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Virgil
Posts:
8,833
Registered:
1/6/11


Re: WMatheology � 193
Posted:
Jan 19, 2013 1:08 PM


In article <0499af551b534314b18a8500fcfb2ece@ho8g2000vbb.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> 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 onesided 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) 6585. English translation: J. van Heijenoort: "From > Frege to Gödel", Harvard Univ. Press, Cambridge, Mass. (1967) 464479] Poison deleted! 



