CONTRADICTION, PRINCIPLE OF (principiurn con tradictionis), in logic, the term applied to the second of the three primary "laws of thought." The oldest statement of the law is that contradictory statements cannot both at the same time be true, e.g., the two propositions "A is B" and "A is not B" are mutually exclusive. A may be B at one time, and not at another; A may be partly B and partly not B at the same time; but it is impossible to predicate of the same thing, at the same time, and in the same sense, the absence and the presence of the same qual ity. This is the statement of the law given by Aristotle. It takes no account of the truth of either proposition; if one is true, the other is not; one must be false.
Modern logicians, following Leibniz and Kant, have generally adopted a different statement, by which the law assumes an es sentially different meaning. Their formula is "A is not not—A"; in other words it is impossible to predicate of a thing a quality which is its contradictory. Unlike Aristotle's law this law deals with the necessary relation between subject and predicate in a single judgment: Whereas Aristotle states that one or other of two contradictory propositions must be false, the Kantian law states that a particular kind of proposition is in itself necessarily false. On the other hand there is a real connection between the two laws. The denial of the statement "A is not—A" presupposes some knowledge of what A is, i.e., the statement A is A. In other words a judgment about A is implied. Kant's analytical propo sitions depend on presupposed concepts which are the same for all people. His statement, regarded as a logical principle purely, does not therefore amount to more than that of Aristotle.