[FOM] ZFC and the Formalisation Thesis
pratt at cs.stanford.edu
Tue Jun 1 02:33:09 EDT 2010
On 5/31/2010 8:23 AM, Arnon Avron wrote:
> On Sun, May 30, 2010 at 12:32:04PM +0200, F.A. Muller wrote:
>> Category Theory works with lots of 'sets' that do not exist
>> according to ZFC. The body of theorems proved in Category
>> Theory surely cannot be neglected, right?
> Category Theory is indeed just a *theory*.
So is evolution, which is an extremely useful theory.
Are you saying that Saunders Mac Lane was living out a private fantasy
when he titled his 1971 book "Categories for the working mathematician,"
with the hope that maybe a few "working mathematicians" might pick it up
and get interested in the subject as an alternative to studying group
theory or linear algebra or number theory?
If so then the fantasy is entirely yours. Your conception of category
theory is like thinking of an automobile factory as a place where people
who like building machinery can amuse themselves and maybe show off
their best work at car shows.
Category theory is an extension of abstract algebra that should be
understood as supplying mathematicians with power tools for their trade.
Many mathematicians use category theory. Pointing out that some
mathematicians don't is like pointing out that some people walk or ride
bicycles and then inferring that automobiles are useless.
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