foundations

[Anand Pillay]

Dear Steve,
I am not sure there is any point in continuing this discussion. In contrast
to the pure rationality you claim to espouse, what I see is caricature and
insinuation. And what is this nonsense about postmodernism?

I think it is not difficult to distinguish between the idea of
axiom-proof-theorem being an important constituent of mathematical
activity, and the idea of it being the defining constituent. (John
Baldwin's point that the axiomatic development in say Bourbaki is now
somewhat out of fashion, is  connected with this distinction.) I was not
even saying what is right here, just that the second idea is more friendly
to a certain conception of foundations of mathematics than the first. I am
sorry to have brought Atiyah's name into this. In any case, if one is to
work in foundations of mathematics, one should make a point of
familiarising oneself with current trends of thought in the heart of the
mathematical community. I will discuss other views of "foundations of
math." when I reply to Harvey.

Regards,
Anand