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[Home]Liar paradox

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The liar paradox, attributed to the Greek philosopher [Eubulides of Miletus]? who lived in the fourth century BC, is the statement
I am lying now.
or more succinctly
This statement is false.
As opposed to the Epimenides paradox, this is a true paradox: assuming that the statement is true, then it must be false; assuming it is false, then it must be true. No truth value can be consistently assigned to the statement.

The proof of Goedels Incompleteness Theorem essentially consists in a formally correct formulation of a variation of this paradox in the context of a sufficiently strong [axiomatic system]?.

To avoid having a sentence refer to its own truth value, one can also construct the paradox

The following sentence is true.
The preceding sentense is false.


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Last edited August 2, 2001 5:36 pm (diff)
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