Contradiction, law of
Contradiction, law of
is given by traditional logicians as “A is B and A is not B cannot both be true.” It is usually taken to be the theorem of the propositional calculus, ~[p~p]. In use, however, the name often seems to refer to the syntactical principle or precept which may be formulated as followsA logical discipline containing (an applied) propositional calculus, or a set of hypotheses or postulates to be added to such a discipline, shall not lead to two theorems or consequences of the forms A and ~A. The law is explicitly stated in a syntactical form, e.g. by Ledger Wood in his The Analysis of Knowledge (1940). — A.C.