CONTRARY.—Aristotle defines contrary, "that which in the same genus differs
most;" as in colour, white and black; in sensation, pleasure and pain; in
morals, good and evil. Contrary, like contradictory, is applied both to
and Propositions. This relation to one another is different from that of
contradictions, e.g., " Pleasure and pain are opposed to each other as
contraries, not as contradictories, that is, the
affirmation of the one implies the negation of the other, but the negation of
the one does not infer the affirmation of the other; for there may be a third or
intermediate state, which is neither one of pleasure nor one of pain, but one of
indifference" (Hamilton, Metaph, lect. XLII. vol. II. p; 436). Of Propositions,
the Universal Affirmative (A) and the Universal Negative (E) are opposed to one
another as contraries, and of these both cannot be true, and both may be false.
Thus, the affirmative of the one implies the negative of the other, but not
vice versâ. Sub-contrary propositions are the particular affirmative (I) and the
particular negative (0). Of these both may be true, and only one can be false.