FOM: Jurassic pebbles (more on Davis/Hersh)

[Martin Davis]

At 09:25 PM 3/16/98 +0300, sazonov at logic.botik.ru wrote:


>But I am very unsatisfied with this irrational explanation because this 
>explains almost nothing.  This seems to be the best way to find 
>ourselves in the prison of our own illusions (about the absolute truth, 
>about the standard model for PA, and the like). 
>
>
Dear Dr. Sazonov,

I understand from some of your previous postings that you take a skeptical
view of the infinitude of the natural numbers (except in the context of a
formal system with exact finitary syntax). So, I'm not surprised by what
you've written.

For me, it has been clear since I was a boy (a very long time ago) that an
acceptable account of G"odel's incompleteness theorem would necessarily take
the natural numbers as given in their totality with objective properties
beyond what could be derived in any particular formal system. As my teacher
Emil Post put it (even longer ago): "this ... must result in at least a
partial reversal of the entire axiomatic trend of the late nineteenth and
early twentieth centuries, with a return to meaning and truth as being of
the essance of mathematics."

Martin