To uphold, or prove by way of syllogism, requires a different procedure. It is a task hard, but not impossible. Most disputants assume without proving their definition, in the same way as the teachers of Geometry and Arithmetic do in their respective sciences. Aristotle tells us that he does not here intend to give a didactic exposition of Definition, nor of the proper way of defining accurately or scientifically. To do this (he says) belongs to the province of Analytic; while in the present treatise he is dealing merely with Dialectic. For the purposes, then, of Dialectic, he declares that syllogistic proof of a definition is practicable, inasmuch as the definition is only a proposition declaring what is essential to the definiend; and nothing is essential except genus (or genera) and differentiæ.[351]
[351] Topic. VII. iii. p. 153, a. 6-22. Compare Analyt. Post. II. iii.-x., where the theory of Scientific Definition is elaborately worked out; supra, Vol. I. ch. viii. [pp. 346-353].
Towards the establishment of the definition which you have to defend, you may find arguments by examining the Contraries and Opposites of the component terms, and of the defining proposition. If the opposite of the definition is allowed as defining properly the opposite of the definiend, you may argue from hence that your own definition is a good one.[352] If you can show that there is declared in your definition a partial correspondence of contraries either separately in the genus, or separately in the differentia, you have a certain force of argument in your favour; and, if you can make out both the two separately, this will suffice for your entire definition.[353] You may also draw arguments from the Derivatives, or Co-ordinates of your own terms; from Analogous Terms, or from Comparates (More or Less). If the definition of any one of these is granted to you, an argument is furnished for the defence of an analogous definition in the case of your own term. If it is conceded as a good definition that forgetfulness is — the casting away of knowledge, then the definition must also hold good that to forget is — to cast away knowledge. If destruction is admitted to be well defined — dissolution of essence, then to be destroyed is well defined — to be dissolved as to essence. If the wholesome may be defined — that which is productive of health, then also the profitable may be defined — that which is productive of good; that is, if the declaration of the special end makes a good definition in one case, so it will also in the other.[354]
[352] Ibid. a. 28: εἰ γὰρ ὁ ἀντικείμενος τοῦ ἀντικειμένου, καὶ τὸν εἰρημένου τοῦ προκειμένου ἀνάγκη εἶναι (ὅρον).
[353] Ibid. b. 14: καθόλου δ’ εἰπεῖν, ἐπεὶ ὁ ὁρισμός ἐστιν ἐκ γένους καὶ διαφορῶν, ἂν ὁ τοῦ ἐναντίου ὁρισμὸς φανερὸς ᾖ, καὶ ὁ τοῦ προκειμένου ὁρισμὸς φανερὸς ἔσται.
[354] Topic. VII. iii. p. 153, b. 25-p. 154, a. 11: ἔτι ἐκ τῶν πτώσεων καὶ τῶν συστοίχων· ἀνάγκη ἀκολουθεῖν τὰ γένη τοῖς γένεσιν καὶ τοὺς ὅρους τοῖς ὅροις. — ἑνὸς οὖν ὁποιουοῦν τῶν εἰρημένων ὁμοληθέντος, ἀνάγκη κὶ τὰ λοιπὰ ὁμολογεῖσθαι. — καὶ ἐκ τῶν ὁμοίως ἐχόντων πρὸς ἄλληλα — ὁμοίως γὰρ ἕκαστον τῶν εἰρημένων πρὸς τὸ οἰκεῖον τέλος ἔχει.
These loci, from Analoga, from Derivatives, from Conjugates, are of the most frequent avail in dialectical debates or definitions. The disputant must acquire promptitude in the employment of them. He must learn, moreover, to test a definition tendered to him by calling to mind particulars and sub-species, so as to determine whether the definition fits them all. Such a procedure will be found especially serviceable in debate with one who upholds the Platonic Ideas. Care must also be taken to see whether the definiend is distorted from its proper signification, or whether it is used in defining itself.[355]
[355] Topic. VII. iv. p. 154, a. 12-22.
These last observations are addressed to the questioner or assailant of the definition. We have already seen however that his task is comparatively easy; the grand difficulty is to defend a definition. The respondent cannot at once see what he ought to aim at; and, even when he does see it, he has farther difficulty in obtaining the requisite concessions from his opponent, who may decline to grant that the two parts of the definition tendered are really the genus and differentia of the definiend; while, if there be any thing besides these two parts contained in the essence of the definiend, there is an excuse for declining to grant it.[356] The opponent succeeds, if he can establish one single contradictory instance; accordingly, a syllogism with particular conclusion will serve his purpose. The respondent on the other hand, must meet each one of these instances, must establish an universal conclusion, and must show that his definition reciprocates with the definiend, so that, wherever the latter is predicable, the former is predicable likewise, and not in any other case whatever.[357]
[356] Topic. VII. v. p. 154, a. 23, seq. καὶ γὰρ ἰδεῖν αὐτὸν καὶ λαβεῖν παρὰ τῶν ἐρωτωμένων τὰς τοιαύτας προτάσεις οὐκ εὐπετές, &c.