Deep into his criticism of the dichotomist method of division, Aristotle and his opponents are deciding what genera and species of animals truly exist.  To discover these natural kinds of animals, the appropriate method of division, that is, a way of separating animals from each other into categories precisely representative of species, is under contentious dispute.

And yet it is necessary to divide by privation, and the dichotomists do divide [in this way].  But there is no difference of a privation qua privation.  For it is impossible for there to be species of what is not, for example of “non-footed” or of “non-winged” just as there are species of “footed” and “winged.”  Furthermore it is necessary that species belong to a generic difference.  For if they do not, why would they belong to a generic difference and not a specific difference? (Aristotle, Parts of Animals, 642b21-26).(1)

Some say that species should be divided into two with each of the two branches always branching off into two more, until the point where a termination results in an actual species.  For example, if we begin by dividing animals into footed and non-footed, and then the footed into bi-pedal and poly-pedal, we can then divide bi-pedal into split-toed and web-toed, etc.  Advocates of this process of dichotomy are called dichotomists.

Aristotle, on the other hand, advocates opening more than one line of division, not limiting himself to the dichotomist method which follows only one of two branches at every step.  In this section of the text, Aristotle, believing that dichotomists commit themselves to “privation” as well, argues that privation is incompatible with dichotomy.  By privation Aristotle simply means a negation of some difference, such as in the example above, “non-footed” as contrasted with “footed.”  The privation objection demonstrates Aristotle’s characteristic subtlety and insight as he, perhaps ironically, forces his opponents into a logical dichotomy: Either the privation is an actual species of animal or it is not, and further division must continue.

Now if we continue with the first option, that there is an actual species of privative animal, say, non-footed, then this seems precluded for the following reasons.  Most obviously, something which is not cannot be said to be.(2) It is also the case that being non-footed would not pick out a species, as it could generically apply to a worm, a whale and a snake, not to mention the variations of each animal.  And yet, even if it were that case that “non-footed” faithfully picked out only a single animal (pretend that earthworms are the only non-footed animals), it is unclear how non-footed is an essential property of earthworms.  After all, earthworms are also furless, wingless, knuckle-less, eyelash-less, and money-less, to name just a few things.

On the other hand, if the privation is not a species, but must be further divided, then Aristotle clearly precludes this possibility in the above text.  Why this is so is unclear, but I will have a preliminary answer in the next post, as well as offer up a Platonic solution which could perhaps stand up under Aristotle’s scrutiny.

REFERENCES:

(1)
Translation mine:
Ἔτι στερήσει μὲν ἀναγκαῖον διαιρεῖν, καὶ διαιροῦσιν οἱ
διχοτομοῦντες. Οὐκ ἔστι δὲ διαφορὰ στερήσεως ᾗ στέρησις·
ἀδύνατον γὰρ εἴδη εἶναι τοῦ μὴ ὄντος, οἷον τῆς ἀποδίας ἢ τοῦ
ἀπτέρου ὥσπερ πτερώσεως καὶ ποδῶν. Δεῖ δὲ τῆς καθόλου δια-
φορᾶς εἴδη εἶναι· εἰ γὰρ μὴ ἔσται, διὰ τί ἂν εἴη τῶν καθόλου
καὶ οὐ τῶν καθ’ ἕκαστον;

(2)
I assume A. would approve this, for he says something logically analogous in the case where we suppose that privations are divided into further species.