FOM: Book on foundations paul.andrews at
Thu Apr 9 18:39:34 EDT 1998

A comment on Till Mossakowski's posting:

Subscribers to fom might be interested to know that as early as 1968,
Hatcher was discussing the foundational status of for category theory.
The first edition of his book is titled "Foundations of Mathematics".  It
includes a section on the language of categories, the category of sets,
and the category of categories.

I also thought I might pass along a few sentences of Hatcher's following
his presentation of the basics of the category of sets.

"As a foundation for set theory itself, it would be difficult to argue
that CS is better than ZF.  But the ultimate value of CS is not as a
classic foundation for classical analysis, but rather as an important
formulation of set theory from a categorical point of view." (pp.315)

What is interesting here is Hatcher's suggestion that category theory and
set theory are complementary tools for investigating the basic machinery
of mathematics rather than mutually exclusive theories.  Each can be used
to shed light on the other.  

Paul Andrews

paul.andrews at

On Thu, 9 Apr 1998, Till Mossakowski wrote:

> Recently, I browsed in the book
>   The Logical Foundations of Mathematics
>    by William S. Hatcher
>   (appeared about 1982, now out of print)
> and found much more discussion on the possibility of categorical
> foundations in it than in most of the "baker's dozen" books
> mentioned by V. Pratt on Fri, 27 Feb 1998 19:15:58.
> Till Mossakowski

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