Epimenides Paradox

A version of the liar's paradox, attributed to the philosopher Epimenides in the sixth century BC. "All Cretans are liars... One of their own poets has said so." This is not a true paradox since the poet may have knowledge that at least one Cretan is, in fact, honest, and so is lying when he says that all Cretans are liars. There therefore need be no self-contradiction in what could simply be a false statement by a person who is himself a liar.

A sharper version of the paradox (which has no such loophole) is the Eubulides paradox, "This statement is false."

REFERENCES

Curry, H. B. Foundations of Mathematical Logic. New York: Dover, pp. 5-6, 1977.

Erickson, G. W. and Fossa, J. A. Dictionary of Paradox. Lanham, MD: University Press of America, pp. 58-60, 1998.

Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. New York: Hyperion, p. 115, 1998.

Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 17, 1989.

Hofstadter, D. R. Metamagical Themas: Questing of Mind and Pattern. New York: BasicBooks, p. 7, 1985.Prior, A. N. "Epimenides the Cretan." J. Symb. Logic 23, 261-266, 1958.