[FOM] ZFC and the Formalisation Thesis

[Vaughan Pratt]

On 5/31/2010 8:23 AM, Arnon Avron wrote:
> On Sun, May 30, 2010 at 12:32:04PM +0200, F.A. Muller wrote:
>>   1.
>>   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.

Vaughan Pratt