Monday, November 5, 2007

i'm not a liar (but Epimenides is)

In my post about the Liar's Paradox (Epimenides the Cretan says, "All Cretans are liars") I discussed the related case of "This sentence is false" but I didn't resolve the oringal paradox from Epimenides. In this case, though, the resolution of the paradox is even easier because although it's called, "The Liar's Paradox" there isn't actually any paradox.

The paradox is usually presented in this way (and I did the same in my post). Epimenides says that ALL Cretans are liars. Therefore Epimenides is a liar and what he says is a lie. Therefore Cretans are not liars, they are honest, and therefore Epimenides is an honest man who tells the truth. So then, all Cretans are liars, and so on forever.

However, if it's a lie to say that ALL Cretans are liars, it is not necessarily the truth that ALL Cretans are honest. The original statement would still be a lie if there were even one honest Cretan. If you take Epimenides' lie to mean that in truth all Cretans are honest men, then Epimenides himelf must be an honest man and you fall into the circular paradox. But if you take his lie to mean that in truth some Cretans are honest and others are liars then the solution is simple: Epimenides is a liar who tells a lie. All Cretans are not liars, but Epimenides is.

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