Date: Jan 19, 2013 3:53 AM Author: mueckenh@rz.fh-augsburg.de Subject: Matheology § 193

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 {{compare Kalenderblatt 101212

to 101214

http://www.hs-augsburg.de/~mueckenh/KB/

}} 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. {{Not to a sufficient degree, unfortunately. --- Then

Hilbert discusses the objections by Russell and Whitehead and finally

Brouwer. Hilbert concludes:}} 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. {{A world discovered by a man

who was behind his times, who did not recognize atoms in the late 19th

century, but rejected evolution, who believed in an infinite set of

angels and took the basis of his mathematics from the holy bible: "in

infinity and beyond".}}

[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]

Regards, WM