FOM: Re: chess challenge to experts

Kanovei kanovei at
Mon Nov 13 06:20:45 EST 2000

> Date: Sun, 12 Nov 2000 09:23:31 -0500
> From: Harvey Friedman <friedman at>
> Rely to Kanovei 1:36PM 11/12/00.
> It appears that you claiming
> "every true mathematical statement is provable"
> Do you wish to claim this or not?

Yes I do. Yet I prefer express this as 
There is no mathematical statement true but not provable, 
as in my letter to fom of Nov 10.  

> If you are not claiming this, then what are you claiming?

The difference between (1) and (2) is of second order 
of importance, if you require me to prove that (1) is equivalent 
to (2) I will not do that.

> If you are claiming that no specific example can be explicitly presented
> together with an explicit refutation, then this is trivially correct 

I claim (2) above. A-claims can be refuted either by 
a concrete counterexample or by a pure existence proof. 
So far there has been neither of the two.
> Thus as far as I can tell, you are either claiming this statement, 

I claim (2) as a sourse of reference, but (1) also goes. 
> why are you bothering to claim a contentless triviality?

(2) was written to demonstrate that the primary dogm of 
modern philosophy of mathematics saying: there are true but 
not provable mathematical statements: -- is a misinterpretation 
of a Goedel's theorem. If you see this contentless then the dogm 
is contentless too, of which I am absolutely satisfied.

> Once you affirm that you are claiming
> "every true mathematical statement is provable"

I affirm.

> there are a number of issues as to what this means. 

That was discussed during last few weeks. 
The moderator does not seem to be tolerable as to this 
discussion any longer, which I have to respect. 

> Under some
> interpretations, it is clearly false. 

If (1) or (2) considered as ZFC statements they 
are refutable by the same G's theorem, this was not an issue. 

> you should make it clear that you are or are not making this claim 

Once again, I am making claim (2). 
Isn't this exchange pointless ? 


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