# FOM: Jurassic pebbles (more on Davis/Hersh)

Mon Mar 16 13:25:39 EST 1998

```Martin Davis wrote replying to Reuben Hersh:

> I claim that the fact about pebbles mentioned above was just as true of
> pebbles on a jurassic beach as on a contemporary beach.
>
> *Do you agree?
>
> Since I can hardly imagine that you would dispute this, I assume your answer
> is "yes". Then I ask, "How do you know?" For me, the answer is clear: it is
> a consequence of Lagrange's theorem which was as true then as it is now.

Dear Professor Davis,

Your position is not sufficiently clear for me because you seems do not
present sufficiently full picture. Does the following, which I consider
as
a possible explication of the above citation, as I see it, correlate in
some way with your point of view?

I would rather say that it was always true that Lagrange's theorem is
PROVABLE in a formal system.  It is even easier than the experimental
truth of its pebble version. It is crucial problem how do we CHOOSE
axioms (and proof rules) for arithmetic to deduce this and other
theorems having consequences in the real world. To which degree this
process is determinate? Are there alternatives? Is the situation in
arithmetic completely different from that in geometry (Fifth
Postulate)?
On the one hand, we do have alternatives. We can freely play with axioms
and proof rules to get some versions of arithmetic which have true
consequences in the real world and reflect this world under another
angle than Peano Arithmetic.  On the other hand there may be (and
actually are) some objections against this freedom, that only one way to
choose axioms is "true" (or fundamental, or the like).  The only coming
to my mind reason for the full determinateness of this process is the
God who knows (or shows us via some prophets?) the correct way so that
we are forced to follow it without understanding how and why. (I do not
know how this corresponds to you point of view. I just try to
extrapolate as I can.)

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).