FOM: Time to park the Jurassic pebbles?

[Vaughan Pratt]

Dear Martin:

>How could the applicability of LT to Jurassic pebbles be possible if LT did
>not possess a validity beyond times when humans inhabited the planet?

I agree with this, as long as "applicability" is understood to mean
"applicability by us".

It might clear the air a bit if I give two circumstances under which I
wouldn't insist on this caveat:

(i) If I shared your apparent perception that at least some of our truths
are independent of ourselves.

(ii) If we were discussing the merits of a new proof of Lagrange's theorem.

The point of (ii) is to illustrate that I distinguish mathematics from
mathematical activity when I'm participating in the latter, but not
when discussing it.  It is hard if not impossible to *do* nontrivial
mathematics without a firm belief in its independent existence.  The point
of (i) is (if I understand you) that you make this distinction in both
situations.

Paradoxically Occam's razor suitably applied supports both our viewpoints,
mine by eliminating unnecessary distinctions, yours by eliminating
unnecessary dependencies on context (participation vs. discussion).

That I instinctively don't distinguish the two when discussing them/it
is the source of my confusion about your intent in "Reuben Hersh makes
the remarkable discovery that mathematical activity is a social process,"
which you've clarified to my satisfaction in

>I can't imagine how anyone could think that mathematical *activity*
>was other than a social process. It's done by people living in society.
>However that simple fact is no help in working out the kind of validity
>that the assertions of mathematics possess.

If Hersh also doesn't make the distinction it would explain his confusion
too.

Vaughan