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Re: Landau letter, Re: Mathematica as a New Approach...

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  • Subject: [mg128135] Re: Landau letter, Re: Mathematica as a New Approach...
  • From: Andrzej Kozlowski <akozlowski at gmail.com>
  • Date: Tue, 18 Sep 2012 03:41:19 -0400 (EDT)
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On 17 Sep 2012, at 09:36, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:

>
> On 17 Sep 2012, at 06:23, J=E1nos L=F6bb <janos at lobb.com> wrote:
>
>> Continuity relies on real numbers and real numbers cannot exist without the continuum hypotheses.
>
> The second part is not true.
>
> Andrzej Kozlowski


I think there is a confusion of terminology involved. What is generally known as "The Continuum Hpothesis" is a statement about cardinal numbers, known to be undecidable in the Zermelo-Fraenkel set theory (and independent of the axiom of choice). It is a mathematical (or "logical" statement and, is not implied by the existence of real numbers (otherwise it would not be undecidable).

It is clear however that what was meant in the post from which the above quote was taken by "continuum hypothesis" was something quite different: an informal "belief" that the real numbers correspond to some physical reality. That of course is a metaphysical statement, which means that it is also "undecidable" but in a very different sense from the sense in which "The Continuum Hypothesis" us undecidable.

Andrzej Kozlowski




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