> >I'm hardly in a position to play Miss Manners, but I think one could > >reasonably complain in both cases. One thing I am very tired of reading > >on this list are the constant attempts to denigrate the mathematical > >work of one distinguished mathematician or another, or one school of > >mathematicians or another. I think ripping in to the positions people > >take on the philosophy of mathematics is one thing, but treating the > >mathematical work of the people involved is quite something else. > > And how exactly does one distinguish one from the other?
If they prove theorems, they are doing mathematics. In which case, keep your greasy paws off of them in terms of philosophy, and look at the proofs and theorems.
People who > call themselves mathematicians invariably work within the context of > one mathematical paradigm or another and one set of axiomatic beliefs > or another.
This is quite false. Mathematicians can, and do, differ sharply on philsophical issues, but can readily agree nonetheless on mathematical issues.
> Their math is no more correct than the paradigm.
This makes no sense. Two people prove the same theorem independently, and send it in for publication. One gets rejected because he holds the wrong philosophical beliefs about mathematics, and hence his proof is invalid. The other, who used the same proof, has his paper accepted because his philosophy of mathematics is correct. What is wrong with this picture?
You seem > to suggest there is some way to distinguish mathematicians from their > philosophy of mathematics.
One is a philosophy, and the other is an actual person. That works for me.