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Re: Hiilbert and Cantor's paradise

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David Petry <davidlpetry@gmail.com> wrote:

> Martin Shobe and Wolfgang Mueckenheim each gave slightly different
> translations of a quote from Hilbert:

> Shobe:
>  This theory is, I think, the finest product of mathematical genius and
>  one of the supreme achievements of purely intellectual human activity.

> Mueckenheim:
>  this appears to me as the most admirable blossom of mathematical
>  spirit and really one of the supreme achievements of purely
>  intellectual human activity.

How about quoting the original, so that we can make up our own minds?
:-)

> There's actually a very big difference between the two.  In the one
> given by Mueckenheim, Hilbert is saying that Cantor's theory of
> infinity is in the spirit of mathematics, and doesn't address the
> question of whether the theory should be accepted as actually part of
> mathematics.

> The translation Shobe gives us leaves the impression that Hilbert
> thinks the theory is some kind of major advance in our understanding of
> mathematics itself, which is bizarre.

???  Why "bizarre"?

> Yes, Cantor's theory of infinity is "in the spirit of mathematics"--it
> consists of axioms, definitions, theorems and proofs, just like
> mathematics.


> But Hilbert also wrote:

> "The infinite is nowhere realized; it is neither present in nature nor
> admissible as the foundation of our rational thinking" 

I'm not aware of any mathematical axiom based on the notion of infinity.
That is likely what Hilbert meant.  The infinite arises as the
consequences of "finite" axioms.

> which suggests he at least understood the reason many mathematicians
> were refusing to accept Cantor's theory of infinity as part of
> mathematics;  if we agree that the purpose of mathematics is to help us
> understand nature and our rational thinking, then infinity doesn't
> belong in mathematics.

That's a very big "if".  I wouldn't agree with it, at least not totally.

> It's interesting how seemingly small differences in two translations
> can make such a big difference in meaning.

-- 
Alan Mackenzie (Nuremberg, Germany).

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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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