FOM: Goedel: truth and misinterpretations

[Martin Davis]

At 07:25 AM 10/26/00 +0200, Kanovei wrote:

>This does not answer the request of mathematical meaning
>of the "sentences".
>I would not be surprized that a skillful number-theorist can even
>convert Con ZFC to a diophantine system,

Actually, based on the work on Hilbert's 10th problem it's a routine 
exercise for a student. In fact it's just a matter of inserting a suitable 
(very large) integer for a parameter in a universal equation.

>  but despite a clear
>METAmathematical meaning of likes of Con ZFC, their mathematical
>meaning is questionable

It's clear that Professor Kanovei and I use the term "mathematical meaning" 
quite differently. I can't imagine what would be clearer than an assertion 
that a particular explicitly displayed system of polynomial equation has a 
solution in natural numbers.

Martin




                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at eipye.com
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