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

[Harvey Friedman]

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