Table of Contents

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.

Reviews

“The selection concerns above all lecture courses on the foundations of arithmetic and logic held between 1917 and 1933. … The edition deserves highest praise. It shows intuitively the development of foundational ideas in the making which finally led to the new mathematical subdiscipline of proof theory.” (Volker Peckhaus, Studia Logica, Vol. 105, 2017)“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Vol. 17 (4), December, 2016)“The volume under review is the third in a projected series of six presenting Hilbert’s unpublished lectures in the foundations of the exact sciences.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)