Pat, (01)
As soon as you go from one to two, you have adopted an inadequate
approximation to infinity: (02)
PH> Well, OK, there are TWO foundations. I agree, CT [category theory]
> is widely treated as a real mathematical foundation in practice. (03)
But if you use "widely treated", you make it a popularity contest. (04)
On foundational issues, I disagree with Avril who is trying legislate
a finitistic foundation. But I also disagree with *everyone* who is
trying to legislate *any* fixed foundation. (05)
But I wouldn't call myself antifoundational, since I am not opposed
to having foundations. I am just opposed to the idea that there must
be exactly one or exactly two foundations or exactly N foundations. (06)
I just say that I agree with CM's friend that practicing mathematicians
don't need foundations, but if anybody wants to define a particular
foundation for a particular purpose, I have no objections to that. (07)
And further that *all* of them would be unnecessary for the practicing
mathematician who actually wants to solve real problems. (08)
John (09)
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