The Liar and related paradoxes

The importance of the Liar paradox to the theory of truth has already become apparent; for Tarski's formal adequacy conditions on definitions of truth are motivated, in large part, by the need to avoid it. It is time, now, to give the Liar and related paradoxes some direct attention on their own account.

Why the ‘Liar paradox’? Well, the Liar sentence, together with apparently obvious principles about truth, leads, by apparently valid reasoning, to contradiction; that is why it is called a paradox (from the Greek, ‘para’ and ‘doxa’ ‘beyond belief’).

The Liar comes in several variants; the classic version concerns the sentence:

Suppose S is true; then what it says is the case; so it is false. Suppose, on the other hand, that S is false; then what it says is not the case, so it is true. So S is true iff S is false. Variants include indirectly self-referential sentences, such as:

Another variant, the ‘Epimenides’ paradox, concerns a Cretan called Epimenides, who is supposed to have said that all Cretans are always liars.