Bourbaki and foundations
Colin McLarty
colin.mclarty at case.edu
Thu May 12 20:33:54 EDT 2022
On Thu, May 12, 2022 at 8:25 PM JOSEPH SHIPMAN <joeshipman at aol.com> wrote:
> So far I have not seen anyone give an explanation that makes sense of what
> is WRONG with set theory. The explanations why you might want to use
> category theory as a basis for formal proof assistant systems are fine, and
> the explanations why you might want to LEARN category theory because it is
> closer to mathematics practice in many areas of mathematics are fine, but
> the fact that you need sets to do certain types of mainstream math even if
> you get them FROM a category-theoretical foundation, and the fact that you
> can formalize all of mathematics in set theory if you want to, are so
> straightforward and easy to understand that I don’t grasp where the
> negativity is coming from!
>
Can you give examples of this negativity? I expect those examples would
say what motivates them.
>
> WHO is forcing anyone to use set theory in a way that requires any
> significant and unnecessary effort?
>
Have you heard anyone say they are forced to use set theory?
Colin
>
> Sent from my iPhone
>
> > On May 9, 2022, at 4:27 PM, Timothy Y. Chow <tchow at math.princeton.edu>
> wrote:
> >
> > Michael Sheard wrote:
> >
> >> (1) How widespread was the belief that category theory is an obviously
> better foundation for mathematics than set theory, among mathematicians in
> 2006 (when the book was published)?
> >>
> >> (2) How widespread is this belief today?
> >>
> >> (3) What is your position on this belief?
> >
> > In the past, there have been many---shall we say---spirited discussions
> on FOM on this topic. You can search the FOM archives circa January 1998
> and circa March 2016 for examples of such discussions.
> >
> > Nowadays we have the advantage of being able to point to Penelope
> Maddy's article, "What do we want a foundation to do?" as a starting point.
> >
> >
> http://www.socsci.uci.edu/%7Epjmaddy/bio/What%20do%20we%20want%20-%20final
> >
> > Depending on what you mean by a "foundation" and depending on what you
> want a foundation to do, the answer may vary. Proponents of category
> theory often lay great emphasis on what Maddy would call "Essential
> Guidance," and less emphasis on (for example) "Risk Assessment."
> >
> > You might want to take a look at the following MathOverflow questions
> for some thoughts on the topic (including my own).
> >
> > https://mathoverflow.net/questions/360578
> > https://mathoverflow.net/questions/376839
> >
> > Tim
>
>
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