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Posted by Alan on July 20, 2003 16:34:04 UTC

It is possible to see ( in my opinion) , that math statements are circular, given Harv's arguments. "

Tarski's theory of truth claims that "X is true if and only if X corresponds to the facts".

Does "2 = 2 = 4" correspond to the facts?

My point is: that this question may be already answered by the DEFINITION of "2 " and "4" as used in math.

So I conclude that you have exposed the circularity in math by asking the questions you did about math and truth.

I suggest that the very definition of numbers themselves involves axioms and inferences that already require correspondence with "the facts"; that math might be pre-defined as true in Tarski perspective.

According to Paul; "three" is defined as the group including all triples. If so; any factual triple has been defined as a three also?


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