[FOM] Foundational Challenge

[Lawrence Paulson]

It might help if more mathematicians were familiar with some basic principles of computer science. To a computer scientist, it's natural that a say a graphics application might be built on top of certain data structures or libraries for computer graphics, which in turn are built on lower-level numerical libraries, and so on down until raw binary is reached. For mathematics, ZFC typically serves as the equivalent of binary, while category theory, et cetera, are the libraries.

I think there is a big cultural difference here. I've read an account of Gödel's theorem that devoted much space to the concept of Gödel-numbering, when coding one thing in terms of another is as natural as breathing to a computer scientist.

Larry Paulson
On 17 Jan 2020, 03:38 +0000, Foundations of Mathematics <fom at cs.nyu.edu>, wrote:
>
> This is based on a confusion. Even if you look at MacClane's
> Categories for a Working Mathematician, category theory is presented
> as a development within set theory where a category is defined as a
> set together with a set of "arrows", etcetera, This is just like a
> normal development of a special mathematical area within the usual set
> theoretic foundations of mathematics.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20200117/86e9b5f5/attachment-0001.html>