Eubulides Liar Paradox

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  2. Goedel's Incompleteness Theorem. Liar's Paradox. Self Reference. By riatlogjuvernde.gqks
  3. Liar paradox
  4. Resolving the Liar’s Paradox

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Goedel's Incompleteness Theorem. Liar's Paradox. Self Reference. By riatlogjuvernde.gqks

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Liar paradox

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Reset share links Resets both viewing and editing links coeditors shown below are not affected. So S is true if and only if it is false. Since S is one or the other, it is both!


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Debate about sentences like S has been going on among philosophers and logicians for more than 2, years without any clear resolution. The roots of the Liar paradox stretch back to the philosopher Epimenides in the sixth century B. Epimenides said: "All Cretans are liars One of their own poets has said so. But actually there is no paradox here. A 'liar,' in everyday language, is someone who on occasions knowingly gives false answers. This leads to no problem at all: the poet, while lying occasionally, this time spoke the truth.

Resolving the Liar’s Paradox

However, most formulations of logic define a 'liar' as an entity that always produces the negation of the true answer, that is, someone who does nothing but lie. Thus, the poet's statement cannot be true: if it were, then he himself would be a liar who just spoke the truth, but liars don't do that.

However, no contradiction arises if the poet's statement is taken to be false: the negation of 'All Cretans are liars' is 'Some Cretans aren't liars', in other words: some Cretans sometimes speak the truth. This doesn't contradict the fact that our Cretan poet just lied.