FOM: the paradoxes

Martin Davis martind at
Fri Jan 2 14:53:14 EST 1998

At 05:05 AM 1/2/98 +0100, Harvey Friedman wrote:

>... they [the paradoxes] are nowhere near having been
>resolved or mined appropriately. Godel felt that they were not properly
>understood, and that a better understanding of them would lead to great
>insights. We have the great mystery of how to approach the axioms of
>mathematics now that we are beginning to see how expansion of the usual
>axioms are essential to give proofs of concrete statements we would like to
>know. How are we to think of the consistency and/or truth of these
>necessary higher principles? Clearly this is likely to be tied up
>inexorably with the paradoxes ...

I would like to draw attention to this important and insightful comment.
(Since it was embedded in an attack on Lou van den Dries, I thought fom'ers
might have missed it.

Martin Davis

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