§ 452. Now the problem of opposition is this: Given the truth or falsity of any one of the four propositions A, E, I, O, what can be ascertained with regard to the truth or falsity of the rest, the matter of them being supposed to be the same?
§ 453. The relations to one another of these four propositions are usually exhibited in the following scheme—
A . . . . Contrary . . . . E
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Subaltern Contradictory Subaltern
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I . . . Sub-contrary . . . O
§ 454. Contrary Opposition is between two universals which differ in quality.
§ 455. Sub-contrary Opposition is between two particulars which differ in quality.
§ 456. Subaltern Opposition is between two propositions which differ only in quantity.
§ 457. Contradictory Opposition is between two propositions which differ both in quantity and in quality.
§ 458. Subaltern Opposition is also known as Subalternation, and of the two propositions involved the universal is called the Subalternant and the particular the Subalternate. Both together are called Subalterns, and similarly in the other forms of opposition the two propositions involved are known respectively as Contraries, Sub-contraries and Contradictories.
§ 459. For the sake of convenience some relations are classed under the head of opposition in which there is, strictly speaking, no opposition at all between the two propositions involved.
§ 460. Between sub-contraries there is an apparent, but not a real opposition, since what is affirmed of one part of a term may often with truth be denied of another. Thus there is no incompatibility between the two statements.