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Showing posts from May, 2006

IN THE MATTER OF ‘EPIMENIDES’

Paradoxes are self-contradictory statements, the meaning of which is revealed only by careful scrutiny. They have function in poetry, however, that go beyond mere wit or getting attention. Highly amusing and often tantalising, logical paradoxes generally lead to searching discussions on the foundations of mathematics.

The most talked about paradox of all times is Epimenides or the liar’s paradox. Epimenides was a Greek poet who lived in Crete in 6th century BC. He remarked, ‘All Cretans are liars’. It is self-contradictory for Epimenides was a Cretan himself.

An English mathematician, PEB Jourdain gave a similar dilemma, in 1913, when he proposed the card paradox. This was a card on one side of which was printed: ‘The sentence on the other side of this card is TRUE.’ On the other side of the card the sentence read: ‘The sentence on the other side of this card is FALSE.’

The same is true of the barber paradox, offered by Bertrand Russell. The only barber in the village declared that he sh…