Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
From: Torkel Franzen (torkel_at_sm.luth.se)
Date: 01/13/05
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Date: 13 Jan 2005 04:49:16 +0100
"LordBeotian" <pokipsy76@CANCELLAMIyahoo.it> writes:
> In the same way I wanted to say something about some "statements that would
> naturally be ragarded as true" without formalizing this notion.
Gödel regarded it as a kind of miracle that the informal concept of
mechanical computability could in fact be captured in a formal
definition. Provability is much more problematic. There was no
disagreement in mathematics over particular algorithms - it was clear
to everybody that Sturm's algorithm was an algorithm, that Euclid's
algorithm was an algorithm, and so on. In the case of provability,
there is disagreement over what constitutes a proof, and there is
a distinction between more or less conclusive or convincing proofs.
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