Stephen Montgomery-Smith wrote: > Gerry Myerson wrote: > > In article <firstname.lastname@example.org>, > > "Gene Ward Smith" <email@example.com> wrote: > > > > > >>Gerry Myerson wrote: > >> > >> > >>>I personally don't put set theory in the same category as astrology > >>>or creation science. Maybe Norm does. I don't know. > >> > >>Norm apparently puts number theory in that category. > > > > > > For what it's worth, Norm has written papers in number theory, > > e.g., > > > > MR1314396 (96a:11029) Wildberger, N. J. Row-reduction and invariants of > > Diophantine equations. Proc. Indian Acad. Sci. Math. Sci. 104 (1994), > > no. 3, 549--555. > > > > Whether this was before he came to his current views on set theory, > > I do not know. > > This affirms what I felt about the OP, that while his views are > unpopular, he is not a crank. (I also just checked him out on > MathSciNet, and it is obvious that he is an active research > mathematician.) In my opinion, his remarks about the natural numbers > are spot on. The only way I disagree with him is that I don't think > that now is the time to work on these problems. > > This whole thread has left a bad taste in my mouth because of the speed > at which people were willing to spew abuse on him. Just because he has > a superficial resemblence to crankpot anti-Cantorians doesn't make him > one. His views are controversial, but that doesn't mean we respond > rudely, rather it gives us an opportunity to engage in civilized > conversation. Even if we end up still disagreeing, we might have > learned something, or at least honed our arguments better. > > Now, one of the respondents said that Norm had rejected the axiom of > infinity, and so how is he supposed to do number theory. But nowhere in > his article has he rejected the axiom of infinity. He has rejected the > whole notion that axioms are the way to go. I would paraphrase what he > said slightly differently - axioms (might) describe the natural numbers, > but they don't define them. There is clearly a problem that there are > numbers between 1 and googolplex that we can never write down or > meaningfully describe. What makes us think that they are really there? > The evidence is at best empirical. Think about your above paragraph for a minute. Do you really think that the Number 2 is more real than some natural number which has never been mentioned or even thought of? Do you really think that "2" is the Number 2 ? "2" is the representation in one particular language of the name in one particular language of the Number 2. The Number 2 is neither its name in any language nor the representation of any such name in any particular language. The Number 2 is something which does not exist physically and can not be experienced by the senses. It is an abstract concept as are all other numbers.
> > The responses have led me to think that some people here believe in the > modern axiomatic system like a religion.
This is also one of Wildberger's assertions, one that has caused much anger. I don't think any serious mathematician "believes" the axioms or in the axioms. Mathematicians agree to use a set of axioms as the foundation of the formal system they are concerned with. Regards.