Re: Provable vs Computable

From: Marchal <marchal.domain.name.hidden>
Date: Sat May 5 07:24:33 2001

scerir wrote:

>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.).


That is basicaly the difference between classical logic
with gap between proof and truth, and intuitionistic
logic, or constructive logic, which equivote truth and provability.
And that is something which will be translated in the language of
the machine ... It is part of the proof I explain currently.


I have begin the explanations of logic with classical logics.
But other logics are fundamental in the derivation (mainly
intuitionist and quantum logics).


Bruno
Received on Sat May 05 2001 - 07:24:33 PDT