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Re: Hiilbert and Cantor's paradise

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Am Dienstag, 15. Mai 2018 08:57:42 UTC+2 schrieb Alan Mackenzie:
> 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?
> :-)

diese erscheint mir aIs die bewundernswerteste Blüte mathematischen Geistes und überhaupt eine der höchsten Leistungen rein verstandesmäßiger menschlicher Tatigkeit.

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

Das Gesamtergebnis ist dann: das Unendliche findet sich nirgends realisiert; es ist weder in der Natur vorhanden, noch als Grundlage in unserem verstandesmäBigen Denken zulässig - eine bemerkenswerte Harmonie zwischen Sein und Denken.
> 
> I'm not aware of any mathematical axiom based on the notion of infinity.

The axiom of infinity is the basis of ZF. ZF is based upon the infinite.

> That is likely what Hilbert meant.  The infinite arises as the
> consequences of "finite" axioms.

noch als Grundlage in unserem verstandesmäBigen Denken zulässig
> 
> > It's interesting how seemingly small differences in two translations
> > can make such a big difference in meaning.

I would prefer my translation.

Regards, WM

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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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