[36] Ibid. xiii. p. 96, a. 22: πῶς δεῖ θηρεύειν τὰ ἐν τῷ τί ἐστι κατηγορούμενα;
[37] Analyt. Post. II. xiii. p. 96, a. 24-b. 14. εἰ τοίνυν μηδενὶ ὑπάρχει ἄλλῳ ἢ ταῖς ἀτόμοις τριάσι, τοῦτ’ ἂν εἴη τὸ τριάδι εἶναι. ὑποκείσθω γὰρ καὶ τοῦτο, ἡ οὐσία ἡ ἑκάστου εἶναι ἡ ἐπὶ ταῖς ἀτόμοις ἔσχατος τοιαύτη κατηγορία. ὥστε ὁμοίως καὶ ἄλλῳ ὁτῳοῦν τῶν οὕτω δειχθέντων τὸ αὐτῷ εἶναι ἔσται.
Where the matter that we study is the entire genus, we must begin by distributing it into its lowest species; e.g. number into dyad, triad, &c.; in like manner, taking straight line, circle, right angle, &c.[38] We must first search out the definitions of each of these lowest species; and these having been ascertained, we must next look above the genus, to the Category in which it is itself comprised, whether Quantum, Quale, &c. Having done thus much we must study the derivative attributes or propria of the lowest species through the common generalities true respecting the larger. We must recollect that these derivative attributes are derived from the essence and definition of the lowest species, the complex flowing from the simple as its principium: they belong per se only to the lowest species thus defined; they belong to the higher genera only through those species.[39] It is in this way, and not in any other, that the logical Division of genera, according to specific differences, can be made serviceable for investigation of essential attributes; that is, it can only be made to demonstrate what is derivative from the essence. We have shown already that it cannot help in demonstrating essence or Definition itself. We learn to marshal in proper order the two constituent elements of our definition, and to attach each specific difference to the genus to which it properly belongs. Thus we must not attempt to distribute the genus animal according to the difference of having the wing divided or undivided: many animals will fall under neither of the two heads; the difference in question belongs to the lower genus winged animal, and distributes the same into two species. The characteristic or specific difference must be enunciated and postulated by itself, and must be attached to its appropriate genus in order to form the definition. It is only by careful attention to the steps of legitimate logical Division that we can make sure of including all the particulars and leaving out none.[40]
[38] Ibid. b. 18. The straight line is the first or lowest of all lines: no other line can be understood, unless we first understand what is meant by a straight line. In like manner the right angle is the first of all angles, the circle the first of all curvilinear figures (Julius Pacius, ad loc. p. 504).
[39] Analyt. Post. II. xiii. p. 96, b. 19-25: μετὰ δὲ τοῦτο, λάβόντα τί τὸ γένος, οἷον πότερον τῶν ποσῶν ἢ τῶν ποιῶν, τὰ ἴδια πάθη θεωρεῖν διὰ τῶν κοινῶν πρώτων. τοῖς γὰρ συντιθεμένοις ἐκ τῶν ἀτόμων (speciebus infimis) τὰ συμβαίνοντα ἐκ τῶν ὁρισμῶν ἔσται δῆλα, διὰ τὸ ἀρχὴν εἶναι πάντων τὸν ὁρισμόν καὶ τὸ ἁπλοῦν, καὶ τοῖς ἁπλοῖς καθ’ αὑτὰ ὑπάρχειν τὰ συμβαίνοντα μόνοις, τοῖς δ’ ἄλλοις κατ’ ἐκεῖνα.
Themistius illustrates this obscure passage, p. 89. The definitions of εὐθεῖα γραμμή, κεκλασμένη γραμμή, περιφερὴς γραμμή, must each of them contain the definition of γραμμή (= μῆκος ἀπλατές), since it is in the Category Ποσόν (ποσὸν μῆκος ἀπλατές). But the derivative properties of the circle (περιφερὴς γραμμή) are deduced from the definition of a circle, and belong to it in the first instance quâ περιφερὴς γραμμή, in a secondary way quâ γραμμή.
[40] Analyt. Post. II. xiii. p. 96, b. 25-p. 97, a. 6.
Some contemporaries of Aristotle, and among them Speusippus, maintained that it was impossible either to define, or to divide logically, unless you knew all particulars without exception. You cannot (they said) know any one thing, except by knowing its differences from all other things; which would imply that you knew also all these other things.[41] To these reasoners Aristotle replies: It is not necessary to know all the differences of every thing; you know a thing as soon as you know its essence, with the properties per se which are derivative therefrom. There are many differences not belonging to the essence, but distinguishing from each other two things having the same essence: you may know the thing, without knowing these accidental differences.[42] When you divide a genus into two species, distinguished by one proximate specific difference, such that there cannot be any thing that does not fall under one or other of these membra condividentia, and when you have traced the subject investigated under one or other of these members, you can always follow this road until no lower specific difference can be found, and you have then the final essence and definition of the subject; even though you may not know how many other subjects each of the two members may include.[43] Thus does Aristotle reply to Speusippus, showing that it is not necessary, for the definition of one thing, that you should know all other things. His reply, as in many other cases, is founded on the distinction between the Essential and the Accidental.
[41] Ibid. p. 97, a. 6-10; Themistius, p. 92. Aristotle does not here expressly name Speusippus, but simply says φασί τινες. It is Themistius who names Speusippus; and one of the Scholiasts refers to Eudemus as having expressly indicated Speusippus (Schol. p. 248, a. 24, Br.).
[42] Analyt. Post. II. xiii. p. 97, a. 12: πολλαὶ γὰρ διαφοραὶ ὑπάρχουσι τοῖς αὐτοῖς τῷ εἴδει, ἀλλ’ οὐ κατ’ οὐσίαν οὐδὲ καθ’ αὑτά.