43. Relations of Opposition and Subordination. -- These relations between propositions may be produced in four different ways: propositions are contradictory, contrary, sub-contrary, or subaltern. The first two are relations of opposition properly so called.

(1) Judgments so opposed to each other as to exclude any intermediate judgment are said to be contradictory. They differ both in form and in quantity. E. g.: Every man is white; some man is not white.^{1}

(2) Judgments which differ only in form, and have the same universal quantity, are so opposed to each other as not to exclude any intermediate judgment, and are called contraries. E. g., every man is just; no man is just -- two extremes between which a third judgment may be slipped in: Some man is not just.

(3) Propositions which differ only in form, and have the same particular quantity, are sub-contrary. E. g.: Some man is just; some man is not just.

(4) Propositions which have the same form, and differ only in quantity, are subaltern. E. g.: Every man is just; some man is just. -- No man is just; some man is not just.

Logicians have adopted the convention of designating by the letters A, E, I, O, the four kinds of propositions as distinguished by quantity and form.

A designates a universal affirmative proposition.

E designates a universal negative proposition.

I designates a particular affirmative proposition.

O designates a particular negative proposition.

The following scheme exhibits the contradictory and contrary modes of opposition.^{2}

{1} Periherm., c. VI.

{2} "A universal affirmative (proposition) and a universal negative are contrary, as Every man is just, No man is just: for a universal negation indeed not only does away with a universal affirmation, but also indicates the extreme distance, inasmuch as it denies all that the affirmative asserts: this is of the essence of contrariety, and therefore the particular affirmative and the particular negative are in the nature of a mean between the contraries. . . . In contradictories the negation does no more than remove the affirmative." St. Thomas, In Periherm., Lect. XI.