FOM: Goedel: truth and misinterpretations

[Martin Davis]

At 07:06 PM 10/26/00 +0200, Kanovei wrote:
> > Date: Thu, 26 Oct 2000 09:26:58 -0700
> > From: Martin Davis <martin at eipye.com>
>
> > I can't imagine what would be clearer than an assertion
> > that a has a
> > solution in natural numbers.
> >
>
>Most assured you cannot be wrong, I only wonder why they
>included the Harrington-Paris note as the only
>(or one of very few) pure research article in the
>"Handbook of Math. Logic", whose (the H-P note) main
>content was to display a true MATHEMATICALLY meaningful
>sentence of PA, not provable in PA.

The Paris-Harrington theorem provides an example of a mathematically 
INTERESTING result not provable in PA. Perhaps when you say that an 
assertion is "meaningful" you mean that it is one that mathematicians would 
a priori tend to find interesting.  The Paris-Harrington theorem and some 
of Harvey Friedman's recent results are of this kind, while the perfectly 
MEANINGFUL results coming from the work on Hibert's 10th problem clearly 
are not.

Martin



                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at eipye.com
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                        http://www.eipye.com