[FOM] Concerning Ultrafinitism.

Bill Taylor W.Taylor at math.canterbury.ac.nz
Sun Nov 5 23:20:02 EST 2006

galathea wrote:

> because they insist mathematics is a physical process
> and one day too may suffer the entropic decay

This is as good a place as any to make an observation.

Ultrafinitists place a lot of significance on *what can physically be done*
in the way of numbers, proofs, etc.  The above quote gives another view
of basically the same idea.

The whole tradition of math for over 2500 years has been to abstract away
from physical matters, whether entropy, the fine structure constant,
the state of human biology and brain power, the state of calculator
technology, and so on.  Sure, all these things are relevant to what
we may ever achieve in math; but not at all to what's IN math itself.
Or so almost all have viewed it, for (as I say) so long a time.

These other matters are highly relevant to other disciplines, such as
sociology, psychology, the history of math, physics, engineering,
medicine and (especially!) computer science.  But they hardly seem
relevant to MATH ITSELF.

The above view (not necessarily Platonist) is almost completely standard
among mathematicians of most stripes.  Math is about abstractions,
and abstraction, NOT physicality.

What, (other than ideological correctness), can possibly be gained
(for math) by these physicalist views?  
                    I can see gain to physics, CS, etc... but to MATH?
W F C Taylor

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