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**From Brouwer to Hilbert. The debate on the foundations of mathematics in the 1920s.**
*(English)*
Zbl 0941.01003

New York, NY: Oxford University Press. x, 337 p. (1998).

This source-book covers 25 major articles in the debate on the foundations of mathematics that took place in the 1920s. It arose out of pedagogical need concerning a course in philosophy of mathematics and tries to fill in the gap that only a few contributions of that central debate between intuitionists and formalists had been translated into English before. The chronologically ordered edition is divided into four sections devoted to “L. E. J. Brouwer”, “H. Weyl”, “P. Bernays and D. Hilbert” and the emergence of “Intuitionistic Logic”, each of it preceded by a detailed introduction instead of elaborate commentary for each article. These introductions into the historical and technical context of the considered program are due to P. Mancosu and W. P. van Stigt. Modern research fields, e.g. the Hilbert Nachlass, are also taken into account. Besides the articles by the entitled mathematicians the book contains six important contributions by Hölder, Borel, Glivenko, Heyting and Kolmogorov. Except the latter they were all written before Gödel’s discoveries which here are not taken into consideration. Useful bibliographies and notes are to be found at the end of the different introducing articles, a name index at the end of the book.

Reviewer: M.Toepell (München)