In syllogistic, a proposition in which the predicate is affirmed or denied of all or part of the subject. Thus, categorical propositions are of four basic forms: “Every S is P,” “No S is P,” “Some S is P,” and “Some S is not P.” These are designated by the letters A, E, I, and O, respectively; thus, “Every man is mortal” is an A-proposition. Categorical propositions are to be distinguished from compound and complex propositions, into which they can enter as integral terms. In particular, they contrast especially with hypothetical propositions, such as “If every man is mortal, then Socrates is mortal.”

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