Another reasonable doubt arises here (ἀπορεῖται δ’ εἰκότως — p. 1036, a. 26) as to which parts belong to the Form alone, which to the entire Concrete. Unless this be made clear, we can define nothing; for that which we define is the Universal and the Form, and, unless we know what parts belong to the Matter and what do not, the definition of the thing can never be made plain (a. 30). Now, wherever the Form is seen to be superinduced upon matters diverse in their own Form, the case presents no difficulty: every one sees circles in brass, stone, wood, &c., and is well aware that neither the brass, nor the stone, belongs to the Form or Essence of the circle, since he easily conceives a circle without either. But, if a man had never seen any circles except brazen circles, he would have more difficulty in detaching mentally the circle from the brass, and would be more likely to look upon brass as belonging to the Form of circle; although, in point of fact, he would have no more logical ground for supposing so than in the case just before supposed; for the brass might still belong only to the Matter of circle (b. 2). This is the case with the Form of man. It is always seen implicated with flesh, bones, and such like parts. Are these parts of the Form of man? Or are they not rather parts of the Matter, though we are unable to conceive the Form apart from them, because we never see it in conjunction with any other Matter? This is at least a possibility, and we cannot see clearly in what cases it must be admitted. Some theorists are so impressed by it as to push the case farther, and apply the same reasoning to the circle and triangle. These theorists contend that it is improper to define a circle and a triangle by figure, lines, continuity, &c., which (they affirm) are only parts of the Matter of circle and triangle; as flesh and bones are parts of the Matter of man. They refer all of them to numbers as the Form, and they affirm that the definition of the dyad is also the definition of a line (b. 12). Among the partisans of Ideas, some call the dyad αὐτογραμμή others call it the Form of a line; saying that in some cases the Form and that of which it is the Form are the same, as the dyad and the Form of the dyad, but that this is not true about line. (These two opinions seem to be substantially the same, and only to differ in the phrase. Αὐτογραμμή means the same as τὸ εἶδος τῆς γραμμῆς: it seems to have been a peculiar phrase adopted by some Platonists, but not by all. Others preferred to say τὸ εἶδος τῆς γραμμῆς.) These reasonings have already misled the Pythagoreans, and are likely to mislead others also: they would conduct us to the recognition of one and the same Form in many cases where the Form is manifestly different: they lead us even to assume one single Form universally, reducing every thing besides to be no Form, but merely Matter to that one single real Form. By such reasoning, we should be forced to consider all things as One (b. 20), which would be obviously absurd.
We see from hence that there are real difficulties respecting the theory of Definition, and how such difficulties arise. It is because some persons are forward overmuch in trying to analyse every thing and in abstracting altogether from Matter; for some things include Matter along with the Form, or determined in a certain way, i.e., this along with that, or these things in this condition (p, 1036, b. 22). The comparison which the younger Sokrates was accustomed to make about the animal is a mistaken one (b. 24): it implies that man may be without his material parts, as the circle may exist without brass. But this analogy will not hold; animal is something perceivable by sense and cannot be defined without motion; of course, therefore, not without bodily members organized in a certain way (b. 30). The hand is not a part of man, when it is in any supposable condition, but only when it can perform its functions, that is, when it is animated; when not animated, it is not a part (b. 32). Clearly the soul is the first Essence or Form, the body is Matter, and man or animal is the compound of both as an Universal; while Sokrates, Koriskus &c., are as particulars to this Universal, whether you choose to take Sokrates as soul without body, or as soul with body (p. 1037, a. 5-10: these words are very obscure).
Respecting Mathematical Entia, why are not the notions of the parts parts of the notion of the whole? e.g., why is not the notion of a semi-circle part of the notion of a circle? Perhaps it will be replied that this circle and semi-circle are not perceivable by sense: but this after all makes no difference; for some things even not perceivable by sense involve Matter along with them, and indeed Matter is involved in every thing which is not τ.η.ε. and Form αὐτὸ καθ’ αὑτό. The semi-circles are not included as parts of the notion of the universal circle; but they are parts of each particular circle: for there is one Matter perceivable and another cogitable (p. 1036, a. 34. — Bonitz remarks that these words from p. 1036, a. 22 to p. 1037, a. 5, are out of their proper place). Whether there be any other Matter, besides the Matter of these Mathematical Entia, and whether we are to seek a distinct Form and Essence for them — such as numbers, must be reserved for future enquiry. This has been one of our reasons for the preceding chapters about perceivable Essences; for these last properly belong to the province of Second Philosophy — of the physical theorist (τῆς φυσικῆς καὶ δευτέρας φιλοσοφίας ἔργον — p. 1037, a. 15). The physical philosopher studies not merely the Matter, but the Form or notional Essence even more (a. 17).
We are now in a position to clear up what was touched upon in the Analytica (Anal. Poster. II. p. 92, a. 27; also, De Interp. v. p. 17, a. 13), but not completed, respecting Definition. How is it that the definition is One? We define man animal bipes: How is it that this is One and not Many? Man and white are two, when the latter does not belong to the former: when it does so belong to and affects the former, the two are One — white man (p. 1037, b. 16): that is, they are One κατὰ πάθος. But the parts included in the definition are not One κατὰ πάθος, nor are they one κατὰ μέθεξιν; for the Genus cannot be said to partake of the Differentiæ. If it did, it would at one and the same time partake of Opposita, for the Differentiæ are Opposita to each other. And, even if we say that the Genus does partake of the Differentiæ, the same difficulty recurs, when the Differentiæ are numerous. The Genus must partake alike and equally of all of them; but how is it that all of them are One, and not Many? It cannot be meant that all of them belong essentially to the thing; for, if that were so, all would be included in the definition, which they are not. We want to know why or how those Differentiæ which are included in the definition coalesce into One, without the rest: for we call the definiend ἕν τι καὶ τόδε τι (b. 27).
In answering this question, we take, as a specimen, a definition which arises out of the logical subdivision of a Genus (p. 1037, b. 28). Definition is given by assigning the Genus and Difference: the Genus is the Matter, the Difference is the Form or Essence; the two coalesce into one as Form and Matter. In the definition of man — animal bipes — animal is the Matter and bipes the Form; so that the two coalescing form an essential One. It does not signify through how many stages the logical subdivision is carried, provided it be well done; that is, provided each stage be a special and appropriate division of all that has preceded. If this condition be complied with, the last differentia will include all the preceding, and will itself be the Form of which the genus serves as Matter. You divide the genus animal first into ζῷον ὑπόπουν — ζῷον ἀποῦν; you next divide ζῷον ὑπόπουν into ζῷον ὑπόπουν δίπουν — ζῷον ὑπόπουν πολύπουν; or perhaps into ζῷον ὑπόπουν σχιζόπυν — ζῷον ὑπόπουν ἄσχιστον. It is essential that the next subdivision applied to ζῷον ὑπόπουν should be founded upon some subordinate differentia specially applying to the feet (p. 1038, a. 14: αὗται γὰρ διαφοραὶ ποδός· ἡ γὰρ σχιζοποδία ποδότης τις). If it does not specially apply to the feet, but takes in some new attribute (e. g., πτερωτόν, ἄπτερον), the division will be unphilosophical. The last differentia ζῷον δίπουν includes the preceding differentia ὑπόπουν: to say ζῷον ὑπόπουν δίπουν would be tautology. Where each differentia is a differentia of the preceding differentiæ, the last differentia includes them all and is itself the Form and Essence, along with the genus as Matter (a. 25). The definition is the rational explanation arising out of these differences, and by specifying the last it virtually includes all the preceding (a. 29: ὁ ὁρισμὸς λόγος ἐστὶν ὁ ἐκ τῶν διαφορῶν, καὶ τούτων τῆς τελευταίας κατά γε τὸ ὀρθόν).
In the constituents of the Essence, there is no distinctive order of parts; no subordination of prius and posterius; all are equally essential and coordinate (τάξις δ’ οὐκ ἔστιν ἐν τῇ οὐσίᾳ — p. 1038, a. 33).
As we are treating now about Essence, it will be convenient to go back to the point from which we departed, when we enumerated the four varieties recognized by different philosophers. These were (1) The Subject — Substratum — Matter, which is a subject of predicates in two different ways: either as already an Hoc Aliquid and affected by various accidents, or as not yet an Hoc Aliquid, but simply Matter implicated with Entelechy (p. 1038, b. 6); (2) Form — Essence — the τ.η.ε.; (3) The Compound or Product of the preceding two; (4) The Universal (τὸ καθόλου). Of these four, we have already examined the first three; we now proceed to the fourth.
Some philosophers consider the Universal to be primarily and eminently Cause and Principle (p. 1038, b. 7). But it seems impossible that any thing which is affirmed universally can be Essence. For that is the First Essence of each thing which belongs to nothing but itself; but the Universal is by its nature common to many things. Of which among these things is it the Essence? Either of all or of no one. Not of all certainly; and, if it be the Essence of any one, the rest of them will be identical with that one; for, where the Essence is one, the things themselves are one (b. 15). Besides, the Essence is that which is not predicated of any subject: but the Universal is always predicated of a subject.
Perhaps, however, we shall be told, that the Universal is not identical with τ.η.ε., but is Essence which is immanent in or belongs to τ.η.ε., as animal in man and horse. But this cannot be admitted. For, whether we suppose animal to be definable or not, if it be essence of any thing, it must be the essence of something to which it belongs peculiarly, as homo is the essence of man peculiarly; but, if animal is to be reckoned as the essence of man, it will be the essence of something to which it does not peculiarly belong; and this contradicts the definition of Essence (p. 1038, b. 15-23. This passage is very obscure, even after Bonitz and Schwegler’s explanatory notes. I incline to Schwegler, and to his remark, Comm. II. p. 115, that the text of b. 23 ought to be written ἐν ᾧ μὴ ὡς ἴδιον ὑπάρχει.).
Again, it is impossible that Essence, if composed of any elements, can be composed of what is not Essence, as of Quality; for this would make Quality prius as regards Essence; which it cannot be, either in reason (λόγῳ), or in time, or in generation. If this were so, the affections would be separable from Essences (p. 1038, b. 28). Essence, if composed of any thing, must be composed of Essence.