[FOM] Absolute truth vs. relative meaning and formal nature of mathematics

Harvey Friedman friedman at math.ohio-state.edu
Tue Feb 7 22:56:36 EST 2006

On 2/6/06 2:46 PM, "Vladimir Sazonov" <V.Sazonov at csc.liv.ac.uk> wrote:

> For example, I ASSERT, not as a mere speculation, that there is a
> simple, but rather unusual FORMAL system of axioms and proof
> rules in which a (semi)set of natural numbers 0,1,2,... < 1000
> is FORMALLY definable which is PROVABLY closed under successor
> and is also upper bounded by the number 1000. Quite intuitive
> informal examples of such semisets from our real world are well
> known (e.g. presented by P. Vopenka).

If this formal system is reasonably simple, I would like to see it presented
here on the FOM. If it is complicated, I would rather not.

It would seem to have to be inconsistent in the strong sense that you can
easily produce an actual electronic file of the inconsistency.

Harvey Friedman 

More information about the FOM mailing list