PRINCIPLE OF

CONTRADICTION (principium contradictionis)  , 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 quality . This is the statement of the law given by Aristotle (TO yap afire inraPXEw TE Kai µi) irrrapXEIV abbac roV nil' ai)rcli Kai Kara TO airrb, Metaph . P 3, 1005 b 19) . It takes no account of the truth of either proposition; if one is true, the other is not; one of the two must be true . Modern logicians, following Leibnitz and Kant, have generally adopted a different statement, by which the law assumes an essentially 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 connexion 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 propositions depend on presupposed concepts which are the same for all people . His statement, regarded as a logical principle purely and apart from material facts, does not therefore amount to more than that of Aristotle, which deals simply with the significance of negation . See text-books of Logic, e.g . C . Sigwart's Logic (trans . Helen Dendy, London, 1895), vol. i. pp . 142 fell . ; for the various expressions of the law see Ueberweg's Logik, § 77; also J . S . Mill, Examination of Hamilton, 471; Venn, Empirical Logic .