# 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 ὑπάρχειν τε καὶ μὴ ὑπάρχειν 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*.