Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Matheology § 193
Posted:
Jan 19, 2013 3:53 AM


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.hsaugsburg.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 onesided 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) 6585. English translation: J. van Heijenoort: "From Frege to Gödel", Harvard Univ. Press, Cambridge, Mass. (1967) 464479]
Regards, WM



