Pat, (01)
A quick remark to your quick remark: (02)
> I just wanted to dispel the impression that there are hundreds
> of competing 'foundations' for mathematics, or that everyone
> agrees that it is fine to just choose your own foundation for
> your own theory. (03)
I agree that ZFC and category theory are the two main systems that
people who worry about the foundations of mathematics decided to
study during the 20th century. But I want to emphasize two points: (04)
1. We have no idea what logicians in the later part of this century
or many centuries to come may decide is a better choice. (05)
2. Mathematicians who use a set of axioms A to solve a problem P
don't choose any foundation whatever. It is irrelevant to them
whether the axioms in A are reducible to ZFC, category theory,
or any other system anyone might invent in the future. (06)
The reason why I emphasize these two points is to dispel Azamat's
claim that there is some pressing need to reduce all the axioms
for everything in the universe to one fixed system. (07)
John (08)
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