I am sure several other readers of this list will have the same reply to this specific point of Paul's message: Paul Taylor wrote:
For example, there is Cantor's "theorem" about a powerset being strictly bigger than a set. This belongs entirely to the dogma of set theory. When set theory is overturned, this miserable and wholely misguided "theorem" will go in the dustbin of mathematical history with it.
There is a very nice paper by Lawvere that shows that the essence of Cantor's theorem is fundamental and beautiful: Originally published in: Diagonal arguments and cartesian closed categories, Lecture Notes in Mathematics, 92 (1969), 134-145. Reprinted in TAC: http://www.tac.mta.ca/tac/reprints/articles/15/tr15abs.html There is also a post by Andrej Bauer in his Mathematics and Computation blog: http://math.andrej.com/2007/04/08/on-a-proof-of-cantors-theorem/ Martin [For admin and other information see: http://www.mta.ca/~cat-dist/ ]