[64] Aristot. Metaph. Γ. iii. p. 1005, a. 19-b. 11.
[65] See Aristot. De Divinat. per Somnum, i. p. 462, b. 15; De CÅ“lo, I. iii. p. 270, b. 3, 20; Metaphys. A. ii. p. 982, a. 4-14. Alexander ap. Scholia, p. 525, b. 36, Br.: ἐν πᾶσιν ἔθος ἀεὶ ταῖς κοιναῖς καὶ φυσικαῖς τῶν ἀνθρώπων προλήψεσιν ἀρχαῖς εἰς τὰ δεικνύμενα πρὸς αὐτοῦ χρῆσθαι.
[66] Aristot. Metaph. A. vi. p. 987, a. 32; M. iv. p. 1078, b. 12. That Plato’s Philosophia Prima involved a partial coincidence with that of Herakleitus is here distinctly announced by Aristotle: that it also included an intimate conjunction or fusion of Parmenides with Herakleitus is made out in the ingenious Dissertation of Herbart, De Platonici Systematis Fundamento, Göttingen (1805), which winds up with the following epigrammatic sentence as result (p. 50):— “Divide Heracliti γένεσιν οὐσίᾳ Parmenidis, et habebis Ideas Platonicas.â€� Compare Plato, Republic VII. p. 515, seq.
[67] Aristot. Metaph. M. iv. p. 1078, b. 17, seq.; ix. p. 1086, a. 37: τὰ μὲν οὖν ἐν τοῖς αἰσθητοῖς καθ’ ἕκαστα ῥεῖν ἐνόμιζον (Platonici) καὶ μένειν οὐθὲν αὐτῶν, τὸ δὲ καθόλου παρὰ ταῦτα εἶναί τε καὶ ἕτερόν τι εἶναι. τοῦτο δ’, ὥσπερ ἐν τοῖς ἔμπροσθεν ἐλέγομεν, ἐκίνησε μὲν Σωκράτης διὰ τοὺς ὁρισμούς, οὐ μὴν ἐχώρισέ γε τῶν καθ’ ἕκαστον. καὶ τοῦτο ὀρθῶς ἐνόησεν οὐ χωρίσας.
The Maxim of Contradiction, which Aristotle proclaims as the first and firmest principium of syllogizing, may be found perpetually applied to particular cases throughout the Memorabilia of Xenophon and the Sokratic dialogues of Plato. Indeed the Elenchus for which Sokrates was so distinguished, is nothing more than an ever-renewed and ingenious application of it; illustrating the painful and humiliating effect produced even upon common minds by the shock of a plain contradiction, when a respondent, having at first confidently laid down some universal affirmative, finds himself unexpectedly compelled to admit, in some particular case, the contradictory negative. As against a Herakleitean, who saw no difficulty in believing both sides of the contradiction to be true at once, the Sokratic Elenchus would have been powerless. What Aristotle did was, to abstract and elicit the general rules of the process; to classify propositions according to their logical value, in such manner that he could formulate clearly the structure of the two propositions between which an exact contradictory antitheses subsisted. The important logical distinctions between propositions contradictory and propositions contrary, was first clearly enunciated by Aristotle; and, until this had been done, the Maxim of Contradiction could not have been laid down in a defensible manner. Indeed we may remark that, while this Maxim is first promulgated as a formula of First Philosophy in Book Γ. of the Metaphysica, it had already been tacitly assumed and applied by Aristotle throughout the De Interpretatione, Analytica, and Topica, as if it were obvious and uncontested. The First Philosophy of Aristotle was adapted to the conditions of ordinary colloquy as amended and tested by Sokrates, furnishing the theoretical basis of his practical Logic.
But, as Aristotle tells us, there were several philosophers and dialecticians who did not recognize the Maxim; maintaining that the same proposition might be at once true and false — that it was possible for the same thing both to be and not to be. How is he to deal with these opponents? He admits that he cannot demonstrate the Maxim against them, and that any attempt to do this would involve Petitio Principii. But he contends for the possibility of demonstrating it in a peculiar way — refutatively or indirectly; that is, provided that the opponents can be induced to grant (not indeed the truth of any proposition, to the exclusion of its contradictory antithesis, which concession he admits would involve Petitio Principii, but) the fixed and uniform signification of terms and propositions. Aristotle contends that the opponents ought to grant thus much, under penalty of being excluded from discussion as incapables or mere plants.[68] I do not imagine that the opponents themselves would have felt obliged to grant as much as he here demands. The onus probandi lay upon him, as advancing a positive theory; and he would have found his indirect or refutative demonstration not more available in convincing them than a direct or ordinary demonstration. Against respondents who proclaim as their thesis the negative of the Maxim of Contradiction, refutation and demonstration are equally impossible. No dialectical discussion could ever lead to any result; for you can never prove more against them than what their own thesis unequivocally avows.[69] As against Herakleitus and Anaxagoras, I do not think that Aristotle’s qualified vindication of the Maxim has any effective bearing.
[68] Aristot. Metaph. Γ. iv. p. 1006, a. 11, seq.
[69] Ibid. a. 26: ἀναιρῶν γὰρ λόγον ὑπομένει λόγον. — p. 1008, a. 30.
But Aristotle is quite right in saying that neither dialectical debate nor demonstration can be carried on unless terms and propositions be defined, and unless to each term there be assigned one special signification, or a limited number of special significations — excluding a certain number of others. This demand for definitions, and also the multiplied use of inductive interrogations, keeping the Universal implicated with and dependent upon its particulars — are the innovations which Aristotle expressly places to the credit of Sokrates. The Sokratic Elenchus operated by first obtaining from the respondent a definition, and then testing it through a variety of particulars: when the test brought out a negative as against the pre-asserted affirmative, the contradiction between the two was felt as an intellectual shock by the respondent, rendering it impossible to believe both at once; and the unrivalled acuteness of Sokrates was exhibited in rendering such shock peculiarly pungent and humiliating. But the Sokratic Elenchus presupposes this psychological fact, common to most minds, ordinary as well as superior, — the intellectual shock felt when incompatible beliefs are presented to the mind at once. If the collocutors of Sokrates had not been so constituted by nature, the magic of his colloquy would have been unfelt and inoperative. Against a Herakleitean, who professed to feel no difficulty in believing both sides of a contradiction at once, he could have effected nothing: and if not he, still less any other dialectician. Proof and disproof, as distinguished one from the other, would have had no meaning; dialectical debate would have led to no result.
Thus, then, although Aristotle was the first to enunciate the Maxim of Contradiction in general terms, after having previously originated that logical distinction of contrary and contradictory Propositions and doctrine of legitimate Antiphasis which rendered such enunciation possible, — yet, when he tries to uphold it against dissentients, it cannot be said that he has correctly estimated the logical position of those whom he was opposing, or the real extent to which the defence of the Maxim can be carried without incurring the charge of Petitio Principii. As against Protagoras, no defence was needed, for the Protagorean “Homo Mensura� is not incompatible with the Maxim of Contradiction; while, as against Herakleitus, Anaxagoras, Parmenides, &c., no defence was practicable, and the attempt of Aristotle to construct one appears to me a failure. All that can be really done in the way of defence is, to prove the Maxim in its general enunciation by an appeal to particular cases: if your opponent is willing to grant these particular cases, you establish the general Maxim against him by way of Induction; if he will not grant them, you cannot prove the general Maxim at all. Suppose you are attempting to prove to an Herakleitean that an universal affirmative and its contradictory particular negative cannot be both true at once. You begin by asking him about particular cases, Whether it is possible that the two propositions — All men are mortal, and, Some men are not mortal — can both be true at once? If he admits that these two propositions cannot both be true at once, if he admits the like with regard to other similar pairs of contradictories, and if he can suggest no similar pair in which both propositions are true at once, then you may consider yourself as having furnished a sufficient inductive proof, and you may call upon him to admit the Maxim of Contradiction in its general enunciation. But, if he will not admit it in the particular cases which you tender, or if, while admitting it in these, he himself can tender other cases in which he considers it inadmissible, then you have effected nothing sufficient to establish the general Maxim against him. The case is not susceptible of any other or better proof. It is in vain that Aristotle tries to diversify the absurdity, and to follow it out into collateral absurd consequences. If the Herakleitean does not feel any repulsive shock of contradiction in a definite particular case, if he directly announces that he believes the two propositions to be both at once true, then the collateral inconsistencies and derivative absurdities, which Aristotle multiplies against him, will not shock him more than the direct contradiction in its naked form. Neither the general reasoning of Aristotle, nor the Elenchus of Sokrates brought to bear in particular cases, would make any impression upon him; since he will not comply with either of the two conditions required for the Sokratic Elenchus: he will neither declare definitions, nor give suitable point and sequence to inductive interrogatories.