Re: Hiilbert and Cantor's paradise

Newsgroups	sci.math
Date	2018-05-14 21:00 -0700
References	<241de154-8ee2-4e40-912b-0383c7fa0626@googlegroups.com> <pd845b$ser$1@dont-email.me> <40265a06-e3cb-4d94-b455-893ef20293d0@googlegroups.com> <pdaocu$2id$1@dont-email.me> <1d5404b7-32bf-4bd6-8d8f-a31c5e558fd3@googlegroups.com>
Message-ID	<cdeb2dbe-797c-4d2e-aff9-0b0bf98698af@googlegroups.com> (permalink)
Subject	Re: Hiilbert and Cantor's paradise
From	David Petry <davidlpetry@gmail.com>

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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.

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.

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"

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.

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

Thread

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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