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


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