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sigurdW
sigurdW is offline
#9
Mar19-12, 01:19 PM
P: 27
Quote Quote by Hurkyl View Post
Edit: I should add that the above isn't the only significance of the paradox. Having the solution for formal logic already, it's easy to forget the more general issue. It clearly demonstrates issues in the semantics of language. (a)"This sentence is false," is perfectly good English, and by the rules of English, the sentence itself really is the referent of the phrase "this sentence", and you run into difficulty when you suppose that we can assign truth values to English propositions.

Second edit: the paradox shows up in the theory of computation too, but with different consequences. With Turing machines (i.e. computer programs), it's fairly straightforward that programs can reference themselves, and we can enact the construction of the liar's paradox: the ensuing argument, however, doesn't yield a paradox: (b)instead, it results in proof by contradiction that there are no algorithms for solving a certain class of problem (e.g. "Does this function return 'true' when given input 'x'?)
You are interesting to read.

(a)
1 This sentence is false.
2 This sentence = "This sentence is false"

Since sentence 2 contradicts the law of identity sentence 2 is false.
Therefore sentence 1 either has no defined subject, or breaks the law of identity.
SO: The paradox cant be derived.
Note. A computer should use the test to exclude the predicate "false" from self referencential use.

(b)
Its probably too tecnical for me to really understand... But I suspect my results (if correct) will affect this class of problem.

PS This insight of yours is unusual:
"Having the solution for formal logic already, it's easy to forget the more general issue."

One cant study the anatomy of paradoxes in a system that doesnt allow self referemce