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[INFO] "All Cretans are liars" - The Liars Paradox
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base2wo
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Joined: 08 Oct 2005
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 		[INFO] "All Cretans are liars" - The Liars Paradox
Matt Viet's Week 3 entry has some nteresting background. First, there's the cretan/cretin homonym that occurs because he's talking and is misunderstood: "cretin" is an "idiot", "cretan" is someone from Crete.

"All idiots are liars" is an interesting thought. But here's some background on what Matt said, for those less familar with Greek philosophy:

From the Wikipedia entry on the Liar Paradox:

"Epimenides paradox" is often considered an equivalent or interchangeable term for "liar paradox" and it is also the kind of supposed "liar paradox" that is best known to the general public. However, an identification of the two is very questionable:

Epimenides was a sixth century BC philosopher-poet. Himself a Cretan, he reportedly wrote:

The Cretans are always liars. (Titus 1:12)
<snip>
The problem of the paradox is that it seems to show that our most cherished common beliefs about truth and falsity actually lead to a contradiction. Sentences can be constructed that cannot consistently be assigned a truth value even though they are completely in accord with grammar and semantic rules. Consider the simplest version of the paradox, the sentence This statement is false. If we suppose that the statement is true, everything asserted in it must be true. However, because the statement asserts that it is itself false, it must be false. So the hypothesis that it is true leads to the contradiction that it is true and false. Yet we cannot conclude that the sentence is false for that hypothesis also leads to contradiction. If the statement is false, then what it says about itself is not true. It says that it is false, so that must not be true. Hence, it is true. Under either hypothesis, we end up concluding that the statement is both true and false. But it has to be either true or false (or so our common intuitions lead us to think), hence there seems to be a contradiction at the heart of our beliefs about truth and falsity.

PostPosted: Sun Oct 09, 2005 9:57 am
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Phaedra
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 		Heh, that used to be my favorite paradox when I was younger, until I realized that it doesn't really work, semantically, in English unless you change it to "All Cretans always lie."
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PostPosted: Sun Oct 09, 2005 12:39 pm
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