1911 Encyclopædia Britannica/Contradiction, Principle of
CONTRADICTION, PRINCIPLE OF (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 (τὸ γὰρ αὐτὸ ὐπάρχειν τε καὶ μὴ ὐπάρχειν ἀδύνατον τῷ αὐτῷ καὶ κατὰ τὸ αὐτό, Metaph. Γ 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 foll.; for the various expressions of the law see Ueberweg's Logik, § 77; also J. S. Mill, Examination of Hamilton, 471; Venn, Empirical Logic.