The Paideia Archive: Twentieth World Congress of Philosophy

Volume 34, 1998

Philosophy of Mathematics

Roger Wertheimer
Pages 48-55

Translation, Quotation and Truth

If logical truth is truth due solely to syntactic form, then mathematics is distinct from logic, even if all mathematical truths are derivable from definitions and logical principles. This is often obscured by the plausibility of the Synonymy Substitution Principle that is implicit in the Fregean conception of analyticity: viz., that synonyms are intersubstitutable without altering sentence sense. Now, unlike logical truth, mathematical truth is not due to syntax, so synonym interchange in mathematical truths preserves sentence syntax, sense, and mathematical necessity. Mathematical necessity, therefore, differs from both logical and lexical necessity.