reply to Friedman FOM: new inductions unimportant

Kanovei kanovei at
Tue Mar 2 13:52:19 EST 1999

> From: cxm7 at (Colin McLarty)
> Date: Mon, 1 Mar 1999 20:48:44 -0500 (EST)

> In the language of any consistent formal theory there are statements, which
> the theory cannot prove, but which you actually accept because of inductive
> arguments not available in that theory. 

This observation sounds very ridiculous. 
Indeed, take PA as a consistent formal theory. 
There are statements of PA which PA really 
cannot prove or reject: say Con PA, the 
Paris--Harrington theorem, and many more. 
Some of them are accepted as true theorems 
just because ZFC (or say 2nd order PA) proves them 
(although PA cannot prove). 
In those ZFC proofs there may happen some 
induction arguments, of course, which cannot 
be justified in PA (say because they appeal 
to real numbers). 

So what ? 

This is a mathematical routine. 

Why one can be so pompous of his own 
discovery of this form of Goedel incompleteness 
theorem ? 


More information about the FOM mailing list