Re: Provable vs Computable

From: scerir <>
Date: Fri, 4 May 2001 16:15:19 +0200

Juergen Schmidhuber wrote:
> Which are the logically possible universes? Max Tegmark mentioned
> a somewhat vaguely defined set of "self-consistent mathematical
> structures'' implying provability of some sort. The postings of Bruno
> Marchal and George Levy and Hal Ruhl also focus on what's provable
> and what's not.
> Is provability really relevant? Philosophers and physicists find
> it sexy for its Goedelian limits. But what does this have to do with
> the set of possible universes?

Many people think that if a formal statement is neither provable nor
refutable, then it should be considered neither true, nor false.
But it is not that way that we - normally - use the term "true".
Somebody wrote: "Suppose that I have a steel safe that nobody
knows the combination to. If I tell you that the safe contains 100
dollars - and it really does contain 100 dollars - then I'm telling the
truth, whether or not anyone can prove it. And if it doesn't contain 100
dollars, then I'm telling a falsehood, whether or not anyone can prove it."
(A multi-valued logics can deal with statements that are either definitely
true or definitely false, but whose actual truth value may, or may not,
be known, or even be knowable.).
- scerir
Received on Fri May 04 2001 - 07:19:41 PDT

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