A paradox is an absurd or self-contradictory statement, so by definition, it’s liable to make your head spin. We’ve got one of the most ancient paradoxes there is, and it’s certainly no different. It’s called the liar paradox.
The liar paradox, also known as the liar sentence, states “this sentence is false.” If that statement makes you go a little crazy, you’re not the first. The liar paradox first came about in ancient Greece, and philosophers have been puzzling over it ever since. It’s even said that the gravestone of scholar Philetas of Cos, from the third century B.C.E., is engraved with the words “‘Twas the Liar who made me die, And the bad nights caused thereby.”
There are many other versions of this ancient puzzle. The French philosopher Jean Buridan used its contradictory logic in his proof of God’s existence: “God exists. None of the sentences in this pair are true.” There’s also the self-referential chain, “The following sentence is true. The following sentence is true. The first sentence in this list is false.”
Here’s why the liar paradox causes philosophers so much grief: if the sentence is true, then it must be false. But if the sentence is false, then it must be true. That’s what makes it a paradox. It’s an argument that leads to a self-contradictory conclusion. There are probably as many schools of thought on how to solve this paradox as there are philosophers in the world, but one thing is true (not false!): it highlights the limitations of classical logic.
How to Resolve the Liar’s Paradox