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Topic: Matheology § 193
Replies: 1   Last Post: Jan 19, 2013 1:08 PM

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Registered: 1/6/11
Re: WMatheology � 193
Posted: Jan 19, 2013 1:08 PM
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In article
WM <> wrote:

> Matheology § 193
> {{In 1927 David Hilbert gave a talk at Hamburg university, where he
> explained his opinions about the foundations of mathematics.}} It is a
> great honour and at the same time a necessity for me to round out and
> develop my thoughts on the foundations of mathematics, which was
> expounded here one day five years ago and which since then have constantly kept me most actively
> occupied. With this new way of providing a foundation for mathematics,
> which we may appropriately call a proof theory, I pursue a significant
> goal, for I should like to eliminate once and for all the questions
> regarding the foundations of mathematics [...]
> I have already set forth the basic features of this proof theory of
> mine on different occasions, in Copenhagen [1922], here in Hamburg
> [1922], in Leipzig [1922], and in Münster [1925]; in the meantime much
> fault has been found with it, and objections of all kinds have been
> raised against it, all of which I consider just as unfair as it can
> be. [...]
> Poincaré already made various statements that conflict with my
> views; above all, he denied from the outset the possibility of a
> consistency proof for the arithmetic axioms, maintaining that the
> consistency of the method of mathematical induction could never be
> proved except through the inductive method itself. [...] Regrettably
> Poincaré, the mathematician who in his generation was the richest in
> ideas and the most fertile, had a decided prejudice against Cantor's
> theory, which prevented him from forming a just opinion of Cantor's
> magnificent conceptions. Under these circumstances Poincaré had to
> reject my theory, which, incidentally, existed at that time only in
> its completely inadequate early stages. Because of his authority,
> Poincaré often exerted a one-sided influence on the younger
> generation. I cannot for the most part agree with
> their tendency; I feel, rather, that they are to a large extent behind
> the times, as if they came from a period when Cantor's majestic world
> of ideas had not yet been discovered.
> [E. Artin et al. (eds.): "D. Hilbert: Die Grundlagen der
> Mathematik" (1927). Abh. Math. Seminar Univ. Hamburg, vol. 6, Teubner,
> Leipzig (1928) 65-85. English translation: J. van Heijenoort: "From
> Frege to Gödel", Harvard Univ. Press, Cambridge, Mass. (1967) 464-479]

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