semantic antinomy [Grk antinomía ‘conflict of laws’] (also semantic paradox)

Contradictory statement(s) whose truth value cannot be determined. Compare, for example, the semantic antinomy from classical times about the (lying) Cretan, who maintained: All Cretans are liars. This statement is true only when it is false. Such a logical contradiction can be resolved through the distinction of different linguistic levels ( object language vs metalanguage) which both occur in this example; the assertion of the Cretan that All Cretans are liars creates an impermissible statement about one’s self, which can only be resolved in the object language assertion All Cretans are liars and in the metalinguistic judgment of this assertion: namely, that it is not true. ( also formal logic, type theory)

References

Brendel, E. 1992. Die Wahrheit über den . Berlin and New York. Kripke, S. 1975. Outline of a theory of truth. JP 72.690-716. Levi, D.S. 1988. The liar parody. Philosophy 63.43-62. Martin, R. (ed) 1970. The paradox of the liar. New Haven, CT. Tarski, A. 1956. Logic, semantics, metamathematics. Oxford.