Grundlagen der Mathematik

Abstract

THAT the foundations of mathematics are A important is a proposition which will find few opponents, for the science of mathematics is commonly regarded as man's securest intellectual possession. What constitutes these foundations is a subject on which agreement has not been reached. There are, however, three main directions into which the body of modern research has branched, namely, the logistic, the intuitionistic and the formalistic theories. Broadly speaking, the logistic theory regards mathematics as a branch of logic, the intuitionistic theory regards the theorems of mathematics as having actual significance, the formalistic theory regards mathe matics as devoid of meaning per se. The most powerful exponent of the formalistic attitude is Hilbert, and the present volume is the first part of a systematic exposition of mathematical foundations from the point of view of the school of thought which he has founded. This is probably the most important book on mathe-matical foundations which has appeared since Whitehead and Russell's “Principia Mathematical Grundlagen der Mathematik Band 1. Von D. Hilbert und P. Bernays. (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Beriick-sichtigung der Anwendungsgebiete, herausgegeben von R. Courant, Band 40.) Pp. xii + 471. (Berlin: Julius Springer, 1934.) 37.80 gold marks.