Obections to Cantor's Theory (Wikipedia article)
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From: Han de Bruijn on 28 Jul 2005 10:03 In response to Martin Shobe. This is actually an old article from 1991, Re: The Political Econony of Sets. But I still consider it as valid. Virtually any kind of Modern Math is based upon Set Theory. Despite the fact that ST suffered from (Russell's) paradoxes from the very beginning. This would have assassinated any other kind of mathematical theory. It is remarkable that Set Theory survived its shortcomings in the first place. Big surprise; it even became the foundation "par exellance" whereupon Modern Mathematics is based. From a rational point of view this must sound like a true miracle. It heavily reminds to the way our Religions are still going strong, despite manifest lack of scientific content. So there must be something out there which is even more convincing than logic. Let's see what it is. A satisfactory explanation can be found only IFF people dare to recognize that Mathematics is a humble activity of human beings. This implies that mathematics is bound to the historical and social restrictions in the first place. Yes (!), I want you to get rid of the idea that Mathematics is independent of society. How can somebody for example conceive the thought that the whole of mathematics is made up from nothing else but Sets? This would be impossible if not society itself had'nt adopted the shape of an "ungeheure Warensammlung" (unprecedented collection of goods: Karl Marx in "Das Kapital"). Is it a coincidence that the birth of Set Theory has its social analogue in the enormous accumulation of all kinds of richness which marks the turn of the century? Is it a coincidence that Georg Cantor's father himself was a merchant, so that his son became *very* familiar with those huge "sets" in the storehouses of his family? So we may conclude in the first place that the birth of Set Theory was inspired by social circumstances. But this is not the end of the story. Even nowadays, nobody can think of an idea which fits better the view of the Capitalist System than Set Theory. (Go to a supermarket, and convince yourself!) This means that no rational arguments can be used in order to deprive ST from its predominant role in mathematics. Read my lips: I *don't want* to get rid of Set Theory as a (less important) part of Mathematics. Mathematical concepts originate and become important within the context of our human society, with all its non-logic and non-scientific taboos. But it is also thinkable that certain concepts will NOT originate in the given social circumstances, simply because such new concepts would have unacceptable economical and political (and personal) consequences. New ideas do not come, essentially because, deep in our heart, we DON'T WANT them. So maybe, yes, further progress in mathematics is *inhibited* by the way our societies are organised ... Han de Bruijn
From: Robert Low on 28 Jul 2005 10:06 Martin Shobe wrote: > But your objections don't cast any doubt, because they are irrelevant > to what you are objecting to. Set theory does not have physics as > it's inspiration, It's a common claim that one of Cantor's motivations in developing sets and ordinal numbers was his attempt to understand Fourier series. Whether you regard that as physics, applied maths, or just maths may affect you opion of whether set theory had any physical motivation :-)
From: stephen on 28 Jul 2005 10:06 In sci.math Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > Just as a matter of prevention, shouldn't we at least _try_ to find > a way of living together, then? > Han de Bruijn You are the one who seems to have a problem living together with mathematicians. What is preventing you from simply living and let live? Stephen
From: Han de Bruijn on 28 Jul 2005 10:30 stephen(a)nomail.com wrote: > In sci.math Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > >>Just as a matter of prevention, shouldn't we at least _try_ to find >>a way of living together, then? > > You are the one who seems to have a problem living together > with mathematicians. What is preventing you from simply > living and let live? We don't care about telling lies ourselves, but we don't want that other people are lying to us. Isn't that so? :-( Han de Bruijn
From: stephen on 28 Jul 2005 10:35
In sci.math Dik T. Winter <Dik.Winter(a)cwi.nl> wrote: > In article <1122503371.218414.268340(a)g47g2000cwa.googlegroups.com> malbrain(a)yahoo.com writes: > > Dik T. Winter wrote: > ... > > > > > > The C language is defined by the C standard, as defined by ISO. > > > > > > There are no "unbounded" standard types in the C language. karl m > > > > > > > > > > Who is talking about C? > > > > > > > > Of the billions of computer systems deployed since the micro-computer > > > > revolution, the overwhelming majority are programmed with C. > > > > > > That is not an answer. > > > > Well, the OBVIOUS answer to your question is, "I'm talking about C" > > However, I'm not that vulgar. I tend to translate discussions into C > > because I find it to be more universally understood than java. karl m > So what? When someone talks about java with "unbounded" standard types, > what is the point stating that C does not have "unbounded" standard types? He probably thinks that if you speak English loudly enough everyone will understand. :) Stephen |