FOM: use and mention, objective, astronomical calculations, etc.

[Vaughan Pratt]

Dear Martin:

>Responding also to your SETI remarks in a different post: Greek mathematics
>was different from ours in just the sort of way I'd expect that developed by
>folks on another planet to be. Based on an entirely different mind set - but
>in the end recognizably the same activity.

You may well be right.  In particular if we met folk from another planet
whose nonmathematical thinking was less like ours than their mathematical
thinking, I would soften my position.  Three independent such encounters
and I'd be quite convinced.

Until then however I regard with suspicion all arguments for or
against the likelihood of this outcome, especially arguments made by
mathematicians whose whole career has been predicated on the absoluteness
of mathematical truth and for whom it is therefore understandable to
see no alternative.

If at some point in their past those aliens had seriously polluted their
planet, I'd feel a strong kinship with them, as well as some relief
if that were an episode well in their past.  Going through such potty
training is a sign of a civilization on a similar track to ours, and
it would be nice to know it's survivable.  But for their pollution at
its peak to roughly equal ours seems to me, on the basis of our current
understanding about these things, about as likely that their mathematics
would roughly equal ours.

In short I don't see any convincing reason why mathematical thinking
should be more absolute or culture independent than other kinds of
thinking.  I agree that the idea is an appealing one, I just don't agree
that the appeal is more than skin deep.

Vaughan