Solving The Epimenides Paradox

By James Donahue

Epimenides was a Cretan philosopher who lived in Knossos about 600 BC. The paradox bearing his name suggests that he once said: "All Cretans are liars." Since Epimenides was a Cretan, he appears to be calling himself a liar. Therefore, can his claim be considered true or false?

The Epimenides Paradox is, like all paradoxes, an exercise in logic. If Epimennides is a Cretan, and if his statement, that all Cretans are liars is true, then his having said it must be considered a lie. And if it is a lie, then all Cretans are not liars. But if true, then Epimenides is himself a liar.

This, of course, is a variation of the Liar Paradox, which we addressed last week. At face value, we can continue on and on, proving that Epimenides and the Cretans are both truthful and untruthful.

In this case, however, there is a suggested solution to this problem. As one philosopher suggested, "if we assume the statement is false, then its correct negation would be: "there exists a Cretan who is honest" would be true.

This does not have to be a contradiction since the honest Cretan does not have to be Epimenides. It just means that Epimenides knows at least one honest Cretan and lies about it. Thus we avoid a paradox by showing that the statement: "all Cretans are liars" is a false statement made by Epimenides, himself a liar.

If you think these paradoxes are silly and perhaps a waste of time to be even thinking about, consider this. Back in the day when philosophers like Epimenides, Socrates and other great thinkers were around, they played with problems like these to help in the development of the kind of logic and mathematics that is in use today.