What is the Epimenides Paradox? – All Cretans are liarsJune 26, 2021
This paradox is actually a problem in logic.
This problem is named after the Cretan philosopher Epimenides of Knossos. The philosopher said: Κρῆτες ἀεί ψεύσται, “Cretans are always liars.” Another version of the problem is found in Douglas R. Hofstadter’s Gödel, Escher, Bach:
Epimenides was a Cretan who made the immortal expression; “All Cretans are liars.”
This statement of Epimenides is called the Epimenides paradox. It is sometimes referred to as the Liar paradox or the Cretan paradox. The paradox arises from:
If we accept the proposition “all Cretans are liars” as true, then Epimenides, who is also Cretan, must be a liar. If Epimenides is a liar, then the proposition “all Cretans are liars” must be false, as they all say. If we believe that he is telling the truth, we know that he is lying. It follows that the proposition is both true and false.
If we take the proposition that “all Cretans are liars” false, then Epimenides, who is also Cretan, must be telling the truth. So the proposition “all Cretans are liars” must be true. Again, a contradictory result emerges.
A proposition cannot be both true and false.
There is a little trick that has been overlooked here that has made mathematicians miscalculate for years, and that is:
The reverse of the proposition “All Cretans are liars” is not “All Cretans are truthful”. In fact, it should be “There is at least one Cretan who is truthful”.
After the discovery that the opposite of EVERY word in logic is at least ONE sentence, this blockage in mathematics was overcome and it was revealed that the Epimenides paradox was not a paradox.
In the light of this information, if the proposition “All Cretans are liars” is false, the proposition “At least one Cretan tells the truth” is true. Since it is possible that one of them was Epimenides, the paradox disappears.
Source: Atatürk University Department of Sociology Lecture Notes for Grade 1 “Introduction to Philosophy” and Grade 3 “History of Contemporary Philosophy” (Ömer YILDIRIM)