Liar Paradox - History

History

The Epimenides paradox (circa 600 BC) has been suggested as an example of the liar paradox, but they are not logically equivalent. The semi-mythical seer Epimenides, a Cretan, reportedly stated that "The Cretans are always liars." However, Epimenides' statement that all Cretans are liars can be resolved as false, given that he knows of at least one other Cretan who does not lie.

One version of the liar paradox is attributed to the Greek philosopher Eubulides of Miletus who lived in the 4th century BC. Eubulides reportedly asked, "A man says that he is lying. Is what he says true or false?"

The paradox was once discussed by St. Jerome in a sermon:

"I said in my alarm, 'Every man is a liar!' "(Psalm. 116:11) Is David telling the truth or is he lying? If it is true that every man is a liar, and David's statement, "Every man is a liar" is true, then David also is lying; he, too, is a man. But if he, too, is lying, his statement: "Every man is a liar," consequently is not true. Whatever way you turn the proposition, the conclusion is a contradiction. Since David himself is a man, it follows that he also is lying; but if he is lying because every man is a liar, his lying is of a different sort."

In early Islamic tradition liar paradox was discussed for at least 5 centuries starting from late 9th century apparently without being influenced by any other tradition. Naṣīr al-Dīn al-Ṭūsī could have been the first logician to identify the liar paradox as self-referential.