FOM: A comment on an old question asked by Professor Pratt
Vaughan Pratt
pratt at CS.Stanford.EDU
Thu Jan 13 02:56:10 EST 2000
From: "Matt Insall" <montez at rollanet.org>
MI>From: "Vaughan R. Pratt" <pratt at cs.Stanford.EDU>
MI>VP>Date: Tue, 21 Oct 1997 02:13:01 -0700
MI>VP>But why is real analysis your litmus test of the worth of a
MI>VP>foundation?
MI>
MI>My response (in case no one has already replied with this type of response)
MI>is that the whole bit began essentially with ``(real) analysis''. Going
MI>back to Cantor, the question of what constitutes a set was actually ``What
MI>constitutes a set *of real numbers*?''
This is the answer to a slightly different question: How did real analysis
influence the *origins* of modern f.o.m.? This is a h.o.m. (or h.f.o.m)
question, h for history, not a f.o.m. question per se. Fom at time t
concerns m at time t, not t-100 (years).
It is also out of context: my (rhetorical) question was in response to
Steve's "The question right now is, how can category theory be used to
explain real analysis?" It had not occurred to me to interpret Steve's
question as meaning, how could Cantor have used category theory to
explain real analysis?
My next sentence in that message was "What if we substitute homological
algebra for real analysis?" Again this makes little sense in the context
of mathematics as understood a century ago, when Betti numbers were just
starting to be grasped by Poincare and homology was still nonexistent.
A healthy fom needs to pay attention across the board to all facets of
important mathematics. Mathematics can certainly derive importance from
its accessibility, but independently one can be doing very important
mathematics despite the fact that only a few are equipped to follow
the reasoning. Homology provides a powerful, hence important, tool of
algebraic topology.
But I do appreciate the importance of real analysis for hfom.
Vaughan
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