I would like to continue writing about the problems Aristotle sees in certain kinds of Platonic division.  In this particular section of Parts of Animals, Aristotle continues to focus on the notion of privation in bifurcatory division, that is, when animals are divided into a category such as wingless (i.e. a privation of wings) and winged.  First we will look at the text:

There are differences of the general kind and they have forms, such as winged.  For there are both unsplit and split wings.  And with regards to footedness also there is the many splitted, or the two splitted, such as the cloven-hoofed, and the uncloven and undivided, such as the single-hoofed animals.  And it is difficult to divide also into such differences of which there are species, so that whatever animal fits under these differences and the same animal does not fit among many animals (for example winged and unwinged.  For both [winged and unwinged] are the same animal [sometimes], for example an ant and a glowworm and some other animals [are both winged and unwinged.]  But it is most difficult of all or impossible to divide animals into bloodless.  For it is necessary for each of the differences to belong to one of the particular animals, so that its opposite also belongs to a particular animal.  And if it is impossible that one single form of essence (εἶδός τι τῆς οὐσίας ἄτομον καὶ ἕν) belongs to those animals differing in form (τοῖς εἴδει διαφέρουσιν) but that the form will always possess a difference (for example bird differs from man— for the two-footedness is other and different.  Even in the case of bloodedness, either the blood [of bird and man] differs or one must discount the blood as belonging to the essence) and if this is so, one difference will belong to two animals.  But if this is so, it is clear that it is impossible for a privation to be a [proper] difference (Aristotle, Parts of Animals, 642b30-643a6). ¹⁾Translation mine. 642b τῶν δὲ διαφορῶν αἱ μὲν καθόλου εἰσὶ καὶ ἔχουσιν εἴδη, οἷον πτερότης· τὸ μὲν γὰρ ἄσχιστον τὸ δ᾿ ἐσχισμένον ἐστὶ πτερόν. καὶ ποδότης ὡσαύτως ἡ μὲν πολυσχιδής, ἡ δὲ δισχιδής, οἷον τὰ δίχαλα, ἡ δ᾿ 30 ἀσχιδὴς καὶ ἀδιαίρετος, οἷον τὰ μώνυχα. χαλεπὸν μὲν οὖν διαλαβεῖν καὶ εἰς τοιαύτας διαφορὰς ὧν ἔστιν εἴδη, ὥσθ᾿ ὁτιοῦν ζῷον ἐν ταύταις ὑπάρχειν καὶ μὴ ἐν πλείοσι ταὐτόν (οἷον πτερωτὸν καὶ ἄπτερον· ἔστι γὰρ ἄμφω ταὐτόν, οἷον μύρμηξ καὶ λαμπυρὶς καὶ ἕτερά τινα), πάντων δὲ χαλεπώτατον ἢ ἀδύνατον 35 εἰς τὰ ἄναιμα. ἀναγκαῖον γὰρ τῶν καθ᾿ ἕκαστον 643a ὑπάρχειν τινὶ τῶν διαφορῶν ἑκάστην, ὥστε καὶ τὴν ἀντικειμένην. εἰ δὲ μὴ ἐνδέχεται τοῖς εἴδει διαφέρουσιν ὑπάρχειν εἶδός τι τῆς οὐσίας ἄτομον καὶ ἕν, ἀλλ᾿ ἀεὶ διαφορὰν ἕξει (οἷον ὄρνις ἀνθρώπου—ἡ διποδία γὰρ ἄλλη καὶ διάφορος· κἂν εἰ ἔναιμα, τὸ αἷμα διάφορον, ἢ οὐδὲν τῆς οὐσίας τὸ αἷμα θετέον)—εἰ δ᾿ οὕτως ἐστίν, ἡ μία διαφορὰ δυσὶν ὑπάρξει· εἰ δὲ τοῦτο, δῆλον ὅτι ἀδύνατον στέρησιν εἶναι διαφοράν.

Aristotle begins with the very obvious point that wings and feet come in easily identifiable and separable categories, such as split and hoofed.  Aristotle’s explanation of the method here is clearly being guided by a concern that each animal has some distinctive difference which is (1) discernible by this process of division and (2) belongs to that animal alone.  Perhaps 2 is a claim made by Platonists themselves for this method of division. However, I think the more likely possibility is that Aristotle construes division in such a way that unless the end of the process results in an actual individual species, it is worthless.  If a terminus of division is two-footed, for example, then this applies to many animals and is unsuccessful in picking any one single animal out. This also makes sense in light of the purpose of Aristotle’s criticisms.  He began (PA 642b5 ff.) by saying how sticking to bifurcatory division alone is either difficult or impossible.  (His alternative is to begin with many lines of division, instead of one.)

Another avenue to get at what Aristotle is saying is this.  When there is no further division possible, we have arrived at a specific difference, i.e., a species or animal, at least on the expectations of a Platonist.  This, as Aristotle shows, is not always so easy, as some differences result in more than one animal belonging to them, such as ants belonging both to the winged and unwinged species.

On the same line of thinking that requires a unique animal for each termination of the division, it also follows that any given termination of a division cannot end in a privation.  For there is no such animal as a “non-footed.”  For there is no existence for non-being.  In Peck’s Loeb translation he notes that the reason why Aristotle does not allow privation in division is that this will result in more than one animal belonging to the species, e.g. non-footed.  If this is so, then non-footed has to be divided to get to individuals, but this cannot occur because non-being cannot be divided (legitimately at least).

Questions:

1. If the process of bifurcatory division does not (always) end in one species, what is it the point?  Could the point be to “narrow down” the candidates, or perhaps this kind of dead end means one has to start over again?

2. Is Aristotle’s use of εἶδός (eidos) consistent in this passage?  (Not necessarily A’s fault, perhaps a difficulty in translation.)  Can it mean body plan, species, shape, body part?

3. Why is “footless, featherless” discounted on the grounds that such things are non-being, while “uncloven, undivided” in Aristotle’s examples are legitimate?  Is it because the latter is merely accidental, or one may even say adjectival, while the former is not?