FOM: Goedel: truth and misinterpretations

[Kanovei]

> Date: Thu, 26 Oct 2000 20:24:57 +0200
> From: Torkel Franzen <torkel at sm.luth.se>
 
> To understand the metaphysical claim "CH is true or false" you
> must understand what difference it makes to our thinking in or
> about mathematics. Can you see any such difference? If you can't,
> what are we arguing about?
> 
>   >I do not see why I must take on trust the prayer 
>   >that either CH is true or CH is false,
> 
>   Take what on trust? What does it mean? What is problematic or
> doubtful about "CH is true or false"? What difference does it make
> whether or not we affirm "CH is true or false"?

I am fully satisfied. I began this discussion a couple of days 
ago, saying that the point of official mathematical philosophy 
that (in the metalanguage of us about mathematics) 
"there are true but unprovable sentences" 
is wrong and basically meaningless, and the related reference 
to Goedel's incompleteness is wrong. 
Now you claim the same in different words. I am happy, the 
effort has not been in vain.
 
> So it does make a difference what axioms we adopt? 

Presumably it does, otherwise 0=1 as the axiom would make 
everybody happy as everybody could prove his favourite theorems.

> Very well, then: what reason do we have to think that
> our current axioms are more likely to survive such justification than
> any other axioms that we might invent?
 
This is competitive. Our current axioms (if you mean ZFC) 
have survived different tests (except for remarkable hatred 
of theorists-categorists to Kuratowski's pair). 
I believe if somebody steps forward with a better concept 
it will be considered, but I personally doubt this happens in 
some observable future. 

V.Kanovei