Stephen Montgomery-Smith wrote: > Norman Wildberger wrote: > > I have posted an article at http://web.maths.unsw.edu.au/~norman/views.htm > > that has caused a bit of discussion in some logic circles. > > > > My claims in short: 1) most of `elementary mathematics' is not sufficiently > > well understood by the mathematical establishment, leading to weaknesses in > > K12 and college curriculum, 2) the current theory of `real numbers' is a > > joke, and sidesteps the crucial issue of understanding the computational > > specification of the continuum, and 3) `infinite sets' are a metaphysical > > concept, and unnecessary for correct mathematics. > > > > Analysts and set theorists are welcome to send me reasoned responses. > > > > Assoc Prof N J Wildberger > > School of Maths > > UNSW > > After casually reading his notes, I think that he is saying this. The > axioms of modern set theory are too burdensome for actual > mathematicians, who in practice take a somewhat Platonic view of their > subject. But he is unsatisfied with the pragmatic Platonist approach > that we take, particular in the manner in which mathematics is taught at > pre-college levels. He thinks we need to roll up our sleeves and > rethink foundations so that we get something that really is usuable, so > that we can finally truly rid ourselves of Platonism, superstition, > instinct, gut reaction, religion, etc, etc. > > Personally I really like the Platonic approach, using set theory as a > highly convenient crutch. I'm not going to preclude the possibility > that one day a set of foundations for mathematics will be found, that > will greatly simplify and advance the extent that we will be able to > think about mathematics, but I think it will take a great genius, and > also some crisis of cicumstance (perhaps the discovery of some horribly > unresolvable contradiction). > > But on the whole, even if his tone was not exactly politic, I liked a > lot of what he said. But I don't think it is going to change the world. > > Stephen
Hi, without any intention of antagonizing you, let me ask you this question: What of what he said did you like and for what reasons? I would like to understand what the appeal of such a rant as Wildberger's is. In my view, it is evidently wrong in many parts, wrong under light scrutiny in many others and falacious for the most part of the rest. The only statement I can think of which is undebatable is the fact that education in mathematics is ever more deficient. But this is also strongly suggested by a lot of other factors, as the ever growing number of crackpots, the ever more present wrong notion that mathematics is dependent on computability and the expanding belief that mathematics is somehow subjected to the constrains of physical reality. Thanks in advance for any effort you may put into your answer. Regards.