> I think Norm would say, 1) you can't form the set (and Norm's reasons > are given in the article), and 2) you don't need to - there's no good > mathematics you can do with the completed infinite set that you can't > do without it.
Norm is also opposed to axioms. Without axioms, how do we know when we are "forming" an infinte set? If I state Euclid's theorem on the infinitude of primes, am I "forming" a set? Am I forming a set just by referencing the integers at all? If Norm won't give a set of axioms he finds acceptable, we can't very well say that measureable cardinals contradict his foundations for mathematics, because he hasn't really given a foundation. He has, in fact, claimed that infinite sets are metaphysics; but if they are metaphysics, he's not talking mathematics at all, but metaphysics. In which case, so what? What do his metaphysical beliefs have to do with mathematics?
> More ad hominem. Norm accepts the axioms of group theory as the > definition of what a group is, and has no problem with them because > he can construct (finite) models of them.
In which case, he can hardly say he is rejecting axioms, and ought to step forward and say what his proposed axioms are. Would ditching the axiom of infinity do it? If not, what would?