Identity, law of
Identity, law of
Given by traditional logicians as “A is A.” Because of the various possible meanings of the copula (q.v.) and the uncertainty as to the range of the variable A, this formulation is ambiguous. The traditional law is perhaps best identified with the theorem x = x, either of the functional calculus of first order with equality, or in the theory of types (with equality defined), or in the algebra of classes, etc. It has been, or may be, also identified with either of the theorems of the propositional calculus, p ? p, p = p, or with the theorem of the functional calculus of first order, F(x) ?x F(x). Many writers understand, however, by the law of identity a semantical principle — that a word or other symbol may (or must) have a fixed referent in its various occurrences in a given context (so, e.g., Ledger Wood in his The Analysis of Knowledge). Some, it would seem, confuse such a semantical principle with a proposition of formal logic. — A.C.