[18] Plato, Republic. v. p. 479, A.; vii. p. 538, E. Compare also the conclusion of the Platonic Parmenides, and the elaborate dialectic or antinomies by which the contradictions involved in it are proved.
[19] Plato, Sophistes, p. 257, B.
While Aristotle mentions these various dissentients, and especially Herakleitus, he seems to imagine that they were not really in earnest[20] in their dissent. Yet he nevertheless goes at length into the case against them, as well as against others, who agreed with him in affirming the Maxim, but who undertook also to demonstrate it. Any such demonstration Aristotle declares to be impossible. The Maxim is assumed in all demonstrations; unless you grant it, no demonstration is valid; but it cannot be itself demonstrated. He had already laid down in the Analytica that the premisses for demonstration could not be carried back indefinitely, and that the attempt so to carry them back was unphilosophical.[21] There must be some primary, undemonstrable truths; and the Maxim of Contradiction he ranks among the first. Still, though in attempting any formal demonstration of the Maxim you cannot avoid assuming the Maxim itself and thus falling into Petitio Principii, Aristotle contends that you can demonstrate it in the way of refutation,[22] relatively to a given opponent, provided such opponent will not content himself with simply denying it, but will besides advance some affirmative thesis of his own, as a truth in which he believes; or provided he will even grant the fixed meaning of words, defining them in a manner significant alike to himself and to others, — each word to have either one fixed meaning, or a limited number of different meanings, clear and well defined.[23] It is impossible for two persons to converse, unless each understands the other. A word which conveys to the mind not one meaning, but a multitude of unconnected meanings, is for all useful purposes unmeaning.[24] If, therefore, the opponent once binds himself to an affirmative definition of any word, this definition may be truly predicated of the definitum as subject; while he must be considered as interdicting himself from predicating of the same subject the negative of that definition. But when you ask for the definition, your opponent must answer the question directly and bonâ fide. He must not enlarge his definition so as to include both the affirmative and negative of the same proposition; nor must he tack on to the real essence (declared in the definition) a multitude of unessential attributes. If he answers in this confused and perplexing manner, he must be treated as not answering at all, and as rendering philosophical discussion impossible.[25] Such a mode of speaking goes to disallow any ultimate essence or determinate subject, and shuts out all predication; for there cannot be an infinite regress of predicates upon predicates, and accidents upon accidents, without arriving at an ultimate substratum — Subject or Essence.[26] If, wherever you can truly affirm a predicate of any subject, you can also truly deny the same predicate of the same subject, it is manifest that all subjects are one: there is nothing to discriminate man, horse, ship, wall, &c., from each other; every one speaks truth, and every one at the same time speaks falsehood; a man believes and disbelieves the same thing at the same time; or he neither believes nor disbelieves, and then his mind is blank, like a vegetable.[27]
[20] Aristot. Metaph. Γ. iii. p. 1005, b. 26; K. v. p. 1062, a. 32. Here Aristotle intimates that Herakleitus may have asserted what he did not believe; though we find him in another place citing Herakleitus as an example of those who adhered as obstinately to their opinions as other persons adhered to demonstrated truth (Ethic. Nik. VII. v. p. 1146, b. 30.).
[21] Aristot. Metaph. Γ. iv. p. 1006, a. 5: ἀξιοῦσι δὴ καὶ τοῦτο ἀποδεικνύναι τινὲς δι’ ἀπαιδευσίαν· ἔστι γὰρ ἀπαιδευσία τὸ μὴ γιγνώσκειν τίνων δεῖ ζητεῖν ἀπόδειξιν καὶ τίνων οὐ δεῖ.
[22] Aristot. Metaph. Γ. iv. p. 1006, a. 11: ἔστι δ’ ἀποδεῖξαι ἐλεγκτικῶς καὶ περὶ τούτου ὅτι ἀδύνατον, ἂν μόνον τι λέγῃ ὁ ἀμφισβητῶν. — K. v. p. 1062, a. 2: καὶ περὶ τῶν τοιούτων ἁπλῶς μὲν οὐκ ἔστιν ἀπόδειξις, πρὸς τόνδε δ’ ἔστιν. — p. 1062, a. 30.
[23] Ibid. Metaph. Γ. iv. p. 1006, a. 18-34. διαφέρει δ’ οὐθὲν οὔδ’ εἰ πλείω τις φαιή σημαίνειν, μόνον δὲ ὡρισμένα. — K. v. p. 1062, a. 12.
[24] Ibid. Γ. iv. p. 1006, b. 7: τὸ γὰρ μὴ ἕν τι σημαίνειν οὐθὲν σημαίνειν ἐστίν, μὴ σημαινόντων δὲ τῶν ὀνομάτων ἀνῄρηται τὸ διαλέγεσθαι πρὸς ἀλλήλους, κατὰ δὲ τὴν ἀλήθειαν καὶ πρὸς αὑτόν· οὐθὲν γὰρ ἐνδέχεται νοεῖν μὴ νοοῦντα ἕν. — K. v. p. 1062, a. 20.
[25] Ibid. Γ. iv. p. 1006, b. 30-p. 1007, a. 20. συμβαίνει τὸ λεχθέν, ἂν ἀποκρίνηται τὸ ἐρωτώμενον. ἐὰν δὲ προστιθῇ ἐρωτῶντος ἁπλῶς καὶ τὰς ἀποφάσεις, οὐκ ἀποκρίνεται τὸ ἐρωτώμενον. — ἐὰν δὲ τοῦτο ποιῇ, οὐ διαλέγεται.
[26] Ibid. p. 1007, a. 20-b. 19: ὅλως δ’ ἀναιροῦσιν οἱ τοῦτο λέγοντες οὐσίαν καὶ τὸ τί ἦν εἶναι. — εἰ δὲ πάντα κατὰ συμβεβηκὸς λέγεται, οὐθὲν ἔσται πρῶτον τὸ καθ’ οὗ, εἰ ἀεὶ τὸ συμβεβηκὸς καθ’ ὑποκειμένου τινὸς σημαίνει τὴν κατηγορίαν· ἀνάγκη ἄρα εἰς ἄπειρον ἰέναι· ἀλλ’ ἀδύνατον.