FOM: Goedel: truth and misinterpretations

[V. Sazonov]

Kanovei wrote:
> 
> > Date: Tue, 31 Oct 2000 08:17:03 +0100
> > From: Torkel Franzen <torkel at sm.luth.se>
> 
> > that a purported observation such as
> >
> >   (1)  Even if Goldbach's conjecture is true, it is not necessarily
> >        provable in ZFC
> >
> > is mysterious. In what way is (1) mysterious?
> 
> Misterious is not a proper word, fraudulent would fit better.
> To be scientifically considerable, "thesis" (1) has to be
> preceded by at least explanation, if not a rigorous definition,
> what is the intended meaning of "true". That has not been made
> clear in the course of the discussion.
> 
> I can see three possible ways to specify the meaning of
> the phrase Goldbach's conjecture is true:

.............

I completely agree with Kanovei's comments. My intention was 
to give an analogous reply. Also "provable in ZFC" can be 
specified in various ways if the author of (1) does not intend 
to do that himself. 

> because (according to modern physics)
> the universe has a finite number of particles.

I would ask what does it mean? May be "bounded (but infinite!)" 
is better. Where is the end of the UNIVERSE, if it is finite? 
What is the number of the last electron if to count all of them 
(if it is meaningful at all to order them as a segment of natural 
numbers)? Is this number even or odd, prime or compound, etc. 
taking in account quantum effects and whatever else we could find 
in physics? 

It seems here we might need in a new concept (or concepts) of natural 
numbers. (Of course, as rigorous as the ordinary ones!) 

Anyway, many things depend on which "glasses" we are using to look at. 
I think we should not take everything what physics or mathematics 
(whose language and system of basic concepts is used by physics) 
says us at its face value. 


Vladimir Sazonov