29 May 2004

This Sentence is False

Posted by Oblivion in General | 7:31pm

Epimenides the Cretan, a philosopher of the 6th century BC, is said to have uttered the sentence, “All Cretans are liars”. As he himself was a Cretan, this gave rise to a paradox—if he were telling the truth, then he would be a liar. Depending on how one defines a liar, the paradox is resolvable; he could have been a habitual liar who was telling the truth in this one instance. However, a stronger version of the paradox, known as the Liar paradox—“this sentence is false”—is not resolvable in conventional logic systems.

Indeed, the circular loop that the sentence induces—if it is false, it must be true, and if true, false—has been used more than once in science-fiction movies to cause marauding computers to lose their sanity and explode. Traditionally, logicians have made a stark distinction between truthhood and falsity. A statement was considered to be either true (given a truth value of one) or false (a value of zero). In the 1960s, Lotfi Zadeh of the University of California at Berkeley came up with the catchy innovation of “fuzzy logic”. In this system, things could be sort-of true, or only partially false. A “truth value” of 0.5 meant that a statement was half-true, and so forth.

On close observation, fuzzy logic is the mathematical equivalent of the 'middle path' advocated by the Buddha. Avoiding the extremes, thus avoiding any conclusions - this helps perception to be undistorted. This is the primary basis for a rational mind. The world absolutely needs this now more than

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