Subject: categories: Organization vs foundations: Kreisel, Lawvere and category theory

From: Robert Seely <[email-masked]>
Date: Thu, 8 Dec 2005 09:36:18 -0500 (EST)

On 29 Nov 2005, the Montreal Category seminar hosted a talk by
Jean-Pierre Marquis on the interaction between Kreisel's and Lawvere's views
on category theory as a foundations for mathematics.  It has been suggested
that many on this list who were not able to attend the talk might find its
contents of interest, and so would be interested to know that the slides for
the talk are available on the triples seminar webpage, at

    http://www.math.mcgill.ca/rags/seminar/

(scroll down to the talk itself - the direct link is

  http://www.math.mcgill.ca/rags/seminar/Marquis_KreiselLawvere.pdf

if you prefer).  The slides are fairly complete, and give a good idea of the
content of the talk itself.

Here is an abstract of the talk:

Jean-Pierre Marquis
Organization vs foundations: Kreisel, Lawvere and category theory

Abstract: it is well-known that in the nineteen-sixties, Bill Lawvere
proposed that category theory could serve as a foundations for
mathematics and logic.  Only one logician reacted officially: Georg
Kreisel.  In a series of notes, appendices and reviews, Kreisel
developed arguments against categorical foundations. In this talk, I
will take a close look at his arguments, examine whether they are still
convincing and propose that Kreisel's position is still underlying most
of the arguments against categorical foundations heard to this day.

-- 
<[email-masked]>
<www.math.mcgill.ca/rags>