Monday, April 06, 2009

Sleight of hand? Judge for yourself.

Crete, a Cretan, says, “All Cretans are liars.”

Suppose every Cretan besides Crete is a liar—then it’s false that ‘all Cretans are liars’, since Crete (who is a Cretan, remember) is telling the truth. If any Cretan tells the truth, then it’s false that ‘all Cretans are liars’.

Suppose every Cretan, including Crete, is a liar—then it would be true that ‘all Cretans are liars’. But if it’s true that all ‘all Cretans are liars’ then whatever Crete says must be false, in which case it’s false that ‘all Cretans are liars’.

How about a third interpretation? Suppose, at t –2, it’s true that ‘all Cretans are liars’. Suppose further, at t –1, Crete says, “All Cretans are liars.” But at t –1 it’s false that ‘all Cretans are liars’ (since Crete is telling the truth), hence Crete is lying when he says, “All Cretans are liars.” So he doesn’t contradict himself when he says, at t –1, that, “All Cretans are liars.” But if this is right, then there is no paradox. For if Crete is lying when he says, “All Cretans are liars,” then we can say, without paradox, “It’s true that ‘all Cretans are liars, including Crete at t-1.’”

I hereby dub the third interpretation, “The non-paradoxical recursive interpretation.”

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4 Comments:

Blogger brianna. said...

i don't get it.

12:52 PM  
Blogger brianna. said...

This comment has been removed by the author.

7:07 PM  
Blogger Derek von Barandy said...

Derek: I lie all the time.
Someone: No you don’t, if it’s true that ‘you lie all the time’, then you just told the truth. In which case you don’t lie all the time.
Derek: Didn’t I just tell you I lie all the time?
Someone: Yes.
Derek: …
Hermogenes: Excuse me, gentlemen; may I interject? I think Derek’s point is that by saying truly “I lie all the time,” he is actually lying, for although the statement “I lie all the time” was true before he said it, at the moment he said it, it no longer remained true, and therefore he was lying at the moment he said “I lie all the time,”—for the proposition ‘Derek lies all the time’ becomes false when he says something true. Someone confirmed this when he said to Derek, “In which case you don’t lie all the time.”
Someone: How so?
Hermogenes: Derek agreed with you when you said “he doesn’t lie all the time,” but since he lies all the time Derek lied when he said, “I lie all the time.”
Someone: I get it.
Derek: You got it all wrong.

10:00 PM  
Blogger brianna. said...

ohhh i get it now.

horse's ass.

12:06 PM  

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