Obections to Cantor's Theory (Wikipedia article)
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From: Jesse F. Hughes on 19 Jul 2005 17:45 "david petry" <david_lawrence_petry(a)yahoo.com> writes: > Jesse F. Hughes wrote: > >> Anyway, what is "Cantor's Theory"? > > The use of the term "Cantor's Theory" has a long history. For > example, it appears in the quote from Kronecker that I included > in the article. Yeah, so what is it? >> > These "anti-Cantorians" see an underlying reality to mathematics, >> > namely, computation. >> >> Petry's own particular nonsense and not a broad program. > > It represents my attempt to understand the arguments of the > anti-Cantorians. It is only your own argument. There are several cranks in this group that criticize Cantor and never once mention computation. >> Science does not proclaim that all truth has observable implications. > > So you say. I'd bet most scientists would disagree with you. Maybe, maybe not. Surely most philosophers of science would not say so and surely such claims ("all truth has observable implications") cannot be considered "scientific" claims in the usual sense at all. >> > The artists see the requirement that mathematical statements must >> > have observable implications as a restriction on their intellectual >> > freedom. >> >> No editorializing in that excerpt, huh? > > No. It's a very objective summary of things that mathematicians > have said in this newsgroup. Uh huh. >> > It is plausible that in the future, mathematics will be split >> > into two disciplines - scientific mathematics (i.e. the science >> > of phenomena observable in the world of computation), and >> > philosophical mathematics, wherein Cantor's Theory is >> > merely one of the many possible "theories" of the infinite. >> >> Bullhonkies. It is plausible only in Petry's feeble imagination. > > Are you seriously saying that it is inconceivable to you that in > the future, mathematics will be split into the two disciplines, as > I have stated? You seem to lack imagination. The negation of "plausible" is not "inconceivable". > -- "Yup, you guessed it. If worse comes to worse, I *will* turn to the Army to help me with mathematicians. And then mathematicians don't think the NSA or CIA can save your asses, as generals LIKE me." -- James Harris's latest foray into mathematical logic.
From: G. Frege on 19 Jul 2005 17:49 On 19 Jul 2005 14:25:47 -0700, "david petry" <david_lawrence_petry(a)yahoo.com> wrote: > > Jesse F. Hughes wrote: > > > > Anyway, what is "Cantor's Theory"? > > > The use of the term "Cantor's Theory" has a long history. For > example, it appears in the quote from Kronecker that I included > in the article. > Look man: "Cantor's Theory" is of no interest any more these days. Mathematics is concerned with modern _axiomatic_ set theory. You might read http://plato.stanford.edu/entries/set-theory/ for a starter. F.
From: Dave Rusin on 19 Jul 2005 17:48 In article <3k58rgFsisjpU1(a)individual.net>, Robert Low <mtx014(a)coventry.ac.uk> wrote: >Tony Orlow (aeo6) wrote: >> Stephen J. Herschkorn said: >>>To those who insist there is a smallest positive real number? >> 000...000.000...001 > >And how many 0's are there after that decimal point? N? log_2(N)? N-1? >N+1? (Whatever the hell any of those answers mean...) Tsk, tsk, Robert, you've not been paying attention! There are N of them; the "1" is in the N-th place, i.e. this decimal expansion is simply of the number 10^(-N). If there had only been N-1 zeros, why, that would be the decimal expansion of 10^(N-1), and THAT certainly isn't the smallest positive real number, now is it? (I mean, it's TEN TIMES as big as 10^(-N).) And if you divide by 10 you get, um, well, see that's now 000...000.000...0001 which is 10^(-(N+1)), and that's different from 10^(-N) (see the extra "0"?). I think. Well, maybe. I mean, it should be smaller than 10^(-N), seeing as how it's only 1/10 as big, but then again, Tony did pronounce this decimal string I'm abbreviating as 10^(-N) to be the smallest positive real, so maybe 10^(-(N+1)) = 10^(-N) after all? Hmm, let's see, I'm sure we can take logs now and get N+1 = N. Ah right, that's it! See, the two decimal thingies are the same because you can kind of line of the zeros of one with the zeros of the other, so that they have the same number of zeros even though one has a zero the other one doesn't have. So that number (I'll just call it X now) has the property that (1/10) X = X. That's just one of those things you've got to get used to here; (9/10)X = 0 doesn't mean X = 0, you know. Ooh, wait, I think I did a bad thing -- that "lining up the zeros" thing sounds a lot like asking for the cardinality of the set of 0's. Can't have that -- cardinality's "wrong". Hmm, looks like I haven't been paying attention either... dave
From: Timothy Little on 19 Jul 2005 18:01 David C Ullrich wrote: > I once had a person tell me the following, with a straight face: > > (*) "You can't say for sure there's no such thing as a square > circle! I mean just because they haven't found one yet doesn't > mean they won't discover one tomorrow." I think the Manhattan metric does a pretty good job of modelling square circles. - Tim
From: Alec McKenzie on 19 Jul 2005 18:04
Chan-Ho Suh <suh(a)math.ucdavis.nospam.edu> wrote: > In article <mckenzie-27AD7F.22290719072005(a)news.aaisp.net.uk>, Alec > McKenzie <mckenzie(a)despammed.com> wrote: > > > In 1879 a proof of the four-colour map theorem was published by > > Arthur Bray Kemp, a member of the London Mathematical Society. > > He became a member of the Royal Society in consideration for his > > achievement. > > > > It was not until eleven years later, in 1890, that the fatal > > flaw in the proof was pointed out by Percy John Heawood in a > > paper in the Quarterly Journal of Mathematics. > > That's a good example. But it's inaccurate to say he became an FRS > because of this. I did not say he became an FRS because of this. I would be very surprised if he ever did become an FRS at all. > And as I alluded to in another post, I seriously doubt Kempe's paper > underwent serious scrutiny by many people. So do I. -- Alec McKenzie mckenzie(a)despammed.com |