In the 1970s, Kripke turned his attention to the problem of semantic paradoxes. It is not surprising that Kripke was interested in this issue, given his interest in puzzles and formal logic. The problem, in a nutshell, is how is it possible to have a truth predicate apply to sentences that themselves contain a truth predicate? This is an ancient problem and it is often called the problem of the liar. According to the ancient version of the liar paradox, Epimenides, a Cretan, is supposed to have asserted the sentence ‘All Cretans are liars’. Given certain empirical assumptions, this sentence yields the result that it is true if and only if it is false. A more direct version of the problem can be seen with the following sentence:
(1) This sentence is false.
(1) is true if and only if it is false. It would be a mistake to think that the problem that is expressed by “liar sentences” such as (1) is only a problem for a very special class of sentences, namely those that involve self-reference, as (1) does. In fact, there are many ways that such paradoxical results can obtain. For example, consider the pair of sentences
(2) Sentence (3) is false.
(3) Sentence (2) is true.
Sentence (2) does not involve self-reference (at least not directly), yet (2) is true if and only if (2) is false. The paradox of the preface is another example.