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53 Aristot. De Interpr. p. 23, a. 27, seq.

54 Scholia ad Arist. pp. 135–139, Br. γυμνάσαι μόνον βουληθέντος τοὺς ἐντυγχάνοντας πρὸς τὴν ἐπίκρισιν τῶν πιθανῶς μὲν οὐ μέντοι ἀληθῶς λεγομένων λόγων &c. (p. 135, b. 15; also p. 136, a. 42).

55 Scholia ad Categorias, p. 83, a. 17–19, b. 10, p. 84, a. 29, p. 86, b. 42, p. 88, a. 30. It seems much referred to by Simplikius, who tells us that the Stoics adopted most of its principles (p. 83, a. 21, b. 7).

Whatever may have been the real origin and purpose of this last paragraph, I think it unsuitable as a portion of the treatise De Interpretatione. It nullifies, or at least overclouds, one of the best parts of that treatise, the clear determination of Anaphasis and its consequences.

If, now, we compare the theory of the Proposition as given by Aristotle in this treatise, with that which we read in the Sophistes of Plato, we shall find Plato already conceiving the proposition as composed indispensably of noun and verb, and as being either affirmative or negative, for both of which he indicates the technical terms.56 He has no technical term for either subject or predicate; but he conceives the proposition as belonging to its subject:57 we may be mistaken in the predicates, but we are not mistaken in the subject. Aristotle enlarges and improves upon this theory. He not only has a technical term for affirmation and negation, and for negative noun and verb, but also for subject and predicate; again, for the mode of signification belonging to noun and verb, each separately, as distinguished from the mode of signification belonging to them conjointly, when brought together in a proposition. He follows Plato in insisting upon the characteristic feature of the proposition aptitude for being true or false; but he gives an ampler definition of it, and he introduces the novel and important distribution of propositions according to the quantity of the subject. Until this last distribution had been made, it was impossible to appreciate the true value and bearing of each Antiphasis and the correct language for expressing it, so as to say neither more nor less. We see, by reading the Sophistes, that Plato did not conceive the Antiphasis correctly, as distinguished from Contrariety on the one hand, and from mere Difference on the other. He saw that the negative of any proposition does not affirm the contrary of its affirmative; but he knew no other alternative except to say, that it affirms only something different from the affirmative. His theory in the Sophistes recognizes nothing but affirmative propositions, with the predicate of contrariety on one hand, or of difference on the other;58 he ignores, or jumps over, the intermediate station of propositions affirming nothing at all, but simply denying a pre-understood affirmative. There were other contemporaries, Antisthenes among them, who declared contradiction to be an impossibility;59 an opinion coinciding at bottom with what I have just cited from Plato himself. We see, in the Thećtętus, the Euthydęmus, the Sophistes, and elsewhere, how great was the difficulty felt by philosophers of that age to find a proper locus standi for false propositions, so as to prove them theoretically possible, to assign a legitimate function for the negative, and to escape from the interdict of Parmenides, who eliminated Non-Ens as unmeaning and incogitable. Even after the death of Aristotle, the acute disputation of Stilpon suggested many problems, but yielded few solutions; and Menedęmus went so far as to disallow negative propositions altogether.60

56 Plato, Sophistes, pp. 261–262. φάσιν καὶ ἀπόφασιν. ib. p. 263 E. In the so-called Platonic Definitions, we read ἐν καταφάσει καὶ ἀποφάσει (p. 413 C); but these are probably after Aristotles time. In another of these Definitions (413 D.) we read ἀπόφασις, where the word ought to be ἀπόφανσις.

57 Plato, Sophist. p. 263 A-C.

58 Ibid. p. 257, B: Οὐκ ἀρ, ἐναντίον ὅταν ἀπόφασις λέγηται σημαίνειν, συγχωρησόμεθα, τοσοῦτον δὲ μόνον, ὅτι τῶν ἄλλων τι μηνύει τὸ μὴ καὶ τὸ οὔ προτιθέμενα τῶν ἐπιόντων ὀνομάτων, μᾶλλον δὲ τῶν πραγμάτων, περὶ ἅττ ἂν κέηται τὰ ἐπιφθεγγόμενα ὕστερον τῆς ἀποφάσεως ὀνόματα.

The term ἀντίφασις, and its derivative ἀντιφατικῶς, are not recognized in the Platonic Lexicon. Compare the same dialogue, Sophistes, p. 263; also Euthydęmus, p. 298, A. Plato does not seem to take account of negative propositions as such. See Plato and the Other Companions of Sokrates, vol. II. ch. xxvii. pp. 446–455.

59 Aristot. Topica, I. xi. p. 104, b. 20; Metaphys. Δ. p. 1024, b. 32; Analytic. Poster. I. xxv. p. 86, b. 34.

60 Diogon. Laert. ii. 134–135. See the long discussion in the Platonic Thećtętus (pp. 187–196), in which Sokrates in vain endeavours to produce some theory whereby ψευδὴς δόξα may be rendered possible. Hobbes, also, in his Computation or Logic (De Corp. c. iii. § 6), followed by Destutt Tracy, disallows the negative proposition per se, and treats it as a clumsy disguise of the affirmative ἐκ μεταθέσεως, to use the phrase of Theophrastus. Mr. John Stuart Mill has justly criticized this part of Hobbess theory (System of Logic, Book I. ch. iv. § 2).

Such being the conditions under which philosophers debated in the age of Aristotle, we can appreciate the full value of a positive theory of propositions such as that which we read in his treatise De Interpretatione. It is, so far as we know, the first positive theory thereof that was ever set out; the first attempt to classify propositions in such a manner that a legitimate Antiphasis could be assigned to each; the first declaration that to each affirmative proposition there belonged one appropriate negative, and to each negative proposition one appropriate counter-affirmative, and one only; the earliest effort to construct a theory for this purpose, such as to hold ground against all the puzzling questions of acute disputants.61 The clear determination of the Antiphasis in each case the distinction of Contradictory antithesis from Contrary antithesis between propositions this was an important logical doctrine never advanced before Aristotle; and the importance of it becomes manifest when we read the arguments of Plato and Antisthenes, the former overleaping and ignoring the contradictory opposition, the latter maintaining that it was a process theoretically indefensible. But in order that these two modes of antithesis should be clearly contrasted, each with its proper characteristic, it was requisite that the distinction of quantity between different propositions should also be brought to view, and considered in conjunction with the distinction of quality. Until this was done, the Maxim of Contradiction, denied by some, could not be shown in its true force or with its proper limits. Now, we find it done,62 for the first time, in the treatise before us. Here the Contradictory antithesis (opposition both in quantity and quality) in which one proposition must be true and the other false, is contrasted with the Contrary (propositions opposite in quality, but both of them universal). Aristotles terminology is not in all respects fully developed; in regard, especially, to the quantity of propositions it is less advanced than in his own later treatises; but from the theory of the De Interpretatione all the distinctions current among later logicians, take their rise.

61 Aristot. De Interpr. p. 17, a. 36: πρὸς τὰς σοφιστικὰς ἐνοχλήσεις.

62 We see, from the argument in the Metaphysica of Aristotle, that there were persons in his day who denied or refused to admit the Maxim of Contradiction; and who held that contradictory propositions might both be true or both false (Aristot. Metaph. Γ. p. 1006, a. 1; p. 1009, a. 24). He employs several pages in confuting them.

See the Antinomies in the Platonic Parmenides (pp. 154–155), some of which destroy or set aside the Maxim of Contradiction (Plato and the Other Companions of Sokrates, vol. II. ch. xxv. p. 306).

The distinction of Contradictory and Contrary is fundamental in ratiocinative Logic, and lies at the bottom of the syllogistic theory as delivered in the Analytica Priora. The precision with which Aristotle designates the Universal proposition with its exact contradictory antithesis, is remarkable in his day. Some, however, of his observations respecting the place and functions of the negative particle (οὐ), must be understood with reference to the variable order of words in a Greek or Latin sentence; for instance, the distinction between Kallias non est justus and Kallias est non justus does not suggest itself to one speaking English or French.63 Moreover, the Aristotelian theory of the Proposition is encumbered with various unnecessary subtleties; and the introduction of the Modals (though they belong, in my opinion, legitimately to a complete logical theory) renders the doctrine so intricate and complicated, that a judicious teacher will prefer, in explaining the subject, to leave them for second or ulterior study, when the simpler relations between categorical propositions have been made evident and familiar. The force of this remark will be felt more when we go through the Analytica Priora. The two principal relations to be considered in the theory of Propositions Opposition and Equipollence would have come out far more clearly in the treatise De Interpretatione, if the discussion of the Modals had been reserved for a separate chapter.

63 The diagram or parallelogram of logical antithesis, which is said to have begun with Apuleius, and to have been transmitted through Boethius and the Schoolmen to modern times (Ueberweg, System der Logik, sect. 72, p. 174) is as follows:

A. Omnis homo est justus.	---	E. Nullus homo est justus.
	✕
I. Aliquis homo est justus.	---	O. Aliquis homo non est justus.

But the parallelogram set out by Aristotle in the treatise De Interpretatione, or at least in the Analytica Priora, is different, and intended for a different purpose. He puts it thus:

1. Omnis homo est justus		2. Non omnis homo est justus.
4. Non omnis homo est non justus		3. Omnis homo est non justus.

Here Proposition (1) is an affirmative, of which (2) is the direct and appropriate negative: also Proposition (3) is an affirmative (Aristotle so considers it), of which (4) is the direct and appropriate negative. The great aim of Aristotle is to mark out clearly what is the appropriate negative or Ἀπόφασις to each Κατάφασις (μία ἀπόφασις μιᾶς καταφάσεως, p. 17, b. 38), making up together the pair which he calls Ἀντίφασις, standing in Contradictory Opposition; and to distinguish this appropriate negative from another proposition which comprises the particle of negation, but which is really a new affirmative.

The true negatives of homo est justus Omnis homo est justus are, Homo non est justus Non omnis homo est justus. If you say, Homo est non justus Omnis homo est non justus, these are not negative propositions, but new affirmatives (ἐκ μεταθέσεως in the language of Theophrastus).