That Logic Blog

December 12, 2005

Kreisel vs Lawvere

(via Robert Seely on the categories mailing list). The slides should be interesting for anyone into foundations, category theory or both:

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

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


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