The Epimenides Paradox

Post 417

‘Epimenides the Cretan says, “All the Cretans are liars”, but Epimenides is himself a Cretan; therefore he is himself a liar. But if he be a liar, what he says is untrue, and consequently the Cretans are veracious; but Epimenides is a Cretan, and therefore what he says is true; saying the Cretans are liars, Epimenides is himself a liar, and what he says is untrue. Thus we may go on alternately proving that Epimenides and the Cretans are truthful and untruthful simultaneously’. So, if a Cretan states all Cretans are liars, is he being truthful or untruthful? ‘Tis the question, readers.

This is a brilliant paradox from the mind of Cretan philosopher Epimenides of Knossos. ‘Epimenides was a Cretan who made one immortal statement: “All Cretans are liars”.’ But from this arises a paradox of self-reference. Has Epimenides spoken the truth? If so, he is a liar. But if he’s a liar, what he said isn’t true, and all Cretans are truthful. But Epimenides was a Cretan, ergo what he says must be true. If you’re not a liar, you’re truthful. But if we believe that it is true, then what he says must be untrue. You see? This could go on for a while.

But it is solvable. Try to figure it out before you read on.

If what Cretan Epimenides says is true, he would be a liar. Therefore the statement ‘all Cretans are liars’ must be false. So assuming the statement is true leads to the conclusion the statement is false. So the statement is false. ‘All Cretans are liars’ is itself a lie. If so, then that means there exists a Cretan who is honest. But that Cretan need not be Epimenides. Meaning he can lie. So if we see the statement as false, it means the statement cannot be true.

Therefore, there is no paradox. It can be solved with logic, readers.

It is a wonderful head scratcher.

Toodle-pip :)(:

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