Obections to Cantor's Theory (Wikipedia article)
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From: Alec McKenzie on 19 Jul 2005 12:33 David Kastrup <dak(a)gnu.org> wrote: > Alec McKenzie <mckenzie(a)despammed.com> writes: > > > David Kastrup <dak(a)gnu.org> wrote: > > > >> Alec McKenzie <mckenzie(a)despammed.com> writes: > >> > It has been known for a proof to be put forward, and fully accepted > >> > by the mathematical community, with a fatal flaw only spotted years > >> > later. > >> > >> In a concise 7 line proof? Bloody likely. > > > > I doubt it had seven lines, but I really don't know how many. > > Probably many more than seven. > > It was seven lines in my posting. You probably skipped over it. I see you have misunderstood what I said. You seemed to be denying that the accepted proof I mentioned (that turned out to have a flaw) was only seven lines, and I was merely saying that I didn't know how many lines it had. -- Alec McKenzie mckenzie(a)despammed.com
From: Michael Stemper on 19 Jul 2005 12:53 In article <1121727755.158001.288300(a)g44g2000cwa.googlegroups.com>, david petry writes: >Cantor's Theory, if taken seriously, would lead us to believe >that while the collection of all objects in the world of >computation is a countable set, and while the collection of all >identifiable abstractions derived from the world of computation >is a countable set, To be consistent with the philosophy that only things that can physically exist are meaningful, you shouldn't say "countable" here, you should say "finite". After all, there are only about 10^78 atoms in the universe, which puts a very definite (and finite) cap on how many computers there can be. In addition to that, each of those computers can only be in a finite number of possible states. Therefore, there's only (by this philosophy) a finite number of "identifiable abstractions derived from the world of computation", rather than a countable number, as you stated. -- Michael F. Stemper #include <Standard_Disclaimer> A bad day sailing is better than a good day at the office.
From: Jesse F. Hughes on 19 Jul 2005 12:50 "Kevin Delaney" <kevind(a)y-intercept.com> writes: > Transfinite theory was the primary reason for removing the study of > logic, grammar and arithematic in American public education and > replacing it with new math. Fascinating. Got any citations for that? Wow. Grammar was removed from public education due to Cantor's theorem. Who'da thunk it? > There are some who think the world was on a better thread with the > classical tradition. There are some who think that one shouldn't make things up and call it an argument. But they're not as persuasive as you. [...] > As pointed out in a different post. The people who are opposed to a > theory are generally a lot more diverse than those who support > it. For example, Brouwer was opposed to the law of excluded > middle. I suspect that others are hoping to pull off a stunt like > Russell. Russell's early work on the reflexive paradox could be > considered "anti-Cantorian". Russell's two step catapulted him to > the top of the intellectual community and led to the decline of > Frege. I suspect that many people toy with anti-Cantorian thoughts > because they hope to repeat the trick. Decline of Frege? Gosh. Of course, Russell continued to be indebted to Frege and Frege continues to be a pillar of philosophy of mathematics. Well, not quite. Frege's reputation grew considerably after his death (and long after Russell's paradox was discovered), if I understand correctly. -- Jesse F. Hughes "Contrariwise," continued Tweedledee, "if it was so, it might be, and if it were so, it would be; but as it isn't, it ain't. That's logic!" -- Lewis Carroll
From: The World Wide Wade on 19 Jul 2005 13:03 In article <r3spd1hlkbptf23frc8pnbqgfgsjfst89k(a)4ax.com>, David C. Ullrich <ullrich(a)math.okstate.edu> 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." > > Please choose one of the following replies: > > (i) No, (*) is nonsense. If it's square then _by definition_ > it's not a circle. So they will _never_ find a square circle. > > (ii) Hmm, good point. > > You really should choose one of (i) or (ii), so people know > how to reply to your post. The point: If you say (ii) then > we know that there's no point worrying about anything you > say. Otoh if you say (i) then there's hope - you agree that > we're _certain_ they will never find a square circle, now > we just have to convince you that our assertions about > enumerations of subsets of N are just as certain, for > entirely similar (although slightly more complicated) > reasons. You need to modify (i) because the definition of a square nowhere specifies a square is not a circle.
From: Kevin Delaney on 19 Jul 2005 14:31
The classical method (Scholastic) method of education leaned primarily on teaching grammar, logic, arithemetic and rhetoric. The modern era felt that these were all artificial edifaces. There was a concerted effort to pull these subjects out of the schools. They were there. They were not there when I went to school. You can verify this if you look at the standard school curriculum in say 1900 and compare it to the curriculum in, say, the 1970s. I used to do stupid things like look up the different books that were taught at different times to try and see how different eras would see the world. Transfinite theory is not the only manifestation of modern thinking. So, I am not saying that transfinite theory alone was the cause for this transformation. The basic idea was that traditional logic, grammar and arithematic were part of this horrible weight keeping people down, and that we would transcend to a higher level of existence. Citing all the places where people attacked classical education would take several years. It is pretty much a fact that in the modern times there was one curriculum replaced by another curriculum. In some cases it was a postive thing, curriculums always need improvement and adjustment. The problem with a wholesale replacement is that you end up losing the promising threads of the previous curriculum. |