David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933

Inbunden, Tyska, 2013

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The bulk of this volume consists of six sets of notes for lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and the early 1930s. The notes detail the increasing dominance of the metamathematical perspective in Hilberts treatment, i.e., the development of modern mathematical logic, the evolution of proof theory, and the parallel emergence of Hilbert's finitist standpoint. The notes are mostly very polished expositions; e.g., the 1917-18 lectures are in effect a first draft of Hilbert and Ackermanns Grundzuge der theoretischen Logik (1928), reprinted in this Volume. They are thus essential for understanding the development of modern mathematical logic leading up to Hilbert and Bernayss Grundlagen der Mathematik (1934, 1938). Also included is a complete version of Bernays Habilitationschrift of 1918, only partially published in 1926.

Produktinformation

Utgivningsdatum2013-06-03
Mått155 x 235 x 63 mm
Vikt1 772 g
FormatInbunden
SpråkTyska
Antal sidor1 062
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783540205784

Tillhör följande kategorier

Introduction.- Hilbert's Lectures on Principles of Mathematics from 1917-18.- Hilbert's Lectures on the Logical Calculus from 1920.- Chapter 3: Hilbert's Lectures on Problems of Mathematical Logic from 1920.- Hilbert's Lectures on Foundations of Mathematics from 1921-22.- Hilbert's Lectures on Logical Foundations of Mathematics from 1922-23.- Hilbert's Lectures on the Infinite from 1924-25.- Hilbert's Typescript on the Foundations of Thought from c. 1925.- Hilbert's Lecture on Infinity from 1933.- Miscellanea.- Appendix A: Bernays's Habilitation Thesis from 1918.- Appendix B: First Edition of Hilbert and Ackermann, 1928.

"The editors have produced an impeccable and exhaustive critical edition of all of Hilbert's papers on mathematical logic and meta-mathematics written between 1917 and 1931 in German. ... this volume is excellently designed for the historian as a working source book for whom it is clearly indispensable. But it should also serve those still interested in the Foundations of Mathematics and its open problems left by Hilbert and his students ... ." (Catharine C. Hennix, Nieuw Archief voor Wiskunde, Vol. 17 (4), December, 2016) "The volume under review is the third in a projected series of six presenting Hilbert's unpublished lectures in the foundations of the exact sciences. ... This volume is a wonderful achievement. ... The book belongs in the library of anyone interested in logic and the foundations of mathematics. Indeed, it should be placed in one of the lower shelves, so as to be ready to hand for frequent use." (Paolo Mancosu, Philosophia Mathematica, Vol. 23 (1), February, 2015)