Philosophy of Arithmetic

Psychologische und logische Untersuchungen) is an 1891 book about the philosophy of mathematics by the philosopher Edmund Husserl.

The first volume is divided in two parts, in the first of which Husserl purports to analyse the "Proper concepts of multiplicity, unity and amount" (Die eigentliche Begriffe von Vielheit, Einheit und Anzahl) and in the second "The symbolic amount-concepts and the logical sources of amount-arithmetic" (Die symbolischen Anzahlbegrife und die logischen Quellen der Anzahlen-Arithmetik).

In order to proceed with this analysis, Husserl, following Brentano and Stumpf, uses the tools of psychology to look for the "origin and content" of the concept of number.

The book is mostly based on his habilitationsschrift of 1887 "On the Concept of Number" (Über den Begriff der Zahl).

Gottlob Frege was critical of Philosophy of Arithmetic, and accused Husserl of relying too much on the metaphysical and not enough on the logical aspects of mathematics.