# 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 (Gr., *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*.

*Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)*