 Remark: The language L3 interpreted by the ground model M3 formalizes the liar's paradox, with the sentence ¬Tλ as the offending liar's sentence. Thus, despite Theorem 2.1, Clauses (1) and (2), Clause (3) strongly suggests that in a semantics for languages capable of expressing their own truth concepts, T cannot, in general, have a classical signification; and the ‘iff’ in the T-biconditionals will not be read as the classical biconditional. We take these suggestions up in Section 4, below.