When the thesis propounded affirms that A is genus of B, you will run over all the cognates of B, and see whether there is any one among them respecting which A cannot be affirmed as genus. If there be, this is a good argument against the thesis; for the genus ought to be predicable of all. Next, whether what is really no more than an accident is affirmed as genus, which ought to belong to the essence of the subject. Perhaps (e.g.) white is affirmed in the thesis as being genus of snow; but white cannot be truly so affirmed; for it is not of the essence of snow, but is only a quality or accident.[152] Examine whether the predicate A comes under the definition already given of an Accident, — that which may or may not be predicated of the subject; also, whether A and B both fall under the same one out of the ten Categories or Predicaments. If B the subject comes under Essentia, or Quale, or Ad Aliquid, the predicate ought also to belong to Essentia, or Quale, or Ad Aliquid: the species and the genus ought to come under the same Category.[153] If this be not the case in a thesis of Genus, the thesis cannot be maintained.
[152] Ibid. b. 23-29.
[153] Ibid. p. 120, b. 36-p. 121, a. 9. καθόλου δ’ εἰπεῖν ὑπὸ τὴν αὐτὴν διαίρεσιν δεῖ τὸ γένος τῷ εἴδει εἶναι.
Aristotle here enunciates this as universally true, whereas if we turn to Categor. p. 11, a. 24, seq. we shall find him declaring it not to be universally true. Compare also Topic. IV. iv. p. 124, b. 15.
You are aware that the species always partakes of the genus, while the genus never partakes of the species; to partake meaning that the species includes the essence or definition of the genus, but the genus never includes the essence or definition of the species. You will examine, therefore, whether in the thesis propounded to you this condition is realized; if not, the thesis may be refuted. Suppose, e.g., that it enunciates some superior genus as including Ens or Unum. If this were true, the genus so assigned would still partake of Ens and Unum; for Ens and Unum maybe predicated of all existences whatever. Therefore what is enunciated in the thesis as a genus, cannot be a real genus.[154]
[154] Topic. IV. i. p. 121, a. 10-19.
Perhaps you may find something respecting which the subject (species) may be truly affirmed, while the predicate (genus) cannot be truly affirmed. If so, the predicate is not a real genus. Thus, the thesis may enunciate Ens or Scibile as being the genus of Opinabile. But this last, the species or subject Opinabile, may be affirmed respecting Non-Ens also; while the predicates Ens or Scibile (given as the pretended genus of Opinabile) cannot be affirmed respecting Non-Ens. You can thus show that Ens or Scibile is not the real genus of Opinabile.[155] The pretended species Opinabile (comprising as it does both Ens and Non-Ens) stretches farther than the pretended genus Ens or Scibile: whereas every real genus ought to stretch farther than any one or any portion of its constituent species.[156] The thesis may thus be overthrown, if there be any one species which stretches even equally far or is co-extensive with the pretended genus.[157]
[155] Ibid. a. 20-26.
[156] Ibid. b. 1-14. στοιχεῖον δὲ πρὸς ἅπαντα τὰ τοιαῦτα, τὸ ἐπὶ πλέον τὸ γένος ἢ τὸ εἶδος καὶ τὴν διαφορὰν λέγεσθαι· ἐπ’ ἔλαττον γὰρ καὶ ἡ διαφορὰ τοῦ γένους λέγεται.
[157] Ibid. b. 4.