FOM: categorical foundations -- an oxymoron

Stephen G Simpson simpson at
Fri Jan 23 12:22:02 EST 1998

In his posting of 23 Jan 1998 11:15:24, Colin McLarty writes:

 > Categorical foundations suggest a wider range of topics. (Simpson
 > and I agree on this fact, but he feels it invalidates the claim to
 > foundationality).

McLarty is grossly misrepresenting my position.  My position is that
"categorical foundations" is an oxymoron, in the sense that category
theory is irrelevant to f.o.m., despite frequently repeated claims by
topos theorists.  Here on the FOM list, these claims have been put to
the test and found severely wanting.

Although category theory is useless for f.o.m., it may be useful as a
technical tool in certain branches of mathematics.  Algebraic
topology?  I'll leave this to the algebraic topologists to judge.

I have clearly stated my position on all of this in my posting of 15
Jan 1998 20:41:29 and 18 Jan 1998 14:39:24 and 21 Nov 1997 20:47:06
and others.  Is McLarty deliberately misrepresenting me?

McLarty continues:

 > (Friedman considers mainstream mathematics intellectually corrupt.)

McLarty is grossly misrepresenting Friedman's position.  I'll let
Harvey Friedman answer this himself.

Does McLarty think that these misreperesentations are useful or

-- Steve

More information about the FOM mailing list