[345] Ibid. p. 152, a. 2.
[346] Topic. VII. p. 152, a. 5-30: σκοπεῖν δὲ καὶ ὧν θάτερον μάλιστα λέγεται ὁτιοῦν, εἰ καὶ θάτερον τῶν αὐτων τούτων κατὰ τὸ αὐτὸ μάλιστα λέγεται, καθάπερ Ξενοκράτης τὸν εὐδαίμονα βίον καὶ τὸν σπουδαῖον ἀποδείκνυσι τὸν αὐτόν, ἐπειδὴ πάντων τῶν βίων αἱρετώτατος ὁ σπουδαῖος καὶ ὁ εὐδαίμων· ἓν γὰρ τὸ αἱρετώτατον καὶ τὸ μέγιστον· &c.
Aristotle remarks that Xenokrates here carried his inference too far: that the application of the same superlative predicate to A and B affords indeed a presumption that they are Idem numero, but not a conclusive proof thereof; that the predicate might be applied in like manner, if B were a species comprised in A as genus.
Xenokrates made the mistake of drawing an affirmative conclusion from syllogistic premisses in the Second figure.
[347] Topic. VII. i. p. 152, a. 31-b. 16.
Farther, in examining the thesis (A is identical numero with B) you must look not merely whether it involves actually any impossible consequences, but also whether any cases can be imagined in which it would involve such;[348] whether the identity is not merely specie or genere; finally, whether the one can exist without the other.[349]
[348] Ibid. b. 17-24. Aristotle illustrates this locus as follows:— Some say that to be void, and to be full of air, are the same. But suppose the air to be drawn away; then the place will no longer be full of air, yet it will still be void, even more than it was before. One of the two terms declared to be identical is thus withdrawn, while the other remains. Accordingly, the two are not really identical. This illustration fits better to the principle laid down, b. 34: εἰ δύνατον θάτερον ἄνευ θατέρου εἶναι· οὐ γὰρ ἂν εἴη ταὐτόν.
[349] Ibid. b. 25-35.
Such are the various loci available for argument against the thesis affirming the equivocal predicate same. All of them may be useful when you are impugning a definition; for the characteristic of this is to declare that the defining proposition is equivalent or identical with the defined name; and, if you can disprove such identity, you upset the definition. But these loci will be of little avail, if your task is to defend or uphold a definition; for, even if you succeed in establishing the above-mentioned identity, the definition may still be open to attack for other weaknesses or defects.[350]
[350] Ibid. ii. p. 152, b. 36-p. 158, a. 5. ἅπαντες οἱ πρὸς ταὐτὸν ἀνασκευαστικοὶ τόποι καὶ πρὸς ὅρον χρήσιμοι — τῶν δὲ κατασκευαστικῶν τόπων οὐδεὶς χρήσιμος πρὸς ὅρον· &c.