FOM: exterminating category theory? grammatical errors? patronizing?

Stephen G Simpson simpson at
Sat Mar 14 18:39:41 EST 1998

Jaap van Oosten writes:
 > Now who do you think you are fooling, Steve?

You misunderstand me.  I'm not trying to fool anyone.  I'm simply
trying to establish a basis for rational discussion with category
theorists who claim not to understand simple mathematical statements
such as "Boolean algebras are not isomorphic to Boolean rings".  I
genuinely want to discuss with them the merits and demerits of what
they call "categorical foundations".  I call it categorical
mis-foundations, pseudo-foundations, etc because I don't concede that
it's foundational.  I'm sorry if that opinion upsets you, but there it

 > (your cause is to exterminate the germ of category theory)

Not at all.  You are not paying attention to what I'm saying.  I've
said repeatedly that I have a lot of respect for category theory as an
organizational tool in certain branches of mathematics, e.g. algebraic
topology and algebraic geometry (Eilenberg/MacLane, Grothendieck).
But I'm not an expert in those areas.  The issue that we are
discussing on the FOM list is whether category theory has anything of
value *for f.o.m.*, and whether it's legitimate in the present state
of knowledge to talk about *"categorical foundations"*.

You seem very upset to find out that not everybody automatically
thinks category theory is wonderful.  Haven't you ever talked with
non-category-theorists before?

 > When I see you relish in dishing it out to people even for minor
 > grammatical errors like the example above (sometimes even errors in
 > English, where another might observe that we're not all native
 > English speakers)

I'm not aware that I have been doing this.  While I strive to write
correctly and clearly and urge everybody to do the same, I don't think
it's appropriate for me or anyone else to nit-pick, expecially if the
errors are merely linguistic.  In the instance to which you refer,
Mossokowski's error was mathematical, not linguistic.  His point was
that the only way to interpret a phrase like "all Boolean algebras" is
in terms of the *category* of all Boolean algebras.  This is a serious
mathematical error, since "all" can be understood more simply, and
therefore correctly, as a universal quantifier.  Perhaps I pounced too
hard, but I wasn't merely quibbling over a grammatical error as you

 > indulge in extremely condescending and patronizing language, for
 > pages and pages on end,

If I sound patronizing and condescending, my excuse is that some
category theorists are forcing me to drag them through some extremely
well-known and elementary mathematics, just to get to the point where
we have a rational basis for discussion, in terms of commonly
understood mathematical notions and distinctions.  (I don't know why
they are doing this.  I suspect that they are deliberately throwing up
a smokescreen, in order to hide the poverty of their f.o.m. ideas.)  I
don't like it any better than you do.  But I'm not prepared to turn
the FOM list over to those who seem to have no appreciation for
genuine f.o.m. issues.

 > I find it revolting.

That's too bad.  But I'm still hoping that something of value will
come out of this discussion.  Remember the watchwords: patience and
intellectual honesty.

-- Steve

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