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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In Immanuel Kant's moral philosophy, an imperative that presents an action as unconditionally necessary (e.g., “Thou shalt not kill”), as opposed to an imperative that presents an action as necessary only on condition that the agent wills something else (e.g., “Pay your debts on time, if you want to be able to obtain a mortgage”). Kant held that there was only one formally categorical imperative, from which all specific moral imperatives could be derived. In one famous formulation, it is: “Act only according to that maxim by which you can at the same time will that it should become a universal law.” Seealso deontological ethics.
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