FOM: card-carrying category theorists; Simpson-bashing

[Stephen G Simpson]

Vaughan Pratt 14 Mar 1998 17:32:01 writes:
 > It used to be that if you defended a communist you were branded one.
 > Nowadays if you defend a category theorist you're branded one.

Well Vaughan, maybe you're not a card-carrying category theorist, only
a fellow-traveler.  I call you a category theorist because, in your
electronic persona here on the FOM list, you *have* advocated
categorical dys-foundations (although your ideas seem to differ from
those of the topos people).  Furthermore, if you look at the FOM
archives, you will see that categorical confusion is responsible for
the current mud-wrestling match on Boolean rings.  It comes from your
obstinate insistence that there is no distinction between Boolean
algebras and Boolean rings, parallel to some of the card-carrying
category theorists' obstinate insistence that there is no distinction
between intuitionistic higher order logic (IHOL) and topos theory.

 > (Those familiar with Bill Lawvere's economics will spot the in joke.)

Yes, I've heard that Lawvere used to be a fanatical Maoist or
something like that.  Maybe Reuben Hersh will use his political
calculus to draw some conclusion concerning the merits of topos
theory.  (More sarcasm.)

I wrote:
 > >move on to more interesting foundational questions: foundational
 > >motivation, general intellectual interest, why algebraic logic is
 > >not the same as f.o.m., etc.
Vaughan Pratt replied:
 > Where is the intellectual interest in prejudged questions?  (This is
 > not a joke.)

Huh?  If a math colloquium speaker states a theorem, does the audience
lose interest because the question is "prejudged"?

Vaughan, I think you are trying to throw up another smoke-screen.  But
I'll try to cut through it:

Obviously I have my opinions about why algebra and category theory
aren't the same thing as f.o.m.  And I will present those opinions
*and the reasons for them*, provided I can overcome the technical
hurdle presented by your obstinate denial of very basic and familiar
mathematical distinctions, e.g. the distinction between Boolean
algebras and Boolean rings.  And conversely, if you think that algebra
= logic = category theory = f.o.m., then I will happily participate in
that discussion, provided you also proceed on a rational basis.

It seems that category theorists such as Pratt, Awodey, and van Oosten
don't want to accept these ground rules.  Why not?

Harvey Friedman 15 Mar 1998 06:41:02 writes:
 > I'm trying to figure out why this kind of complaint is more often
 > directed at Simpson than at me, since I claim to be "worse" than
 > Simpson. For example, I claim to also use subject headers like
 > "categorical pseudo foundations."

Harvey, I also am trying to figure out why I have been the target of
so much vituperation from card-carrying category theorists, while you
have gotten away almost scott-free.  Maybe the category theorists
attack me because they think I'm an easy target; maybe they are more
afraid of you.

Want to switch roles for a while?  I guess I'm going soft.  Can't I be
the good cop for a change?  :-)

 > I have said on the fom that categorical foundationalists have a
 > profound misunderstanding of f.o.m. I claim that this is worse than
 > Simpson.

Yes indeed, that's "worse" (i.e. more pointed and provative) than
anything I've said on the FOM list.  But many mathematicians routinely
say even worse things, e.g. when they refer to category theory as
"abstract nonsense".

-- Steve