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# Darling

'This statement is false.' What do we make of this statement (call it S)? If S is true, then S is false. On the other hand, if S is false, then it is true to say S is false; but, because the Liar sentence is saying precisely that (namely that it is false), S is true. So S is true if and only if it is false. Since S is one or the other, it is both! Debate about sentences like S has been going on among philosophers and logicians for more than 2,000 years without any clear resolution.

Various elaborations of the basic Eubulides Liar paradox have appeared over the ages. In the fourteenth century, the French philosopher Jean Buridan applied it in his argument for the existence of God. In 1913, the English mathematician Philip Jourdain (1879-1921) offered a version that is sometimes referred to as 'Jourdain's Card Paradox.' On one side of a card is written:

THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS TRUE.

On the other side is written:

THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS FALSE.

Yet another popular version of the Liar paradox, guaranteed to perplex, is given by the following three sentences written on a card:

(1) THIS SENTENCE CONTAINS FIVE WORDS.
(2) THIS SENTENCE CONTAINS EIGHT WORDS.
(3) EXACTLY ONE SENTENCE ON THIS CARD IS TRUE.