This volume provides an English translation of 14 texts on the foundation of mathematics written by the German mathematician Moritz Pasch (1843–1930). These texts were originally published between 1917 and 1926, half of them also in Pasch’s own collection of papers “Mathematik am Ursprung” from 1927 [M. Pasch, Mathematik am Ursprung. Gesammelte Abhandlungen über Grundfragen der Mathematik. Leipzig: Felix Meiner (1927; JFM 53.0038.01)]. They give deep insights into Pasch’s philosophy of mathematics, e.g., his empiricist epistemology of geometry, and his contributions to the axiomatic method, in particular his theory of implicit definitions.
The translator opens the volume with an introduction of 43 pages length, focusing not on Pasch’s contributions to the foundations of geometry, but on his arithmetical writings. In his preface the translator characterizes his goal as “to produce a text that might have been composed by a mathematically and philosophically competent writer whose first language is [today’s] English” (p.v). The papers are chosen to introduce the English speakers to an important body of work in foundations, going “beyond the familiar triad of formalism, intuitionism, and logicism”. These goals might have been reached, but one has to state, that this translation does not serve scholarly purposes. Producing an easy readable English text from old-fashioned German leads to changes in the presentation of the argument and connotations including some “corrections”. A telling example for the scholarly level is the translator’s decision to render in English the titles of German works cited by Pasch. This might be a helpful service for readers with only a little command of German (p.vi), but a constraint for those intending to look up the literature.