[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.

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.

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