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Re: Endorsement of Wolfgang Mueckenheim from a serious mathematician
Posted:
Jan 31, 2013 5:35 PM
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On Thursday, January 31, 2013 7:35:47 AM UTC-8, David C. Ullrich wrote:
> On Tue, 29 Jan 2013 20:30:12 -0800 (PST), david petry
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> <david_lawrence_petry@yahoo.com> wrote:
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> >On Tuesday, January 29, 2013 5:26:38 PM UTC-8, W. Dale Hall wrote:
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> >> david petry wrote:
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> >> >
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> >> > Doron Zeilberger wrote the following in an opinion piece on his website:
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> >> > "Read Wolfgang Mueckenheim's fascinating book ! I especially like the bottom
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> >> > of page 112 and the top of page 113, that prove, once and for all,
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> >> that (at least)
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> >> > the actual infinity is pure nonsense."
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> >> >
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> >> > http://www.math.rutgers.edu/~zeilberg/Opinion68.html
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> >> > I'd be interested in seeing an English translation of the bottom of page 112 and the top of page 113.
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> >> >
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> >> I suppose you missed the statement that immediately followed that:
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> >> Clarification added Aug. 25, 2011: My endorsement of Wolfgang
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> >> Mueckenheim's wonderful book is purely philosophical. I have no
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> >> expertise, or interest, in checking any possible technical
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> >> claims that he may have made.
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> >Of course I did not miss that. Is that extremely important?
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> Yes, it's certainly important if you're going to say he has an
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> endorsement from a serious mathematician.
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> Because people here don't object to his "philosophy".
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> A person can do standard mathematics, including all
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> that stuff about infinite sets, without believing
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> that infinite sets "really" exist.
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> The problem is that WM's version of the technical
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> details is always nonsense. His arguments about
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> binary trees are simply _wrong_. Wrong in basic
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> simply ways, totally independent of one's attitude
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> on any sort of "philosophical" question.
I admit that I don't understand WM's technical claims. However, when I see you and other mathematicians fail to comprehend, or at least fail to respond coherently to, very simple, clear and straightforward informal arguments, it doesn't inspire confidence in me that you are qualified to judge whether WM's technical claims are valid.
Here is a simple, clear and straightforward informal argument, which I believe Mueckenheim would endorse, that I have never seen a Cantorian mathematician respond to in a coherent way:
It is eminently reasonable to believe that the purpose of mathematics is to provide a rigorous and practically useful conceptual framework for reasoning quantitatively about real world phenomena. The objects that exist in a conceptual framework are concepts; the universe of mathematical objects is a collection of concepts. Concepts can be encoded in language. Languages are countable. The Cantorian claim that "uncountable" infinite collections exist is tantamount to the claim that mathematics should assert the existence of things that are not within the mathematical conceptual framework. That is a truly extraordinary and even bizarre claim that requires truly extraordinary evidence, and such evidence is lacking, and prominent and well respected mathematicians have pointed out that such evidence is lacking.
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