Shut up. You are not a rhetoric major and You Don't Know what "ad hominem" means. The literal translation is "against the man" but that does NOT mean that EVERY time somebody insults a person, he is committing a sin of type "ad hominem". What is going on here is an ARGUMENT. Arguments are characterized by mutual attempts at LOGICAL rebuttal. If you have logically demonstrated that somebody is flaunting his ignorance and being a dipshit then it is NOT "ad hominem" Or Any Other fallacy to point this out.
> Norm accepts the axioms of group theory as the > definition of what a group is,
Shut up. You don't know Norm, either. Norm attacks "logicians" and the axiomatic method generally. IF he accepted axioms as legitimate for defining things then he wouldn't have anything to argue about.
> and has no problem with them
> because he can construct (finite) models of them.
Obviously, he AND EVERYBODY ELSE can ALSO construct INFINITE models of them -- AND HE DEALS with infinite groups ALL THE TIME in his work. So this is simply not a legitimate distinction.
> He argues that the axioms > of set theory (in particular, ZFC) don't define what a set is
That is completely incoherent. Since, in ZFC, EVERYthing is a set, the axioms of ZFC could NOT POSSIBLY DO ANYTHING BUT define what a set is.
> and don't lead to sensible constructions of infinite sets.
That is ridiculous too. He is not even saying that. You need to quote him. What he DOES say is that textbooks aren't much on defining what an infinite set is, and he has looked. That just makes HIM look stupid. Arthur Rubin and others have posted 5 different definitions of infinite set, in case he was too stupid to find one. More to the point, classical FOL IN GENERAL is NOT constructive and one NEVER looks to the axioms themselves to construct ANYthing -- the model construction language is ALWAYS something DIFFERENT.
> It seems to me Norm is making several points, two of which are > that ZFC sucks and that mathematics doesn't need axioms in the first > place.
Well, now you are a lot closer to reading him rightly, but you do need to understand that your 2nd point here (about math not needing axioms in the first place) contradicts your point above about Norm respecting the axioms of group theory because he can construct finite models of them. Group theory is in fact defined by its axioms. Norm canNOT simultaneously appreciate that AND think that math doesn't need axioms. Neither can you.
> I'm dismayed by the level of vituperation in some of the posts in > this thread.
Well, you shouldn't be. That's what you get for farting in church. NW is presuming to pontificate about something he has not studied.
> Norm is not presenting a high-school algebra proof of > Fermat's Last Theorem, nor is he insisting that the reals are countable > because you can always take that real number that you left off your > list and stick it on at the end. He's adopting a finitistic, or > constructivist, or computational view of mathematics.
He IS NOT, you IDIOT! IF he were doing that, he would've actually GOOGLED "constructive mathematics" before presuming to pontificate, and would've SAID something about it in his article! NW * doesn't know SHIT * about constructive mathematics!
> It's an unpopular view,
And one that he has never heard of; the only thing that is even MOTIVATING him to LEAN in that direction are the things he DOES ACTUALLY TALK about in his article, things you would've been WISE TO QUOTE, IF you were going to be stupid enough to be attributing views to another person, things like the failure of the profession at large to logically ground its concepts. If this was what was actually bothering him then (obviously) he should've been supporting axioms, not attacking them.
> it doesn't particularly appeal to me, but I don't see the need > to go ballistic in response.
The going ballistic is NOT in response to constructivism. NW didn't cite Bishop or anybody who is trying to go that way. He HIMSELF FIRST went ballistic vs. "logicians" by calling them a priesthood. He embarrassed himself by sounding like James Harris.