be separate and be substances: so that animal too. (a30–33)

Aristotle is explicit about uniformity again in Zeta 15: 9.4 But in fact, they too [= the genus, animal, and the differentia, two-footed] are also separate, if man is separate: for either none < is separate>, or both ; if then, nothing , the genus will not exist apart from (para) the species; but if it will do, then so the differentia. (1040a18–21, my emphasis)

Aristotle makes one further preliminary point before he turns to his detailed criticisms. He is about to question the status of the genus-form on Plato’s theory, and ask whether the genus-form can be the same or not in the different species of which it is a constituent. But he is not worried about whether the genus is the same in definition in its various occurrences (a28–30): it goes without saying that it is, and this kind of sameness presents no difficulty. What will matter is whether the genus will be the same in number in its different occurrences. Aristotle suggests in 9.2 (“from these very points”, a24) that the arguments of the preceding chapter 13 are a source of difficulties for Plato in particular. In part, he may have in mind the use he is about to make of Partial Functionality not only in Zeta 14, but also in 16 (9.8 and 10.4, cf. 13, 8.7 and 8.8 above, and this chapter, n. 9). More broadly, Aristotle will argue that the conclusions of Zeta 13 and a variety of assumptions from the Platonic theory of forms do not sit well together. As already noted in the introduction to this chapter, it is not clear to what extent Plato would disagree.

2 Aristotle’s Dilemma The entirety of Zeta 14 is devoted to a dilemma challenging the different views Plato may want to take regarding the relation between a Platonic genus-form and its various species. Aristotle pictures a succession of difficulties on each side of his dilemma—whether we think that the genus is numerically the same in the various species, or whether it is not numerically the same there. The dilemma in outline is as follows:

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the genus-form, animal

numerically the same form in every species;

not numerically the same same form in every species;

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B1

the form is separate from itself;

infinitely many things have animal as their ousia;

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contrary differentiae will be true of one and the same thing.

animal-itself will be many;

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b2 & the composition of the different animals in each species is a mystery; b3 & similar if not worse problems arise for the relation of Platonic forms to sensibles. b4

3 “The Genus is Numerically the Same in the Different Species” In part A1 (the left-hand horn) of Aristotle’s dilemma, we are to suppose that the genus-form, animal, is the same in each of the different species. But Plato assumes that the genus and the different species alike are “one and separate”: how can the genus be one in the sense specified, if it exists in things that are separate (sc. separate from each other)? Aristotle sees two sets of consequences, each unappetizing. It will follow, first (a1), that animal itself is separate from itself: 9.5 If the animal in man and the animal in horse is the same and one, just as you are the same as yourself, how will what exists in things that exist apart be one, and why will this animal [“animal so conceived”] not be separate from itself ? (1039a33–b2)

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In 9.5, Aristotle has in mind the relation of the genus-form to its various species-forms; he will return to this complaint, reworked for the relation of Platonic forms in general to particulars, with the dismissive remarks in (b4) (Section 5) and in Zeta 16 (10.6 in Chapter 10, Section 6). This latter question about the relation of a single Platonic form to each of the many particulars that participate in it, comes from Plato himself in the first part of the Parmenides at 131a–e.3 Thus—parallel to the dilemma Aristotle construct in Zeta 14—is the form the very same entity in each particular? Or is it a different form—as Plato understands it, a different part of the original form—in each? It will also follow, (a2), that contrary differentiae will be true of one and the same thing: animal is both two-footed and four-footed, and so forth: 9.6 Then if is to participate in two-footed and in many-footed, the consequence is something impossible, for opposites will belong simultaneously to it—it being one and a this; but if not, what is the form of speech, when one says that the animal is two-footed or footed? But perhaps they are situated together and are in contact, or have been mixed: but these are all absurd. (1039b2–6)

This same complaint also makes a brief appearance in Zeta 12, 1037b18–21, and Aristotle’s dismissive attitude towards metaphor—perhaps genus and differentia are “put together”, or “in contact”, or “mixed”—as a way of evading difficulty is echoed in Eta 6, 1045b7–16. Of the two objections on this side of Aristotle’s dilemma, (a1) suggests that Plato is condemned to applying to genus-universals the “logic proper for particulars”.4 No particular can be wholly and completely present in distinct (non-overlapping) things at the same time; but if the genus, animal, is “one and separate”, as Plato says, then is it not subject to the logic of particulars? The question is a variant on a question Plato himself raises in the Parmenides: if a Platonic form is in the various particulars that fall under it, then is it not like a sail, that must be cut up and the parts allocated to the different particulars? Or is the sail to reappear in different places at the same time (Parmenides 131bc)? Perhaps it is no advance to respond that it is not the ordinary sense of “in”, in which the wine (say) is in the bottle, but a technical use, much like that Aristotle appropriates for himself in the Categories. Behind Aristotle’s expression of distaste for metaphor perhaps lies the deeper objection, that Plato’s view of the genus-form as one and separate, simply allows no escape from the “logic of particulars” objection. The same point perhaps applies in the case of the second objection, (a2), that one and the same genus, animal, must participate simultaneously in contrary differentiae. 3 Ross (1924) II, 212, points out the verbal similarities between Aristotle at b1–2 and Parmenides 131b1–2. It is worth remembering that the two works are more or less contemporaneous—to the extent that it has been suggested that the first part of Plato’s Parmenides reacts to Aristotle’s Zeta 14, rather than vice versa as usually thought; Ross (1924). 4 The phrase is from D. Lewis (1983), 345. The use of this phrase should not be thought to open the door to paradigmatism, understood as vicious self-predication, in Plato’s case (as Aristotle views him here) any more than in Lewis’s. (Equally, the view that Izzing is reflexive, so that for each form, X, X Is itself, X (Chapter 6, Section 4), commits Plato only to syntactic self-predication, but is logically innocuous.)

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Now, Aristotle says elsewhere that all the co-ordinate differentiae will be true of the genus: 9.7 Or see if, though the contrasted differentia exists, it yet is not true of the genus; for then, clearly, neither of them could be a differentia of the genus; for differentiae that are co-ordinates in a division with the differentia of a thing are all true of the genus to which the thing belongs. (Topics Z5, 143b2–5, Pickard-Cambridge)

So, for example, it will be true that animal is both two-footed and many- (= more than two-) footed: Aristotle himself will have no trouble distributing the predicates, “twofooted”, “many-footed”, over different individual members of the genus.5 But the assumption that a Platonic form “has the logic of particulars” makes impossible to interpret the different differentia-predicates distributively on Plato’s behalf.6 A sentence asserting a given differentia of the genus for Plato must have the form of a simple singular predication. So, sentences asserting different differentiae of the same genus-form must be contraries: no single entity can be simultaneously two-footed and many- (= more than two-) footed. As before, then, it will be the special assumptions that hold in the case of Platonic genus- and differentia-forms—that these are all alike “one and separate”—that make the trouble.

4 “The Genus is Not Numerically the Same in the Different Species” If Plato can find no comfort on one horn of Aristotle’s dilemma, how will he fare on its other horn? We suppose now that the genus-form, animal, is different in each different species. Aristotle points first, (b1), to the sheer number of different species that will have animal as their substance: 9.8 Then there will be so to speak indefinitely many things (apeira ho¯s epos eipein) whose substance is animal; for man is not out of animal as a matter of accident. (1039b7–9)

It is not a matter of accident that man has animal as a constituent: so—consistent with Plato’s assumption that the genus-form, animal, is a substance—we come naturally to the conclusion that animal must be the substance of man and of all its different species.7

5

While Aristotle allows that the differentiae will be true of the genus, he will deny that the genus participates in its differentiae (Topics ˜2, 123a7–8); presumably, this is because he defines “participates” in such cases as “admits the definition of” (˜1, 121a11–12), so that the differentia-term would force an unwanted restriction in the application of the genus-term. At the same time, the species will participate in its (constitutive) differentia, E4, 132b35–133a3. 6 Again (this chapter, n. 4), to say that, for Plato (as Aristotle understands him), genus- and other forms “have the logic of particulars” is not to say that they are particular members of the very kind they represent. This is paradigmatism, and it is not needed for the purposes of the present argument. 7 AristotIe’s argument requires us to ignore the difficulty that animal can hardly be the full substance of each of the different species (Chapter 8, Section 5, with n. 28).

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More dramatically, as Aristotle puts it, each of the virtually infinite number of different species will have animal as its substance. If Aristotle is justified in reaching this conclusion, what about it are we supposed to find objectionable? After all, it is the leading assumption of this side of Aristotle’s dilemma that the genus is a different entity in each of the different species.8 Rather than find the result objectionable in itself, we may perhaps see it as supplying a premiss for the argument that follows, where Aristotle does seem to have a genuine difficulty in mind. For possible future use, then, suppose without further comment that animal-1 is the substance of man, animal-2 the substance of horse, and so on, for each of the indefinitely many species of animal—where apparently we are to suppose that animal-1 6¼ animal-2. (It will be remembered that Aristotle himself is exempt from these consequences, given his view that the genus is not a substance at all—and hence also not the substance of anything.) In the argument that follows, (b2), Aristotle urges against Plato the difficulty that “the animal-itself will be many”. 9.9 Again, animal itself will be many: for, (i), (b9) the animal in each is substance (for, (b10) it [the species] is not spoken of in virtue of something else: otherwise, man would be out of that and it would be its genus), and again, (ii), (b11) they are all forms from which man ; therefore, (b12) a thing will not be the form of one thing, and the substance of another (for this is impossible); therefore, (b13) animal-itself will be each one of the in each . (1039b9–14)

A first task is to understand the nature of the complaint. In particular, the complaint may seem simply to repeat the initial assumption on this limb of Aristotle’s dilemma, that the genus is different in each species (heteron en hekasto¯i)—if this is right, then why argue the point? In fact, however, the conclusion of the argument does not merely repeat its initial assumption. Help here can come from Plato’s Parmenides. In the Parmenides, Plato

8 It is tempting to attribute to Aristotle the objection that if the genus animal is the substance both of the species, man, and the species, horse (and the substance of inordinately many other species as well), it follows, by the Partial Functionality assumption from Zeta 13 (Chapter 8, Section 3), either that the different species are identical with each other, or if the species are different from each other, that animal will be different from itself—the “many animals” result about to come (9.9 below, and see Ross (1924) II, 212). In fact, I think, the role of Partial Functionality in the argument is harder won, given the opening hypothesis on this limb of Aristotle’s dilemma, that the genus, animal, is different in each of its different species. If we add that hypothesis to the argument, we get the relatively bland result that there will be indefinitely many different genera, animal, distributed among the different species as the substance of each. It requires the argument that follows in (b2) (given in 9.9 below) to make room for Partial Functionality and to achieve the “many animals” result.

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supposes that either the whole form is present in each of the things that fall under it, or that just a part of the whole form is present in each. So Aristotle’s option that the genusform, animal, is different in each species can be understood to say that a different part of the whole form is present in each species. On this view, we will have, on the one hand, animal-itself, and on the other, animalman, animalhorse, and so on. Aristotle conclusion in (b2) will not be the bromide that there are many parts, animalman and the rest, of the genus, animal; he will say instead that the genus, animal, itself is not one but many, in a sense to be explained (see (11) below). We now have the following argument, which will hinge on the point that on this limb of the dilemma, as presently understood, we are now offered two choices for the substance of a given species: by 9.8, the genus, animal, but also, as we are about to see, the different parts of the genus, animalman and the rest. Thus, for example, (1)

Animalman is the substance of man. b9–10.

(Aristotle supports (1) with the lemma at b10–11: if the species were called what it is in virtue of something other than animalman, then that other entity would be its genus and also, presumably, its substance. Importantly, then, we are to understand by (1) that animalman is the one and only substance of man.) Again, by hypothesis, (2)

Animalman is a Platonic form. (b11–12)

At the same time, (3) Where x is a Platonic form, x is the substance of y if and only if x is the Platonic form of y. (b12–13) Aristotle does not argue for (3), but merely comments that it is “impossible” otherwise. Given (1), (2), and (3), we know that (4)

Animalman is the Platonic form of man.

We can add as a further assumption the conclusion of (b1), that the genus, animal, is the substance of each of its indefinitely many species. For example, (5)

Animal is the substance of man.

By a second application of (3), along with the assumption (in force throughout the passage) that the genus animal is a Platonic form, namely, animal-itself, it follows that (6)

Animal is the Platonic form of man.

(1) and (5) together give us two choices for the substance of man (and a similar result for horse and every other species). Comparably, by (4) and (6), we also have two choices

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for the Platonic form of man and the rest. A pair of principles now apply—one proprietary to Plato, the other due to Aristotle: (7)

x and y are both the Platonic form of z, only if x = y.

(8)

x and y are both the substance of z, only if x = y. b9–11. Partial Functionality

That is, echoing a Platonic principle that a thing has at most one Platonic form, Aristotle holds that a thing has at most one substance.9 The inference to (9) (ara, “therefore”, b13) is now overdetermined: Animal-itself = animalman, and animal-itself = animalhorse.

(9)

(9) comes from (1), (5), and (8), or equally well from (4), (6), and (7). The “many animals” result now follows almost immediately. By our initial hypothesis, (10)

animalman 6¼ animalhorse.

It follows from (7) and (8), absurdly, that (11)

Animal-itself 6¼ animal-itself.

Or, if you like, there are many animals.

5 Two Final Negative Consequences Aristotle completes his argument in two further steps. The first, (b3), concerns the relation of the genus-form, animal-itself, to the different forms, animalman and the rest, lodged in the different species: 9.10 From what is this [ = animalman and the rest] < composed>, and how from animal-itself ? Or, (b15) [sc. if not constructed from it, following Ross], how can the animal [= the animal in each species?] exist that has just this [= animal] as its substance, alongside (para) animal-itself ? (b14–16)

Of the two objections in 9.10, the first may show Aristotle simply throwing up his hands: as in 9.6 and elsewhere, the complaint is that Plato has no coherent account of

9 The presence of Partial Functionality in the present argument is unannounced, but I take the uniqueness of a thing’s substance to be implied, if not explicit, at b9–10 in 9.9 above: “the animal in each is substance for, it [the species] is not spoken of in virtue of something else” (my emphasis); see the comment on premiss (1) in the main text above. In any case, subject to the reservations in this chapter, n. 8, the assumption is indispensable to the argument as I reconstruct it. For Plato’s commitment to (7), meanwhile, see Parmenides 147de and Wedberg (1955), 30–1, where the principle is explained as “a condensed way of saying that, corresponding to each plurality of objects to which we apply a common name, there is a unique Idea which justifies the application of that name”—an explanation, as Wedberg notes, that is given by Aristotle at M4, 1078b34–1079a4, cf. A6, 987b9–10.

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the relation between the genus, animal, and the various parts, animalman, animaltiger, and the rest, distributed among the various species. Next—Aristotle’s second objection at b15—whatever else we say about the relation of the genus, animal itself, to its various parts, animalman, and the rest, we surely can assume at least this, that the genus, animal itself, is the substance of its various parts. Then how can animalman and animaltiger (say) “exist alongside” animal itself ? Plato is already credited with the assumption that the genus- and differentia-forms that are parts of the species-form are separate substances (9.2, 9.3, and 9.4 above): are the parts of the genus-form, animalman and the rest, separate in the same way? If, as we have assumed, the genus-form is the substance of the single part, animalman, then by the Identity Thesis above, the genus and its part are identical: how, then, can the one be separate from the other? Again, if the genus-form is also the substance of a second part, animaltiger, the two parts will be identical with each other, by Partial Functionality; they will also both be identical with the genus; and the conflict with the separation assumption is complete. Finally (b4), there comes the blanket condemnation: just these and even worse consequences follow for the relation of Platonic forms to sensibles. So, the thesis of Platonic forms cannot be sustained. At the end of Zeta 16 (Chapter 10, Section 6), Aristotle explains Plato’s underlying error. In Aristotle’s view, Plato identifies the wrong set of entities—namely, the universals under scrutiny in these chapters—as “separate substances”. Much less are they the eternal non-sensible substances that metaphysics demands. Aristotle will have more to say about Plato’s forms in Zeta 15 and 16; these chapters of Zeta are our topic in the next chapter.

10 Substance and Universals (III): Zeta 15 and 16, and Plato’s Fundamental Mistake The segment on substances and universals that occupies chapters Zeta 13–16 is bracketed by statements of one or both of Aristotle’s negative conclusions: from the closing lines of the segment, again (= 8.1), 8.1 Accordingly, (i), that none of the things said universally is substance and, (ii), that no substance is out of substances, is clear.

How far into the different chapters of the segment does the negative tone highlighted in 8.1 extend? On one view of how the discussion of substance and universals unfolds in 13–16, the shift from received views to Aristotle’s own theory is finally under way in Zeta 15. If this is correct, we may reasonably expect in the last two chapters of the segment to find the lessons learned in the earlier chapters 13 and 14 applied within the “in-house” ontology of form, matter, and form–matter compound. So how does the expected application go? In this chapter I will suggest that the expectations of the previous paragraph are largely in vain. In chapters 15 and 16, Aristotle continues to be occupied in large part with the missteps that disqualify a Platonic theory of universals. Now, we know from the Analytics that universals are required for demonstration (see the epigraph at the beginning of Chapter 8) and for definition; the discussion in Zeta 15 too strongly suggests that they are required for definition. So—for all the strictures of 8.1 and elsewhere—there must be room in what Aristotle will deem a sound metaphysics for universals and, if substances are to be defined, for a connection between the notions of universal and substance. But we are not told in these chapters how these accommodations are to be achieved. Perhaps for this reason, we also learn little about how the discussion of universals in the present segment 13 through 16 bears on the main project of Zeta, which is to produce a definition of substance, to be accomplished in the “new start” in Zeta 17. Zeta 15 is concerned with the topic of definition—briefly inside Aristotle’s own metaphysical theory, but largely in non-partisan terms in the ontology of others. Thereafter, Zeta 16 is almost entirely partisan, but with a tantalizingly brief suggestion

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of how Plato’s error over the identity of the eternal non-perceptible substances is remedied in Aristotle’s own theory of the unmoved movers (10.7 below). I begin with the discussion of definition in Zeta 15.

1 “Received” and “Partisan” Mode in Zeta 15 Aristotle begins Zeta 15 in overtly partisan mode, noting two different kinds of substance in his own theory: the compound, which is the logos (or form) with matter—the compound material substance—and the logos by itself. Only the first, but not the second, is destroyed (and also comes into being). The fact that the compound undergoes destruction, and the role matter plays in this,1 explains why “substances that are perceptible and also particular” (to¯n kath’ hekasta, 1039b28) cannot be defined. Aristotle’s argument here—call it the argument from perishability—may not be the prettiest: 10.1 If, then, demonstration is of necessary things, and definition is tied up with scientific knowledge (episte¯monikon), and if, just as it is impossible that scientific knowledge (episte¯me¯) be at one time knowledge and at another time ignorance, but rather it is opinion that is like that, in the same way it cannot be demonstration or definition, but rather it is opinion that is of what is capable of being otherwise— plainly of these (sc. particular perceptible objects) there can be neither definition nor demonstration. For they are unclear, the perishing things, to those who have knowledge, as soon as they have passed from perception, and although the same formulae are preserved in the soul, there will not be either definition nor proof. (1039b31–1040a5, following Furth’s translation)

Aristotle’s remarks about the resistance of particulars to definition echoes a similar sentiment in Zeta 10: 10.2 (excerpted from 7.8 above) But when we get to the composite, e.g. this circle, i.e. one of the particular ones, whether perceptible or intelligible—by “intelligible” I mean e.g. mathematical ones, by “perceptible’ e.g. brazen or wooden ones—of these there is no definition, they are known by thinking or perceiving, but when they depart from this completedness it is not clear whether they are or are not; but they are always formulated or known through the universal formula. (a8) But matter, in respect of itself, is unknowable. (1036a2–9, following Furth’s translation)

Although Aristotle does not say so, the terminology and doctrine in 10.1 in particular draws heavily on the Analytics (see, for example, An. Pr. B21, 67a39–b3; the contrast between knowledge strictly construed and opinion is also the subject of An. Po. A33). Demonstration, Aristotle tells us in 10.1, “is of necessary things”: that is to say, with respect to the products of demonstration: 1

1039b29–31, cf. Z7, 1032a20–21.

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10.3 We think we know (epistasthai) something simpliciter, and not in the sophistical way, incidentally, when we think we know the cause through which the thing is , and that it is not possible for it [= the thing] to be otherwise . . . if there is knowledge (episte¯me¯) of a thing without qualification, it is impossible for it to be otherwise. (An. Po. A2, 71b10–12, 15–16, cf. A4, 73a21–3)

Knowledge that is the product of demonstration is of what cannot be otherwise, and is of the universal (An. Po. A4, 73a25–74a3, 31, 87b37–88a5); and the definitions obtained from demonstrations are themselves of the universal (7.3 above and An. Po. B3, 90b3–7; and for how such definitions are to be obtained, see Chapter 11, Sections 2 and 3). But these are quite severely restrictive notions of knowledge and definition; and Aristotle’s arguments in 10.1 and 10.2 appear to overstate the case against having knowledge (even in a less restricted sense?) of particular perishable things. The argument of 10.1, outside of the restrictive context of the Analytics, can seem open to challenge on two fronts. There is, first, the general worry that the view that the object of knowledge must be necessary, rests on a modal fallacy. From the fact that necessarily, if I know that P, then P is true, it does not follow that if I know that P, then P is necessarily true. So, from the fact that any property that belongs contingently to a particular may cease to be true of it—in particular, will no longer be true of it when the particular ceases to exist—it does not follow that, at a time when the property holds of the particular, I cannot know that it holds of it at that time, or that later, when the particular no longer exists, that the property did hold of it at that earlier time. What, then, of the counter, that knowledge is an internal state of the knower that stays fixed, even as the corresponding objects in the world change, or even cease to exist? But—the second difficulty—it is not clear that our knowledge claims are thereby undermined. We might think that the content of our knowledge claims—for, example, “I know that my tomato plants are flowering”—is implicitly indexed as to time (the time at which the knowledge claim is issued). So the relevant state in the soul, if this is how we think of knowledge, will not be disturbed by a subsequent change in how things are. Aristotle extends his claims of indefinability beyond the compound material substances of his own ontology, to apply also to Plato’s forms (1040a8–27, b2–4). And eternal things in general get swept up in the mix, especially those that are the sole representatives of their kind (monacha, 1040a29), like the sun and the moon. Because these are all eternal, they are exempt from Aristotle’s perishability argument, and so their indefinability is harder to detect (1040a27–b2).2 2

The cross-reference between Metaphysics Z15 and Plato Theaetetus 209aff. has long since been noted; see Cornford, (1957), 162. According to Cornford, the appearance of the sun in both contexts guarantees that Aristotle is following Plato, but I am not sure that we are entitled to say more than that the issue was a matter of contemporaneous debate between the two philosophers. Plato asks how our thoughts in terms of the general characteristics of one individual, Theaetetus (say), can reliably pick out that person rather than Theodorus or some other. Aristotle’s application of this puzzle to Platonic forms is not entirely obvious; the explanation by Ross (1924) II, 215–16, is given in this chapter, n. 3.

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But indefinable they all are. With Plato’s forms, Aristotle is insistent that the issue is again separation among the forms—as in Zeta 14 (Chapter 9), the idea that even where one form is a constituent in another, as in the construction of a species-form out of genus- and differentia-forms, all are equally forms and, hence, equally substances, so that a substance has actual substances as its parts. Suppose, now, we try to define the (Platonic) species-form, man, in terms of its constituents, animal and two-footed. If the words we use are not simply invented for the occasion, Aristotle thinks, each “will apply to something else as well”. So, Aristotle tells us, the definition that results cannot apply uniquely to the form being defined. This result may seem to be challenged by Aristotle’s own remarks in the Analytics. In An. Po. B13, Aristotle suggests that while various terms apply singly to things other than the thing to be defined, in combination they apply uniquely to it (B13, 96a32–5). But thanks to separation, apparently, the suggestion of the An. Po. is of no help. The genus- and differentia-forms must be predicable of more than one thing, not just singly but also in combination: no set of defining terms can apply uniquely to the speciesform. But why separation in this way disables the move proposed in the Analytics is not entirely clear.3 Different arguments apply in the case of things that are the sole example of their kind—the sun and moon, for example. In such cases we cannot tell when accidents get wrongly counted into their definition; and we cannot tell when the definition includes items that can apply to other things even if in fact they do not. In the latter case there might exist a second thing in addition to the first, with all and only the features given in the definition; or just one thing—but some other thing, and not the very thing that in fact answers to the definition.4 These arguments too, however, are hardly conclusive. From the fact that under adverse circumstances we can get a definition wrong—even that we can never tell for sure that our definition is correct—it does not obviously follow that no definition is available.

2 An Aristotelian Condition on Definition? To this point in the chapter, Aristotle has offered a wave of negative comments ruling out the possibility of definition for certain kinds of items. How are these negative conclusions related to the discussion of substances and universals in Zeta 13 and 14? All the examples in Zeta 15 are substances—even Platonic forms are substances, if you have a Platonic ontology—so they are all prima facie candidates for definition. But they are all particulars, not universals (compound substances are ta kath’ hekasta, 1039b27, 30–1, 3 Ross (1924) II, 215–16, explains that the would-be definition, “two-footed animal” is predicable in sum of animal (but not universally), of the two-footed (universally, since the differentia applies only within the genus), and of man—all three separately existing Platonic forms. Without this last assumption, supposedly, there will not be three distinct items vying for the same definition. 4 For this alternative reading, see Cohen (1984), 54.

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1040a6; Platonic forms are “kath’ hekasta and separate”, 1040a8–9; the sun and moon are to¯n kath’ hekasta, like Cleon or Socrates, 1040b1–2). The emphasis on particularity suggests a blanket reason why in all these different cases, no definition is available. Instead, it seems that Aristotle is committed to thinking that the proper objects of definition must be universals.5 Plausibly, he requires that: A thing is a (primary) definable, only if it is both a universal and a (primary) substance. An Aristotelian Condition on Definition We can think of this Condition as an enhancement of the requirement already set out in Zeta 4 and 5, that a thing is a (primary) definable, only if it is a (primary) substance (see, for example, 3.22 and 3.23 above).6 The enhancement takes up the suggestion that motivates the present segment of Zeta, that substances are universals. The result accords exactly with the stipulation in Zeta 11, in the “partisan” portion of the preceding segment, that “definition is of form and the universal” (1036a28–9).7 For these and other reasons, it is hard to think that the Aristotelian Condition given would not be a cornerstone of Aristotle’s larger theory. In addition to the explicit arguments of the chapter, then, Aristotle’s discussion leaves room for a positive Condition connecting the notions of substance and universal that produces the same negative result, that no particular, not even Platonic forms (themselves counted as particulars), can have a definition. I say that Aristotle “leaves room for” the Condition on Definition: Aristotle’s primary aim in the body of Zeta is to examine the received views about substance set out in Zeta 3 (1.4 above), preparatory to advancing his own definition of (primary) substance and of the substance of a thing in Zeta 17. But accord with received views, suitably adapted, is an important source of support for his “official” theory of form and matter, and it is welcome if his theory can deliver results that are also desirable on independent grounds. So much the better, then, for the Condition on Definition, which gets its support from the contrast with a range of examples of particular substances that cannot be defined, drawn from both inside and outside Aristotle’s own “official” theory. So much the better too for the long-term prospects of the connection between substance and universals that is the motivating idea (8.2 above) under discussion in the entire segment and which is advertised in the Condition given. All of this, however, ignores the fact that the connection between substances and universals put to use in the Condition is antecedently impossible, by Aristotle’s own 5

For this use of the argument of Z15, see also Code (1984), n. 22. Appeal to these earlier passages does not violate principles about moving across levels: importing the partisan into the non-partisan is not permitted (see Chapter 1, Section 8); but the whole point of the separation between levels is to allow, at the appropriate time, the application of results obtained in “nonpartisan” mode to concepts at the partisan level. For form as a universal, see also M8, 1084b5. Note too that the case against Cleon and Socrates as primary definables is over-determined, since they are not only particulars but also (in Aristotle’s more developed theory) not primary substances. 7 The point that for Aristotle particulars cannot be defined is scarcely news: in addition to the examples in Z15 noted above (and the express statement at 1039b27), see Z10, 1035b33–1036a8 (in 10.2 above), M10, 1086b32–7. 6

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pronouncements from Zeta 13 on, summarized for all to see in 8.1 above. In the bulk of 13–16, Aristotle argues, against Plato and against the motivating idea with which Zeta 13 began, that no universal is a substance. How, then, in Zeta 15 can he require that the object of definition be both? If Aristotle’s rule that no universal is a substance holds in its bald form, as in 8.1, then nothing can satisfy the Condition, and on Aristotle’s own terms the Condition is not a coherent requirement on definition, and not a significant weapon against Plato nor anyone else.

3 The Revised Aristotelian Condition The difficulties noted at the end of the previous section disappear, however, given the appropriate relational formulation of the Condition on Definition. As written, the Condition on its right-hand side simply reproduces, in non-relational form, the received view of substances as universals that motivates this segment of Zeta. Even in the agenda passage, 1.4, however, where the received view is introduced, a relational version of the view is only just around the corner: we are told there that the universal “is thought to be the substance of each thing”. As with the motivating view itself, more than one relational formulation of the Condition on Definition is available. We can begin with a relational formulation that, arguably, represents more exactly a Platonic view of how the notions of substance and universal are connected: A thing is a (primary) definable, only if it is both a substance and a universal, and universal to and the substance of the very same things. A Platonic Condition on Definition The Platonic view in this more exact formulation is something Aristotle himself will reject, for reasons already set out in Zeta 13 (Chapter 8, Sections 2 and 3). His rejection will be based on his more nuanced rule, not simply, No universal is a substance, but rather, as before, No universal is the substance of the very things it is universal to: For all x, y, z (y 6¼ z), x is universal to y and z, only if x is not the substance of y or of z. Mutual Exclusivity

A version of the Condition on Definition that Aristotle will find acceptable will incorporate the relational formulation given in Mutual Exclusivity: x is a (primary) definable, only if (i) x is a primary substance, so that for some y, x is the substance of y, and (ii) for some z, u (z 6¼ u), x is universal to z and u, and (iii) for all v, w, such that x is universal to v and w, x is not the substance of v or of w. The Revised Aristotelian Condition on Definition That is to say, a thing is a primary definable, only if it is both a substance and a universal (the substance of something and universal to something), but not the substance of and universal to the same thing(s). The principle of Mutual Exclusivity that doomed the

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Platonic Condition above has no bite against the Revised Condition. The Revised Condition requires that the objects of definition be the substance of one thing, but universal to another. Plato’s forms are not substances and universals in this way and so, by the Revised Condition, they are not primary definables. Not all would-be definables need fail the Revised Condition, however. In particular, the primary definables in Aristotle’s own theory, I suspect, do not fail it.

4 A Comment on Aristotle’s Silence, and the Constructive Dilemma (CD) Strategy Revisited On the point raised at the end of the previous section as to how Aristotle’s own views on definition satisfy the Revised Condition given, Aristotle himself is of less help than one might want. I have suggested (Chapter 8, Sections 2 and 15) that in disagreeing with Plato over substances and universals, Aristotle leaves room for a positive account of how the two notions might after all be connected—an account (on my view) realized in his own theory of (Aristotelian) form. He does not tell us that he has a positive view in mind, however, let alone tell us what that view is, or how it applies within his own theory. What are we to make of this silence? His silence need not mean that Aristotle holds no positive views on these topics after all. But it does bring into relief the preliminary, exploratory nature of his discussion to this point—for all the brave start in the opening lines of the chapter with the analysis of perceptible substances in partisan terms as compounds of form and matter. The very question of substances and universals comes up in the chapter only indirectly, thanks to the emphasis on particularity and the (at best) oblique hint that not particulars but only universals may be defined. But Aristotle does not venture beyond this, into distinctively Aristotelian territory. Of the various examples in the chapter, Platonic forms are Plato’s not Aristotle’s, and the sun and the moon belong in (virtually) everyone’s ontology. And in the case of Plato’s forms, Aristotle’s main move is to take up and modify a point from the Analytics, so that this part of his discussion falls squarely on the “non-partisan” side of the ledger. Only the case of perceptible particular substances obviously involves distinctively Aristotelian “partisan” notions. And even the point about matter and perishability Aristotle appeals to here is not essential to his case. Plato, for example, does not accept Aristotle’s analysis of sensible individuals as compounds of form and matter; but he can readily construct his own version of an argument from perishability to argue that sensible particulars cannot properly be defined or known. On this account, Aristotle in Zeta 15 never seriously engages with his own ontology of form, matter, and compound, let alone spell out explicitly how on his theory he avoids the objections he directs against Plato’s universals. To this point, we may be disappointed that his account takes us no further—but no more serious harm is done.8 8

For discussion, see the Appendix to this chapter.

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But his silence is far more damaging on the Constructive Dilemma (CD) view (Chapter 1, Section 4) of how Aristotle follows through on the details of the agenda (1.4 above) he sets himself at the beginning of Zeta 3. The CD view is my formalization of the suggestion that each segment of Zeta set in motion by the opening agenda in Zeta 3 contains an independent argument, with the governing assumption of the segment as primary assumption, and with all segments driving towards the same single conclusion, that in Aristotle’s “official” theory, (Aristotelian) form is primary substance. In the present case, for example, we might expect an argument in outline as follows: Suppose that a thing is a (primary) substance if and only if it is a universal9 (the “primary assumption”). Universals are to be defined by the condition, C. (Aristotelian) forms satisfy condition C. Therefore, (Aristotelian) forms are universals and, thereby, the primary substances. Virtually none of the material required for this argument appears in Zeta 13 through 16.10 The most conspicuous absence is that of the primary assumption. Aristotle’s express aim in the segment is to demolish the connection Plato sees between substance and universal. So we cannot without further work use the motivating claim connecting the two as our primary assumption—for that claim is the very one Aristotle takes himself to be refuting. Without express word from Aristotle as to how to replace the discredited Platonic idea with his own positive view of how substances may also be universals, the argument cannot even get started. At the same time, the required definition of universal appears only parenthetically at 13, 1038b11–12 (8.7 above). And Aristotle does not say that (Aristotelian) form satisfies this definition, and asserts that form is a universal only (obliquely) in 10, 1035b33– 1036a2, and (outright) in 11, 1036a26–31 (= 7.3 above)—in both cases, outside (and inaccessible at?11) the present segment where it is needed. Finally, the would-be argument also seems to lack its required conclusion. On the CD view, somewhere in Zeta 15 and 16 Aristotle will use the results of 13 and 14 to drive towards the positive, “partisan” conclusion that form is primary substance. Aristotle does refer parenthetically in Zeta 15 to a variant idea, that form is definable

For “universal” here, read “substance-universal”; see the introduction to Chapter 8, and that chapter, n. 8. With the critique that follows in the main text, we may compare the remarks about the segment on essence, and the similar absence of a sub-derivation of the kind the CD strategy would require, in Chapter 1, Section 8. 11 The claim that form is a universal in Z10 and 11 will be inaccessible at Z13–16, on the Non-Linearity assumption of Burnyeat (2001), if that claim depends on the assumption governing the segment of which 10 and 11 form a part, that a thing’s substance is its essence, or on results obtained in that segment on the basis of that assumption; see Chapter 1, Section 9. 9

10

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substance. Let us grant that this is close enough to the result we need. Even so, it is not advanced as a conclusion to anything, let alone a conclusion to the opening assumption of the chapters, that substance is a universal.12 Given the relative dearth of positive, partisan results in Zeta 15, we have little justification for seeing the bulk of the chapter as anything other than “non-partisan”. Much the same verdict applies to the final chapter, 16, in the segment on universals, as we will see in Section 5.

5 The Critique Continued in Zeta 16 In Zeta 16, Aristotle focusses squarely on the two rules announced in Zeta 13, and cited as the conclusion of the segment in the final lines of Zeta 16. His conclusion is given as 8.1 from Chapter 8, repeated here: 8.1 Accordingly, (i), that none of the things said universally is substance and, (ii), that no substance is out of substances, is clear. (Zeta 16, 1041a3–5)

According to the second rule, (ii), of 8.1, if a thing is a substance and has another thing as its part, then the second is not a substance. In the opening lines of Zeta 16, Aristotle suggests that the majority of things popularly thought to be substances are not: although he does not say so, the cases all fall foul of the rule (ii) in 8.1. The parts of the living animal, for example, are not substances (even while the animal itself is one); and the elements, earth, air, fire, and water amount to no more than a heap until they are worked up into a proper unity (and it, not they, will be the substance). These applications of the rule are not trivial: Aristotle’s own views in the Categories 3a29–32, and the views he passes along without comment in Metaphysics Delta 8, 1017b10–14, and in Zeta 2, 1028b9–15 with promise of later scrutiny, contribute to the list of cases that he now rejects. The applications of rule (ii) at the beginning of Zeta 16 continue the hodge-podge of applications already made in Zeta 13. In the summary midway through 13, for example (8.13 above), the topic is species and genera: if man is a substance and has animal as a part, then animal is not a substance, and it is not the substance of anything. Later in Zeta 13, as we have seen (Chapter 8, Section 13), he applies the more nuanced version of the rule, that no substance is composed of two substances existing in actuality, to lines, to Democritus’s atoms, and to numbers conceived as collections of units. In the last two cases in Zeta 13 (atoms, numbers as collections of units), the examples are not from Aristotle’s own ontology; but the point about lines is something with which almost anyone can be comfortable. Similarly in Zeta 16, the parts of animals and the elements have a place in his and perhaps in almost any of his contemporaries’ ontology. To this point, then, the discussion in Zeta 16 has no special bearing on a distinctively Aristotelian

12 Burnyeat denies that the argument under discussion in the main text belongs within the larger context of a CD argument, but he seems committed to something like the argument given, stripped of the trappings of the CD account; see his (2001), 54.

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ontology (it is not especially “partisan”); if anything, it reads as a correction of the received list of substances in Zeta 2 and elsewhere. At 1040b16–24 in Zeta 16, it is the turn of rule (i) from 8.1. The rule is stated separately towards the beginning of Zeta 13, and this separate statement appears as 8.3 above, repeated here: 8.3 For it seems impossible that any whatsoever of the things said universally should be substance. (Zeta 13, 1038b8)

Aristotle quotes the rule in 8.3 in 10.5 below, in company with an assortment of associated principles in both 10.4 and in 10.5: 10.4 Since one is said like being, and the substance of what is one is one, and things whose is one in number are one in number, (b18) it is evident that neither one nor being is capable of being the substance of things, (b19) just as neither the to-be for an element or for a principle ; but we seek what, then, the principle is, so that we may reduce to what is more knowable. (1040b16–21, following Furth) 10.5 (the immediate continuation of 10.4) Now indeed, of these, being and one are more substance than principle and element and cause, but still, not even these are , (b23) if indeed nothing else that is common is substance [= 8.3]; for (gar, b23) substance belongs to nothing but itself and what has it, of which it is the substance. (b21–24, following Furth)

In the stretch of argument contained in 10.4 and 10.5, the rule in 8.3 together with various related principles are brought to bear on a topic from the book of problems, Metaphysics Beta. The present problem involves the view attributed to Plato and to Pythagoras, that being and one, which are universal to everything, are also substances, or the substance of everything (B1, 996a4–7, 3, 998b9–11, 4, 1001a4–b25, cf. I2). Now, because Plato is one proponent of the view Aristotle has as his target, and because the whole issue in this segment of Zeta is whether Plato is right in general about the connection he sees between substances and universals, it might seem to beg the question against Plato if Aristotle were simply to enforce his rule, 8.3, or some more nuanced version of it, in the case of being and one.13 Perhaps to purchase protection against this objection, Aristotle begins in 10.4 with two principles about substance which applied to being and one give the same result that the more nuanced version of 8.3 requires.14 The net effect will be to uphold Aristotle’s side of the disagreement, and to tend to confirm the anti-Platonic rule.

13 For the record, Plato’s view of being and one violates 8.3 not only in its bald (non-relational) form, but also in its more nuanced form as Mutual Exclusivity; see Chapter 8, Sections 2 and 3, also (3) in the present chapter, Section 3. By hypothesis, being and one are universal to everything. By Mutual Exclusivity, however, nothing may be both universal to and the substance of one and the same thing. Neither being nor one, then, can be the substance of anything. 14 “The more nuanced version of 8.3”: see Mutual Exclusivity, this chapter, n. 13.

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According to the two principles in 10.4, “the substance of what is one is one”, and “those things whose substance is one in number are one in number” (b16–18). That is, with some simplification, (11)

x is the substance of y and z is the substance of y, only if x = z.

and (12)

x is the substance of y and x is the substance of z, only if y = z.15 Partial Functionality

As noted, of these two principles, (12) is our old friend, Partial Functionality, and records the partial functionality of the substance-of relation; (11) attributes the same property to the converse relation. Like Partial Functionality in (12), (11) too is a consequence of the Identity Thesis (Chapter 6, Section 1, cf. Chapter 8, n. 20). Aristotle states his conclusion without argument: in light of these principles, it is impossible that being or one be the substance of things (b18–19 from 10.4 above). It is not hard to supply the arguments Aristotle has in mind but fails to state. (i). For purposes of reductio, suppose that being and one are each the substance of the very things they are universal to. (This an instance of the relational version of 8.3 above that Aristotle rejects, in contrast to the relational version represented by Mutual Exclusivity, which I have argued he favours.) Now being and one are each universal to everything so that, by hypothesis, each is also the substance of everything. It follows trivially that they are the substance of the same things; impossibly, then, by (11), they are themselves the same. At the same time, by (regular) Partial Functionality in (12), the things that have being and one (= one and the same things) as their substance will be the same as each other. This is the result that “all things will be one”, that Aristotle attributes to Plato and to the Pythagoreans together in Zeta 11; see 7.9 above. (Similarly, being an element and being a principle belong, if not to everything, to at least one thing in common; so if they are also the substance of what they belong to, then impossibly they too are the same, as are the things to which they belong.) Again, (ii), being and one belong to and, hence, by hypothesis, are each the substance of everything; but by (12), each can be the substance of at most one thing. (Similarly, being an element and being a principle belong, if not to everything, at least to many things; but if they are the substance of what they belong to, each can be the substance of no more than one thing.) I turn next to the argument in our second passage, 10.5 above. The argument hangs on the principle that appears in the last line of 10.5:

15 “with some simplification”: by “one” and “one in number”, I suppose that Aristotle has in mind the relation of one thing’s being one, or one in number, with another, and that for present purposes these two can be treated as equivalent to our identity.

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From 10.5 . . . not even these [being and one] are , if indeed nothing else that’s common is substance [= 8.3]; for (gar, b23), substance belongs (huparchei) to nothing but itself and what has it, of which it is the substance. (1040b22–4; see 8.12 in Chapter 8)

That is, as I understand that difficult last line, (13) x is the substance of y, only if x is the substance of itself and otherwise of y but of nothing else.16 As Aristotle notes (gar, b23), the rule in 8.3, that “nothing that’s common is substance”, applies to Plato’s one and being, in light of the difficult (13). Thus, for the sake of reductio and (again) contrary to Mutual Exclusivity, we are to suppose that being is both a substance and a universal, and universal to and the substance of the very same things. (This is an instance (not of Mutual Exclusivity, but) of the relational version of 8.3 that Aristotle finds objectionable.) Since being is universal to everything, it follows that it is the substance of everything. But by (13), if being is the substance of so much as one thing, then it is the substance of itself and of that thing, but of nothing else.17 So being is both the substance of and not the substance of everything. Equally, perhaps, everything will be one. Accordingly, we should drop the (Platonic) view that being is the substance of the things it is universal to. (I omit the counterpart of this argument for being an element and being a principle, and for being a cause.)

6 A Final Jab at Plato, and a Summary of Conclusions in the Segment Aristotle ends the chapter with a point that connects his critique of universals with Plato’s choice—a misguided choice, in Aristotle’s eyes—for his “eternal substances”: 10.6 (= the immediate continuation of 10.5 above) Again, what is one could not be in many places at once, but what is common does occur at many places; so that clearly none of the universal things occurs apart from (para) the particulars, separately. (b27) But those who speak of the forms in one way speak rightly, that they are separate, if they are substance, that is; but in another way wrongly, in that they say that the one-over-many is a form. (1040b25–30, following Furth)

16 For the difficulties in understanding the last line from 10.5 (= 8.12), see Chapter 8, Section 11, with that chapter, n. 49. On a different understanding of huparchei from that in (13), Aristotle will mean that

(13') x is the substance of y if and only if x is predicated of itself and otherwise of y but of nothing else. The huparchein at Z13, 1038b9–11, from 8.7 (Chapter 8) offers the same set of choices; see Chapter 8, n. 20. Given the difficulty of deciphering 10.5 (= 8.12 above), the support for (13) is correspondingly uncertain: for an alternative argument based on (13'); see this chapter, n. 17. 17 Alternatively, if we read Aristotle’s principle as (13') (this chapter, n. 16), being is the substance of itself and of the thing in question, but of nothing else. But we have already seen that it is the substance of everything. By reductio, then, as in the main text, being is not the substance of and universal to the very same things.

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Unlike what is common, what is one “cannot be in many places at once”. That is, one and the same thing cannot both be wholly and completely present at a single place at a given time, and also wholly and completely present at some distinct (non-overlapping) place at that same time.18 No universal, then, can also be one and a separate substance, “over and above” the particulars. A universal, by definition, can be common to many things, but for that very reason it cannot also be one in the sense of “one and separate”, as Plato envisions. So Plato is part right, part wrong. If Platonic forms are genuinely substances, Plato is right to think of them as separate. But the one-over-many cannot be separate, in Plato’s sense of “separate”; so he is wrong to think it is a genuine substance, or that it can rise to the level that he expects of a Platonic form.19 Plato has made the wrong choice for eternal substances: his are merely modelled after the substances we know—man itself, horse itself (1040b32–4, cf. B2, 997b5–12). A better choice, Aristotle will say elsewhere—but not here—is the unmoved mover or movers responsible for the motions of the heavenly bodies. These final criticisms of Plato are the parting shots in an extended attack on the Platonic conception of kinds that has been underway throughout chapters 13–17. Aristotle’s criticisms have pretty much discredited Platonic-style universals as true substances and, hence, as candidates for the eternal, non-perceptible substances that first philosophy, or metaphysics, apparently demands. So we have made negative progress, so to speak, on the question raised in Zeta 2 on the existence of eternal non-perceptible substances (Chapter 1, Section 1, n. 16): Plato’s forms will not do. As to Aristotle’s own thinking on this topic, all we have in Zeta 16 is the enigmatic comment: 10.7 And yet, even if we have never seen the stars, nonetheless, I imagine, they would still have been eternal substances besides (para) the ones we knew; so that as things are, too, if we can not say which ones these are, all the same perhaps it is necessary that some such do exist. (1040b34– 1041a3, following Furth)

This is the largest concession Aristotle makes in Zeta towards his avowed goal of uncovering the nature of the eternal substances—in fact, the unmoved movers of Metaphysics Lambda—that are the ultimate subject-matter of first philosophy.20

Again, perhaps, an appeal to “the logic of particulars”; Chapter 9, Section 3, cf. this chapter, n. 19. Aristotle himself is more guarded that he will allow Plato to be over the sense in which his Aristotelian forms are separate: the forms of objects in the sublunary world are separate only “in account” (Chapter 2, n. 17); and only the Unmoved Mover (if this is a special case of a form) is separate without qualification. 20 In the end, neither the Aristotelian forms of sublunary objects nor Plato’s forms are the true separate substances or true first principles for which both philosophers are looking. Rather, Aristotle’s theory of form and matter is only the starting point for the study of the true separate substances, and belongs in the first instance not in first philosophy, whose proper business is the study of true separate substances, but in physics. So physics—but not Plato’s choice, mathematics—is the correct starting point for the study of the true separate substances that are the genuinely first principles: namely, the Unmoved Movers of Metaphysics Lambda. See Burnyeat (2001) passim, especially 125. 18 19

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Meanwhile, with respect to the line of thought promoting Aristotle’s own choice of primary substance in the sublunary world—namely, the forms of sensible objects, in particular, and the souls of living things—Aristotle is here silent,21 as he is in general on the subject of how his own Aristotelian forms survive the critique directed at Plato’s. The final lines 1041a3–5 of Zeta 16 offer a summary of the two main conclusions of the segment: that no universal is a substance, and that no substance is composed of (two actual) substances (8.1 above). With these negative conclusions, part of a more or less sustained criticism of the Platonic theory of forms in these four chapters, Aristotle will have completed the survey of received views he set himself in the agenda passage 1.4 of Zeta 3. We may now recapitulate the events of the four chapters in the segment on substance as universal. After the polemics of Zeta 13, the two negative conclusions of the chapter are summarized at the end of Zeta 16 (8.1 above). Zeta 14 continues the attack on Platonic forms, and calls in question the unity of a species-form, composed as it is on Plato’s view from genus- and differentia-forms. In Zeta 15 we learn that particulars cannot be defined—where for Aristotle’s negative purposes, Platonic forms too are to be counted as particulars; and finally in Zeta 16, Aristotle directs the two negative conclusions from Zeta 13 against Plato’s “transcendental” universals, being and one. As a coda to Zeta 16, Aristotle comments that a one-over-many—a run-of-the-mill universal—cannot be a separate substance in the style Plato expects of Platonic forms: the one-over-many cannot be the eternal substance both he and Aristotle are looking for (this chapter, n. 20). After this spate of negative conclusions in the present segment, occupying all but a small corner of Zeta 15, how much survives of the received view of substance as universal with which the segment began? This much, perhaps, is clear: if substances are after all in some way universals, the manner in which this is accomplished in Aristotle’s official theory must be very different from what we find in Plato. But (despite the lengthy discussion in Section 15 and later sections in Chapter 8) Aristotle is not explicit on how the connection between the notion of substance and that of universal, which his own theory must surely require, is to be safely accomplished. (For speculative remarks on this last topic, see the Appendix to this chapter.) Given the negative character of so much of what has preceded, what positive moral or, more hopefully, morals are we to carry away from the discussion? As I read Zeta, hopes for a positive outcome must wait for the “new start” about to come in Zeta 17. This new start will produce Aristotle’s “official” definition of substance, and to all appearances, the discussion in 17 proceeds independently of the entire inquiry spanning the preceding chapters 3–16. (The following chapter, Eta 1, goes some way to showing how the received views in 3–16 can be accommodated to the extent necessary to conform to the causal account of substance put forward in Zeta 17.)

21

For a more optimistic assessment on this score, see Burnyeat (2001), 55–6.

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Perhaps because of the new and positive start under way in Zeta 17, the connection is usually missed between Zeta 17 and the (“non-partisan”) discussion of Plato’s and Pythagoras’ conceptions of being and one in the preceding chapter 16. Contrary to Plato and Pythagoras, these two, being and one, which are universal to everything, are not themselves substances, and not the substance of anything. Instead, on Aristotle’s view, we find that substance—better, primary substance, which is also the substance of a given thing—is the cause for each thing of its being one, or a being. This piecemeal approach to questions of one and of being is in contrast to the sweeping approach he associates with Plato, and it is as striking an example as any of the “flight from the general” that separates his larger metaphysical preferences from those of Plato.22 The two ideas of substance—that is, the substance of a given thing—as the cause of being for that thing, and also of the thing’s being one, are the topics of the two halves of Zeta 17, where Plato will offer his own positive account—in particular, the long-awaited definition of substance or, better, the substance of a thing.23

Appendix: Definition, Substance, and Universals: A Puzzle, and Some Speculative Conclusions In Zeta 4 from the segment on essence, Aristotle’s inquiry after substance seemed to make progress in two ways. In the first place, the initial link that gives the starting point of the segment, that the essence of a thing is its substance, appears to survive intact:

(1)

x is the substance of y, just in case x is the essence of y.

Zeta 4 endorses a similar connection between the notions of essence and (metaphysical) definition:

(2)

x is the essence of y, just in case x is the definition of y.

Now, the discussion in Zeta 15 and 16 suggests a connection between the notions of definition and of universal. Individuals cannot, strictly, be defined; only repeatable universals can. An obvious thought will be to frame the connection between universals and definition along lines similar to those connecting substance and essence, and essence and definition, in (1) and (2) above:

Burnyeat (2001), 36–7, cf. 13, writes eloquently on “the Platonists’ unscientific craving for generality and abstractness”. 23 Z17, 1041a10–b11, b11–25; the two strands are pulled together in the final summary at b25–33. For more on the structure of Z17, see Lewis (1995) 1996. 22

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x is universal to y and z (y 6¼ z), just in case x is the definition of y and z.

And from (1) through (3), it is but a short step to a connection between the notions of substance and universal, in line with the leading idea of the segment:

(4)

x is universal to y and z (y 6¼ z), just in case x is the substance of y and z.

Now, (4) will not amount to satisfying Aristotle’s goal of giving a definition of substance. But it may seem that (4) supplies a condition that will constrain the definition once one is forthcoming. But of course, Aristotle will say that (4) is flat-out false—indeed, he warns us against much the argument sketched above (8.8 in Chapter 8, Section 7). (4) is contrary to one of the two main results of the segment, as set out in Mutual Exclusivity (Chapter 8, Section 2): x is universal to y and z (y 6¼ z), just in case x is not the substance of y and not the substance of z. Mutual Exclusivity If there are any sure results to be gained from the segment on universals, the argument to (4) is headed in precisely the wrong direction. A first thought for how to repair the damage might be to take a closer look at the notion of definition. To take a stock example from the Organon,24 repeated in Metaphysics Zeta 12: where the definiendum, “man”, names the species, man, the definiens, “rational animal” (let us suppose), in the correct linguistic definition names the combination of the genus with the differentia, namely, rational animal. Aristotle also recognizes a notion of definition as a relation between entities: for example, the entity, rational animal, is the (metaphysical) definition of man. Suppose the item being defined is a genus. Then the entity that defines it will apply to exactly that genus, and to no other genera besides.25 Similarly, if the item being defined is a species, then the entity that defines it will apply to exactly that species, and to that species and to no other species besides. At the same time, Aristotle also tells us that “definition is always universal”. Consider, for example, the definition of health in the eye, where different definitions will be appropriate for the eyes of different kinds of animal: one definition of health will be universal to all members of the genus, eye; and a different definition will be universal to all the members of a given species of eye, An. Po. B13, 97b25–8. Accordingly, the entity that defines the genus will be predicated of all the members of the genus. And the entity that defines the species will be predicated of all the members of that species. To accommodate the differences noted in the preceding two paragraphs, we can formally separate the different levels in the notion of (metaphysical) definition into definition (unstarred) and definition*.26 For example, we may compare these two quite different results:

(5)

Rational animal is the definition [unstarred] of man.

(6) Rational animal is universal to and the definition* of Archimedes, Speusippus, and the rest. 24 For definition by genus and differentia, see, for example, Topics Z5 and 6, and for advice about the method of dividing a genus by the appropriate differentiae, in the appropriate order, omitting none, An. Po. B13, 96b25–97b6, with B14 and Metaphysics Z12. 25 Plausible though this may seem, Aristotle puts pressure on the idea at Z15, 1040a8–21; see Section 1. 26 For the “starred”/“unstarred” distinction in use throughout this section, see Chapter 3, n. 11 and Chapter 8, Section 5, with that chapter, n. 25.

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So the connection between the notions of definition and universal will be significantly weaker than envisioned in (3) above. In place of (3), we will have

(3*)

x is universal to y and z (y 6¼ z), just in case x is the definition* of y and z.

From (3*), there is no route to (4) above, and the clash between (4) and Mutual Exclusivity is avoided. Instead, we assume, first, a version of the connection Aristotle sees between definability and substance:

(5)

x is the definition* of y, just in case x is the substance* of y.

Given (3*) and (5), in place of the unwanted (4) we can now derive the result that

(4*)

x is universal to y and z (y 6¼ z), just in case x is the substance* of y and z.

The new (4*) offers the prospect of a more innocuous link between the notions of substance and universal. We now have within reach a fresh version of Compatibility (see Appendix to Chapter 8), formally consistent with Mutual Exclusivity:

For some y, z (y 6¼ z), x is universal to y and z, and x is the substance* of y and of z. Compatibility C x is universal to y and z (y 6¼ z), just in case x is not the substance of y and not the substance of z. Mutual Exclusivity Alas for the prospects of reconciliation, Compatibility C accommodates a view of universals represented by Plato’s theory of forms that Aristotle cannot accept. If Aristotle allows himself a theory of universals in which a universal is the substance (unstarred) of only itself, but is the substance* of each of the many things to which it is universal, then he must be willing to credit Plato with a comparable set of views. A Platonic form will be the substance (unstarred) only of itself, and will stand in the reduced substance* relation to the many sensibles that participate in it. To avoid the relapse into Platonism, Aristotle must take a sterner view of Aristotelian kinds than he allows himself elsewhere. In Metaphysics Zeta 4, for example, Aristotle makes use of the received view according to which genous eide¯—the (lowest) species of a genus—occupy the position of primary substances (3.21 above). In Zeta 10 and 11, by contrast (7.1 = 8.6 above, cf. Zeta 11, 1037a6–7), he is clear that kinds are not substances of any grade. And if kinds do not count as substances of any rank, then they will not be even the substance* of their members. A theory of kinds is also active in the Analytics, which is (Aristotelian)-form-free. In Zeta 17, by contrast, which is the capstone of the discussion of substance in Zeta and devotes the core of its argument to the official theory of form and matter, Aristotle’s forms displace kinds as the appropriate causal middle terms in the structure he takes over from the theory of demonstration in the Analytics. In the “in-house” Aristotelian theory of form and matter, Aristotelian forms are the primary substances, and kinds are not substances at all. How might Aristotle adapt the account of substances and universals so as to fit the “in-house” theory of (Aristotelian) form and matter? We start with the idea that an Aristotelian form is a primary substance, and at the same time, the substance* of the compound material substances of which it is a constituent. So, for example, where Archimedes and Speusippus are each compounds of form and matter,

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Archimedes = m1 + ł, Speusippus = m2 + ł, the following two assumptions hold: ł is a primary substance. ł is the substance* of Archimedes (= m1 + ł), and ł is the substance* of Speusippus (= m2 + ł).27 In this account, an Aristotelian form is a primary substance, but the substance* of the relevant compound material substance. This starred result is altogether appropriate, since if we ask of a primary substance, what is its substance (unstarred), the only possible answer can be: itself (for the reasoning behind this view, see Chapter 6, Section 1). That is, we also have this result: ł is the substance [unstarred] of ł. As we will see in Chapter 11, it is the presence of one and the same form, ł, to the different cases m1 and m2 of matter that constitutes the cause of being for the two individual substances, Archimedes and Speusippus. Accordingly, if forms are universals for Aristotle,28 it will be because one and the same form exercises the same causal role with respect to the two different matters, m1 and m2. Speculatively, then, where (as before) Archimedes = m1 + ł and Speusippus = m2 + ł, we have the following connection between substances and universals in the official theory of (Aristotelian) form and matter:

(i) ł is universal to m1 and to m2; and ł is the substance* of Archimedes (= m1 + ł) and of Speusippus (= m2 + ł); and (ii) ł is the substance [unstarred] of ł. For (i), compare Compatibility B, and for (ii), Compatibility A, both in the Appendix of Chapter 8. Meanwhile, if kinds are not substances of any grade, the role of a kind as universal to its members is of no relevance to the limits Aristotle places on the relation between substances and universals.

27 In the formulae in the main text I assume that ł is what commentators call “substantial” or “last” form, while m1 and m2 are proximate matter. That is, where Archimedes = m1 + ł, ł is substantial, last form, and m1 proximate matter, we say that there are no forms, łn, łn + 1, and no matter, mn, such that m1 + łn = mn and mn + łn + 1 = Archimedes. Intuitively, you cannot insert two layers of forms to take us from m1 to the finished substance, Archimedes. But while it can be the business of metaphysics to say that boundaries of this sort exist, it falls to another—the natural philosopher, perhaps, or the craftsman—to fill in the real-world details. 28 For a caution about the notion of universal here, see Appendix to Chapter 8, n. 77. Others are outright sceptical whether (Aristotelian) forms are universals; see Chapter 8, n. 64; for ambivalence on this question, Code (1984), 18–20, and see also his (1985) and (1986).

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PART FIVE

Back to the Definition of Substance: The End-Game

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11 The Posterior Analytics, and a Fresh Approach to Defining Substance 1 The Search for Substance: Are We There Yet? With the end of Zeta 16, Aristotle completes his review, set in motion at the beginning of Zeta 3, of received opinions about how to define substance (1.4 above). Given the seriously negative cast of much of his discussion, documented in previous chapters, how much closer are we to the wanted definition? Can the leading conceptions of substance taken up in the three segments that form the body of Zeta—of substance as a subject, or as a universal, or as the essence of a thing—can these be salvaged in some form acceptable to Aristotle? And if, for all Aristotle’s silence, not just one, but two, perhaps even all three, of those views can be suitably revised and refined to warrant a place in his own, partisan theory, do they combine to form a single, unified notion of substance? In the meantime, the definitional project is about to get still more complicated. At the beginning of the final chapter, 17, of Zeta, Aristotle offers yet another “new start” on the attempt at definition—one that supersedes the new starts that originate in the agenda passage of Zeta 3:1 11.1 What, and what sort of thing, substance should be said to be, let us formulate this again, making as it were another beginning . . . Since, then, substance is a certain principle and cause, let us pursue it from that point. (1041a6–7, 9–10, Furth’s translation)

The leading idea in this new new start is that substance is a cause. Now, we will find that the notion of substance that most interests Aristotle—that of primary substance—is that of the substance of a given thing; and he will expand the formulation in 11.1, that substance is a cause, to say that a substance is the substance of a thing and the cause of that thing:

My “supersedes” is not intended to endorse Bostock’s “no relevance” thesis, to the effect that the argument of Z17 is “independent of anything else in book Z” (Bostock (1994), 236), as the discussion in Chapter 12 should make clear. In defence of relevance, see also Frede and Patzig (1998) II, 308, and Wedin (2000), 407, with his n. 3. 1

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11.2 This [= the cause of unity in a thing] is the substance of each thing, for it the primary cause of its being. (Z17, 1041b27–8, cf. a31–2, H2, 1043a2–4, H3, 1043b13, and de Anima B4, 415b12–14)

Aristotle moves freely between the different formulations—non-relational and relational—in 11.1 and 11.2, and in most contexts as we go along, I follow his lead and do not separate these different views out.2 Even so, it will be helpful to keep them apart when it comes to saying exactly what kind of property I take being a substance to be (Section 6). Back now to Aristotle’s new start in Zeta 17. In contrast to his previous new starts, which he represents as the product of received opinion, Aristotle proceeds here without an overt appeal to the work of others: as we shall see, the causal idea is one he and others have had before, but he is happy to state it in propria persona. But how does the conception of substance as a cause bring us closer than earlier chapters have done to the definition we are after? In particular, again, how does this new definitional proposal bear on the earlier attempts at definition? We will turn later to Aristotle’s own attempt to summarize what is to be learned from the different segments of Zeta in the first chapter of Eta (see Chapter 12). But a provisional answer is in order to the question how the new approach to substance in Zeta 17 is related to, even improves on, earlier endeavours in Zeta. The best hypothesis is that the new notion of substance as a cause in one way or another incorporates the different approaches listed in 1.4 and pursued in the body of Zeta, so that there are causal dimensions (in a suitably Aristotelian sense of “causal”) to all three conceptions of substance—as a subject, as a thing’s essence, and as a universal, alike. It will also be important to see Zeta 17 in the context of the summary in Eta 1 (always remembering that the division between books is not Aristotle’s work, but an editor’s). While Zeta 17 is embedded in various ways in its larger context in Zeta–Eta, we cannot read far into the chapter before becoming aware of a further debt, this time to one of Aristotle’s own other selves in the An. Po.3 As we shall see, just how we are to understand the first half of Zeta 17 against the background of the Analytics is a major factor in settling on an interpretation of the chapter. In some respects, Aristotle appears to take over directly ideas from the Analytics. In other respects, it seems that he must modify the apparatus of the Analytics, if it is to fit its new context—the inquiry into substance—in the Metaphysics. As in the body of Zeta, the discussion in Zeta 17 is a mix of “received views” and partisan: at first “received views” (11.6 and Chapter 11, n. 16), thanks principally (although not quite exclusively) to Aristotle’s own views in the An. Po. For Aristotle’s movement between relational and non-relational notions of substance (“substance of ” and “substance(s)” tout court), see the remarks in the Introduction and in Chapter 8, Sections 2 and 3, with that chapter, nn. 11 and 18. 3 Aristotle suggests that antecedents of the causal idea can be found in Plato (8.5 above); see Chapter 8, Section 2. But there is no trace of Platonic ancestry in Z17. O the contrary, the chapter silently offers a substitute for Plato’s notions of one and being; see Section 2, and the final paragraph of Chapter 10. As we shall see, the main influence external to Zeta is Aristotle’s other self in the Analytics. 2

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Meanwhile, later in the chapter the apparatus of the An. Po. is folded into Aristotle’s distinctive “partisan” theory of form and matter (11.8, matter, and 11.9, matter and form). In the case of the Analytics, there is especially good reason for making room for its views in the pursuit of Aristotle’s own partisan conclusions in metaphysics. As Aristotle says elsewhere, a knowledge of the principles of syllogistic (to¯n sullogistiko¯n archo¯n), along with perhaps a knowledge of his Analytics more generally, is an essential prerequisite for work in metaphysics or first philosophy. Thus, students of metaphysics must beware of 11.3 . . . a want of education in analytics (en tois analutikois, “in the Analytics”?); for they should come knowing these things already, and not be inquiring into them while they are listening [sc. to Aristotle’s lectures?]. (Metaphysics ˆ3, 1005b3–5)

Contrary to what some have argued, however, in Zeta the influence of the Analytics, and work in the science of metaphysics in the sense of “science” established there, is largely confined to Zeta 17.4 So I would not agree that because Zeta is taken up with attempts to define substance, and because attempts at constructing definitions are not a part of dialectic (De Int. 11, 20b26–30), the body of Zeta is not dialectical (though it contains dialectical passages), but rather pursues the science of metaphysics.5 Such an account does not fit the bulk of Zeta, but it captures exactly the change of approach embodied in the “new start” in the final chapter 17 of Zeta. The chapters in which Aristotle works through the attempts at definition featured in the agenda passage of Zeta 3 are in large part dialectical, especially given Aristotle’s generally destructive approach to the definitions he passes under review. But the science of metaphysics comes roaring in in Zeta 17. In this chapter Aristotle draws heavily on the theoretical apparatus of the Analytics in order to produce a successful definition of substance in terms of causes, as required for a definition of the kind the Analytics favours. The borrowings from the Analytics count as one “outside” source for Aristotle’s views in Zeta 17. His agenda in the chapter also represents his attempt to put his own stamp on two major issues discussed at the end of the preceding chapter, 16, and associated elsewhere with the names of Plato and Pythagoras (Chapter 10, Section 5). For Plato and Pythagoras, being and unity are both transcendental universals, applying equally to everything and, perhaps, masquerading (as Aristotle regards it) as the substance of everything—so that in the end, he complains, “everything is one” (7.9; see Chapter 10, Section 5). Aristotle himself favours, rather, a piecemeal approach,

4 This is not to deny that there are occasional glimpses of the Organon at different points elsewhere in Zeta: the Organon supplies important background to the discussion in Zeta 4 (Chapter 3), for example; see also 10.1 from Z15 above. References in Zeta to the Organon are collected in Charles (2000), 276ff. Charles (2000) and Bolton (1995) 1996 both place more weight on the presence of the Organon in the chapters of Zeta prior to Z17 than I am inclined to do. 5 The argument is from Bolton (1995) 1996, 251. I would also argue that the idea of substance as a cause, which is key to the Analytics account, is almost entirely absent from the discussion of substance in the earlier chapters that take up the agenda passage of Z3; see Chapter 8, n. 6.

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where questions of the being and unity of a thing are explained differently for each different kind of thing—one explanation for man, another for house, and so on. The two topics, being and unity, are discussed separately, with issues of being in the first half of Zeta 17, and questions of unity in the second. As I read the chapter the discussion in the first half motivates the move to a discussion of unity in the second, for as it turns out, our account of the being of a thing requires us to see the thing as a whole, with constituent parts: if a thing has parts, how do we guarantee that it is a genuine whole—that its parts form a genuine unity? Elements of his solution appear in the second half of the chapter, where the discussion of unity runs in parallel with the earlier discussion of being.6 My main interest in what follows, however, will be in the discussion of being in the first half of the chapter.

2 Substance as a Cause Aristotle’s new start on substance in Zeta 17 is framed around the idea of substance as a cause. Now, causes are things we cite in answer to Why? questions. But there is work to be done on the nature of the relevant Why? questions, which Aristotle suggests must be understood as asking, why one thing belongs to another. There follow a series of remarks separating the kind of question he has in mind from its pretenders; the result will be to motivate his conception of Why? questions as involving the structure given—namely, asking why one thing belongs to another: 11.4 Since, then, substance is a certain principle and cause, let us pursue it from that point. Now, the why is always sought in this form: why does one thing belong to something else? For to inquire why the musical man is a musical man is either to inquire what was just said, namely, why the man is musical [= why one thing belongs to another], or something else. Now, why a thing is itself (dia ti auto estin auto, a14) is to inquire after nothing. For the that and the being (to hoti kai to einai) clearly must obtain—I mean for example that the moon is eclipsed; but that a thing is itself (auto de hoti auto, a16) is a single formula and a single cause that applies to everything, Why is the man a man? or the musical musical?—unless one were to say that each thing is indivisible with respect to itself and is what it was to be one [= “is essentially one”]; but that is common to everything and cut from the same cloth (koinon ge kata panto¯n kai suntomon).7 (1041a9–20, after Furth’s translation) 11.5 (immediately following 11.4) One might inquire, why is such-and-such an animal (a) man?8 This much, then, is clear, that one is not asking why he who is a man is a man; so one is 6 The later chapter, Eta 6, on questions about unity—in particular, the unity of form and matter— represents what I take to be Aristotle’s best attempt to settle questions that have arisen repeatedly in Zeta; see Chapter 8, n. 58. 7 I translate Aristotle’s suntomon by “cut from the same cloth”, repeating in more colourful terms his koinon kata panto¯n, “common to everything”; I owe to John Malcolm the attractive alternative, that Aristotle means that the answer that everything is itself “cuts too short” what might otherwise have been an informative explanation. 8 For this translation, see this chapter, n. 13.

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asking, where something is of something, why does it belong? That it belongs must be plain; for if it is not so, then there is no question. For example, why does it thunder? Why does noise occur in the clouds? For what is being asked after is something in this manner of something else. And why are these, bricks and stones, say, a house? (1041a20–7, after Furth’s translation)

A first task on Aristotle’s mind in 11.4 and 11.5 is to clear out of the way what he regards as unhelpful readings of Why? questions. In part, we will be tempted to say, the difficulties he sees involve what we would regard as the scope of the question-word, Why? Suppose we ask why a musical man is a musical man. Either this is to ask of the musical man why he is musical (giving the question-word narrow scope), or we are asking “why the thing is the thing” (a14, 16, with the question-word having wide scope). We must beware of interpretations of our question that return answers that are vacuous (that “it is it”, a16) or, at the least, are overly generic (so that “everything has a single account and a single cause”, a17). These are the interpretations we might be tempted to put down to problems over the scope of the question-word, Why? So, the questions why the man is a man, or why the musical is musical, are out of court. And the answer that everything is itself is (presumably not false, but) “common to everything”, and “cut from the same cloth” (suntomon) in every case. In the absence of our distinction between wide and narrow scope of the question-word, and needing to avoid asking the trivial question, Why is a man a man?, what is Aristotle to do? In 11.5 he introduces his solution: we are to find some new subject for the predicate, “man”—a subject non-identical with the thing—the man—with which he began. Before we turn to the details of this new proposal, it is clear from both 11.4 and 11.5 that there is one old puzzle that the appeal to some different item as subject is not intended to address. We are to suppose that the fact of the matter (the hoti) and the being—that the thing exists?—do in fact obtain (a15–16, 23–4). It is already established, for example, that the moon is eclipsed (the example, prominent in the Analytics, is our first warning that the An. Po. will be of importance in the present chapter). Since Aristotle here already assumes a positive answer to questions about whether the fact obtains, or the thing exists, his move to some new entity at the end of 11.5 is not directed at resolving a familiar problem about assertions of existence. A standard difficulty in discussions of existence is that, in the very act of asking whether a given thing exists, we prejudice the answer by apparently referring to the thing concerned in our question. Since the existence of the thing is not at issue in Zeta 17, it is not obvious that the move he will suggest to some new entity is meant to protect against this old objection.9 While the topic of existence is before us, a caveat is in order. It is perfectly proper to ascribe to Aristotle an interest in such questions, without committing ourselves or him to an interest in the so-called “is” of existence. Neither Aristotle nor we need to have a semantic theory involving the alleged ambiguity of “is” or its Greek equivalent, esti, in 9 Code (unpublished) argues that the problem of existence noted may influence Aristotle’s thinking in the Analytics, and if so, we cannot rule out that the discussion in Z17 is crafted partly in that light.

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order to be able to discuss intelligibly conditions under which things of a given type exist.10 In the An. Po. it appears that for Aristotle, questions about the existence of a given event-type, thunder (say), can be settled quite early in the process of scientific inquiry.11 Exactly in line with the Analytics, in Zeta 17 we are to assume early on that the thing exists, or that the event occurs (11.4, 11.5 above, and 11.8 below). So we begin with the assumption that a particular man exists—that we have an individual man before us. The question remains: what about that object ensures that it is a man? That is to say, Why is it a man? As we shall see, this is an unarticulated Why? question of the sort Aristotle thinks must be reformulated in the way the Analytics treatment of thunder and the rest suggests, to ask why one thing belongs to another. Aristotle turns to the problem of being he does mean to discuss, and to the move to a new entity that he offers as its solution, in 11.5. He finds what he regards as solid ground with the example of thunder at the end of 11.5: the question, Why does it thunder?, is to be parsed as (a) Why does noise come about in the clouds? a25.12 Or (also from 11.5 above) with a house, or with a man,

10

Against Owen (1956) 1986, see Matthews (1995), and for further discussion see Dancy (1983) and (2006), and Hintikka (2006). 11 In Charles (2000), Charles distinguishes three stages of inquiry in Aristotle’s account, starting at stage 1 with knowledge of what a name signifies (loosely, we have what commentators have sometimes called a nominal definition of the phenomenon at hand); proceeding to stage 2, where we know only that some middle term exists, without perhaps knowing what that middle term is; and ending at stage 3, with discovering what the middle term is, and so being in command of both explanation—the why—and definition—the what (Greek dia ti and ti respectively). On this account, knowing just that some middle exists at stage 2 is sufficient warrant for thinking we have a single natural kind in view. (According to Charles, Stages 2 and 3 can come simultaneously in our knowledge, but they need not do so. As to the boundary between the two stages, An. Po. 93a36–b2 gives an example of knowing that there is an eclipse by way of a middle term that is not “causally fundamental”, Charles (2000), 54; but as Charles suggests, there are “major gaps” in Aristotle’s account that leave it unclear how much of the essence of the thing we should know in order to know that the thing exists. For more on these topics, see An. Po. B8–10, with Charles (2000), chapters 1 and 2.) On other accounts (Bolton 1976), knowledge that members of the kind exist is said to come even earlier, as an essential part of our knowledge of what the term signifies. On either view, Aristotle is not much inclined towards scepticism about the existence of a genuine kind. There is little sign that for him, further investigation of the nature of the middle term might reveal that the supposed middle term is bogus, so that no kind exists after all; or that there is in fact more than one middle term, each an equally good candidate for supplying an explanation and a definition, so that we have more than one natural kind, not just one. 12 The parsing required reproduces what in the An. Po. is a preliminary to constructing a demonstration, with the move from a single term for the phenomenon to be explained, “thunder” (say), to a “nominal” definition (this chapter, n. 11), “noise in the clouds”, which in the successful case will reappear as the conclusion to the completed demonstration. Of equal interest is the technique of “transformation” in the An. Po, whereby the different terms in a demonstration are reassembled to form the defininens for the phenomenon under investigation; see this chapter, n. 25.

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(b) Why are these, e.g. these bricks and stones, a house? a26–7. (c) Why is such-and-such an animal a man?13 a20–1. Aristotle insists that this last question is not to ask why he who is a man is a man (our widescope “why”). Rather, for Aristotle, the question takes the form, Why is one thing another? We might begin by noticing an apparent mismatch between Aristotle’s example, (a), and the remaining two, (b) and (c). As we will see, example (a) comes from the An. Po, and has to do with the explanation of events or event-types—thunder, for example— while the remaining two examples, (b) and (c), involve the explanation of substances or substance-types. Aristotle is emphatic about the relevance of cases of the first kind to those of the second; but it is not obvious that what holds of thunder transfers unchanged to man and the rest.14 How, then, in Aristotle’s view does the example of thunder advance our understanding of questions about man, house, and the rest? We should begin with some details about the thunder example. When Aristotle admonishes us in 11.5 to “articulate out” the term “thunder” to become “noise in the clouds”, he presents the move as support for his solution to establishing an acceptable interpretation of Why? questions—to what we would regard as the problem of settling on the appropriate scope of the question word, Why? But—as the appeal to the event-type, thunder, suggests—the roots of the manoeuvre lie deeper, in the An. Po. In Beta of the An. Po., Aristotle is concerned with how to reach a definition by means of constructing the relevant demonstration. In the case of thunder, for example, the route to the needed demonstration begins with “articulating out” the term “thunder” as “noise in the clouds”; this will count as a nominal definition of thunder, and it supplies us with the major and minor terms, “noise”, “clouds”, that can be incorporated into a demonstration. The demonstration is completed with the introduction of the needed middle term, “the extinction of fire”, which cites the appropriate cause of thunder: Noise belongs to extinction of fire. Extinction of fire belongs to the clouds. 13

How to read this example is controversial (my choice of text and the accompanying interpretation appears also in Furth; see his note, 125). The translation in the main text requires that we omit the definite article before the Greek for “man”, with Ab. If the article is retained, then the translation must be, Why is the man such-and-such an animal?, where the “such-and-such” will seem a place-marker for an appropriate differentia-predicate, “two-footed” (say). On this reading, Aristotle is veering towards the topic of genus and differentia, in particular, definition by genus and differentia (see An. Po. B8, 93a23–4, with Charles (2000), 229), and perhaps towards the problems of unity he says more than once in Metaphysics Zeta–Eta are associated with these. But Aristotle’s next examples, like those later in the chapter, point to questions about matter, and how we get from matter to examples of the kind, and I read the present example (with Ab’s text) in that light. As to the definition of individual substances and their kinds, I would suggest that the topic is not broached in Z17, but must wait for H2’ see also Section 5. 14 One difference is immediately obvious: in (a), the term “thunder” itself does not appear in the result of “articulating out” the term. In (b) and (c), where the topic is substances or substance-types like man (and second-rate substances or substance-types like house), the result of articulating out retains the term under treatment. The importance of this will emerge in Section 4; see this chapter, n. 35.

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So Noise belongs to the clouds. Once this causal ingredient is in place, we can read off from the demonstration the real definition of thunder as “noise in the clouds thanks to the extinction of fire”. The definition includes the cause of the phenomenon in question, so that it can be seen as answering the question, Why does it thunder?15 On this account, Aristotle’s thunder example does not begin life as a treatment for the difficulties over scope we are inclined to see in Zeta 17. Instead, I am tempted to say, in Zeta 17 Aristotle finds a solution to the treatment of Why? questions, in the solution to a different problem over the early stages in the construction of a demonstration in the An. Po. And his adaptation of his old solution brings a special bonus to the discussion of substance in Zeta 17. The process of “articulating out” that stands at the beginning of a search for a demonstration in the Analytics, brings to its new context in the Metaphysics the causal notions that Aristotle now thinks key to his search for the definition of substance. As Zeta 17 develops, Aristotle expands on the different kinds of cause appropriate to different kinds of thing. If the text in 11.6 below can be trusted (Ross ad loc. argues that it can), questions as to a thing’s cause (speaking logiko¯s, this chapter, n. 16) address the essence of the thing. In the case of a house, perhaps, or a bed, our causal questions are headed for an answer in terms of a final cause, but elsewhere, a moving cause, or even both kinds of cause: 11.6 (= the continuation of 11.5 above) So it is evident that one is inquiring after the cause, and that is the essence, as we say logiko¯s,16 which in the case of some things is the “for the sake of something” [= the final cause], as for example in the case of a house or a bed; in other cases it is what first set the movement going, for that is a cause too. But while the latter sort of cause [= the efficient cause] is sought in the case of coming to be and passing away, the former [= the final cause] in the case of being also [= in the case of being as well as becoming].17 (1041a27–32, following Furth’s translation)

15

There is considerable variation in detail in Aristotle’s account of the demonstrations from which a definition can be extracted, see An. Po. B8, 93a29–b12, and B10, 94a1–7 (included in 11.10, this chapter, n. 25), and for discussion, (Barnes) 1994, 220 and 224. The example in the main text, which is recalled in Metaphysics Z17 (see 11.5 above), is from An. Po. B10, 94a1–9. 16 The text translated here is defended in Chapter 12, n. 16. For the credentials in the Organon for the link between cause and essence, see An. Po. B2, 90a14–23, 31–4, cf. B8, 93a3–4. Text 11.6 contains the third and final occurrence of the term of art, logiko¯s, in Zeta. The use of the term here may be intended only as a reminder of its use when Aristotle introduces the topic of essence in Z4. Minimally, as perhaps there (3.5 with Chapter 3, n. 20), Aristotle may mean only to appeal to how informed people speak, outside the framework of the official Aristotelian theory of form and matter. Charles’s “to speak in general terms” (Charles (2010), 310), serves equally well to separate the appeal to essence from the technical notions proprietary to Aristotle’s own theory. 17 If I read Aristotle right, he suggests that a moving cause is appropriate to cases of coming to be and perishing, but the final cause applies to a thing’s being as well as to its coming to be (but less obviously to its perishing). Notably, where in the explanation of event-types in the An. Po. the efficient cause is given pride of place as middle term in the relevant demonstration, in Eta 6 the efficient cause is bracketed, and the account

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As in the case of thunder, so in the case of men and houses there is first some unpacking to be done, if our causal account is to proceed: 11.7 (continuing 11.6 above) But the thing being inquired after escapes notice most of all in those cases where things are not said of one another, as when it is asked, Why is man? (b1),18 because it is said simpliciter (“simply”, haplo¯s), and it is not articulated out, that these are this. (1041a32–b2, following Furth’s translation) 11.8 (= the immediate continuation of 11.7) But before we inquire it needs to be articulated out; if it is not then it is all one whether we are inquiring into something or nothing. But since the being must hold and be assured, clearly the question is why the matter is [= constitutes]19 some thing (ti); for example, Why are these things a house?—Because there belongs what it is to be for a house. Why is this, or better, this body in such-and-such a state, a man? (1041b2–7, following Furth’s translation) 11.9 (= the immediate continuation of 11.8) So the cause is being sought (and this is the form)20 of the matter’s being [= constituting]21 some thing (ti); and this is the [its?] substance [sc. the substance of the result]. (1041b7–9, following Furth’s translation)

That is to say (in 11.7): it can be difficult to see how the initial question, Why?, invites an answer that fits the desired causal paradigm. “Why is it a man?”, for example, does not obviously ask why one thing belongs to another (and does not obviously avoid the problems of scope already noted). But (11.8) we must “articulate things out”, if our inquiry is to mean anything.22 Thus, our question will be, with respect to the matter, why it is a this—a thing of this or that kind. For example, Why are these—these bricks and stones—a house? Why are these, or better, this body in such and such a state, a man? Because the essence of house, or of man, belongs to them. Accordingly—lining runs in terms of form and matter by themselves. For the different assignments of causes for different kinds of explananda, see the discussion in the main text. 18 At 1041b1, I read dia ti (“on account of what?”, “why?”) with E and Asclepius, rather than the unadorned ti (“what?”) of the other manuscripts. With the latter reading, Aristotle turns to the definitional question, What is (a) man? Now, Why? questions of the kind under discussion in Z17 in the An. Po. are his replacement for definitional questions of the form, What is it?, applied to the definition of events or eventtypes, thunder, eclipse, and the like. But while the main object of Zeta 17 is to make good on the definition of the substance of a thing as the cause of its being, I do not see that the chapter is concerned with a quite different set of definables: individuals, perhaps, or their types, or even (Aristotelian) forms (see Sections 4 and 5). The reading I reject at the beginning of this note would represent the only place in Z17 where Aristotle explicitly introduces the topic of defining entities of any such sort; see this chapter, n. 13, and Section 5. As to the special character of the property of being the substance of a thing that I take to be properly the object of definition in the chapter, see Section 6. For further discussion of the text, see Wedin (2000), 420 with n. 18, and Frede and Patzig (1988) II, 315. 19 The relations between matter, the thing of a given kind, and the kind, all three of which enter into Aristotle’s picture here, are not easy. Given the switch from thinking of the man, Archimedes (say) as subject to the kind, man, to his matter as its subject, the predicate “is a man”, as applied to Archimedes’ matter as subject, must be read as “constitutes a thing of the kind, man”. I will assume a reading of this sort as needed below. 20 For the text translated here, see Chapter 12, Section 2, with that chapter, n. 18. 21 See this chapter, n. 19. 22 For the process of “articulating out” see this chapter, nn. 12 and 25.

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up the mention of essence in 11.6 and 11.8 with that of form in 11.9—the cause thanks to which the matter is, better, constitutes, a this, is the form; and the form is a substance, and also the substance of the finished thing. In this account, to the all-important question, what item in the Metaphysics ontology serves as the cause of particular substances?, Aristotle answers: form. At its best, explanation includes all four causes.23 At the same time, different kinds of cause are favoured for different classes of explananda. For what we would think of as an event—the occurrence of thunder, or an eclipse—there is perhaps no final cause, and the efficient cause will be all-important (Eta 4, 1044b8–15). In the explanation of the being of particular substances, other kinds of cause—material and efficient—are also at work, but the starring role goes to form: a form is that real item in the constitution of a thing that answers to both its formal and final cause. Because form is now the favoured kind of cause, it occupies (more or less) the place given in the Analytics to the middle term in the demonstration that gives the cause of events, thunder, and the rest.24 The move from the An. Po. to Metaphysics Zeta 17 is our next topic.

3 From the An. Po. to the Metaphysics The formulation of how to approach questions about being in 11.7 through 11.9 above puts in place an explanatory structure that brings the devices of the An. Po. well within reach. The examples of thunder and eclipse make it clear that the An. Po. is in Aristotle’s mind all along—always allowing for the accommodations required for the shift from the explanation of events in the Analytics, to giving the cause of being for substances in Metaphysics Zeta 17. I start with the treatment of events, or event-types, in the Analytics. In the Analytics, as we have seen (in Section 2), Aristotle links the examples of thunder and eclipse to syllogisms that count as demonstrations. These start from a “nominal” definition (this chapter, n. 11) of thunder (say) as noise in the clouds, and then supply a middle term that is the cause and the essence of thunder, so that we are able to read the definition of thunder, “noise in the clouds due to the extinction of fire”, from the relevant demonstration, which I repeat from Section 2:

23

Aristotle is usually taken to be explicit in An. Po. B11 that four kinds of cause can act as middle term in a causal demonstration; this is a chapter Ross (1949), 638, describes as “one of the most difficult in Aristotle . . . it is only by exercising measure of goodwill that we can consider as syllogisms some of the ‘syllogisms’ put forward by A. in this chapter”. (But for an argument that Aristotle may not after all require in B11that all four causes be capable of performing in the role of middle term, see Leunissen (2010).) I argue in Sections 4 and 5 that difficulties similar to those traditionally seen in B11 stand in the way of extending the causal demonstrations of the An. Po. into the account of substance as the cause of being for things in Metaphysics Z17. 24 For the starring role given to the cause that occupies the position given to the middle term, see An. Po. B2.

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Noise belongs to extinction of fire. Extinction of fire belongs to the clouds. So Noise belongs to the clouds.25 Since the argument given is a genuine demonstration, it is a “scientific deduction” (sullogismon episte¯monikon); that is to say, it gives us knowledge of “the cause through which the thing is , and that it is not possible for it [= the thing] to be otherwise” (An. Po. A2, 71b10–12). Accordingly, the demonstration shows how to insert the cause of thunder into its definition: thunder is exactly this kind of noise in the clouds—the kind caused by the extinction of fire there (in contrast, as we might say—but Aristotle could not—to the kind of noise in the clouds caused by a passing plane).26 A further requirement on a demonstration (from the list at An. Po. B2, 71b29–33) is that its premisses be immediate: so the connection above between the extinction of fire and noise in the major premiss, and between the extinction of fire and the clouds in the minor premiss, is immediate in both cases. There are no further middle terms to come. This apparatus is relevant in important ways to the discussion in Zeta 17. At the same time, there is no exact fit: the apparatus of the Analytics must be adapted in certain ways to fit its new context. The similarities and the adaptations are our next topic.

25 For the demonstration in the main text, see this chapter, n. 15. Aristotle explains the connection between demonstration and definition in the An. Po:

11.10 Another definition is an account which shows why something exists . . . will clearly be like a demonstration of what something is, differing in arrangement from a demonstration (te¯i thesei diaphero¯n te¯s apodeixeo¯s). For there is a difference between saying why it thunders and what thunder is. In the one case you will say: Because the fire is extinguished in the clouds. But: What is thunder?—A noise of fire being extinguished in the clouds. Hence, the same account is given in different ways: in one way it is a continuous demonstration, in the other a definition . . . is a deduction of what something is, differing in grammatical form (pto¯sei diaphero¯n) from a demonstration. An. Po. B10, 93b38-39, 94a1–7, 12–13, following Barnes’ translation. Noteworthy here is the “transformation” or “transposition” of terms (the terminology is from Mendell (2007), 9), taking us from the separate occurrences of “noise”, “extinction-of-fire”, and “clouds” in the demonstration to the single term as definiens, “noise-in-the-clouds-due-to-the-extinction-of-fire”, in the definition of thunder. Interestingly, the technique of transformation is the mirror image of the technique prominent in Zeta 17 of “articulating out” the term “thunder” (say) as “noise in the clouds”, which echoes the procedure for producing a nominal definition of thunder from which in the Analytics come the major and minor terms, “noise” and “clouds”, that together with the appropriate middle term yield the completed demonstration. (What I call “articulating out” is, presumably, Aristotle’s eis arithmon thentes at An. Po. B1, 89b25–6, as John Malcolm reminds me; see Ross (1949), 610.) In the scheme 11.10 describes, Aristotle sees the cause of an event-type as a key component in its definition. From the explanatory schema that gives the cause of a given event-type, then, we must be able to read off the definition of the event. With this move, it may seem that the dominance of the Socratic What is it? question over definition is over at a stroke: the definitions we want will emerge in answer to the question, not What is it?, but Why is it? But (I will argue) Aristotle does not in Zeta 17 extend the technique for defining events or event-types to the definition of substances or substance-types; see this chapter, nn. 31 and 33, and Sections 4 and 7. 26 For a more Aristotelian example, see the two kinds of pride (as resentment of insult and as indifference to fortune) at An. Po. B13, 97b15–25; see Charles (2000), 209–10, 327.

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4 Some Questions of Fit For all the apparent closeness between Zeta 17 and the apparatus of the An. Po, the adaptation of the latter to the former may not come so easily. I begin with some points at which the contact between the two accounts seems close. In the Analytics, Aristotle sees an occurrence of thunder as a complex entity, with noise and the clouds as constituents, compresent thanks to the extinction of fire. The connection between noise and the extinction of fire is immediate, as also is that between the clouds and the extinction of fire. (The connection between the clouds and the noise is of course a mediated one, thanks to the extinction of fire as middle term.) Because the connection between terms is immediate in the two cases noted, there is no further middle term to be found, and the middle term given can plausibly count as the (one and only nonaccidental) cause of the occurrence in question. Comparably to the triad, noise—extinction of fire—clouds, from the Analytics, Aristotle in Zeta 17 offers the triad, matter—form—kind. The relevant texts are 11.8 and 11.9 (Section 2), in part repeated here: 11.8 . . . clearly the question is why the matter is [= constitutes]27 some thing (ti); for example, Why are these things a house?—Because there belongs what it is to be for a house . . . 11.9 So the cause is being sought (and this is the form)28 of the matter’s being [= constituting]29 some thing (ti); and this is the [its?] substance.

On the picture presented in 11.8 and 11.9, the matter of a given man, for example, is connected to the kind, man, thanks to the relevant essence or form, where this last appears in a role comparable to that given to the middle term in the demonstration attached to the occurrence of thunder. And a given individual man is a compound of matter and form, with no “connecting relation” (no logos henopoios, H6, 1045b17) between its constituent matter and form. There is, as it were, an “immediate” connection between them. (While Aristotle makes remarks in the second half of Zeta 17 about how the matter, or the various material parts of a thing, are unified by some different kind of item—a principle as opposed to an element, and presumably the form of the thing—he reserves the details of how the “unmediated” unity of form with matter is accomplished for Eta 6.)30 But the fit these correspondences suggest between the theory laid out in the Analytics and the discussion in Zeta 17 is not exact.31 Five questions are relevant here; I list the questions first, and follow with answers where appropriate: 27

See this chapter, n. 19. For the text translated here, see Chapter 12, Section 2, with that chapter, n. 18. 29 See this chapter, n. 19. 30 See Chapter 8, n. 58 and this chapter, n. 6. 31 On the limits to how deep the reach is of the An. Po into the theories of Metaphysics Z17, see also the cautionary remarks in Wedin (2000), 414, 423–4. A contrary account is given in Charles (1994), revisited in his (2000) and (2010), and the remarks that follow in the main text are directed at his (2010). The questions, Whether a thing exists, and What a thing is, even Why it exists? are designed in the An. Po. for complexes like the occurrence of eclipse in the moon, where eclipse is an attribute of the moon as subject (see, for example, 28

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(1) In Zeta 17, we are to associate the matter of a thing with its kind, thanks to the form. Can we construct out of the triad made up of these three, matter, form, and kind, a demonstration in the case of man (say), like that constructed in the Analytics for thunder or for eclipse, and the rest? (2) If a demonstration as in (1) can be found, will it be a suitable platform for framing a definition of man, in the way that an Analytics-style demonstration in the case of thunder leads directly to a definition of the event-type, thunder? (3) Uncontroversially, the task Aristotle sets himself in Zeta 3 is to define (primary) substance (singular), or the relational property of being the substance of certain kinds of thing. Even if in Zeta 17, Aristotle were to provide the demonstrations from which to construct definitions of substance-types (plural), how would that contribute to the real task of the chapter, of defining substance (singular)? Does Aristotle in Zeta 17 explicitly tell us how to get from the former kind of definition to the latter? If he does not, then the entire argument set in motion in Zeta 3 and apparently brought to an end in Zeta 17 may be one giant non sequitur. (4) Prima facie, the work required under (1) through (3) above is brought to a finish within Zeta 17 itself, where plausibly, Aristotle’s task is complete prior to the summary in the first half of H1.32 Looking beyond Zeta 17 and bringing in material from H2 and later chapters in order to construct the account Aristotle could or should have given us in Zeta 17, seems contrary to Aristotle’s own assessment of the state of his argument. (5) If Aristotle’s project does after all require that he bring in new material in order to complete his project, is the textual evidence in H2 any stronger than in Zeta 17? And if this later chapter does offer some textual basis on which to construct a demonstration, will the result pass muster as a genuine demonstration? That is, will the proposed demonstration be valid? On (1) and (2). I do not see how to construct the demonstrations that would be needed to lead to the definition of substance-types (plural), given the resources available to us in Zeta 17 by itself. In Zeta 17, we are told that a body of a given type is (constitutes) a man, thanks to the relevant form or essence. At best, the resources of this triad suggest a demonstration along the following lines: An. Po. B2, 90a15–23). But, as Ross asks, “how can [these questions] applied to a substance be supposed to be concerned with a middle term? . . . there are no two terms between which a middle term is to be found”; Ross (1949), 612. I argue below that Aristotle does not attempt in Metaphysics Z17 to extend the Analytics scheme of causal demonstrations for event-types to construct similar demonstrations in the account of substance-types. 32 For a contrary view, and a contrarian account of the opening sentence of H1, which on the usual interpretation marks the end of Aristotle’s project in Zeta, see Burnyeat (2001), 65–73, and Chapter 12, n. 2. But Burnyeat says nothing to encourage the thought that H2 contributes to the project of constructing demonstrations preparatory to the task of defining substance–types, which Charles supposes is under way in Z17.

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The kind, man (being a man) belongs to the essence as of man. The essence as of man belongs to a body of the relevant type as matter. So The kind, man (being a man) belongs to a body of the relevant type as matter. This hand-me-down argument is imperfect in two obvious but important ways. Above all, it is hard to see how the argument constitutes a respectable syllogism.33 If the argument is to be valid, we will need a consistent reading of the connective, “belongs to”, throughout the argument. The second premiss, to the effect that a given form is (metaphysically) predicated of a given matter, reflects standard doctrine in the Metaphysics. But the first premiss and the conclusion alike require different but equally tortured readings: the kind, man, is typified by [“belongs to”?] the form in question; an example of the kind, man, is constituted by matter of the relevant type. Without a consistent reading of “belongs to”, the argument is not a proper syllogism, and has no hope of being valid. It is also difficult to see how the proposed demonstration can support a definition. As Aristotle develops the thunder example in Zeta 17, the kind, thunder, stands outside the demonstration altogether.34 This is why we can read the definition of thunder off from the relevant demonstration: thunder is defined as noise in the clouds thanks to the extinction of fire. There is no counterpart to this in the case of man. We can hardly define the kind, man, as such-and-such matter worked up into a man thanks to the relevant essence or form. The reason is obvious: the alleged definiens contains the very term, ‘man,’ supposedly being defined.35 One further difficulty with the syllogism given deserves mention. The definition of thunder suggests that an episode of thunder is a complex entity, in which noise and the clouds go together to make up thunder in the presence of the extinction of fire. But the composition of an individual substance is a two-piece affair, from matter and form by themselves. In terms of the hand-me-down sketch above of how a demonstration for compound material substances might look, the compound material substance would have only the minor term and the middle term—the matter and the form—as constituents, while the major term—the kind—is not a constituent of the individual substance at all. (To the contrary, the kind has the relevant form and matter as its constituents, 8.6 above, with Chapter 8, Section 15.)

33

For scepticism about assembling the triad, matter—form—kind, into a syllogism, see, for example, Lewis (1991), 178–9, with nn. 12 and 13, and Section 4. On incorporating thunder into a syllogism (but not a demonstration), see perhaps An. Po. B8, 93b7–14, with Barnes (1994), ad loc.; see also this chapter, n. 34. 34 Aristotle’s examples in An. Po. B8 and 10 seem to go either way, at times suggesting the kind-term goes into the demonstration, and at times excluding it; see Barnes (1994), 219–20, 224, for discussion. But Aristotle’s statement of the thunder example in Z17 (11.5 above) suggests that the kind-term is excluded, so that the demonstration takes the form of Barnes’ (7)–(9), his 220. This is how I have represented Aristotle in setting out the relevant demonstration in the main text, Sections 2 and 3. 35 The difficulty noted here enters Aristotle’s text with the examples (a), (b), and (c) in Section 2; see this chapter, n. 14.

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It is reasonable to conclude that if there is a demonstration for substance–types to be found, it will not be found in Zeta 17. On (3). Suppose that successful demonstrations for substance-types can be found elsewhere. Is there a route from the definitions of substance-types (plural) that these demonstrations make possible to Aristotle’s target, namely, the definition of (primary) substance or the substance of a thing? Perhaps an answer will come if we scrutinize a series of demonstrations for different substance-types (plural), where in each demonstration the role of the form or essence as (primary) substance and the substance of a thing, thanks to its causal role as middle term, is plain to see. The resultant definition of the substance of a thing may seem no different from the definition in terms of a second-level functional property, as in Section 6. But we must first find a more persuasive version of the demonstration for different substance-types than the straw man assembled earlier in this section. This brings us to our final two questions. On (4) and (5). What evidence is there for thinking that—despite the objections in (4)—Aristotle is occupied in H2 in assembling the materials for a demonstration that will lead to the definition of different substance-types, parallel to the demonstrations assembled for thunder and for other event-types in the Analytics?36 Charles gives us a syllogism that does supposedly parallel that for thunder in the An. Po.: Charles’ [E.4]. (iv) Being two-footed [a certain mode of arrangement??] belongs to what it is to be a man [= soul of a given type]. (v)

What it is to be a man [= soul of a given type] belongs to a body of this type.

Hence, (vi) Being two-footed [the mode of arrangement already noted?] belongs to a body of this type. (The material in square brackets indicates the “more articulated” version of [E.4] that Aristotle omits to give.) Can we read off from [E.4] a definition of the kind, man, in the way that in the Analytics we can read off from the relevant demonstration the definition of the eventtype, thunder? The resultant definition would seem to be this: man is a body of a given type to which is present the arrangement, being two-footed, thanks to soul of the relevant type. The mode of arrangement is the remnant of form, after the final cause supposedly incorporated in the middle term, the essence as of man, or what it is to be for a man (= a certain variety of soul), has been peeled away. That is, [E.4] presupposes a division in the form of a man, or a house (say), into the final cause (the psychic 36 By H2, 1041b8, according to Charles, Aristotle “has the basis for a demonstration which parallels the one he gave for thunder”, but the result (his [E.3]) at this point is provisional and “not his [Aristotle’s] finished product”, and I will not discuss it further.

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capacities of a man, the function of a house in protecting men and goods) on the one side, and various structural features (the physiology of a man, the arrangement of boards and timbers in a house) on the other. The textual evidence for this division of labour, which we are to find in H2, is slight. Aristotle begins H2 by remarking that his (Aristotelian) form is his counterpart of Democritus’ differentiae. (Aristotelian) form, as a thing’s essence, will include the final cause (“include” is the most that is supported at 1043a16 ff.), in the same way that it may include the efficient cause in the explanation of event-types (H4, 1044b8–15). Harmlessly, then, with Charles, “a house will be bricks and stones arranged in a given way for the sake of protection”, following 1043a9, and in line with 1043a8–9, “or again the for-the-sake-of-which too applies to some cases” (cited by Charles, 312). But it is a far cry from this to thinking that Aristotle is here assembling the materials for a demonstration, assigning to a core notion of form-as-final-cause the role of middle term in a demonstration, with the thing’s structure relegated to the major term. As we have seen, in the sample demonstration [E.4], form is conceived in terms of its teleological core, stripped of any structural components, being two footed, and the rest. The division between structure and function is familiar, but it is typically put to a quite different end. Thus, on a “thin”, perhaps Democritean view of form,37 form is structure alone, while on an appropriately “thick” view, form will include both structure and goal. It is surprising to find this “thick” view dropped in favour of an (admittedly different) “thin” view of form as goal, divorced from structure. On this showing we succeed in constructing a demonstration that presents form as middle term, at the price of undercutting a properly robust conception of form in its most important role as (primary) substance and the substance of a thing. Finally, what is perhaps the most serious difficulty. [E.4] may seem well contrived as a source for a definition of man, but it is not a demonstration that Aristotle could find acceptable. We might wonder how it is in (iv) that being two-footed belongs to the form or essence, what-it-is-to-be-(a)-man: surely we are not to suppose that just as Archimedes is two-footed, so too is his form (for a comparable objection, see Wedin (2000), 423). Charles heads off this reading with a different account of what “belongs to” must come to. He tells us (his n. 31) that “there are per se connections at each stage in this demonstration”: in (iv) “belongs to” amounts to, “is defined in terms of ”, while in (v) it amounts to “defines”. This reading of [v] is surprising, given Aristotle’s settled view that form is (metaphysically) predicated of matter. Worse, if, as Charles suggests, these are different per se connections, the proposed syllogism is patently invalid. There remains the use of “belongs to” in (vi). Presumably, we read (vi) to say that bodies of the given type are two-footed, in just the way that that individual men are two-footed. But exactly this is the reading of “belongs to” that we must avoid to make sense of (iv).

37

“Democritean”: see PA A1, 640b30–641a14.

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Still more reason for thinking we cannot find a univocal reading of “belongs to”, and still less hope for validity.

5 On Why Aristotle Does Not Mean for the Fit to be Exact The lack of fit between the Analytics and Metaphysics Zeta 17 in the various regards just noted is not because of oversight or mistake on Aristotle’s part, but because the topic has changed. In the relevant chapters of the Analytics, Aristotle is interested in the use of demonstration to yield, first, the definition of a given event or event-type—thunder, eclipse, and the like. At the same time, the finished demonstration will include, second, a causal component, which also forms part of the target definition. Once the single appropriate cause is found, we are able to move beyond the nominal definition (that thunder is noise in the clouds) to give the proper definition, that thunder is noise in the clouds thanks to the extinction of fire there. On my reading of Zeta 17, the second of these interests, in the cause, remains, while the first, in defining the phenomenon in question, drops away. As I understand the argument of Zeta 17, Aristotle is interested more in the explanatory story offered by the scheme of the Analytics, and his interest in defining individual substances or substancetypes is tangential or (as I prefer) in this chapter of Zeta non-existent. Much this point is made in Wedin (2000): I do not see that Z17 aspires to extend, unproblematically, the framework of the Posterior Analytics to form–matter compounds. Like the conclusion of demonstrative syllogisms, we explain why “these” bricks and stones are a house by appealing to a third factor, in this case the form of house. This is enough justification for summoning the apparatus of the Posterior Analytics, but it is not enough to make the explanation of hylomorphic compounds a simple case of demonstrative syllogism. (Wedin (2000), 415)

In the relevant chapters B8–10 of the Analytics, Aristotle is interested in the use of demonstration as a route to a definition of different events or event-types, thunder and the rest, and in identifying the causal middle term that will give the essence of the kind in question. Aristotle’s main aim in Zeta 17 too is to develop a definition—but this is a different definition, the definition of substance (singular), not substances (plural). And the causal structure Aristotle takes over from the technique of demonstration is an essential component in his definitional project—not in constructing the actual definition of substance, but in spelling out how the reference to causes in that definition applies in different cases. The definition of substance—that is, of primary substance, or the substance of a thing—and questions of just how the causal contributions of form add to that definition, give us our next topic.

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6 Causes and the Definition of Substance Aristotle begins Zeta 17, as we have seen, with a reminder of his project of defining (primary) substance,38 and with the offer of a “new start” that ushers in his own, perhaps authoritative account of how the definition will go: substance is a cause of some sort (arche¯ kai aitia tis, 11.1 above). Or, as he works around to saying, the substance of a thing is the cause of that thing, or the cause of being for the thing (11.2 above). It is Aristotle’s business in the remainder of the discussion to explain what these characterizations amount to. After the bare statement of the definition, Aristotle’s next move is to say which items they are in the official Aristotelian ontology that satisfy the definition.39 With the help of the causal scheme that he adapts from the An. Po., he identifies the cause of being for a thing and, hence, what counts as its substance, as the (Aristotelian) form of the thing, which belongs to its matter (11.9 above). So being the substance of a thing and also, presumably, being a (primary) substance, both turn out to be properties of forms. This answer to the Application Problem, which Aristotle anticipates frequently in earlier partisan parts of Zeta, helps confirm the new definition of substance with which Zeta 17 began. But, I will argue, being a substance is no ordinary property of a form. To explain what is distinctive about the property, we should begin with the nature of (Aristotelian) forms and their place in the constitution of compound material substances. Aristotle thinks of each of his forms in terms of a complex of active powers thanks to which, in combination with the corresponding passive powers in the appropriate matter, the matter is worked up so that it constitutes a thing of the kind typified by the form.40 Meanwhile, a given stuff or structure is the appropriate matter, if it is matter for a thing of that same kind. Active and passive powers alike are the powers for a thing of the kind

38

I say that Aristotle’s project is to define primary substance, or the substance of a thing. It is not his intention to define the notion of substance that applies to compound material substances; see this chapter, n. 48 and the opening paragraphs of the Introduction. Compound material substances qualify as substances, thanks to the form that is their substance and the cause of their being. It may be that—to extend the remarks at H3, 1043a29–37—the notion of substance as it applies to the compound material substance stands in a relation of core-dependent homonymy on substance as form, which is primary substance and the target of Aristotle’s definition. 39 The passage from stating the definition to identifying the items in his own ontology that answer to the definition is familiar from Physics B1; see Chapter 1, Section 2. 40 The (first-level) causal properties of the stuff or structure that serves as matter in a given case are passive powers for being made into a thing of a given kind (“matter qua matter is capable of being acted on”, GC A7, 324b18). Corresponding to a given passive power in a given matter is the active power associated with the relevant form and lodged in the agent, thanks to which, under the appropriate conditions of realization, the agent produces a product of the kind typified by the form. As to the conditions under which the two powers are actualized, what has the active power and what has the passive power must be “together” or otherwise in suitable proximity, Phys. ¨4, 255a34–b1, GC A7, 324b13–18, De Long. Vitae 3, 465b15–16; and the two powers must be suited to each other and to the product in various ways, De Caelo ˜3, 311a4–6, De anima ˆ5, 430a10–13, De Motu 8, 702a10–15, 20–1, GA B4, 740b22–6, Metaph. ¨5, 1048a5–7.

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typified by the form, so the conception of the form establishes from the very start the teleological framework within which the matter and the kind too belong. The complex of active powers associated with the form of a natural object constitutes (at least part of) the content of that form: the form includes in its content a variety of capacities for acting on the stuffs or structures that serve as its matter, in all the various ways that are determined by the nature of the capacities in question.41 What now of Aristotle’s claim that the form is (primary) substance, and the substance of the finished thing? The property of a given form, that it is a substance, or the (relational) property that it is the substance of this or that thing—these are not members of the class of active powers associated with the form. The property of being a substance is not part of the content of the form. The correct view, rather, in modern dress, appears to be this: The property of being a substance is a second-level functional property of a form in virtue of the role of the form as the cause of being for individuals of a given kind; the content of the form includes the various first-order “realizer” properties that are the active causal powers for producing and maintaining42 individuals of the kind in question. The Second-Level Functional Property View

According to the Functional Property View, we may think of forms as having the property of being a substance in virtue of a certain role property of forms—their role as the cause of being for individual substances43—while the appropriate active causal powers in the content of a given form are the corresponding realizer properties. (For the distinction between role and realizer properties, compare the role property of being Prime Minister in the government of the UK, for example, with the realizer properties of leading discussion in meetings of the cabinet, answering questions in Parliament, and the like.)44

41 In saying that a given form is associated with the cluster of active powers that collectively make up its content, I come uncomfortably close to questions of how we are to think of the causal efficacy of form. It is worth saying that we do not commit Aristotle to the view that the form itself has the capacity to act in this or that way when brought to bear in the appropriate circumstances on the appropriate matter. Rather, the form is or, perhaps, has as its content the set of capacities in light of which the efficient cause—the craftsman’s arm, the male parent, the various intermediate “instruments” of form—acts on the matter in the appropriate way so as to bring the product into existence. The efficient cause implements the form in different but equally complex ways in the case of human action and craftsmanship and in the natural world, but the details (where they are available) are not properly our concern here. 42 I count among the realizer properties for a given form the active powers responsible for producing as well as for maintaining an individual of the relevant kind. Strictly, form as the cause of being for a thing will seem to limit the causal powers to those responsible for maintaining a thing as a functioning member of its kind, leaving questions of becoming to one side; but the same form serves as the goal in the production of the thing, so that we may broaden the class of realizer properties to include the causal powers associated with the goal in production and with the various “instruments” required to attain it. Support comes from the reading I give to 11.6, Section 2, where Aristotle allows that the final cause—more broadly, the formal/final cause?— is in force in cases of both being and becoming. 43 “the cause of being for individual substances” as before, this chapter, n. 38, the use of “substance” here is not the notion of (primary) substance that is Aristotle’s target here and throughout Zeta; see also this chapter, n. 48. 44 For second-level functional properties in general, see Heil (2004a) and (2004b), and Prior, Pargetter, and Jackson (1982); and for the view of the property of being matter as a second-level property of a given stuff

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The functional property of form—that of being a (primary) substance—is defined in terms of the role of form as the cause of being for individual substances. There is a major virtue to this kind of account. Because it is defined in terms of a certain causal role, the notion of substance stays constant, as it should do, across the whole range of forms, even while it leaves the needed room for the different sets of causal powers required to match the variety of things that have this or that form as their substance. At the same time, only a form will have the causal role Aristotle’s definition demands, and only a form will be the substance of a given thing. The role property in the definition calls for a range of different forms, but it will not be satisfied by anything but a form. The direction of metaphysical priority is also of interest. Different causal properties realize the role of the form as the cause of being for things of different kinds, and it might seem that without the realizer properties the role property would be idle. Does a given form have the role property because it has certain causal realizer properties? Or does it have the realizer properties it does because it has the role property? Aristotle would surely give the second answer. The causal powers associated with a given form are the powers for a thing of the very kind typified by that form. They realize the role of the form as the cause of being for individual things because they are the causal powers for things of the kind prescribed by the form. Accordingly, determination is from the top down, from a given form with the role property, to the realizers in the content of that form and in the appropriate matter. A given form is primary substance in virtue of its role property as the cause of being for a thing of a given kind, a man (say) or a horse; and this is the basis on which it has the causal realizer properties that, when matched with the appropriate matter, conduce to the production and maintenance of the expected result. The distinction between first- and second-level properties, or between realizer and role properties, should put sufficient distance between the causal properties of a given form that go into its definable content, and the status of the form as primary substance and as the substance of individual things. Accordingly, Aristotle’s project of explaining what it is for a given form to be a substance in no way requires defining that form. The relevant realizer properties in the content of a given form, and spelled out in its definition, are in the service of the role the form plays as the cause of a thing’s being or structure, Lewis (2008). I emphasize that a functional property counts as a second-level property of a thing (a property that the thing possesses in virtue of itself possessing some lower-level “realizer” property), but not a second-order property (a property of some lower-level property of the thing). The distinction between role and realizer properties is a standard feature of contemporary discussions in the philosophy of mind: the functionalist, for example, will identify pain with a role property, that is or may be realized differently in different kinds of creatures, so that perhaps even martians can feel pain. For discussion, see, for example, chapter 8, “Functionalism”, in Heil (2004a). On a minority view, due to D. Lewis (1966) and (1994), functional properties are identical with the realizer properties, and so are first-level. The result would be a different notion of pain for each different type of physical realization in different kinds of animals; on the view of the property of being matter as a functional property, a different notion of matter for each different type of opposites involved in generation and destruction; and finally, a different notion of substance for each different kind of form and the different active powers associated with it. So I will persist in saying that Aristotle is better served by the second-level idea.

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and, hence, as its substance. But the role property itself is not among the realizer properties, and is not part of the definable content of the form. We may revisit one last time the definition Aristotle gives of the property of being a substance that has been his target throughout Zeta, together with the theory that follows in the train of that definition. In Aristotle’s finished theory, the definition of the property runs in terms of its causal role: (1)

x is a (primary) substance = df. for some y, x is the cause of being for y.45 Definition.46

The notion being defined in the Definition is the (non-relational) property of being a (primary) substance; but the causal idea introduced in the definiens provides a bridge to the relational idea of being the substance of a certain class of entities: namely, those for which the substance in question is put forward as a cause.47 Zeta 17 is our source for how the causal idea in the definiens of the Definition will apply to the analysis of individual substances in the official Aristotelian theory. Thus, on the subject of causes, where y is a given particular substance,48 we are told (11.9 above) that (2) x is the cause of being for y if and only if for some form, ł, ł is the cause thanks to which the matter, m, of y constitutes a thing of the appropriate lowest kind, and x = ł. 45 This will not be a definition of what it is to be a potential substance (a property of the matter), nor, as before (this chapter, n. 38), a definition of being a compound material substance. Note that (1) defines the substance of a thing in terms of its role in the economy of individual substances in general. How that role is cashed out in a given case is determined by the different sets of realizer properties—the different sets of active powers—associated with different forms. 46 Although Aristotle does not say so, it may be that the Definition is incomplete, in that the term “cause” in the definiens is left undefined. We know from 11.6 above that a thing’s cause is its essence, where the notion of cause (and so also of essence) is sufficiently fluid to allow for an efficient cause as well as a formal or final cause. In the case of a natural object (rather than, say, an event), the relevant kind of cause will be a formal/final cause. Accordingly, perhaps, a full-blown definition of (primary) substance, understood to be the substance of a natural object, will specify the cause as the formal/final cause of the object. I am simply not clear whether the Definition should also include reference to the formal/final cause as the essence of the thing. 47 As Aristotle intends his Definition in Z17, the variable y ranges over individual substances, so that Definition targets the role of forms as causes for these. I leave it open whether he would allow that y also range over forms; if so, I suspect he would in this case hold to a principle of self-sufficiency and stipulate that y = x, so that a form is the cause of being for itself. In Z17, strictly speaking, given the restriction to individual substances, forms qualify as primary substances because they are the substance* of a given set of individual substances: primacy for primary substances consists in their dominance over this second set of entities. Meanwhile, a form will also be the substance (unstarred) of itself. (Similarly, a form will be the essence* of the relevant individual substances, but the essence (unstarred) of itself; see Chapter 6.) As frequently in earlier chapters, I omit the apparatus of asterisks where their absence does not invite misunderstanding; the starred– unstarred distinction is explicit as needed; see, for example, Chapter 3, n. 11, Chapter 8, n. 25, and Chapter 10, n. 26, and the Appendix to Chapter 10. 48 These will be the individual substances from the commonsense, “non-partisan” framework, now revealed in Aristotle’s official theory to be compounds of form and matter, thanks to the causal role of form in (1), as spelled out in (2). The property of being a primary substance, or the substance of a thing (in fact, of a natural object), that is the object of definition in Z17 is a fundamental part of the same official theory.

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According to (2), being the cause of being for an individual substance, or compound material substance, is a property of (Aristotelian) forms. By (1) together with (2), then, being a (primary) substance too is a property of forms. As in the Second-Level Functional Property view highlighted above, being a (primary) substance is, in effect, the second-level property of a given form, that the form itself have a certain causal role as set out in (2). As 11.6 above suggests, this will be the causal role relevant to questions of being and becoming—to the coming to be and subsequent constitution of individual substances. In Aristotle’s finished account, accordingly, the place of the forms of natural objects as primary substances is secure. So, for example: (3) The matter of a given compound material substance, Archimedes (say), constitutes a man thanks to the form, ł, only if, and only because, ł is a (primary) substance and ł is the substance of Archimedes. That is, the property of being a substance (along with the property of being the substance of Archimedes and his fellow men) belongs to the form, ł. At the same time, in the case of forms of natural objects49 we can add that, (4) The form, ł, is a (primary) substance, only because there exists some compound material substance, y, such that ł is the cause of being for y. That is to say, as the definition in (1) also tells us, ł possesses the second-level property of being a substance—the substance of a given thing—in virtue of the causal role that has ł at its centre, and is realized in the case of Archimedes or some other. Finally, the causal role accorded to the form in the present account is spelled out in terms of the required “realizer” (first-order) properties or powers: (5) The first-level “realizer” properties accorded to the form, ł, in the present account are just those active powers set out in the content of ł that, in combination with the appropriate passive powers in the appropriate matter (and in the presence of the appropriate efficient cause), conduce to the production of a thing of the relevant kind. In short, the form, ł, fulfills the causal role accorded to it, thanks to the content of ł. Meanwhile—though not strictly our business here—the matter and the efficient cause play subsidiary roles in the causal account, in a way that is also governed by the content of the form. In all this, the order of determination is again worth remarking. A form is (primary) substance, and the substance of this or that individual substance, in virtue of its role as the 49

I add the restriction to forms of natural objects to meet the point (due to Michael Wedin) that (4) will fail for the Unmoved Mover, should it too turn out to be a form. (4) ties the existence of the form of a natural object to the existence of a given natural object with that form. I do not address the question of how the form of an artifact can exist, so far unrealized, in the craftsman’s mind.

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cause of being for individual substances. As is proper, the account to this point leaves unspecified the different causal powers that are the “realizer” properties appropriate in a given case. The various active powers that realize the causal role of a given form, even if not known (or not fully known) by us, owe their presence in a given case to the fact that the form is the form for a thing of a given kind, and to the role of the form as the cause of being for a thing of that kind. As before, then, determination is from the top down—from the role properties of a given form, to the realizer properties that must be part of its content. Study of the content of the form required for natural substances of a given kind, meanwhile, lies outside metaphysics or first philosophy altogether, and for the most part is not on Aristotle’s mind in Zeta.50 As to the general shape of this larger story, omitted here: as we have seen, in the case of Archimedes (say), his form has as its content a certain complex of active powers, with their appropriate counterparts in the passive powers lodged in the matter; and it falls to the biology to discover which powers, active and passive alike, are required for his coming to be and eventual constitution as a man. So in the real order of things, the project of understanding the forms of natural objects begins with Aristotle’s natural philosophy. Finally, a word in praise of what Aristotle can plausibly take himself to have accomplished with the closing chapter of Zeta. Richard Rorty once asked: If the conclusion to Zeta is that the form of a thing—its constitutive form—is the thing’s substance, how much has this conclusion really taught us? (Rorty (1973), 393–4). The view of the property of being a substance as a second-level functional property of forms, and the promise of the different first-level causal properties that are the “realizer” properties associated with the second-level property, as explained above, may go some way to countering the scepticism that Rorty’s question implies.

7 Conclusion I have argued in Section 2 that Aristotle borrows from the practice of inserting a causal middle term into the appropriate demonstrative syllogism in the explanation of events in the Analytics, in order to inject the required causal notions into the discussion of substance in Zeta 17. In Section 6 I set out what I take to be the relevance of causal notions to the definition of substance: it is because Aristotelian forms do the causal work they do in the coming-to-be and maintenance of individual substances (plural), that forms satisfy the definition of substance (singular) that is Aristotle’s main target in Zeta 17. Being the substance of a thing is in effect a role property, accompanied by the required realizer properties in the content of the form: that cluster of causal properties

50 Issues in natural philosophy (so-called “second philosophy”) make an appearance in Zeta 7–9, but these chapters are usually thought to be an intrusion into the main argument of Zeta; see the Introduction, Section 3.

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that in the natural philosophy are manifested in the creation of fresh individuals of the species, in the creature’s nourishing itself, in its perceiving, its locomoting, and the rest. Now, the larger topic in the relevant parts of the Analytics is definition: how locating the cause of an event completes the demonstration from which we hope to obtain a definition of the event or event-type in question. But I am doubtful whether Aristotle’s preoccupation with defining events (plural) in the Analytics is matched by a similar interest in defining individual substances (plural) in Zeta 17. In this chapter, at any rate, only the definition of (primary) substance (singular) or, better, the substance of a thing is on Aristotle’s agenda.

12 Aristotle on the Positive Contributions of Zeta 1 The Retrospective in Eta 1 The opening lines of Zeta 17, and the new start announced there (11.1 above), are the last we hear of the project of defining substance. I will suppose that Aristotle actually accomplishes his goal in Zeta 17, and that the causal account of the substance of a thing outlined in Chapter 11 constitutes a successful definition in his eyes. In light of this assessment, what are we to make of the opening of the first chapter of book Eta, which follows next? At the beginning of Eta 1, Aristotle acknowledges a need to 12.1 . . . reckon things up and, after summarizing the upshot, to add the finishing touches (sullogisasthai dei kai sunagagontas to kephalaion telos epitheinai). (1042a3–4)

What follows is a review—part summary, part critical assessment—of the different segments of Zeta (as before, Zeta 7–9 and 12 are exempted), directed exclusively at Aristotle’s discussion of “received” views, and with no mention of the brief appearances of form and matter in the different segments. Thereafter, abruptly at 1042a24, Aristotle turns to the topic of the “agreed-upon substances”, namely, perceptible substances, now openly acknowledged as compounds of form and matter: in particular, in Eta 1, their matter, then in Eta 2 “the substance as actuality”—that is, the form (Eta 3, 1043a30–1)—of sensible substances. With this, Aristotle shifts decisively to “partisan” mode. He is now well and truly launched on the analysis of (perceptible) substances as compounds of form and matter; and in contrast with the studied reticence of Zeta, not just form and matter but also some of the questions and difficulties that come up in connection with them, are unashamedly on the front burner all through Eta. These further developments aside, how does the first part of Eta 1 fit with proceedings earlier in Zeta—with the original agenda Aristotle sets himself in Zeta 3, and with the new causal account of substance offered in Zeta 17? An immediate question concerns the “finishing touches” (if this is how telos should be translated) promised in the opening lines of Eta. Does the telos come in Eta 1 itself ?

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Or must we wait until the end of Eta (perhaps the account of unity in Eta 6)?1 And exactly what telos needs to be added to the discussion so far?2 If the telos yet to be added is the definition itself of (primary) substance, then Aristotle cannot already have given us the definition in Zeta 17, and (worse) nothing in the remainder of Eta looks remotely like the definition we would still need. On the contrary, the telos does not consist in some yet-to-come conclusion later in Eta but, rather, in taking stock now that the discussion of traditional takes on the definition has been completed. Suprisingly, as we have already noted, he is not concerned in Eta 1 with how the successful definition of (primary) substance in Zeta 17 meshes with the discussion in the three main segments of Zeta. Notions of subject, essence, and universal, have all figured in the discussion largely in terms of “received” views, during which no successful definition is found: how much of those notions survive, now that the definition is done? Aristotle’s immediate topic in Eta 1, then, is confined to the final scoresheet for the received views about substance that shaped the three main segments of Zeta. He begins with a summary, repeating first the (more or less undigested) list of substances—both the “agreed-upon” ones and some more idiosyncratic choices—from the wind-up to definition in Zeta 2.3 In a different vein,4 next, taking up again the discussion of received views5 dominant in Zeta, we have again the unedited list of options taken to be constitutive of substance from the beginning of Zeta 3: the essence and the subject and, different from these again, the genus rather than its species, and the universal in preference to individuals. These last two options, both genus and the universal, are in

1

As always, it is worth remembering that the division into separate books, Zeta and Eta, is not Aristotle’s, but the work of a later editor. (On the contrary, Aristotle himself thinks of Zeta and Eta together as forming a unit, ¨1, 1045b27–29; see Ross (1924) II, ad loc.) The same point holds of the division into chapters. As will be obvious, the topics of the present book come to an end once we reach the middle of what we today read as Eta 1. 2 Burnyeat (2001), 65ff., argues that the promised telos must be not the summary Aristotle is about to offer, but rather “the completion of Z [that] is the rest of H”. Burnyeat is right to emphasize the positive contributions the balance of Eta makes to the official Aristotelian theory of form and matter. But with two reservations, the summary in the first part of Eta 1 is an appropriate telos to what has gone before in Zeta. The first reservation is that Aristotle says nothing about the smaller portion of the different segments of Zeta in which he refers to form and matter. Equally surprising, second, he says virtually nothing in Eta 1 (apart from a passing reference to “the causes and principles and elements of substances” at 1042a5–6) to remind us of the new start and the new definition of (primary) substance in Z17. So his summary is of no help in supporting the definition of substance in Z17, which he locates within the official or partisan theory of matter and form, or in showing how it fits with, even adjudicates among, the different “received” opinions about substance in Zeta 3 that set the agenda for the bulk of Zeta. I add some speculative remarks about what Aristotle might have said on these various scores later in this section. 3 He lists earth, air, fire, water, and the other simple bodies (see Ross (1924) II, 227, ad loc.); plants, animals, and their parts; finally, the universe and its parts (1042a7–11); he does not mention his corrections to this list in Z16. As against these, next come the partisan ontologies of others, in which (Platonic) forms and the mathematicals are said to be substances (idiai . . . legousin, a11–12). 4 allo¯s, H1, 1042a12, with Christ and Jaeger. 5 ek to¯n logo¯n, H1, 1042a12–13; see Burnyeat (2001), 62–3.

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the same neighbourhood as Plato’s forms (kai hai ideai sunaptousin, a15–16) since, as he says (a16), the same argument lies behind making any of them substance.6 There follows (a17ff.) Aristotle’s assessment of how the different options fare in the body of Zeta. He begins with a positive conclusion, and some consequences. Because the essence (of a thing) is (its) substance (a17), and because the account of essence is a definition, we made some decisions about definition and about what a thing is per se; and because a definition is an account with parts, we were obliged to see what were the parts of the substance, and whether these were the same as the parts of the definition. Next (a21), on the negative side, neither the genus nor the universal is substance; but discussion of the forms and the mathematicals, “which some [the Platonists] say are over and above (para) the sensible substances”, is reserved for later (presumably, Books Mu and Nu). The association of both genus and universal with Plato noted in the previous paragraph makes it decisive that like Aristotle’s kinds, Plato’s forms are not substances; as always, Aristotle is silent about whether his own Aristotelian forms can be universals and also in some manner substances (I argue above that he leaves room for a theory on which they can be both).7 Aristotle’s review ends at 1042a24 with the entry of the “agreed-upon” substances, namely, sensible substances, and with a discussion of substances as subjects.8 Mention of Aristotle’s “official” theory now enters the mix: matter, form, and the individual all alike are substances of a kind, and all count as subjects in their different ways. Aristotle goes on to justify thinking of matter as substance—that is, as potential substance (1042a27–8, Eta 2, 1042b10)—thus paving the way for the other side of the story, namely, substance as the actuality of perceptible substances—that is, substance as form—in the body of Eta 2. Such, in bare outline, is Aristotle’s review of his work in Zeta. As he tells it, the three received views about how to define substance or of the substance of a thing from the agenda passage in Zeta 3, do not all fare equally well. The view that the essence of a thing is its substance is sustained.9 Essences are the only items on the original list of Zeta 3 to survive Aristotle’s critique without major damage; accordingly, those items in Aristotle’s partisan ontology that count as the substance of a given thing and, thereby, count also as primary substance will also be the essence of the thing.10 The discussion in Zeta 17 makes it plain that this is the space occupied by (Aristotelian) forms. Meanwhile, universals and genera—think Platonic forms, and Aristotelian kinds— are officially out as substances. They are out too, presumably, as the substances of No universal—no “one-over-many”—is a substance; above all, no universal can be a Platonic form (as Plato conceives of his forms, each is a substance and therefore separate, 1040b27–30 from 10.6 above). 7 Chapter 8, Sections 2, 15, and 19; the Appendices to Chapters 8 and 10; and Wedin (2000), 426–7. I say more about a role for universals in the account of substance later in this section. 8 For the link between particular substances and the subject criterion, see Z13, 1038b4–6, cf. ˜8, 1017b10–14. 9 This is not to say, however, that the substance of a thing is defined as its essence; see Chapter 3, n. 1, and the introduction in Chapter 7. 10 As before (Chapter 11, n. 47), where Archimedes is a compound of a given form with a given matter, m + ł, ł is his essence* and Archimedes 6¼ ł; but the essence (unstarred) of ł = ł itself. 6

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whatever they may be universal to. (As to whether other, more promising options are open for Aristotelian forms, which I take to be universals, Aristotle remains silent; this chapter, n. 7.) Aristotle’s summary also leaves the status of the subject criterion in some doubt. He brings into the discussion form and matter, which have pride of place in his own “partisan” ontology; and he appears to say that matter, form, and compound material substance alike count as subjects. But he does not say how forms qualify as subjects. Instead, he emphasizes the status of matter as substance (more exactly, as potential substance), and reviews the different notions of matter involved as a subject in different kinds of change. He says nothing, however, to encourage the idea that matter is the substance of anything. The biconditional connection between the essence of a thing and the substance of that thing seems solid. But if a comparable connection exists between the notion of (primary) substance and the other entries—subjects and universals—on his list, Aristotle does not give us the help we need to find the formulations that survive his discussion in the body of Zeta. Other questions about Aristotle’s opening menu of options are also outstanding. To begin with, is his list is exhaustive? The answer now is clear, that it is not. Throughout Zeta, he introduces further constraints on substance, beginning with thisness and separability towards the end of Zeta 3 itself, which while not perhaps definitory of substance, can trump the would-be definition of substance as subject offered in Zeta 3. More important, the conception of substance as a cause, which is expressly offered as a definition in Zeta 17, is entirely new as compared with Aristotle’s initial list. Once a more promising approach to the definition of substance has made its appearance in Zeta 17, and after the exhaustive critique in the body of Zeta directed at the initial menu of options from Zeta 3, should we conclude that those initial options have now been entirely superceded? Events in the body of Zeta itself, as well as in Aristotle’s summary in Eta 1, suggest strongly that Aristotle wants to salvage as much as he can from the received options recorded in the agenda passage of Zeta 3. Precisely how those various options can be preserved is less clear. A primary question involves the coherence or otherwise among the four options on the agenda in Zeta 3. Two, apparently—the genus and the universal—can be rolled into one (Chapter 1, n. 54). But for the resulting three options, it is from the start an open question whether each excludes the other two, or whether two or even all three can be true together. Is it Aristotle’s opening position in Zeta 3 that all the received views can be true together? Once the work of Zeta is done, and if we suppose that only one of the received views is the clear winner—are there in prospect accommodations to the runners-up, that will allow them (suitably revised) a contributing role in the characterization of (a thing’s) substance? Finally—going beyond anything Aristotle tells us in his summary in Eta 1—how does the final disposition of the received views from Zeta 3 bear on what we supposed is the bona fide causal definition of substance in Zeta 17? Convergence. The questions raised in the previous paragraph are primarily questions about the conceptual unity of the varying notions of substance that pass before us in

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Zeta, and there is evidence to support rather different kinds of answer. On one approach, the different notions converge. We are to identify a single item from Aristotle’s official, “partisan” ontology, and show that it satisfies all three characterizations from the Zeta 3 agenda. The obvious single candidate is (Aristotelian) form. According to Aristotle, arguably, form counts as a substance, better, as the substance of a thing, on each of the three characterizations of substance—suitably adapted where needed as a “response to justified criticism”—under discussion in the different segments of Zeta. In the “partisan” part of Zeta 3, form is classed as a subject along with the matter, and the form–matter compound. Again, the essence of a thing is its form; and in contrast to Platonic forms and Aristotelian kinds, there may be reason to think that form is both a substance and a universal. There is some support for this reading in Aristotle’s text.11 The Distributive Option. A rival account of how to accommodate the Zeta 3 agenda of received views within Aristotle’s own “partisan” ontology of form and matter takes the distributive option. On this view, we follow the lead of Zeta 17, where arguably, Aristotle distributes the three criteria for substance that originate in Zeta 3 among (perhaps) all three of the different sorts of entity featured in the causal scheme of the chapter. Distributing the different characterizations of substance in this way among these different entities can be justified by the position each occupies in the causal scheme of Zeta 17. The explanatory power of the scheme Aristotle models after the demonstrations involved in the explanation of events in the Analytics, promises to bring coherence among the different views of substance under review in Zeta. Aristotle is explicit in Zeta 17 that the cause of being for each thing is the essence of the thing, which is also its form.12 Again, the matter of a thing is the first (although not the primary) element in the causal triad of Zeta 17; there as elsewhere, the matter acts as subject to the essence or form. When Aristotle explains in Eta 1 how subjects are substances, he emphasizes that matter too is a substance thanks to its role as subject of change (1042a32–b3).13 So the causal connection is alive and well in the case of the matter too.14 11

Form as subject: Z3, 1029a1–3, Z8, 1033a31–2 (following Ross ad loc. and Alexander), H1, 1042a26–9, and arguably ˜18, 1022a29–32 (but with De Anima A4, 408b11–18, 25–9, to the contrary); form as universal: Z10, 1035b33–1036a2, Z11, 1036a28–9. For the form of a thing as its essence, see 11.6 and 11.9 above from Z17, along with Physics B1, 193b1–3, 2, 194a20–1, 3, 194b26–9, Metaphysics A3, 983a27–8, ˜2, 1013b22–3, Z7, 1032b1–2, Z10, 1035b14–16, 32, Z11, 1036a28–9, H3, 1043b1–2, H4, 1044a36; see Chapter 4, n. 2. 12 See this chapter, n. 11. 13 The discussion of matter at a32–b3 is non-standard, for it counts the subject of accidental change (the compound material substance itself) as a case of matter. The causal conception of subjects by which matter qualifies as a subject is a significant departure from the Categories-based view of subjects, and is not obviously a factor in Aristotle’s initial discussion of matter’s candidacy for substance in Metaphysics Z3. The causal role for matter aligns more with the conception in Physics B1 (Chapter 2), and is perhaps presaged at Metaphysics Z13 in 8.5 above (“the universal too (sc. in addition to the essence and the subject?) is thought in some quarters to be most of all a cause”). Similarly, Plato’s view of universals as a cause in Z13 helps introduce the universal as a candidate for the substance of a thing, but (pace Bolton (1995) 1996) the causal view plays no role in the arguments of the chapter. Discussion of substance as a cause is reserved for Z17, where Aristotle turns to the Analytics for help in constructing his own partisan definition of (primary) substance. 14 But the causal role is not the same in the three cases. The essence of a substance—that is, its form—is the cause par excellence of the thing, and the form is the substance of the thing and thereby primary substance. But

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Finally, thanks to the form, the matter constitutes a thing of the appropriate (Aristotelian) kind: does this scheme leave room for universals of one style or another? Two possibilities come to mind. In the first place, Aristotle’s kinds are universals, and universals too have a place in the causal scheme of Zeta 17, despite their diminished status in Zeta. Aristotle has already cut the kind down to size in Zeta 10 and 11, judging it to be not a substance at all, but only a “compound of this form and this matter, taken universally” (Chapter 8, Section 15). Equally in Zeta 17, kinds are not robust members of the causal threesome, since they have no work to do over and above what is done already by the form and the matter of a thing. Given these doubts about kinds, if the substance of a thing is also a universal, we may do better to suppose that the relevant conception of universal is not that of an Aristotelian kind at all but, rather, that of an Aristotelian form,15 which if a universal at all, is so in a very different way, as we have seen (Chapter 8, Section 19, and the references in this chapter, n. 7). The Mixed Strategy. This last suggestion points to a mixed strategy, in which one of the three candidates from the Zeta 3 agenda is assigned to a single element from the causal threesome of Zeta 17, while the remaining two are consolidated around a single favoured item: namely, Aristotelian form. On this view, the role of subject is assigned to matter, while essence and universal are consolidated around form. The consolidation of these two makes sense in the context of Zeta 17. The intuitions inherited from Zeta 3 earn a place in Aristotle’s studied account of substance in Zeta 17, only to the extent that they contribute to the causal story that is paramount in the chapter. In particular, if Aristotelian form is primary substance because it is the cause of being for a thing, how does the conception of form as a universal enhance its causal role? Plausibly, it is part of the causal idea that the cause is repeatable: one and the same form can be applied to different stuffs or structures as matter, to produce different examples of the same kind (see Zeta 8, 1034a5–8). Aristotle’s account in 11.6 through 11.9 above is consistent with thinking that a given form is universal to different stuffs and structures as matter, and plays the same causal role across the board, in the constitution of all the specimens of the relevant kind. There is, then, a unity of a sort among the three candidates for substances, stemming from their respective positions in Aristotle’s causal scheme. The preeminent causal role on the part of a thing’s form qualifies the form as the one and only substance of the thing (11.6 and 11.9 above); but the causal idea does not require that the form is the

matter in the strict sense (this chapter, n. 13) is only a potential substance, and in the case of the compound material substance, it is a cause but not its cause par excellence. Arguably, the causal role that Plato assigns to his universals (his Platonic forms) is reassigned to Aristotelian forms: for further discussion, see the two paragraphs that follow in the main text. 15 Form as (primary) substance, Z10, 1035b14–16, 11, 1037a5, 28–9, 17, 1041b7–9 (= 11.9 above); form as universal, this chapter, n. 11 and the Appendices to Chapters 8 and 10.

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one and only cause. Rather, the form has a place in a causal nexus among two, or perhaps three, items: the matter, the form, and (even) the kind, seen as in a certain way the product of the causal interaction between the first two. In the explanation of the being of a substance, form is the substance and simultaneously the essence of the thing in question; matter plays the role of subject and material cause or potential substance; while role of universal falls to either the kind or, as explained above, to the form. So there is, and can be, only one thing that qualifies as the substance of a given thing: here, the form of the thing is the clear, and sole, winner. At the same time, other entities in addition to the thing’s substance or form enter into the causal story of Zeta 17, which is made to engage, to some degree, the governing ideas of all three segments. (I say “to some degree” because the kind contributes nothing to the explanation of a given individual substance that is not already contributed by its matter and its form by themselves.) So Zeta 17 does not altogether displace the earlier characterizations of substance. And it preserves unity among them, by assigning them different roles in a single, wider explanatory context.

2 A Closing Note About Levels We have been concerned with two distinct aspects of Aristotle’s discussion of substance initiated by the agenda passage in Zeta 3, and ending with the retrospective in the first chapter of Eta. On the one side, we find Aristotle engaged with his philosophical friends and foes, even his own philosophical self in other works—all part of the philosophical tradition. Then again, there is Aristotle’s ultimate goal, which is to articulate his own “partisan” theory in terms of form and matter. Of these two approaches to the question of substance, perhaps both are on display in Z17; but the decisive move from received views to the “in-house,” “partisan” theory of (Aristotelian) form and matter takes place in the middle of Eta 1, and it is this latter viewpoint that occupies the remaining chapters of Eta. The presence of received views is beyond dispute in Zeta 17. The point is even explicit in the text (unless we are the beneficiaries of a friendly scholiast): From 11.6 So it is evident that one is inquiring after the cause, and that’s the essence, as we say logiko¯s, which in the case of some things is the “for the sake of something” [= the final cause], as for example in the case of a house or a bed; in other cases it is what first set the movement going, for that is a cause too . . . 1041a27-30, my emphasis.16

16 Alexander doubts that the remark in italics is authentic, and it is bracketed by Jaeger. But the remark is defended by Ross, who thinks that the fresh start under way in Z17 is designed to show, what was left inconclusive before, that a thing’s essence is its substance, Ross (1924) II, 222–3. The manuscript reading is defended also in Frede and Patzig (1988) II, 312–13, and Burnyeat (2001), 58. For Aristotle’s logiko¯s, see Chapter 3, n. 7.

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Just so, in giving the cause of being for a thing, a house (say) or a bed (a29–30), Aristotle glosses “cause” with a reference to the notion of essence, itself from the resources of the Analytics17 and part of the framework of received views in Zeta 4 through 6. But we may also turn, as Aristotle also does in Zeta 17, to the resources of the “partisan” theory of form and matter. In terms of the partisan theory, the role assigned to essence in 11.6 is now assigned to form. The connection between essence and form is clear from 11.6 in combination with 11.9, repeated here: 11.9 So the cause is being sought—and this is the form—of the matter’s being some thing (ti); and this is the substance. (1041b7–9, my emphasis.)18

Accordingly, what we offer at one level as the explanation for Archimedes’ being— that he is a man, where man is his lowest kind—within the partisan theory is replaced by the more refined account of the cause of being for Archimedes in terms of form and matter. In this new account, kinds are still in the ontology, but the form and the stuffs or structures that are the matter appropriate to that form in a given case, are now explanatorily prior. On this view, Aristotle’s account of substance as a cause involves him again in the project of engineering the shift from the concepts and explanations available in the “received” theory or theories that are innocent of the notions of matter and (Aristotelian) form, over into the explanatory scheme of the official theory in which those notions have pride of place.

17 For the association of essence with the middle term in a demonstration, see, for example, An. Po. B8 and B11, 94a36. The view that the efficient cause may be included in the form or account of an event or event-type appears in the discussion of eclipse in Metaphysics H4, 1044b9–15. 18 Again, the phrase in italics has been seen as the work of a friendly scholiast (so Christ, cited by Jaeger); but even if Christ is right, so is the scholiast. In any event, the cat is already out of the bag, since the reference to matter—an element in the “partisan” theory—is undisputed.

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Index abductive argument 37–40, 188 see also argumentative strategies Accidental Compound Theory (ACT) 10 n3, 56, 87 n41, 143 see also “No ACT” Assumption accidental compounds 10, 14 n11, 70, 71 n6, 128, 236 accidental occurrence 107 n33 accidents 79 n27 see also fallacy of accident; Principle of Substitution; snub addition, see prosthesis “all or nothing” principle 167–8 anti-platonism 24–8 see also Platonism Dramatis Personae, expansion of 26–8 polemics, place for 24–6 aquiline 79 n26 Argumentative Man Argument (AMA) 131 n12 argumentative strategies alternative 37–40 see also abductive argument Aristotelianism Aristotle on Zeta’s positive contributions 295–302 levels 16, 17, 18, 19, 29–32, 301–2 retrospective in Eta 1 295–301 Aristotle’s definition of the essence of a thing 88 nn43–44 Aristotle’s dilemma 245–6 Aristotle’s silence 4, 23, 24, 34, 48, 103, 161, 195, 197 n4, 241, 256–258, 263, 271, 288–298 condition on definition 253–5 hypothetical necessity, notion of 123 n70 revised 255–6 individuals and kinds 128–34 lack of fit between Analytics and Metaphysics Zeta 17, 289 per se accidents, notion of 98 nn6–7 problem of friendly fire 209–210 unity, account of 89 n45, 200 n17, 226 n58 see also Platonism; universals asymmetry 162 n40 babbling 27, 97, 103, 109–10, 113 n42, 120 in defence of 121–2 bare substrates bare substrate ontology and 59–61 Basic Argument Plato and elaboration of 154–59

“black-and-white view” 73, 92 body 62, 122–3, 180, 183 see also soul causal principle 156 n25 “cloak” manoeuvre 144–5 cluster theory of properties 55 n26 common conclusion assumption 21 n24, 32–3, 34, 36 compatibilism 196 n5, 200, 238–9, 266 see also mutual exclusivity compound material substances 172 n57, 178–179, 181, 235 condition on definition Aristotlean 255–6 Platonic 255–6 revised 255–6 constancy assumption of meaning 111 n40, 121–2 Constructive Dilemma (CD) 35–7, 256–58 convergence 298–9 see also distributive option, mixed strategy core-dependent homonymy 10 n1, 91, 179 de re essentialism 140 n23 definition see condition on definition; substance; universals democritean atoms 223–4 see also Metaphysics Zeta 13 dependency, ontological 15 n13, 70 n1 see also ontological dependency diachronic analysis 63 dialectic 13–14, 104 differentia, see under Platonism distributive option 299 see also convergence, mixed strategy double bundle theory 61 n34 eclipse 302 n17 elements 45 English language pseudo-cleft constructions 92–4 essence composite essences 144–5 conducted Logiko¯s 76–83 connection with definition 83–4 definition and 90–2 grades of being 90–2 hierarchy of essences (Aristotle) 129–30

310

INDEX

essence (cont.) in Metaphysics Zeta 4 69–94 ownership vs content 74–6 referential opacity 142–4 philosophical tradition of 71–4 Plato “as friend” 148–73 puzzles in Metaphysics Zeta 5 97–104 making room for 104–10 referential opacity and 140–6 sameness, substitution and 95–146 substance and 21–2, 69–189 substance as 5, 69–188 “things that are the same as their essences” 129–30 Thisness Test and 84–7 two conditions on definition and 87–90 “under a description” 140–1 see also pale man argument; referential opacity; substance Eta 1 retrospective in 295–301 event-types 4–5 fallacy of accident non-sameness result and 137–40 referential opacity and 135–7 focal meaning, see core-dependent homonymy form as primary substance 183–6 and the Common Conclusion Assumption, Introduction 9 see also Nonlinearity, Abductive Argument form–matter compounds 11 n6, 11, 25, 29, 202 n17, 239 friendly fire 209–10, 221–2 see also universals full-expansion condition on definition 183–6 Functional Property View 289–4 genus, see under Platonism God nature of 12 n8 see also theology Governing Assumption and essence 151–4, 156 grades of being 10–11, 13, 70, 90–2 homonymy 181 n10 of matter 61–4 see also core-dependent homonymy; metaphysical predication hoper 84–6 pseudo-cleft English constructions and 92–4 hypothetical necessity 123 n70 identity 152, 158 n15 see also Izzing and Having, Theory of; severance

identity premiss 153, 205, 207, 240–2, 261 see also primary argument identity result 153, 159, 172 n57, 204 inaccessibility requirement 33, 35, 37 incompatibility ranges 79 n26 individuals, see kinds infinite regress 152 n14 intensional isomorphism 116 n52 Izzing and Having, Theory of 11 n6, 60 n32, 228–9 severance and 162–4 kath’ hauto terms 147 kinds 70, 181 Aristotlean theory 234–6 individuals and kinds: metaphysical analysis of kinds 231–4 statement predication 229–31 theory of 227–8 see also universals L-equivalence 116 n52 levels 16, 17, 18, 19, 29–32, 301–2 see also non-linearity linguistic predication 11 n4 linguistics 88 n44 logiko¯s 48 n13, 72 n7, 76–83, 104 n22 terminology 29 n34 Masker Paradox 124 n73 matter homonymy of 61–4 stripping away and 57–9 trouble with 59 metaphysical predication 11, 44, 49 difficulties for 61–4 see also homonymy; universals metaphysics definition 12 n8 Metaphysics Zeta 3 “received” and “partisan” in 51–7 Aristotle’s target in 49–51 subjects in 43–65 see also subjects Metaphysics Zeta 4 essence in 69–94 Metaphysics Zeta 5 Aristotle’s argument: absence of target 125 systematic considerations 126 wideness of target 122–5 sameness, substitution, and essence in 95–126 three puzzles in 97–102 accidents and compounds 106–7 contextual definition 107–8 issue of validity 108–10 making room for 104–10

INDEX

non-solution solution 105–6 strategy 117 substitution and reformulation in 118–21 Metaphysics Zeta 6 pale man argument from 127–46 primary argument and Metaphysics Zeta 13 204–5 see also pale man argument Metaphysics Zeta 10 “partisan” mode, shift to 173–87 Metaphysics Zeta 11 “partisan” mode, shift to 173–87, 182–3 Metaphysics Zeta 13 191–239 closing dilemma (1039a14–23) 225–7 general results (1038b30–4) 222–3 lines, numbers and democritean atoms (1039a3–14) 224 Metaphysics Zeta 6 and 204–5 primary argument (1038b8–15) 201–4 programme of 192–5 reprise of primary argument (1038b16–23) 211–19 substance and its parts, a (1038b23–29, 29–30) 219–21 substance and predication (1038b15–16) 214–17 universals and this-such distinction (1038b34–1039a3) 217–19 see also primary argument; universals Metaphysics Zeta 15 received and partisan mode in 251–3 substance and universals 250–67 Metaphysics Zeta 16 critique 259–62 substance and universals 250–67 Metaphysics Zeta 17 fresh approach to defining substance 271–94 see also Functional Property View mixed strategy 302–3 see also convergence, distributive option monolithic conception 64 see also subjects mutual exclusivity 198–9, 203, 205–11, 119, 221–2, 227, 239–40, 255, 259 n13, 260–1, 265–6 see also compatibilism; primary argument natural philosophy 12 n8, 293 n50 “No ACT” Assumption 137–9 see also Accidental Compound Theory (ACT) “no relevance” thesis 271 n1 non-circularity condition 82 Non-Linearity Assumption 6, 32–4 common conclusion assumption 32–4 inaccessibility requirement 32–4 logic of 34–7 see also levels

311

ontological dependency 11, 13, 91 ownership, see essence pale man argument 27, 75, 85–6 from Metaphysics Zeta 61 28–47 “things that are not the same as their essences” 130–4 referential opacity and 135–40 various arguments 134–5 see also essence; Metaphysics Zeta 6 partial functionality 202–5, 207–10, 213, 220–2, 240–2, 249, 260 see also primary argument partisan view, see received view pedagogy 12 n8 perishability argument 252 Platonism 161 n38 critique of Plato 261–4 individuals and kinds 227–39 Plato as “friend” in essence theory 147–71 elaboration of basic sameness argument 154–9 Plato’s forms, inessentiality of 170–2 purity in engagement 151–59 sameness, basic argument for 151–54 severance and Platonic separation 159–62 uniformity and true Platonic doctrine 165–70 Plato on genus, species and differentia 240–49 assumptions that make Plato vulnerable 242–3 negative consequences 248–9 “The genus is not numerically the same in the different species” 245–8 “The genus is numerically the same in the different species” 243–5 Platonic condition on definition 255–6 Plato’s fundamental mistake 250–67 see also anti-platonism; Aristotleanism; severance predication substance and 214–7 see also linguistic predication; metaphysical predication Presocratics 46–7 primacy condition 87–90 see also essence primary argument argument of Zeta 6 and 204–5 limits of 205–9 reprise of, in Metaphysics Zeta 13 (1038b8–15) 201–4 (1038B16–23) 211–19 see also identity premise; Metaphysics Zeta 13; mutual exclusivity; partial functionality; uniformity; universals prime matter 60 n33, 61 n35

312

INDEX

Principle of Identity 110, 114 n46, 115 n47 Principle of Substitution 109–11, 114, 117 n55, 111–21, 135–8 extended sameness test 115–17 see also under substitution priority, ontological 15 n13, 70 n1 proleptic interpretation 14, 30 n36, 31 n40 propositionalist interpretation 234 n69 prosthesis 80 n30, 84, 98–101, 105, 108–9, 119 n62 see also addition purity 151 n9, 157–8 in engagement with Plato 151–9 puzzles, see Metaphysics Zeta 5; SE, the; sameness; substitution; snub quality 10 n2 quasi-propositional structured entity 235 received view 16 n18, 18, 21, 25, 30, 37, 95 n1 “received” and “partisan”, distribution of 51–7 “received” to “partisan”, shift from 57–9 managing the shift 183–7 in Metaphysics Zeta 10 and 11, 173–88 non-partisan views 18 partisan developments 74 received and partisan mode in Metaphysics Zeta 15 251–3 sources of 45–9 terminology 29 n34 see also full-expansion condition on definition; stripping away; subjects; universals referential opacity fallacy of accident and 135–7 pale man argument and 135–40 theory of essence and 140–6 composite essences 144–5 ownership vs content 141–3 “under a description” 140–1 relational notion 201 relevance, see “no relevance” thesis retrospective interpretation 15 sameness basic argument for 151–4 Plato and elaboration of 154–9 definition and 115–17 non-sameness result: fallacy of accident and 137–40 substitution and 113–17 puzzles and principles of sameness 114–15 puzzles, sameness and definition 113–14 substitution, essence and 95–146 see also snub; substitution SE, the “double” in 110–11 repetition of the ‘same thing’ 112–13

sameness, substitution and essence in 95–146 snub nosedness in 102–4 second-level functional property view 289, 292–3 separability 25, 59, 65 severance 150 n7 consequences of 159–62 Platonic separation and 159–62 severance assumption 160–2 Theory of Izzing and Having and 162–4 uniformity and 165–72 see also Platonism snub 79 n26, 97, 98 n7, 99 n9, 100–2, 105 in the SE 102–4 see also accidents; sameness; substitution Socrates the Younger 124 n69, 183 n12 sophistic puzzles 71 n5 soul 180, 183 definition 19 see also body species, see under Platonism stripping away 52–7, 63–4 matter and 57–9 see also received view subjects in Metaphysics Zeta 3 43–65 primary subjects 43 subject criterion 48 n13 substance and 21 see also received view; monolithic conception of substance “no substance can can actual substance as its parts” 219–27 actual substances 226–7 alien presences 4–5 and its parts 219–21 approach to, in Zeta 10–20 definition of substance 16–20 Metaphysics Zeta 1 10–16 compositional dependency 14 constraints on 28–37 definition of 271–94 causes and 288–93 from An. Po. to Metaphysics 280–1 questions of fit 282–7 search for substance 271–4 substance as a cause 274–80 translation 13 n8 essence and 21–2 substance as essence 5, 11, 69–186, 228 non-substances 10, 70 oblique approach to 2–4 perceptible substances 15 predication and 214–17 primary substances 1–2, 10, 13, 22 n25, 40, 43, 95, 157, 178, 181, 183–6, 226, 264, 271 secondary substances 11 n7, 181

INDEX

subject, as 43–65 subjects and 21 unexpected absences 5–6 see also absences universals and 22–3 definition and 264–67 no substance is a universal 194–5 Plato as foe 191–240 Plato on genus, species, and differentia 240–49 Plato’s fundamental mistake 250–67 see also essence; individuals; kinds; universals substitution extended sameness test and 115–17 reformulation and: in three puzzles of Metaphysics Zeta 5 118–21 sameness and 113–17 sameness, essence and 95–146 see also sameness; snub subtraction rule 115 syntactic unity 89 n45 “the for-you to be” 75 theology 15–16, 167 n49 theory of forms 5, 181 see also Platonism Third Man Argument 85 n37 thisness 15 n13, 25, 59, 65 Thisness Test essence and 84–7 this-such distinction This-Such Assumption 218 universals and 217–9 transitivity 134 true doctrine, see Platonism uniformity 166, 202–7, 210, 242 applications of 165–9 fallacy and 165–70

313

severance and 165–72 true Platonic doctrine and 165–70 see also primary argument unity condition 87–90 see also Aristotle; essence Universal Generalization (UG), rule of 126 Universal Introduction (UI), rule of 166–7 universals substance and 22–3 “no universal is a substance” 201–10 Aristotelian forms 209–10 definition and 264–67 friendly fire 209–10, 222–3 Plato as foe 191–240 Plato on genus, species, and differentia 240–49 Platonic view in Zeta 13–16, 196–200 Plato’s fundamental mistake 250–67 primary argument and Zeta 6 204–5 primary argument, limits of 205–9 structure of universals 224–6 substance and its parts 219–21 substance and predication in Metaphysics Zeta 13 (1038b15–16) 213–7 summary of conclusions 262–5 this-such distinction and universals 217–9 see also Aristotelianism; kinds; Metaphysics Zeta 13; Platonism; primary argument; substance Unmoved Mover 13 n8 veneer theory of properties, see cluster theory of properties What a Thing is per se 76–83 What is it? Question 73 What is the for-cloak to be? 83–5 what it was to be 89 Zeta, see under Metaphysics Zeta 1–16

Index Locorum Alexander of Aphrodisias In Metaphysica (in Met.) 160.30–161.1: 153 n14 G. E. M. Anscombe “Under A Description” 219: 141 n22 G. E. M. Anscombe and Peter Geach Three Philosophers: Aristotle, Aquinas, Frege 16: 55 n26 53–4: 230 n63 Aristotle Categories 1, 1a12–15: 228 2, 1b3–6: 214 n37 2a34–5: 45 3a29–32: 258 5, 2b37: 45 5, 2a11–14: 214 n37 5, 3a8–9: 214 n37 5, 3a29–32: 49 5, 3b10–13: 50 n17 5, 3b10–21: 217 n43 5, 3b13–21: 50 n17 5, 3b36–9: 93 7, 6a39–b11: 93 10, 12b5–16: 234 n69 De Anima 412a3: 19 G5, 430a10–13: 290 n40 A4, 408b11–18, 25–9: 301 n11 B4, 415b12–14: 274 De Caelo 278a29 ff: 79 n26 D 311a4–6: 290 n40 De Generatione Animalium (GA) B4, 740b22–2: 290 n40 De Generatione et Corruptione (GC) A3, 318b32: 15 n13 A7, 324b13–18: 290 n40 A7, 324b18: 290 n40 De Int. 1, 16a3–9: 233 n69 11, 20b26–30: 275 11, 20b31ff.: 113 n42 De Long. Vitae 3, 465b15–16: 290 n40

De Motu Animalium 8, 702a10–15, 20–1: 290 n40 Metaphysics 3, 998b14–999a23: 168 n51, 194 n1 7, 988b4–5: 24 n27 Æ2, 994b16–18: 153 n14 Alpha: A3, 983a27–8: 301 n11 A6, 987b9–10: 251 n9 A6, 988b4–5: 152 n10 A6, 988a8–11: 24 n27, 152 n10 A9, 991a31: 90 n48 Beta: B1, 995a24–b4: 103 n21 B1, 995b35: 44 n4 B1, 996a4–7: 262 B2, 997b5–12: 265 B3, 995b29–31: 90 n49, 168 n51, 194 n1 B3, 998b5–6: 88 n43 B3, 998b9–11: 262 B3, 998b14–999a23: 70 n3, 71 n5, 90 n49, 211 n29 B3, 999a14–16: 90 n49, 168 n51 B4, 999a33–4: 44 n4 B4, 1001a4–b25: 262 B5, 1001b26–1002a11: 52–3 B5, 1001b32: 50 n17 B5, 1002a8–11: 46 B6, 1003a7–9: 217 B6, 1003a7–12: 201 n18, 217 n43 B6, 1003a9–12: 201 n18 Gamma: G3, 1005b3–5: 275 G4, 1007a33: 86 n39 Delta: D2 1013b22–3: 301 n11 D6 1015b16–36: 131 n11 1016a33: 83 n34 1017a6: 83 n34 D7 1017a22–3: 155 n20 D8 25 n29, 34 n51 1017b10–14: 47–8, 214 n37, 261, 299 n8 1017b14–16: 50 n15 1017b21–2: 83 n34

I N D E X L O C O RU M

1017b25: 15 n13 D9 1018a2–3: 131 n11 D11 1019a1–4: 48, 50 n17 D18 1022a25–7: 164 1022a26: 75 n16 1022a26–7: 142 n24 1022a29–32: 301 n11 D28 1024b4–6: 88 n43 D29 1024b30–31: 131 n11 Epsilon E1, 1025b28–1026a6: 179 n5 E2, 1026b15–18: 131 n11 Zeta Iota 9, 1058b3–5: 145 Metaphysics Zeta 1 1028a14–18: 10 n1 1028a20–31: 13 1028a31–4: 50 n17 1028a31–b2: 219 n46 1028b2–7: 12 1028b7: 95 2, 1028b31–2: 12 17, 1041a6: 12 a18–20, Ch. 3 s 8: 10 n1 a20–9, n. 3: 10 n1 Metaphysics Zeta 2 1028b9–15: 261 1028b28–32: 15 n16 1028b31: 34 n49 1028b31–2: 95 3, 1029b3–12: 15 n16 11, 1037a10–17: 15 n16 16, 1040b27–1041a3: 15 n16 17, 1041a7–9: 15 n16 Metaphysics Zeta 3 1028b23–4: 39 n59 1028b33–6: 3, 16, 43, 69, 157 n23 1028b36–7: 43 1028b37: 50 n16 1029a1–2: 43 1029a1–3: 301 n11 1029a2–3: 50 n15 1029a5–7: 49 1029a7–8: 34 n49 1029a7–9: 23 n26 1029a8–9: 43 1029a21–6: 54 1029a23: 195 n3 1029a23–4: 44

315

1029a27–33: 59 1029a28: 15 n13 1029a29–30: 43 n3 1029a30–2: 195 n3 1033a31–2: 301 n11 Metaphysics Zeta 4 1029b1–3: 32 n42, 69, 152, 157 n23, 195 n3 1029b13: 28 n34, 104 n22 1029b13–14: 72, 74 1029b13–16: 76–7 1029b16–18: 76–7 1029b19: 82 1029b19–20: 82, 99 n8, 124 1029b22–7: 11 n3, 145 1029b22–31: 83 1029b29–1030a2: 99 1030a10–14: 71 1029b21–2: 115 n48, 129 n3 1029b28–9: 84 1030a1–2: 84, 169 n54 1030a2–7: 84, 87 1030a7–11: 88 1030a10: 96 1030a11–14: 85 n37, 187 1030a11–17: 89 1030a13–14: 24 n27 1030a17–32: 91 1030a17–b13: 208 n25 1030a25: 28 n34 1030a27: 104 n23 1030a27–8: 72 n7 1030a33: 98 n7 1030b4–13: 92, 147 1030b7–13: 226 n58 1030b10–13: 145 Metaphysics Zeta 5 1030b14–15: 109 n36 1030b14–16, 26–28: 99 1030b16: 98 n7 1030b16, cf. 23–6: 108 n35 1030b17–18: 98 n7 1030b23–5: 79 n26 1030b26–8: 99 1030b28–1031a2, a11–14: 100 1030b28–32: 100, 129 n3 1030b29, 30: 98 n7 1030b30–1: 98 n7 1030b31–2: 103 1031a1: 101 1031a2: 100 1031a2–5: 108 n35 1031a6: 98 n7 1031a9–14: 92, 96 1031a11–14: 71 1031a12: 83 n34 Metaphysics Zeta 6

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Aristotle (cont.) 1031a15–18: 128, 147, 149 1031a17–18: 243 n1 1031a18: 152 1031a19: 11 n3, 154 n17 1031a19–25: 129, 131 1031a19–28: 115 n48, 128 n2, 149 n1, 150 1031a24–5: 135 1031a28 ff, cf.10: 21 1031a28–b3: 155 1031a29: 148 1031a31–b3: 158 n27 1031b2–3: 152 n11 1031b3–11: 159, 165 1031b11–15: 170–171 1031b14–15: 151 n9 1031b18–20: 217 n42 1031b22–8: 131 n11, 155 n20 1031b31–2: 152 n11 1032a2–4: 172 n57 1032a6–10: 115 n48 1032a8: 75 n16, 142 n24 1032b12–13: 71 n6 1036a1–2, 11: 21 1037a33–b7: 21 M2, 1077b4–9: 11 n3 Metaphysics Zeta 7 1032a20–1: 254 n1 1032b1–2: 152 n11, 301 n11 Metaphysics Zeta 8 1034a5–8: 302 Metaphysics Zeta 10 1034b20–2: 172 n57, 223 1034b20–4, 28–30: 17 1034b22: 176 1034b22–4: 185 1035a1: 174 1035a4–9: 178 1035a7–8: 180 1035a9–23: 123 n69 1035a18–20: 182 n10 1035b1–3: 180 1035b14ff.: 181 1035b14–16: 18, 96 n2, 152 n11, 187 n14 1035b14–16, 32: 301 n11, 302 n15 1035b14–18: 124 n69 1035b16, 32: 176 1035b33–1036a2: 301 n11 1035a23: 179 n5 1035b3ff: 179 1035b23–5: 182 1035b25–7: 182 1035b27–30: 201, 231 1035b31–1036a9: 186 1035b33ff: 15 n13 1035b33–1036a1: 187

1035b33–1036a2: 260 1035b33–1036a8: 257 n7 1035b34: 186 1036a1, 18: 176 1036a1–3: 180 1036a2: 186 1036a2–9: 178 n4, 254 1036a12ff: 15 n13 1036a22: 179 1036b21–32: 123 n69 Metaphysics Zeta 11 1036a26–31: 260 1036a27–31: 183 1036a28–29: 96 n2, 257, 301 n11 1036b17–20: 183 1036b22–32: 98 n7, 179 n5 1037a5: 22 1037a5, 28–9: 187 n14, 302 n15 1037a6–7: 194 n1, 269 1037a9–10: 231 1037a21–2: 95 n1 1037a26–30: 179 n4 1037a27: 179 n5 1039b31–1040a5: 178 n4 Metaphysics Zeta 12 1037b18–21: 247 1037b29–30: 88 n43 1038a13–33: 90 n49 1038a23: 213 Metaphysics Zeta 13 1038b1: 194 1038b1–2: 32 n42 1038b1–3: 195 1038b2–3: 16 n18, 198 1038b4–6: 44 1038b6–8: 199 1038b8: 195, 214, 262 1038b8–15: 201 1038b8–23: 196 1038b9–11: 264 n16 1038b9–15: 216 1038b10: 160 n37 1038b11–12: 260 1038b12–13: 167 n49 1038b14–15: 152 n11 1038b15: 25 1038b15–16: 213 1038b16–17: 26 1038b16–23: 210 1038b17: 200 1038b23: 219 1038b23–9: 197, 216, 225 n54 1038b23–30: 196 1038b23–34: 196, 217 1038b26–9: 219 n46 1038b29–30, 30–34: 197, 199 n7, 217

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1038b30–2: 200 n11, 201 n18 1038b30–4: 217, 222–3 1038b34–1039a3: 196, 217 1038b35–1039a3: 50 n17, 85 n37 1039a3–14: 223–4 1039a3–14: 197 1039a3–23: 196 1039a7–11: 202 n17 1039a14–18: 197 1039a14–23: 197, 224–6 1039a16–23: 203 1039a19: 225 1039a19–21: 197 1039a22–3: 202 n17 34–1039a3: 196 Metaphysics Zeta 14 1036b9–11, b14–16: 206 n23 1039a24–6: 244 1039a30–3: 245 1039a33–b2: 246 1039b2–6: 247 1039b7–9: 152 n10, 248 1039b8–9: 210 n27, 220 n47 1039b9–10: 251 n9 1039b9–14: 249 1039b14–16: 251 1039b16–19: 203, 244 Metaphysics Zeta 15 1039b27: 257 n7 1039b27–30: 179 n4 1039b27, 30–1: 256 1039b28: 254 1039b29–31: 254 n1 1039b31–1040a5: 254 1040a6: 257 1040a8–21: 268 n25 1040a8–27: 255 1040a8–9: 257 1040a18–21: 245 1040a27–b2: 255 1040a28–30: 245 1040a29: 255 1040b1–2: 257 1040b2–4: 255 Metaphysics Zeta 16 1040b16–18: 206 n23 1040b16–21: 262 1040b16–24: 262 1040b17: 202 n21 1040b18–19: 200 n11 1040b21–3: 201 n18 1040b22–4: 264 1040b23–4: 221 1040b25–30: 264 1040b27–30: 299 n6 1040b32–4: 265 1040b34–1041a3: 265

1041a3–5: 194, 261, 266 Metaphysics Zeta 17 1041a3–4: 201 n18 1041a6–7: 273 1041a6–10: 199 n10 1041a9–10: 199, 273 1041a9–20: 276 1041a10–b11: 267 n23 1041a28: 28 n34, 164 n44, 200 n10 1041a20–7: 277 1041a32–b2: 281 1041b1: 281 n18 1041b2–7: 281 1041b5–9: 229 1041b7–9: 281, 302 n15, 304 1041b11–25: 267 n23 1041b25–33: 267 n23 1041b27–8: 274 1041a27–30: 303 Eta Eta 1 1042a3–4: 297 1042a5–6: 298 n2 1042a7–11: 298 n3 1042 a11–12: 298 n3 1042a12: 298 n4 1042a12–13: 298 n5 1042a13–15: 35 n54, 90 n49, 168 n51 1042a17: 83 n34, 152 n11, 175 1042a21–2: 201 n18 1042a26–9: 50 n15, 301 n11 1042a24: 297, 299 1042a27–8: 299 1042a29: 15 n13, 50 n17 194 n1 1042a29–31: 195 n3 Eta 2 1042a32–b3: 301 1042b10: 299 1042b25–31: 230 1042b26–8: 230 n62, 233 1042b26–7: 74 1042b27–8: 74 1043a2–4: 274 1043a5: 230 1043a5–6: 44 n4, 230 1043a7–8: 74 1043a8–9: 288 1043a9: 288 1043a9–10: 74 1043a16 ff.: 288 Eta 3 1043a29–37: 290 n38 1043a30–1: 297 1043b1–2: 301 n11 1043b2–4: 180 1043b13: 274

317

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Aristotle (cont.) 1044a36: 301 n11 1044b8–15: 288 1044b9–15: 304 n17 1045a12–14: 88 1045a14–20: 211 n30 1045b17: 284 Eta 4 1044b8–15: 282 Eta 6 1045b7–16: 247 Iota ¨1, 1045b27–9: 298 n1 ¨5, 1048a5–7: 290 n40 ¨7, 1049a18–36: 236 ¨7, 1049a19–36: 53 n22 ¨7, 1049a27–30, 34–6: 44 ¨7, 1049a35: 15 n13 I2, 1053b16–18: 201 n18 Kappa K2, 1060b21: 201 n18 Lambda ¸1, 1069a26–8: 199 n6 ¸3, 1070a11, 13–15: 15 n13 ¸10, 1075b35: 230 n62 Mu M4, 1078b30–4: 50 n17 M4, 1078b34–1079a4: 251 n9 M5, 1079b15–17: 152 n10 M5, 1080a1: 24 n27, 152 n10 M8, 1084b5: 257 n6 M9, 1086a32–b13: 201 n18 M10, 1086b32–7: 257 n7 M10, 1086b37–1087a4: 225 M10, 1087a2: 201 n18 De Partibus Animalium (PA) A4, 644a24–5: 168 n51 B1, 646b11–27: 124 n70 Poetics 20, 1457a28-30: 88 Posterior Analytics 31, 87b37–88a5: 255 93a36–b2: 278 n11 Alpha A2, 71b10–12: 255, 283 A2, 71b15–16: 255 A4, 73a21–3: 255 A4, 73a25–74a3: 255 A4, 73a34 ff, b16 ff, 74b5–12: 79 n26 A4, 73b5–9: 84, 89 n47 A4, 73b7: 50 n17 A4, 73b16 ff: 79 n26 A4, 73b23–4, 74b5–12: 79 n26

A4, 644a24–5: 90 n49 A11, 77a5-9: 193 A21, 83a24–32: 154 n18 A22, 82b37–83a1: 88 n43 A22, 83a24–5: 93 A22, 83a32–5: 227 A22, 84a11–17: 79 n26 A39, 49b6–9: 86 n39 Beta B1, 89b25–6: 283 n25 B2, 71b29–33: 283 B2, 90a15–23: 285 n31 B11, 94a36: 304 n17 B2, 90a14–23, 31–34: 280 n16 B3, 90b16: 88 B3, 90b3–7: 255 B3, 91a1: 83 n34 B7, 92b5–8: 89 n46 B7, 92b28–32: 89 B7, 92b31–2: 88 B8, 93a3–4: 280 n16 B8, 93a23–4: 279 n13 B8, 93a29–b12: 280 B8, 93b7–14: 286 n33 B10, 93b29, 94a11: 83 n34 B10, 93b35–7: 88 B10, 93b38-9: 283 n25 B10, 94a1–7: 280 n15, 283 n25 B10, 94a1–9: 280 n16 B10, 94a12–13: 283 n 25 B13, 96a32–5: 256 B13, 96b25–97b6: 268 B13, 96b30–5: 88 n43 B13, 97b15–25: 283 n26 B13, 97b25–8: 268 B13, 97b32–9: 98 n6 B13, 96b35–97a6, a25–6, 35–b6: 88 n43 B13, 97a23–b6: 88 n43 B13, 97a25, 28–34: 88 n43 B21, 67a39–b3: 254 B22, 83a25–8: 86 n39 Iota I.22, 82b37–83a1: 153 n14 I.22, 84a25–6: 153 n14 De Sophisticis Elenchis (SE) 1, 164a20–1: 97 1, 165a3–19: 111 n39 3, 165b15–17: 102 6, 168a34–b10: 135 n15, 144 n28 13, 173a34–8: 102, 110 13, 173b5–11: 98 n7 13, 173b8–11: 102 13, 173b12–16: 103, 110–111 22, 178b36–179a10: 201 n18, 217 n43 22, 178b37–9: 50 n17

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22, 179a3–4: 85 n37 24, 179a26–b7: 135 n15, 144 n28 24, 179a37: 172 n57 24, 179a37–9: 116 n52, 129 n2, 135 n15, 144 n28 31, 173b15–16: 120 n64 31, 182a2–3: 119 31, 182a3–4: 119 n64–65 31, 182a4: 119 31, 182a24: 121 31, 181b25–8: 112 31, 181b32–4: 112 31, 181b35–182a3–5: 112 31, 182a5–6: 119 31, 181b35–182a7: 104 n21 31, 182a4: 102 n18, 103 n20 31, 182a4–5: 103 Topics 5, 126a17–20, 90 n48 5, 143a18–19: 90 n49 9, 147b12–25: 99 n8 14, 151a33–4, b16–17: 202 n21 Alpha A4, 101b21–2: 83 n34 A5, 101b38: 83 n34 A5, 101b38–102a5: 83 n33 A5, 102a7–14: 115 A5, 102a7–17: 99 n8, 144 A5, 102a15–16: 115 n49 A5, 102a18–22: 163 n41 A8, 103b9–10: 83 n34 A14, 105b19 ff: 104 n22 A15, 106a12ff: 98 n6 A15, 107a36–b5: 113 n41 Epsilon E2, 130a29ff: 113 n42 E2, 130b25–8: 84 n35 E4, 132b35–133a3: 248 n5 E4, 133b15–21, 31–6: 131 n11 E4, 133b17–21: 135 n15 E11, 162b11–15: 158 n28 Gamma ˆ1, 116a26–7: 86 n39 Delta ˜1, 120b23, 27-8: 86 n39 ˜1, 121a11–12: 248 n5 ˜1, 121a11–14: 90 n48 ˜2, 122b25–6, 123a2: 86 n39 ˜2, 123a7–8: 248 n5 ˜4, 124a17–18: 86 n39 Zeta Z1, 139a29–31: 90 n49, 211 n29 Z1, 139b15–17: 84 n35 Z3, 140a24–32: 84 n35

319

Z3, 141a4–6: 113 n42 Z4, 141a35: 202 n21 Z4, 142a34–b6: 82, 99 n8 Z5, 143b2–5: 248 Z5, 142b27–9: 88 n43, 211 n29 Z5, 142b35: 202 n21 Z5, 143a18–19: 211 n29 Z9, 147b12–25: 82 Z11, 148b32–149a7: 83, 124 Z11, 149a1–4: 83 n33 Z11, 149a8–11: 88 Eta H1, 152a33–7: 114 n44 H1, 152a33–7, b25–9: 135 n15 H1, 152b10–15: 82, 114, 132 H1, 152b25–9: 114 H2, 152b36–153a5: 99 n8, 115 n49 H3, 153a12–22: 83 n34 H3, 153a15–22: 88 n43 H5, 154a31–2: 83 n34 Theta ¨14, 163b3–4: 26 n31 Jonathan Barnes Aristotle: Posterior Analytics 286 n33 174: 75 n18 113–14: 78 n23 117: 89 n47 219: 286 n34 220: 280 n15, 286 n34 224: 280 n15, 286 n34 Robert Bolton “Science and the Science of Substance in Aristotle Metaphysics Z” (Lewis and Bolton) 15 n15, 199 n6, 275 n4, 301 n13 249–50: 33 n46 251: 275 n5 272: 211 n32 Herman Bonitz Aristotelis Metaphysica 308: 86 II, 317–18: 166 n48 Index Aristotelicus 296a2: 103 533b44–534a23: 86 n39 764b45–57: 83 n34 David Bostock Aristotle Metaphysics Books Z and H 96: 105 n28 96–7: 99 n8 97–8: 101 n14 97–9: 105 n28 98: 102 n16 99: 105 n25

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David Bostock (cont.) 99–100: 113 n41 107–8: 150 n6 108: 151 n9, 156 n21 109: 165 n45 109–10: 165 n46 110: 166 n48, 169 n53 112–13: 152 n14 116: 30 n36 236: 273 n1 Myles Burnyeat Notes on Book Zeta of Aristotle’s Metaphysics 101 n14 A Map of Metaphysics Zeta 6, 22 n25, 28 nn33–4, 30 n36, 76 n20, 104 n23, 158 nn26–7, 195 n3, 260 n11 4–5: 32 n44 13–15: 23 n26 15–16: 35 n53 19–24: 29 n34 19–25: 72 n7 22–3: 72 n7 26: 152 n12, 153 n15, 154 n18 27: 151 n9, 170–1 28–9: 31 n40 29–38 (on Z7–9): 5 n5 36–7: 267 n22 39: 179 n6 41: 39 n58 42–4 (on Z12): 5 n5 46: 31 n40, 36–7 49: 223 n52 54: 261 n12 55: 31 n40 55–6: 266 n21 58: 303 n16 62–3: 298 n5 65ff: 298 n2 65–73: 285 n32 81: 33 n48 82 (note): 35 n55 103: 26 n31 125: 30 n37, 265 n20 David Charles Aristotle on Meaning and Essence 284 n31 54: 278 n11 209–10: 283 n26 229: 279 n13 276ff: 275 n4 312: 288 327: 283 n26 Ch. 1: 278 n11 Ch. 2: 278 n11 Ch. 10, s 10.3: 72 n9 Definition in Greek Philosophy 149 n1, 284 n31 310: 280 n16

“Some Remarks on Substance and Essence in Metaphysics Z6” (Morison and Ierodiakonou) 129 n2, 171 n57 Harold Cherniss Aristotle’s Criticism of Plato and the Academy 151 n7 334–6: 158 Kai Chiba “Aristotle on Essence and Defining Phrase in his Dialectic” (Charles) 29 n34, 72 n7 Noam Chomsky Language and Mind 171–2: 40 n60 Alan Code “No Universal is a Substance: An Interpretation of Metaphysics Z13, 1038b8–15” 233 n63 67–8: 202 n20 70: 167 n49, 202 n19 “Aristotle on the Sameness of Each Thing With Its Essence” 11 n5, 162 n39 “The Aporematic Approach to Primary Being in Metaphysics Z” n.22: 257 n5 18–20: 270 n28 “On the Origins of Some Aristotelian Theses About Predication” (Bogen and McGuire) 185 n13, 270 n28 “Aristotle: Essence and Accident” (Grandy and Warner) 11 n5, 162 n39, 215 n40, 270 n28 “Aristotle’s Metaphysics as a Science of Principles” 30 n36, 151 n9 “Commentary on Devereux” (Gurtier and Wians) 179 n5 Marc Cohen “Kooky Objects Revisited: Aristotle’s Ontology” 141 n22 J. Cook Wilson Statement and Inference I, 159–66: 48 n13 Francis Macdonald Cornford Plato’s Theory of Knowledge 162: 252 n2 Paolo Crivelli Aristotle on Truth 233–4 n69

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Norman Dahl “Two Kinds of Essence in Aristotle” 129 n5 256: 137 n17 “On Substance Being the Same As Its Essence in Metaphysics Z6: The Pale Man Argument” n.15: 75 n17, 129 n5 n.29: 131 n11 “On Substance Being the Same As Its Essence in Metaphysics vii6: The Argument About Platonic Forms” 129 n2, 149 n1, 171 n57 Russell M. Dancy Sense and Contradiction: A Study in Aristotle 100: 151 n9 “On Some of Aristotle’s Second Thoughts About Substances: Matter” 394: 51 n20, 73 n12 394–6: 54 n25 “Aristotle and Existence” (Knuuttila and Hintikka) 278 n10 “Hintikka, Aristotle, and Existence” (Auxier and Hahn) 278 n10 Daniel Devereux “Aristotle on the Form and Definition of a Human Being: Definitions and Their Parts In Metaphysics Z 10 and 11” (Gurtler and Wians) 179 n5, 184 n12 L.-A. Dorion Aristote: Les Re´futations sophistiques 216, n.25: 113 n42 310, n.216: 110 nn37–8 312, n.222: 111 n40 398, n.430: 112 n41 Michael Ferejohn “The Definition of Generated Composites in Aristotle’s Metaphysics” (Scaltsas et al.) 30 n36, 104 nn21–2 n.35: 105 n25 296–7: 107 n32 297–300: 101 n14 299–300: 102 n16

321

Michael Frede and Gunther Patzig Aristoteles “ Metaphysik Z” 75 n18, 223 n52 I, 39: 231 n64 I, 52: 231 n64 II: 151 n7 II, 82–4: 101 n14 II, 85: 101 n13, 102 n17 II, 88: 152 n12 II, 95: 165 n46 II, 96–7: 159 n32, 160 n38 II, 97–8: 169 n55 II, 241–2: 195 n3 II, 244: 24 n28 II, 256–7: 231 n64 II, 308: 273 n1 II, 312–13: 303 n16 II, 315: 281 n18 Cynthia Freeland “Accidental Causes and Real Explanations” (Judson) 141 n22 Christopher Frey “Organic Unity and the Matter of Man” 182 n10 Montgomery Furth 12–13, 71, 92, 96, 99, 101 n14, 177, 178, 180, 183, 186, 223 n52, 244, 252, 262, 264, 265, 273, 276–7, 279 n13, 280–1 “Transtemporal Stability in Aristotelian Substances” 631: 1 n1 Aristotle Metaphysics, Books VII–X. 126–7: 230 n63 Substance, Form, and Psyche: An Aristotelean Metaphysics 250–7: 230 n63

Kit Fine “The Problem of De Re Modality” (Almog et al.) 116 n53, 117 n55, 126 “Ontological Dependence” 70 n1

Mary Louise Gill “Aristotle’s Attack on Universals” 210 n32 n.6: 195 n3 238: 217 n42 246: 217 n42 248–9: 221 n48 252: 221 n50 253: 221 n50 253–4: 221 n48 Granger, Herbert 70 n3, 79 n26

Michael Frede 1990: 179 n5 (2000) 12–14: 46 n9 Frede, M. and Patzig, G. 169–70

Herbert Granger “Aristotle on the Subjecthood of Form” 135–59: 50 n15 “The Subjecthood of Form: A Reply to Shields” 177–85: 50 n15

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D. W. Hamlyn “Aristotle on Predication” 123–4: 230 n63 J. E. Hare “Aristotle and the Definition of Natural Things” 113 n32 168: 101 n13 172–3: 119 n61 173: 102 n18, 106 n29, 119 n61 John Heil Philosophy of Mind: A Contemporary Introduction 291 n44, 292 n44 “Properties and Powers” 291 n44 Francis Roger Higgins “The Pseudo-Cleft Construction in English” 92 n52 Risto Hilpinen “Peirce’s Logic” (Gabbay and Woods) 644–53: 40 n60 Jaako Hintikka “Reply to R. M. Dancy” (Auxier and Hahn) 278 n10 Terence Irwin Aristotle’s First Principles Ch. 2, ss 20 ff: 103 n21, 104 n24 Ch. 2, n46: 104 n22 Ch. 2, n48: 104 n22 Ch. 2, n49: 104 n22 Ch. 7, n15: 104 n22 Ch.12: 231 n64 Carrie Jenkins Grounding Concepts: An Empirical Basis for Arithmetical Knowledge 124: 74 n14 David Kaplan “Quantifying In” (Davidson and Hintikka) 107 n33, 111 n40 “What is Russell’s Theory of Descriptions?” (Pears) 233–4: 107 n32 David Keyt “The Mad Craftsman of theTimaeus” 168 n50 Jeffrey King “Two Sorts of Claim About “Logical Form” (Preyer and Peter) 233 n65 Christopher Kirwan Aristotle’s Metaphysics Books G, D, ¯ 186: 103 n21

Kathrin Koslicki The Structure of Objects 70 n1, 202 n17 Joan Kung “Can Substance be Predicated of Matter” 48 n13 “Aristotle on Thises, Suches, and the Third Man Argument” 234 n70 255, n48: 153 n14 255, n49: 153 n14 Mariska Leunissen “Aristotle and Philoponus on Final Causes in Demonstrations in Posterior Analytics II 11” (de Haas et al.) 282 n23 David Lewis “New Work for a Theory of Universals” 345: 247 n4 “Reduction of Mind” (Guttenplan) 234 n70 Frank A. Lewis “What Is Aristotle’s Theory of Essence?” n. 14: 208 n25 30 n36, 149 n3, 155 n20 91–118: 96 n3 117–18: 73 n11 “Plato’s Third Man Argument and the ‘Platonism’ of Aristotle” (Bogen and McGuire) 215 n40, 230 n63, 234 n70 Substance and Predication in Aristotle’s Metaphysics 10 n3, 215 n40, 234 n70 63–73: 63 n38 72–3: 25 n29 73–4: 194 n2 73–8: 218 n44 101, n27: 131 n11 108–14: 56 n28 108–28: 144 n29 110: 144 n29 149: 230 116–21: 114 n44, 129 n2 119: 115 n47 119–20: 132 n13 154: 231 178–9: 286 n33 207–10: 141 n22 289: 54 n24 291: 54 n25 301–4: 45 n7 309–21: 201 n18 312 n10: 73 n11 313: 167 n49 340–1, n72: 73 n11 344: 167 n49, 202 n19 Ch. 4: 116 n52 Ch. 4, s 1: 135 n15

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1992: 313–14: 200 n11 “Aristotle on the Relation between a Thing and its Matter” (Scaltsas et al.) 63 n37 “Substance, Predication, and Unity in Aristotle” 529: 96 n3, 149 n3 “Aristotle on the Unity of Substance” 202 n17, 267 n23 “The Hitchhiker’s Guide to Metaphysics Zeta” 33 n48 63 n75: 225 n55 “Friend or Foe?: Some Encounters With Plato in Aristotle Metaphysics Zeta” 151 n9 Review of Burnyeat (2001) 91 n50 (2008) 10 n3, 44 n5, 60 n33, 215 n40, 292 n44 144–5: 61 n34 s 2: 61 n35 “Predication, Things, and Kinds in Aristotle’s Metaphysics” 44 n5, 215 n40, 230 n62 s 2: 233 n69 A. C. Lloyd “The Principle That the Cause is Greater Than the Effect” 157 n25, 168 n50 Michael J. Loux 1979: 230 n63 18: 230 19: 230 1984: 234 n70 Primary Ousia: An Essay on Aristotle’s Metaphysics Z and H 230 n63 132–3: 234 n70 132–5: 234 n70 Ch. 3: 96 n3, 153 n14 Ch. 7: 149 n3 “Composition and Unity” (Sim) 202 n17 Gareth Matthews 1982: 10 n3 “Aristotelian Essentialism” 256–7: 141 n23 259, n7: 71 n6 “Aristotle on Existence” 211 n30 Tim Maudlin “Substances and Spacetime: What Aristotle Would Have Said to Einstein” 62 n36 G. E. L. Owen “Logic and Metaphysics in Some Earlier Works of Aristotle” (During and Owen) 166, n. 7: 98 n7 173: 91 n50

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“Plato on Not-being” (Nussbaum) 249: 54 n23 “Particular and General” (Nussbaum) 12 n7, 15 n13 Gunther Patzig “Logical Aspects of Some Arguments in Aristotle’s Metaphysics” (Aubenque) 134 Francis Jeffrey Pelletier “Sameness and Referential Opacity in Aristotle” 289: 153 n15 Michail Peramatzis “Essence and Per Se Predication in Aristotle’s Metaphysics Z4” 29 n34, 72 n7, 78 n24, 89 n47 47–9: 74 n13 Priority in Aristotle’s Metaphysics 70 n1 E. W. Prior , R. Pargetter, and F. Jackson “Three Theses about Dispositions” 291 n44 Plato Parmenides 131b1–2: 247 n3 147 de: 251 n9 Physics 2, 194a20–1: 301 n11 2, 209b7–11: 54 n25 3, 194b26–9: 301 n11 Alpha A1, 184a26–b13: 176–7 A3, 186b18–23: 79 n26 A7, 191a19–20: 46, 47 Beta B1, 193a5: 50 n17 B1, 193a14–28: 47 n11 B1, 193a29: 47 B1, 193a21–26: 45, 47 B1, 193a30–31, b3–5: 1 n2 B1, 193b1–3: 301 n11 B1, 193b5–6: 47 B1, 193b6–7: 46 B2, 193b31–194a7: 179 n5 B9, 192a31–2: 182 n10 Gamma G3, 202b4–6: 129 n2 G3, 202b14–16: 116 n52, 135 n15, 144 n28, 171 n57 Delta D1, 209a4–6: 54 n25 Eta H4, 248b7–10: 98 n6 Theta ¨4, 255a34–b1: 290 n40 Republic IV 435a5–8: 111 n39

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Plato (cont.) Theaetetus 209aff: 255 n2 Richard Rorty “Genus as Matter: A Reading of Metaphysics Z-H” 22 n25 393–4: 295 W. D. Ross Aristotle’s Metaphysics I: 48 n12 I, xv: 19 n23 I, xcv, n. 1: 75 n16, 142 n24 I, xcix: 104 n22, 148 I, lxxvii, xciv: 32 n43 II: 84, 90 n48, 298 n1 II, 168: 80 n30, 104 n22, 104 n23 II, 169: 169 n54 II, 174: 101 n12, 101 n14, 106 n29 II, 177: 148, 150 n6, 155 n19, 165 n45 I, 178: 159 n36, 169 n54, 171 n56 II, 196: 178 II, 209: 24 n28 II, 210: 202 n19, 210 n32 II, 212: 247 n3, 249 n8 II, 215–16: 255 n2, 256 n3 II, 222–3: 303 n16 II, 227: 298 n3 (1949) 70–1: 48 n13 519: 79 n26 574: 93 610: 284 n25 612: 285 n31 638: 282 n23 Alber Schwegler Die metaphysik des Aristoteles I–IV IV, 43: 51 n20 IV, 115–16: 213 n36 Donald E. Stahl “Stripped Away: Some Contemporary Obscurities Surrounding Metaphysics Z3 (1029a10–26)” 55 n27, 56 n27

J. Van Cleve “Three Versions of the Bundle Theory” 99–100: 61 n34 Julie K. Ward Aristotle on Homonymy: Dialectic and Science 91 n50 Anders Wedberg Plato’s Philosophy of Mathematics 30–1: 251 n9 Michael Wedin (1973) n. 9: 79 n26 Aristotle’s Theory of Substance: The Categories and Metaphysics Zeta 30 n36, 33 n48, 151 n9 35–6: 10 n2 202–3: 123 n72 221–7: 123 n69 230–47: 85 n37, 90 n49 264–5: 71 n4, 130 n7 276: 130 n9 278: 130 n9 282–3: 71 n4, 130 n7 407, n. 3: 273 n1 414: 284 n31 415: 289 420 n. 18: 281 n18 423: 288 423–4: 284 n31 426–7: 299 n7 Ch. VII: 149 n2 Nicholas P. White “Origins of Aristotle’s Essentialism” 60: 141 n23 Michael Woods “Substance and Essence in Aristotle” 104 n23 173–4: 80 n31