It is a general truth that the same species cannot belong to two distinct genera, unless one of the two be subordinate to the other, or unless both of them be comprehended under some common higher genus. You will examine, therefore, whether there is any other genus, besides the predicate of the thesis, to which the subject of the thesis can be referred. If there be some other genus, not under either of the two conditions above indicated, the predicate enunciated by the thesis cannot be the real genus of the subject. Thus, if the thesis declares justice to be science (or to belong to the genus science), you may remark that there is another distinct genus (virtue) to which justice also belongs. In this particular case, however, it would be replied that science and virtue can both be referred to one and the same higher genus, viz., habit and disposition. Therefore the thesis, Justice is science, will not be truly open to objection on this ground.[158]
[158] Topic. IV. ii. p. 121, b. 24, seq.
Again, if the predicate of the thesis be the true genus of the subject, all the higher genera in which the predicate is contained must also be predicated in Quid (as the predicate itself is) respecting the subject. This you must show by an induction of particular instances, no counter-instance being producible.[159] If the thesis enunciated does not conform to this condition, you will have a good argument against it. You will also run over the sub-species that are comprehended in the subject of the thesis, considered as a genus; and you will examine whether the predicate of the thesis (together with all its superior genera) is predicable essentially or in Quid of all these sub-species. If you can find any one among these sub-species, of which it is not essentially predicable, the predicate of the thesis is not the true genus of the subject;[160] the like also, if the definitions of those genera are not predicable of the subject or its sub-species.[161]
[159] Ibid. p. 122, a. 5-19. ὅτι δὲ ἑνὸς ἐν τῷ τί ἐστι κατηγορουμένου πάντα τὰ λοιπά, ἄνπερ κατηγορῆται, ἐν τῷ τί ἐστι κατηγορηθήσεται, δι’ ἐπαγωγῆς ληπτέον.
[160] Ibid. a. 21-b. 6.
[161] Ibid. b. 7-11. εἰ οὖν διαφωνεῖ, δῆλον ὅτι οὐ γένος τὸ ἀποδοθέν.
Perhaps the thesis may enunciate as a genus what is really nothing more than a differentia. It may also enunciate the differentia either as a part of the genus or as a part of the species; or it may enunciate the genus either as a part of the differentia or as a part of the species. All these are attackable. The differentia is not a genus, nor does it respond to the question Quid est, but to the question Quale quid est. It is always either more extensive than the species, or co-extensive therewith.[162] If none of the differentiæ belonging to a genus can be predicated of a species, neither can the genus itself be predicated thereof. Thus, neither odd nor even can be predicated of the soul; accordingly, neither can the genus (number) be predicated of the soul.[163] If the species be prius naturâ, so that when it disappears the enunciated genus disappears along with it, this cannot be the real genus; nor, if the enunciated genus or differentia can be supposed to disappear and yet the species does not disappear along with them.[164] If the species partakes of (includes in its essence) something contrary to the enunciated genus, this last cannot be the real genus; nor, if the species includes something which cannot possibly belong to what is in that genus. Thus, if the soul partakes of (or includes in its essence) life, and if no number can possibly live, the soul cannot be a species of number.[165]
[162] Ibid. b. 12-p. 123, a. 10. οὐδὲ δοκεῖ μετέχειν ἡ διαφορὰ τοῦ γένους· πᾶν γὰρ τὸ μετέχον τοῦ γένους ἢ εἶδος ἢ ἄτομόν ἐστιν. ἀεὶ γὰρ ἡ διαφορὰ ἐπ’ ἴσης ἢ ἐπὶ πλεῖον τοῦ εἴδους λέγεται. — ἐπὶ πλέον τε γὰρ τὸ γένος τῆς διαφορᾶς δεῖ λέγεσθαι, καὶ μὴ μετέχειν τῆς διαφορᾶς.
As an example to illustrate the enclosing of the genus within the species (εἰ τὸ γένος εἰς τὸ εἶδος ἔθηκεν), Aristotle cites a definition given by Plato, who defined τὴν κατὰ τόπον κίνησιν, as φοράν. Now φορὰ is less extensive in its meaning than ἡ κατὰ τόπον κίνησις, which includes βάδισις and other terms of motion apart from or foreign to φορά. — Example of enunciating differentia as a genus is, if immortal be given as the genus to which a god belongs. Immortal is the differentia belonging to ζῷον, and constituting therewith the species god. — Example of enclosing the differentia in the genus is, if odd be given as the essence of number (ὅπερ ἀριθμόν). — Example of enclosing differentia in the species is, if immortal be put forward as the essence of a god (ὅπερ θεόν). — Example of enclosing the genus in the differentia is, number given as the essence of the odd. — Example of enunciating the genus as a differentia is, when change of place is given as the differentia of φορά.
[163] Topic. IV. ii. p. 123, a. 11-14.