[321] Ibid. b. 32-p. 149, a. 13.
The definiend, being compound, will contain both a generic and a differential term. In general, the generic term will be the better known of the two; yet sometimes the other is the better known. Whichever of the two is the better known, the definer ought to choose that, if all that he aims at is a mere substitution of one name in place of another. But, if he aims at something more or at the substitution of an explanatory proposition in place of a name (without which there can be no true definition), he ought then to choose the differentia in preference to the genus; for the definition is produced for the purpose of imparting knowledge, and the differentia, being usually less known than the genus, stands most in need of extraneous help to cognition.[322] When the definition of the differentia has thus been tendered, you will examine whether it will be equally suitable for any other definiend also. If it be, you have an argument against the goodness of the definition. For example, the definition of odd number tendered to you may be — number having a middle. Here, since number is common both to the definiend and to the definition, having-a-middle is evidently put forward as the equivalent of odd. But this cannot stand as equivalent to odd; since various other subjects which are not odd (such, for example, as a body or a line), nevertheless have a middle. Since, then, we see that having-a-middle would be suitable in defining definiends which are not odd, it cannot be admitted, without some qualifying adjunct, as a good definition of odd. The adjunct annexed must declare in what sense middle is intended, since it is an equivocal phrase.[323]
[322] Ibid. p. 149, a. 14-28.
[323] Ibid. a. 29-37.
29. If the definiend be a something really existent, the definition given of it ought not to be a proposition declaring an incompatible combination, such as neither does nor can exist. Some, for example, define white — colour mingled with fire; which is incompatible, since that which is incorporeal (colour) cannot be mingled with a body (fire).[324]
[324] Topic. VI. xii. p. 149, a. 38-b. 3.
30. Again, suppose the definiend to be a Relatum: the correlate thereof must of course be declared in the definition. Care, however, must be taken that it shall be declared, not in vague generality but, distinctly and with proper specialization; otherwise, the definition will be incorrect either entirely or partially. Thus, if the respondent defines medicine — the science of the really existent, he is incorrect either wholly or partially. The relatum ought to reciprocate or to be co-extensive with its correlate.[325] When the correlate, however, is properly specialized in the definition, it may be declared under several different descriptions; for the same real thing may be at once ens, album, bonum. None of these descriptions will be incorrect. Yet, if the correlate is thus described in the definition of a relatum, the definition cannot be considered good or sufficient. For it applies to more things besides the definiend; and a good definition ought to reciprocate or to be co-extensive with its definiend.[326]
[325] Ibid. b. 4, seq.: ἔτι ὅσοι μὴ διαιροῦσιν ἐν τοῖς πρός τι πρὸς ὃ λέγεται, ἀλλ’ ἐν πλείοσι περιλαβόντες εἶπαν, ἢ ὅλως ἢ ἐπί τι ψεύδονται, οἷον εἴ τις τὴν ἰατρικὴν ἐπιστήμην ὄντος εἶπεν — ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων, ἐπειδὴ ἀντιστρέφει πάντα τὰ πρός τι.
[326] Ibid. b. 12-23. ἔτι δ’ ἀδύνατον τὸν τοιοῦτον λόγον ἴδιον τοῦ ἀποδοθέντος εἶναι· — δῆλον οὖν ὅτι ὁ τοιοῦτος οὐδεμιᾶς ἐστὶν ἐπιστήμης ὁρισμός· ἴδιον γὰρ καὶ οὐ κοινὸν δεῖ τὸν ὁρισμὸν εἶναι.
31. Another mistake in defining is committed, when a man defines, not the subject purely and simply but, the subject in a high measure of excellence. Sometimes the rhetor (e.g.) is defined — one who can perceive and produce without omission all that there is plausible in any cause; the thief is defined — one who takes away secretly what belongs to another. But these are the definitions, not of a rhetor and a thief generally but, of a skilful rhetor and skilful thief. The thief is one who is bent on taking away secretly, not one who does take away secretly.[327]