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This is a law of truth. Roughly speaking, a contradictory of a proposition p is one that can be expressed in the form not-p, or, if p can be expressed in the form not-q, then a contradictory is one that can be expressed in the form q. Thus, e.g., if p is 2 + 1 = 4, then 2 + 1 ≠ 4 is the contradictory of p, for 2 + 1 ≠ 4 can be expressed in the form not-(2 + 1 = 4). If p is 2 + 1 ≠ 4, then 2 + 1 = 4 is a contradictory of p, since 2 + 1 ≠ 4 can be expressed in the form not-(2 + 1 = 4). Thus, mutually contradictory propositions can be expressed in the form, r, not-r. The Principle of Contradiction says that mutually contradictory propositions cannot both be true and cannot both be false. Thus, by this principle, since if p is true, not-p is false, no proposition p can be at once true and false (otherwise bothp and its contradictory would be false). In particular, for any predicate p and object x, it cannot be that p is at once true of x and also false of x. This is the classical formulation of the Principle of Contradiction. There are some senses in which the Principle of Contradiction is not above controversy (see Priest, 1985).: The Development of Logic (Oxford: Clarendon Press, 1962). eds: Paraconsistent Logics (Munich: Philosophia Verlag, 1985). ... log in or subscribe to read full text