Introduction to mathematical philosophy. With an introduction by Michael Otte. Edited by Johannes Lenhard and Michael Otte (Q2778902)

This is a German textbook edition of \textit{B. Russell}'s seminal ``Introduction to mathematical philosophy'' [London, G. Allen \& Unwin, New York, Macmillan (1919; JFM 47.0036.12; reprint Zbl 0877.03001)], based on E. J. Gumbel's (slightly revised) translation, first published in 1923 [Drei Masken-Verlag, München (1923, 2nd ed. 1930; JFM 56.0037.08)].NEWLINENEWLINENEWLINEIn his comprehensive introduction (pp. VII--LIX), M. Otte presents a readable analysis of the text, also providing the context in which Russell's ideas have to be placed and discussing their relevance for today's philosophy of mathematics. He especially relates Russell's set-theoretic approach to the concept of number, necessitating the introduction of the axiom of infinity, to the approach of formal axiomatics criticized by Russell. Obviously, the author assumes, Russell preferred an ontological meaning of the axiom of infinity according to which it is more plausible to accept the existence of infinite multiplicities in the world than the opposite finitistic hypothesis (p. XXIV).NEWLINENEWLINENEWLINEOtte sees a similarity between Russell's approach and I. Kant's constructive-genetical approach to mathematics (cf. pp. XXV--XXIX). He presents Russell's theory as a logically turned Kantianism and summarizes its basic features in one single thesis: Russell's epistemology and especially his philosophy of mathematics is based on the attempt to specify the application problem and the relation of our mathematical knowledge to reality by characterizing it in an absolute, aprioristic way, and thereby to get rid of its specific dynamics and uncertainties (p. LVIII).