>I'm dismayed by the level of vituperation in some of the posts in >this thread. 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. It's an unpopular >view, it doesn't particularly appeal to me, but I don't see the need >to go ballistic in response.
Norm's paper is not a discussion of finitistic methods. It's not a discussion of the computational view of mathematics. It is a mean-spirited, sneering attacking on a huge swath of modern mathematics and modern mathematicians. It is *full* of vituperation.
When it comes to reasonableness, I don't see why Norm's equating set theory with a religious is *more* reasonable than Peter Webb's equating Norm's paper with crank babble. Norm's paper is not a mathematical paper, it is a polemic. There is really no way to give a reasoned, mathematical response to it.
In contrast, a paper that starts off saying that the author is rejecting the axiom of infinity because he wishes to see how much of mathematics can be done with minimal ontological commitment could be the start of a reasonable mathematical paper. An exploration of finitistic mathematics could be interesting mathematics. Nobody would accuse Norm of being a crank for writing such a paper, or even for dedicating his life to the development of finitistic methods. People accuse him of being a crank when he says things such as comparing set theory with a religious cult. *That's* what's crank material, not finitistic methods, and not the computational view of mathematics.
However, I understand why Norm might prefer to write the inflamatory type of paper: because at least it generates a response, while the more reasonable exploration of finitistic methods would generate polite indifference and yawns.