> >Gerry Myerson wrote: > >> 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.
Isn't everyone? The only reason for axioms is that people are too lazy or stupid to demonstrate the truth of their assumptions.
> 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? ~v~~