Aristotle

by George Grote

VII.

In the Seventh Book of the Topica Aristotle continues his review of the manner of debating theses which profess to define, but enters also on a collateral question connected with that discussion: viz., By what arguments are we to determine whether two Subjects or Predicates are the same Numero (modo maxime proprio), as distinguished from being the same merely Specie or Genere? To measure the extent of identity between any two subjects, is important towards the attack and defence of a definition.[344]

[344] Ibid. VII. i. p. 151, b. 28: πότερον δὲ ταὐτὸν ἢ ἕτερον κατὰ τὸν κυριώτατον τῶν ῥηθέντων περὶ ταὐτοῦ τρόπων (ἐλέγετο δὲ κυριώτατα ταὐτὸν τὸ τῷ ἀριθμῷ ἕν) &c.

Two subjects (A and B) being affirmed as the same numero, you may test this by examining the Derivatives, the Co-ordinates, and the Opposites, of each. Thus, if courage is identical with justice, the courageous man will be identical with the just man; courageously will be identical with justly. Likewise, the opposite of courage (in all the four modes of Opposition) will be identical with the opposite of justice. Then, again, the generators and destroyers, the generations and destructions, of courage, will be identical with those of justice.[345] If there be any predicate applied to courage in the superlative degree, the same predicate will also be applied to justice in the superlative degree.[346] If there be a third subject C with which A is identical, B also will be identical therewith. The same attributes predicable of A will also be predicable of B; and, if the two be attributes, each will be predicable of the same subjects of which the other is predicable. Both will be comprised in the same Category, and will have the same genus and differentia. Both will increase or diminish under the same circumstances. Each, when added to or subtracted from any third subject, will yield the same result.[347]

[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.

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.

[357] Ibid. a. 32-b. 12.

So much greater are the difficulties belonging to the defence of a Definition, as compared with the attack upon it; and the same may be said about attack and defence of a Proprium, and of a Genus. In both cases, the assailant will carry his point, if he can show that the predicate in question is not predicable, in this relation, of all, or that it is not predicable, in this relation, of any one. But the defendant is required to make good the universal against every separate objection advanced against any one of the particulars. It is a general rule, that the work of destruction is easier than that of construction; and the present cases come under that rule.[358] The hardest of all theses to defend, and the easiest to overthrow, is where Definition is affirmed; for the respondent in this case is required to declare well the essence of his subject, and he stands in need of the greatest number of auxiliary data; while all the Loci for attack, even those properly belonging to the Proprium, the Genus, and the Accident, are available against him.[359] Next in order, as regards difficulty of defence, comes the theses affirming Proprium; where the respondent has to make out, not merely that the predicate belongs to the subject, but that it belongs thereunto exclusively and reciprocally: here also all the Loci for attack, even those properly belonging to Accident, are available.[360] Easiest of all theses to defend, while it is the hardest to impugn, is that in which Accident alone is affirmed — the naked fact, that the predicate A belongs to the Subject B, without investing it with the character either of Genus or Proprium. Here what is affirmed is a minimum, requiring the smallest array of data to be conceded; moreover, the Loci available for attack are the fewest, since many of those which may be employed against Genus, Proprium, and Definition, have no application against a thesis affirming merely Accident.[361] Indeed, if the thesis affirmed be only a proposition particular (and not universal), affirming Accident (and nothing more), the task of refuting it will be more difficult than that of maintaining it.[362]

[358] Ibid. b. 13-32. ἔοικε δ’, ὥσπερ καὶ ἐν τοῖς ἄλλοις τὸ διαφθεῖραι τοῖ ποιῆσαι ῥᾷον, οὕτω καὶ ἐπὶ τούτων τὸ ἀνασκευάσαι τοῦ κατασκευάσαι.

[359] Topic. VII. v. p. 155, a. 3-21: φανερὸν δὲ καὶ διότι πάντων ῥᾷστον ὅρον ἀνασκευάσαι.

[360] Ibid. a. 23-27. Aristotle has in view the most complete Proprium: belonging omni, soli, et semper.

[361] Ibid. a. 28-36: ῥᾷστον δὲ πάντων κατασκευάσαι τὸ συμβεβηκός· — ἀνασκευάζειν δὲ χαλεπώτατον τὸ συμβεβηκός, ὅτι ἐλάχιστα ἐν αὐτῷ δέδοται, &c.

[362] Ibid. p. 154, b. 36-p. 155, a. 2: τὸ δ’ ἐπὶ μέρους ἀνάπαλιν ῥᾷον κατασκευάσαι ἢ ἀνασκευάσαι· κατασκευάζοντι μὲν γὰρ ἀπόχρη δεῖξαι τινὶ ὑπάρχον, ἀνασκευάζοντι δὲ δεικτέον ὅτι οὐδενὶ ὑπάρχει.