Once more, if the individual man or horse are Essences, nothing which is in the definition of these can be Essence; nor apart from that of which it is Essence; nor in any thing else. There cannot be any man, apart from individual men (p. 1038, b. 34).
Hence we see clearly that none of the universal predicates are Essence: none of them signify Hoc Aliquid, but Tale. To suppose otherwise, would open the door to many inadmissible consequences, especially to the argument of the ‘Third Man’ (p. 1039, a. 2).
Another argument to the same purpose:— It is impossible that Essence can be composed of different Essences immanent in one Entelechy. Two in the same Entelechy can never be One in Entelechy. If indeed they be two in potentiâ, they may coalesce into one Entelechy, like one double out of two potential halves. But Entelechy establishes a separate and complete existence (p. 1039, a. 7); so that, if Essence is One, it cannot be made up of distinct Essences immanent or inherent. Demokritus, who recognized only the atoms as Essences, was right in saying, that two of them could not be One, nor one of them Two. The like is true about number, if number be, as some contend, a synthesis of monads. For either the dyad is not One; or else the monads included therein are not monads ἐντελεχείᾳ (a. 14).
Here however we stumble upon a difficulty. For, if no Essence can be put together out of Universals, nor any compound Essence out of other Essences existing as Entelechies, all Essence must necessarily be simple and uncompounded, so that no definition can be given of it. But this is opposed to every one’s opinion, and to what has been said long ago, that Essence alone could be defined; or at least Essence most of all. It now appears that there can be no definition of Essence, nor by consequence of any thing else. Perhaps, however this may be only true in a certain sense: in one way, definition is possible; in another way, not. We shall endeavour to clear up the point presently (p. 1039, a. 22. — Schwegler says in his note upon this passage: “Die von Aristoteles häufig berührte, doch nie zur abschliessenden Lösung gebrachte, Grundaporie des aristotelischen Systems� — Comm. II. p. 117).
Those who maintain that Ideas are self-existent are involved in farther contradictions by admitting at the same time that the Species is composed out of Genus and Differentia. For, suppose that these Ideas are self-existent and that αὐτοζῷον exists both in man and horse: αὐτοζῷον is, in these two, either the same or different numerically. It is, of course, the same in definition or notion (λόγῳ); of that there can be no doubt. If it be numerically same (ὥσπερ σῦ σαυτῷ) in man and in horse, how can this same exist at once in separate beings, unless we suppose the absurdity that it exists apart from itself (p. 1039, b. 1)? Again, are we to imagine that this generic Ens, αὐτοζῷον, partakes at the same time of contrary differentiæ — the dipod, polypod, apod? If it does not, how can dipodic or polypodic animals really exist? Nor is the difficulty at all lessened, if, instead of saying that the generic Ens partakes of differentiæ, you say that it is mixed with them, or compounded of them, or in contact with them. There is nothing but a tissue of absurdities (πάντα ἄτομα — b. 6).
But take the contrary supposition and suppose that the αὐτοζῷον is numerically different in man, horse, &c. On this admission, there will be an infinite number of distinct beings of whom the αὐτοζῷον is the Essence; man, for example, since animal is not accidental, but essential, as a constituent of man (p. 1039, b. 8). Αὐτοζῷον will thus be Many (“ein Vielerleiâ€� — Schwegler); for it will be the Essence of each particular animal, of whom it will be predicated essentially and not accidentally (οὐ γὰρ κάτ’ ἄλλο λέγεται — i.e., this is not a case where the predicate is something distinct from the subject). Moreover all the constituents of man will be alike Ideas (e.g., not merely ζῷον, but δίπουν): now the same cannot be Idea of one thing and Essence of another; accordingly, αὐτοζῷον will be each one of the essential constituents of particular animals (δίπουν, πολύπουν, b. 14).
Again, whence comes αὐτοζῷον itself, and how do the particular animals arise out of it? How can the ζῷον which is Essence, exist apart from and alongside of αὐτὸ τὸ ζῷον? (p. 1039, b. 15.)
These arguments show how impossible it is that there can exist any such Ideas as some philosophers affirm (p. 1039, b. 18).
We have already said that there are two varieties of Essence: (1) The Form alone, (2) The Form embodied in Matter. The Form or Essence in the first meaning, is neither generable nor destructible; in the second meaning it is both. Τὸ οἰκίᾳ εἶναι is neither generable nor destructible; τὸ τῇδε τῇ οἰκίᾳ εἶναι is both the one and the other (p. 1039, b. 25). Of these last, therefore, the perceivable or concrete Essences, there can be no definition nor demonstration, because they are implicated with Matter, which is noway necessary, or unchangeable, but may exist or not exist, change or not change. Demonstration belongs only to what is necessary; Definition only to Science, which cannot be to-day Science and to-morrow Ignorance. Neither Science, nor Demonstration, nor Definition, applies to such things as may be otherwise: these latter belong to Opinion (τοῦ ἐνδεχομένου ἄλλως ἔχειν — p. 1040, a. 1). You cannot have Science or Demonstration or Definition about particular or perceivable things, because they are destroyed and pass out of perception, so that you do not know what continues to be true about them; even though you preserve the definition in your memory, you cannot tell how far it continues applicable to them (a. 7). Any definition given is liable to be overthrown.
Upon the same principle, there cannot be any definition of the Platonic Ideas; each of which is announced as a particular, distinct, separable, Ens (p. 1040, a. 8). The definition must be composed of words — of the words of a language generally understood — and of words which, being used by many persons, are applicable to other particulars besides the definiend (you define Alexander as white, thin, a philosopher, a native of Aphrodisias, &c., all of which are characteristics applicable to many other persons besides). The definer may say that each characteristic taken separately will apply to many things, but that the aggregate of all together will apply to none except the definiend. We reply however, that ζῷον δίπουν must have at least two subjects to which it applies — τὸ ζῷον and τὸ δίπουν. Of course this is all the more evident about eternal Entia like the Platonic Ideas, which are prior to the compound and parts thereof (ζῷον and δίπουν are each prior and both of them parts of αὐτοάνθρωπος), and separable, just as αὐτοάνθρωπος is separable (a. 14-20); for either neither of them is separable, or both are so. If neither of them is separable, then the Genus is nothing apart from the Species, and the Platonic assumption of self-existent Ideas falls to the ground; if both are separable, then the Differentia is self-existent as well as the Genus (a. 21): there exist some Ideas prior to other Ideas. Moreover, the Genus and Differentia, the component elements of the Species, are logically prior to the Species: suppress the Species, and you do not suppress its component elements; suppress these, and you do suppress the Species (a. 21). We reply farther that, if the more compound Ideas arise out of the less compound, the component elements (like ζῷον δίπουν) must needs be predicable of many distinct subjects. If this be not so always, how are we to distinguish the cases in which it is true from those in which it is not? You must assume the existence of some Idea which can only be predicated of some one subject, and no others. But this seems impossible. Every Idea is participable (a. 27).