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 ([Greek: ou)]), 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. [Footnote 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. |X| 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 [Greek: A)po/phasis] to each [Greek: Kata/phasis (mi/a a)po/phasis mia=s katapha/seôs], p. 17, b. 38), making up together the pair which he calls [Greek: A)nti/phasis], 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.