FOM: NYT culture wars; topos axioms; Brouwer's mysticism
Stephen G Simpson
simpson at math.psu.edu
Tue Feb 10 20:48:13 EST 1998
New York Times culture wars:
I thank Martin Schlottman for posting the URL of the article on
"quasi-empiricism" in today's New York Times. I also thank Martin
Davis for his superb reply to that article; I hope it gets
published! All of this is related to Tymoczko's book, which I
reviewed here on the FOM list a few days ago (1 Feb 1998 22:17:36).
F.o.m. is very fashionable nowadays. It seems that almost every
issue of the New York Times (and even the Wall Street Journal!)
contains something about f.o.m. For instance, the January 24 NYT
has an article entitled "Science Confronts the Unknowable",
subtitled "Less Is Known Than People Think", pages A17-A18. The
article misuses quantum physics and G"odel's theorem in the usual
way.
Why is f.o.m. so relevant to wider cultural issues? I think it's
because mathematics has traditionally been resented and revered as
the most rigorous of the sciences; it is therefore a natural target
for those who wish to attack reason and objectivity.
Topos axioms:
McLarty's "final draft" (6 Feb 1998 09:21:21) presents axioms for a
nontrivial Boolean topos, and for a well-pointed topos with natural
number object and choice. But it doesn't present axioms for a
topos! Why not? Too hard to motivate from the f.o.m. perspective?
As always, my real question about all of this is, what's the
motivating picture? I don't think there is any, except perhaps set
theory.
Regarding the issue of simplicity, I believe that Awodey wanted to
claim that the topos axioms are in some sense algebraically simple.
Could Awodey please elaborate on this, in light of McLarty's "final
draft"?
Brouwer's mysticism:
Van Oosten 6 Feb 1998 14:02:30 mentions Brouwer's mystical views.
I'm pretty certain that Brouwer's mysticism is of a piece with his
intuitionistic (or perhaps more accurately solipsistic) philosophy
of mathematics. I regard Heyting's work as a valiant attempt to
make logical sense of Brouwer's ideas, but ultimately this may be
doomed to failure.
-- Steve
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