Bryn Mawr Classical Review

Bryn Mawr Classical Review 2002.03.44

Myles Burnyeat, A Map of Metaphysics Zeta.   Pittsburgh:  Mathesis Publications, 2001.  Pp. x + 176.  ISBN 0-935225-03-X.  

Reviewed by Mohan Matthen, Department of Philosophy, The University of British Columbia, Vancouver (

"Metaphysics Zeta has been aptly described as the Mount Everest of ancient philosophy." So begins this brilliant book, which undertakes the project of constructing a trail to the peak, amply furnished with rest areas and view-points and with rewards for the frequent climber. Until now, fearsomeness has been a part of Zeta's appeal. Confident young metaphysicians set out bravely to the peak through snow flurries, advancing with steady steps, using the very latest equipment. They disappear and are never heard from again, though there are rumours of them living in exile, preparing editions in foreign languages. Myles Burnyeat wants to change all of this. His project is to make Metaphysics Zeta no more difficult to traverse than any other contested work -- Nicomachean Ethics I, for instance. It will still be possible to disagree about the details of the argument and the validity of the conclusions, but the route to the peak, and the peak itself, will be almost completely clear.

Burnyeat proposes the following interpretive schema.

(A) Zeta consists of five parts, (1) an introduction to the problem in chapters 1 and 2, (2) chapter 3, (3) chapters 4-12, (4) chapters 13-16, and (5) chapter 17.

(B) Each of these parts (aside from the introduction) starts afresh from a different proposal of what substantial being (as οὐσία is translated) is: respectively, that it is subject, essence, universal, and genus.

(C) At the start of each section, Aristotle proceeds λογικῶς. That is, he invokes "only concepts familiar from the Organon: substantial being, essence, definition, subject and predicate, species and genus, universal and particular, the categories" [p. 8].

(D) The next stage in each section consists of "metaphysical" discourse. These subsections "presuppose familiarity with the role of form and matter as omnipresent principles of explanation in the study of nature," though in first philosophy we focus on nature not so much as a principle of change, but as a principle of being for natural things.

(E) Each section arrives by an independent route at the conclusion that substantial being is form. (Henceforth, I'll label this thesis SBF.)

The distinction between logical and metaphysical discourse is important. The extension of this distinction is clear: in metaphysical discourse, but not in logical, substance is analysed into form and matter. What is the intent and origin of this distinction? This is controversial. The account I prefer is a little different from Burnyeat's, and I'll start by explaining it in my terms.

In the first five chapters of the Categories, Aristotle discusses substance in the context of a logical and conceptual analysis of a restricted corpus of fact-structures, namely those that consist of a subject possessing a predicable at a moment -- these facts are expressed by sentences that use the static copula "is," sentences like "The man is pale," "Socrates is a man," The man is seated," and so on. Change is discussed in this work but only in these static terms: "numerically one and the same substance is able to receive contraries," he says, thus defining change in terms of a pair of momentary facts, expressed by the pair of sentences, "X is F" and "X is contrary-to-F," obtaining at different times. As a result of his analysis of this corpus of static facts, Aristotle arrives at the conception of individual substance as the subject required for the existence of everything else.

In Physics I 7, Aristotle turns his attention to a different corpus of fact-structures, namely those expressed by sentences expressed in terms of the kinetic copula "becomes," sentences like "The man becomes musical," "What is not-musical becomes musical," and "The not-musical man becomes a musical man." Now, the syntactic parallels between 'be' and 'become' are well known, but the underlying semantic connection is more controversial.1 According to one theory, becoming is subordinate to being in exactly the way implied in Categories 5. To quote Kahn, "as Jesperson saw: X becomes Y presupposes X was not Y and implies X will be Y" (ibid, p. 205). According to another theory (with which I am in greater sympathy), the semantic content of 'becomes' cannot be reduced to that of 'is'. However this may be, what is interesting about Aristotle's analysis of the facts expressed by the kinetic copula is that their subjects are not all the same as those of static facts. The ultimate subjects of static facts, as revealed by the Categories analysis, are individual substances; dynamic facts have subjects that go below the unity of these substances, and this reveals the predicative sub-structure of substances. Aristotle's analysis of kinetic facts in Physics I 7 thus leads him to regard individual substance as composite, that is, as composed of matter and form. These two components of substance are held together by a predicative link; form is predicated of matter within composite substance.

In Physics I 7, the predicative link in question is kinetic. Having revealed it in this way, Aristotle then extends the matter-form analysis to static predications. For example, in De Anima II 1, form is predicated of matter in a non-kinetic context. Thus, the hylomorphic analysis is brought into the domain of first philosophy. But there are notoriously sticky difficulties here: since an animal's body is not a substrate for the process by which it comes to be, it is unclear how the kinetic analysis of matter and form can be smoothly transferred to the De Anima II 1 discussion of soul and actuality. In Zeta, Aristotle acknowledges these difficulties by making a distinction: "There are two ways in which something can underlie as subject: as a "this", in the way that an animal underlies its attributes, or in the way that matter underlies the actuality" (Z 13, 1038b4-6).

Elementary though they are, these remarks have consequences a little at odds with Burnyeat's conclusions, though largely friendly to them.

I. The distinction between "logical" and "physical" (or "metaphysical") discourse does not rest on distinct methodological stances. Burnyeat argues that logical discourse is "content-neutral" and preliminary, completely concerned with the methodology of argumentation, whether demonstrative or dialectical. It is only when Aristotle broaches the content-specific questions of physics that matter and form enter the picture. This, according to Burnyeat, is why form and matter occur only in metaphysical discourse.

But, as I see it, Aristotle does not adopt, in Physics I 7, a less analytic, more content-specific stance than he takes up in logical discourse. As I see it, Categories achieves a result perfectly parallel to that of I 7: the former finds substance to be a subject of "is," and the latter finds the persisting substrate, or matter, to be similarly a subject of "becomes."2 The difference between the discourse of Physics I 7 and that of the Organon lies, I would contend, in the corpus of facts being analysed, not in the method used. (Significantly, Burnyeat says that he starts introductory survey courses on Aristotle with Physics I 7 as an alternative to the Categories [p. 113].) The introduction of the kinetic copula compels an acknowledgement of the predicative component structure of individual substance and in particular of matter and form. Of course, Physics I-II does discuss certain dialectical principles appropriate to the kinetic context -- for instance, the ex nihilo principle, and the dictum that what happens always or for the most part cannot be due to chance. Of course, these principles are not mentioned in the Organon. But (a) the introduction of matter in I 7 does not depend on these principles, and in any case (b) they are not really content-specific: they hold right across the domain of things that are, and the components of substance that they force us to acknowledge help us understand even the non-sensible, unchanging substance, God.

II. The results of physical discourse are compatible (as Burnyeat rightly insists) with those of logical discourse. To say that individual substance is composite is not to undermine the claim that it is the subject for everything else (including its components). Thus, there is no reason to believe that the Categories belongs to an earlier phase of Aristotle's development, in which he has not yet discovered matter and form. (After all, Plato, and others like Philolaus and Empedocles, had already discovered matter and form: "Aristotle sees the rudiments of a two-factor analysis outside as well as inside the Academy. He does not claim originality for his type of analysis, only that he does it better than other people" [p. 96].) Nor should we think that in Metaphysics Z 3 the hylomorphic analysis leads to a reversal of the "logical" doctrine of substance.

However, the conception of individual substance as subject does impose constraints on the hylomorphic account of substance, for it has the consequence that form and matter be predicated in some way of the composite in addition to form being predicated of matter. As noted above, this raises notoriously knotty problems of ontological priority. Burnyeat rightly says, "Aristotle's view [is] that form or actuality must first be predicated of some matter to constitute a substantial being and this then serves as subject for predicates in the dependent categories" (p. 45; cf. Z 3, 1029a23-24). But this raises difficulties: what does "first...then" mean? Does it imply that matter is, in some sense, prior to form, i.e., to substantial being? (It had better not have this consequence!) When Aristotle discovered that dynamic facts have substance-components as subjects, he must have had to revise a great many of his thoughts about metaphysics. It is striking that the Organon did not have to be revised as a consequence to include discussions of form and matter. This is very much in line with Burnyeat's take on the role of logical discourse in the corpus as a whole, namely, that it is preparatory to physics and metaphysics. It also agrees with what I have said above, namely, that it takes an analysis of the kinetic copula to reveal matter and form, which are then recognized in discussions of first philosophy. The only amendment that I would make to Burnyeat's way of looking at the matter is to suggest that Physics I 7 is also preparatory, also "logical." Metaphysical discourse is distinguished not by the occurrence of matter and form as such but by the occurrence of these concepts in contexts defined by the static copula.

Despite the relatively minor disagreement related above, I found Burnyeat's treatment of the logical/metaphysical distinction in chapter 5 enthralling to read and extremely illuminating. He presents us with a largely original and (to me) almost completely convincing account of the relationship between the logical treatises and Aristotle's metaphysics. Readers should take special note of his defence of the view that almost all of the Corpus Aristotelicum is a simultaneous utterance, each part in constant revision as other parts get written and revised. I had heard bits of this view in conversation before: I cannot say that I found it even slightly moving. After having read chapter 5, I find it compelling. Developmental accounts of Aristotle's philosophy will need to start afresh and recheck their evidence at just about every point.

III. The above analysis of metaphysical discourse leads us to the following account of a problem addressed by Z-H-Θ. Individual substance consists of form predicated of matter. But not every predicable that belongs to a material substrate constitutes a new substance over and above the substrate. Thus, a piece of matter could be reshaped in certain ways, put in a new position, painted, put into motion, etc. without a new substance coming to be -- a lump of matter could receive these predicables, and just stay itself. Only a few predicables, then, are going to be substance-making. What sort of predicable is substance-making? This is the question Aristotle means to ask when he asks what ousia is. The answer is form: this is the SBF thesis.

What kind of predicable is form? This question is discussed further in Book H, and a highly technical answer is offered there: form is actuality. But a simpler answer (an answer from second-philosophy, as Burnyeat says [p. 129]) is also available. Aristotle implicitly links form, at least in the sensible realm, to nature, as nature is defined in Physics II. Nature is an innate principle of change or stasis. It follows that if matter acquires a predicable which gives the composite an innate principle of change over and above that which is present in its matter, then a new substance has been created. Form, then, is something predicated of matter that results, in virtue of that predication, in an entity with a new innate principle of change. Or at least this is what the form of sensible substance is.

What counts as an innate principle of change over and above that which is present in matter? With regard to substance-making predicates, Burnyeat sets the bar very high. He says, "Of the candidates for substantial being enumerated in Z 2, the four elements and the parts of animals or plants will be disqualified in Z 16...The net result will be that within the sensible world only living organisms qualify as substantial beings" [p. 13]. In effect, the claim is that only soul counts as form and substantial being. This seems not quite right. In the first place, the οὐρανός and its parts -- i.e., the heavenly bodies -- are mentioned in Z 2, and they are not eliminated in Z 16. These are not living organisms. Secondly, Z 16, 1040b5-10 does eliminate the parts of animals but does not say that the elements are not substances in actuality. "Earth and fire and air" are allowed to be substances when they have been "worked up" and a unity is made out of them. What reason is there to think that an earthen sphere is not a unity of this sort? It is, after all, possible to hold that an earthen sphere has an innate principle of change that a mere lump of earth does not -- it rolls down a hill under the impetus of its own weight. It is certainly possible that Aristotle did not think of this and would have modified his conception of form if he had, but even if so, I think it is a mistake to interpret the definition of form to fit Aristotle's applications rather than his intentions. All in all, I would suggest that the conclusion, "Within the sensible world the base line of Aristotle's ontology is souls" (p. 56) needs adjustment. At a minimum, it needs to be noted that the "οὐρανός and its parts" are sensible substances but lack a soul.3

The central chapter of Burnyeat's book is devoted to "signposts," the divisions of the text in conformity with the schema outlined above. This is specialist work, in which fine details of the presentation are offered as indications of structure. I wonder how many people there are in the world who can just read this through without the help of a mountain of texts, editions, and commentaries -- in any case, I am not one of them. (Most will treat it as commentary, reading quickly through for the main points, and returning to it as the need arises -- while preparing for class, or in the context of some research project.) Much effort is invested in exposing indications in the text of how the logical parts of the exposition relate to the metaphysical. For example, Burnyeat discusses in considerable detail the pointers that connect the discussion in chapters 4-5 of the "logical" thesis that a thing is the same as its essence and the account in metaphysical terms in chapters 10-11 of the conditions under which the parts of a thing figure as parts of its definition. However, he does not, in the chapter on signposts at least, explain exactly how, in his own view, the discussion of parts of a defining formula (λόγος) in Z 10 sheds light on the discussion of the identity of essence and individual substance in Z 4-5. (That explanation comes only later, at pp. 83-86.) Generally speaking, the philosophical discussions in this book are (intentionally) abbreviated; most of it is devoted to "mapping" the text, and "a map deals with form rather than content" (p. 4).

A similar problem occurs with respect to Z 15. How does Burnyeat propose to explain Aristotle's use of the term λόγος Z 15 to denote form, in the context of a metaphysical discussion? (And it must denote form if these chapters are to be counted as metaphysical.) What he actually says is: "The use of the word λόγος for form is probably significant . . . [It] is to insist that substantial being as form can be defined" (p. 53). Perhaps, but the word εἶδος does not occur in Z 15-16 (except to denote species at 1040a20, and Platonic Forms later on), nor does the SBF thesis.

I'll end with praise for Burnyeat, and some criticism of the publisher. This is a wonderful book; it gives the Metaphysics, especially the central books, structure, context, and continuity. Some parts remain obscure (to me), but one can learn more from this small book than from any other work published on this subject in the last thirty years or so (with the exception of Frede and Patzig's commentary).

But why is it so poorly produced? True the paper and binding are good, but the design is very poor. The cover is ugly. The page lay-out is poor, with notes that snake about the foot of the page with unnecessarily deep tab settings. The Greek font does not flow with the English. Ideally, a book like this should lie flat; for, as I have said, most people will want to read it together with texts and other commentaries. The inside margins are too narrow, and it is difficult even to hold it open with one hand. Mathesis should get its act together.


1.   See the pellucid account in Charles Kahn, The Verb 'Be' in Ancient Greek (Dordrecht-Holland: Reidel, 1973), chapter 5.
2.   To complete the argument, one must establish that the Categories consists of logical discourse, not metaphysical. Burnyeat argues this thesis, pp. 106-108, citing a 1995 article by Stephen Menn as anticipating his argument. I rather wish he had been aware of my own very first publication, Matthen, "The Categories and Aristotle's Ontology," Dialogue XVII (1978): 228-43. It makes a similar point.
3.   For an exploration of the treatment of the οὐρανός as a sensible substance, see Mohan Matthen, "The Holistic Presuppositions of Aristotle's Cosmology," Oxford Studies in Ancient Philosophy, vol XX (Summer 2001): pp. 171-99.

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