What is the ancient Greek paradox "catch 22"?

Chris asked:

What is the name or source, assume it will be titled in one of a Greek’s dialogues, on a logical paradox, catch 22.

Like Kurt Godel’s incompleteness theorem, in layperson aphorism, ‘this cannot be proven’.

Answer by Shaun Williamson

There were certain paradoxes which were known to the ancient Greeks which I think of as paradoxes of self-reference. I don’t know of any other name for this type of paradox nor do I know of any source documents for them.

A typical example is as follows.

An Athenian who is thinking of travelling to Crete meets a Cretan in Athens and ask him ‘What are the people of Crete like?’ The Cretan answers ‘All Cretans are liars’.

The question is ‘Is this Cretan telling the truth?’. If he is telling the truth then he is lying, if he is lying then he is telling the truth (and so on). This paradox is attributed to the Cretan philosopher Epimenides who lived around 600BC.

Godel applied this idea in his proof because he realised that our system of mathematics allows self referential sentences such as ‘This sentence contains five words’. If we disallow self reference then Godel’s proof would no longer hold but our system of mathematics would be very different.

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