29 Nov 2005
2:35 - 4:00

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.