Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 01/17/05
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Date: Mon, 17 Jan 2005 11:42:50 +0100
Torkel Franzen wrote:
>
> 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.
Do you have any references/can you provide any further explanation
for these? the miracle: was that Goedel's reaction to Turing's
undecidability result? What is the "more or less convincing" you are
referring to; is that the range of formality or something else (is
that a technical disagreement or philosophical one)?
-- Mitch Harris (remove q to reply)
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