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Re: Hiilbert and Cantor's paradise

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On 5/13/2018 4:59 PM, David Petry wrote:
> Martin Shobe wrote:
> 
>> David Petry wrote:
> 
>>> Hilbert is famous for the quote, "mathematicians will never be evicted from the paradise Cantor created for us".  However, ten years later he wrote:
>>>
>>> "The infinite is nowhere realized; it is neither present in nature nor admissible as the foundation of our rational thinking" [D. Hilbert: "Über das Unendliche", Math. Annalen 95 (1925) p. 190]
>>>
>>>
>>> I think that's interesting because so often people claim that the first quote is that last word in the debate over whether Cantor's ideas about infinity should be accepted as part of mathematics.  But the second quote shows clearly that Hilbert had second thoughts about the issue.
> 
>>
>> Quote mining is can be fun. In the same paper.
> 
>> But analysis alone does not provide us with the deepest insight into the
>> nature of the infinite. This insight is procured for us by a discipline
>> which comes closer to a general philosophical way of thinking and which
>> was designed to cast new light on the whole complex of questions about
>> the infinite. This discipline, created by George Cantor, is set theory.
>> In this paper, we are interested only in that unique and original part
>> of set theory which forms the central core of Cantor's doctrine, viz.,
>> the theory of transfinite numbers. This theory is, I think, the finest
>> product of mathematical genius and one of the supreme achievements of
>> purely intellectual human activity. What, then, is this theory?
>   
> 
> Well that's very interesting.
> 
> If I'm reading him correctly, he's acknowledging that mathematics has a major role to play in understanding nature, and it has a major role to play in understanding our own rational thinking, but infinity has no role to play in those things.

You're not understanding him. He has a role for infinity in 
understanding nature but that doesn't make infinity part of nature. 
Similarly infinity is not part of our notion of proof or rational thought.

> Furthermore, he asserts that our understanding of infinity does not come from our understanding of mathematics, but rather from "a general philosophical way of thinking".
> 
> But then he says that Cantor's theory of infinity is "the finest product of mathematical genius".
> 
> If he had said that the theory of infinity is the finest achievement in philosophy and/or art, then I would say that he is being consistent, even though I disagree with him.  But what he wrote suggests that he is actually quite confused.

The confusion is not his.

Martin Shobe

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Hiilbert and Cantor's paradise David Petry <davidlpetry@gmail.com> - 2018-05-12 13:26 -0700
  Re: Hiilbert and Cantor's paradise "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-05-12 20:24 -0500
    Re: Hiilbert and Cantor's paradise David Petry <davidlpetry@gmail.com> - 2018-05-13 14:59 -0700
      Re: Hiilbert and Cantor's paradise "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-05-13 20:22 -0500
        Re: Hiilbert and Cantor's paradise WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-14 00:54 -0700
          Re: Hiilbert and Cantor's paradise "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-05-14 19:17 -0500
          Re: Hiilbert and Cantor's paradise David Petry <davidlpetry@gmail.com> - 2018-05-14 21:00 -0700
            Re: Hiilbert and Cantor's paradise Alan Mackenzie <acm@muc.de> - 2018-05-15 06:57 +0000
              Re: Hiilbert and Cantor's paradise WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-05-15 06:04 -0700
                Re: Hiilbert and Cantor's paradise Alan Mackenzie <acm@muc.de> - 2018-05-15 19:41 +0000
                Re: Hiilbert and Cantor's paradise "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-05-15 19:54 -0500
                Re: Hiilbert and Cantor's paradise Python <python@python.invalid> - 2018-05-16 03:04 +0200
                Re: Hiilbert and Cantor's paradise David Petry <davidlpetry@gmail.com> - 2018-05-16 17:53 -0700
                Re: Hiilbert and Cantor's paradise "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-05-16 20:44 -0700
                Re: Hiilbert and Cantor's paradise Alan Mackenzie <acm@muc.de> - 2018-05-17 18:32 +0000
                Re: Hiilbert and Cantor's paradise David Petry <davidlpetry@gmail.com> - 2018-05-18 21:56 -0700
                Re: Hiilbert and Cantor's paradise Alan Mackenzie <acm@muc.de> - 2018-05-20 18:54 +0000
                Re: Hiilbert and Cantor's paradise David Petry <davidlpetry@gmail.com> - 2018-05-20 12:13 -0700
                Re: Hiilbert and Cantor's paradise bursejan@gmail.com - 2018-05-20 14:15 -0700
                Re: Hiilbert and Cantor's paradise bursejan@gmail.com - 2018-05-20 14:21 -0700
                Re: Hiilbert and Cantor's paradise bursejan@gmail.com - 2018-05-20 14:26 -0700
              Re: Hiilbert and Cantor's paradise FredJeffries <fredjeffries@gmail.com> - 2018-05-15 08:47 -0700
            Re: Hiilbert and Cantor's paradise "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-05-15 20:09 -0500
              Re: Hiilbert and Cantor's paradise David Petry <davidlpetry@gmail.com> - 2018-05-16 17:57 -0700
                Re: Hiilbert and Cantor's paradise "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-05-16 20:39 -0500
                Re: Hiilbert and Cantor's paradise David Petry <davidlpetry@gmail.com> - 2018-05-16 20:02 -0700
                Re: Hiilbert and Cantor's paradise "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-05-17 06:56 -0500
    Re: Hiilbert and Cantor's paradise "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2018-05-15 13:55 -0700
  Re: Hiilbert and Cantor's paradise bursejan@gmail.com - 2018-05-12 18:50 -0700

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