Obections to Cantor's Theory (Wikipedia article)
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From: Han de Bruijn on 25 Jul 2005 03:57 David Kastrup wrote: > Uh, no. I don't want to recreate the whole building of mathematics > whenever physics discovers something new. The whole point of > mathematics is that it is not subject to external influences. New > math models don't invalidate previous ones, new physics models _do_ > invalidate previous ones. It's not that bad. The Theory of Relativity didn't invalidate the use of Newtonian Mechanics with designing bridges and cars. And what would be wrong with a mathematics which evolves in time, like everything else in life ? Han de Bruijn
From: MoeBlee on 25 Jul 2005 04:15 >From a post by Han de Bruijn: > Set theory doesn't deserve such a predominant place in mathematics. Mathematical logic and set theory provide a rigorous basis for notions such as proof, set, function, sequence, etc. This provides me a better understanding and appreciation of mathematics, even as I am only learning about it. If there are significantly better bases, then I'm happy to hear about them. However, I wouldn't invest my time in your inconsistent system. > After the discovery of Russell's paradox et all, everybody should have > become most reluctant. Whether anyone should or should not have been reluctant, within a few years, a solution was devised that has withstood nearly a century. Set theory was not conceived as an allegory of the physical world. Your criterion that set theory be such an allegory is extrinsic to the purpose, usefulness, and sublimity of the subject. Meanwhile, set theory does provide a rigorous technical and conceptual basis for mathematics that is used to figure out things about the physical world.
From: Han de Bruijn on 25 Jul 2005 04:19 david petry wrote: > Cantor's set theory has been intertwined with modern analysis to > such an extent that it sometimes appears that analysis would fall > apart without the glue of set theory to hold it together. > > My claim is that all the results of analysis which have observable > implications, an hence have the potential to be applied as models > of the real world, necessarily do not need Cantor's Theory. Affirmative. After I discovered (in 1973) that Set Theory was just a burden on analysis (Lie groups), I've managed to do analysis without set theory for another 30 years. And I still cannot imagine what its additional value is, I mean as a general foundation of mathematics. (I'm not talking about a few applications which use set theory quite explictly, such as CSG: Constructive Solid Geometry). Han de Bruijn
From: MoeBlee on 25 Jul 2005 04:33 >From a post by Han de Bruijn: > I've managed to do analysis without > set theory for another 30 years. With no theory of sets whatsoever? Or do you allow yourself the inconsistent theory you have on your web site? MoeBlee
From: Han de Bruijn on 25 Jul 2005 04:39
Virgil wrote: > So that the "observability" of an area of pure mathematics may not be > observable until after, possibly long after, the time of its > developement, and no one at that time of development is likely to be a > good judge of whether it will ever become "observable". "Observable" is not the same as "observed", inasmuch as "applicable" is not the same as "applied". I disagree with your suggestion as if it would be impossible to decide about these issues and make predictions. Han de Bruijn |