Epimedes and “Self-Referential Paradoxes”

This is a replica of a Roman copy of a Greek fifth-century original of a man called Epimedes. We actually don’t know if he looked like this, because he lived earlier (6th-c BCE). But the eyes closed thing Epimedes has going on here is what I liked, because it’s the face many of us make when confronted by “self-referential paradoxes.” And this man gave his name to one of the first.

Self-referential paradoxes twist your brain because they sound logical but cannot make sense. For instance, “if God is all powerful, can he create a stone that he cannot lift?” See what I mean?

Epimedes’ paradox comes from a poem he wrote praising Zeus, and in it he claims that all Cretans are liars — but Epimedes was a Cretan. Actually, it was later philosophers who labeled this a self-referential paradox, because the statement isn’t as inconsistent as it may seem. (And why? Because you have to assume that all Cretan statements are false. Also, what if Epimedes is a liar but he knows one honest Cretan?)

Regardless, the logical difficulties in self-referential paradoxes ended up having very important implications for mathematics and computing — the mathematicians Kurt Gödel and Alan Turing derived key components of their work from them to argue that “no formal consistent system of mathematics can ever contain all possible mathematical truths” and that there will always be some task a computer cannot perform, “namely reasoning about itself”.