Wittgenstein on Why the Liar Paradox Belongs to a Language Game

(i) Introduction
(ii) On the Liar Paradox as a Language Game
(iii) The Liar Paradox Was Created, Not Found

The following passage offers us a short account of the Liar Paradox:

“[T]he classical liar paradox [] is the statement of a liar that they are lying: for instance, declaring that ‘I am lying’. If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In ‘this sentence is a lie’ the paradox is strengthened in order to make it amenable to more rigorous logical analysis. [] Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction.

“If ‘this sentence is false’ is true, then it is false, but the sentence states that it is false, and if it is false, then it must be true, and so on.”