As Aristotle proceeds in his criticism of division (Parts of Animals 642b ff.), he indirectly illuminates a methodological point about how the ‘branches’ of the tree of the division are supposed to work.  When we have a given animal before us, we first might determine what it has: feet.  Thus we have some first genus (footed) from which we can have differentiae.  These differentiae might be two-footed and four-footed, as in his example.

What this shows is that this process is empirically based on two counts.  The first is that  the divider is aware of a given animal in both what it possesses and what it is.  Secondly, there is a contextual awareness of the animals that are alike, in some way, to this animal.  In other words, the would-be divider knows that there are no one-footed or 563-footed animals.  How does he know this?  By experience.

There might even be an allowance on Aristotle’s part that there is a kind of wisdom of the crowd in understanding animal divisions.  He says that the “bird and the fish are named,” but adds that others “are nameless, such as the blooded and unblooded [animal] (642b14-15).  If this is so, it is reasonable to believe that Greeks, from Aristotle’s perspective, have got it right with regards to birds and fish due to generations of people having seen various birds and fish.  There is thus a kind of group empirical gathering of facts.

This emphasis on the actual is also why, it turns out, that Aristotle says there can be no privations in divisions.  “And yet it is necessary to divide by privation and the dichotomists do divide by privation. But there is no difference of privation qua privation: it is impossible for there to be a species of something that does not exist, such as footless or wingless in the same way there is of winged and footed” (PA 642b21-24 Greek follows below).  This is another indication that for Aristotle, a proper division is always empirically based, since one cannot go out and find footless animals.  What he means by this is that the animal will not have “footless” as part of its definition or essence.  Now of course, a slug, for example, is without feet, but it is also without feathers, and this hardly seems worthy of being remarked upon, much less to make it an opportunity for division.  Thus another way of stating why to exclude privation: whatever privation we choose to divide by certainly is vulnerable to the charge of being arbitrary.  For every animal is deprived of many attributes and features.

Ἔτι στερήσει μὲν ἀναγκαῖον διαιρεῖν, καὶ διαιροῦσιν οἱ
διχοτομοῦντες. Οὐκ ἔστι δὲ διαφορὰ στερήσεως ᾗ στέρησις· ἀ-
δύνατον γὰρ εἴδη εἶναι τοῦ μὴ ὄντος, οἷον τῆς ἀποδίας ἢ τοῦ
ἀπτέρου ὥσπερ πτερώσεως καὶ ποδῶν. (PA 642b21-24)