Criterion of meaning

Statement

According to Ayer, analytic statements are tautologies. A tautology is a statement that is necessarily true, true by definition, and true under any conditions. A tautology is a repetition of the meaning of a statement, using different words or symbols. According to Ayer, the statements of logic and mathematics are tautologies. Tautologies are true by definition, and thus their validity does not depend on empirical testing.

Synthetic statements, or empirical propositions, assert or deny something about the real world. The validity of synthetic statements is not established merely by the definition of the words or symbols they contain. According to Ayer, if a statement expresses an empirical proposition, then the validity of the proposition is established by its empirical verifiability.

Propositions are statements that have conditions under which they can be verified. By the verification principle, meaningful statements have conditions under which their validity can be affirmed or denied.

Statements that are not meaningful cannot be expressed as propositions. Every verifiable proposition is meaningful, although it may be either true or false. Every proposition asserts or denies something, and thus is either true or false.