Freges Weg vom Logizismus zum Versuch einer geometrischen Grundlegung der Arithmetik

Abstract

This article has two parts. In the first part, I trace the development of Gottlob Frege's views on the foundations of arithmetic, from the conception of logicism to the attempt to lay geometrical foundations for arithmetic. I trace Frege's path from 1902, when he learned of Russell's paradox in the system of The Basic Laws of Arithmetic, to the late manuscripts "Sources of Knowledge of Mathematics and Mathematical Sciences", "Numbers and Arithmetic" and "A New Attempt at the Foundations of Arithmetic", written in 1924/25, but not published until 1969. Between 1910 and 1924/25, Frege abandoned important theses of logicism.

In the second part of the article, I discuss the philosophical sources of mathematics. There were fundamental philosophical influences on Frege's new position. The views on the philosophy of mathematics, especially on the concept of geometric intuition, of the neo-Kantian philosophers Bruno Bauch and Richard Hönigswald provided the intellectual background to Frege's ideas. Bauch, who was a good friend of Hönigswald, was Frege's colleague at Jena University between 1911 and 1918. He had very good relations with Frege during this period.

I want to examine Bauch's and Hönigswald's influences on Frege. Therefore I analyse the papers of these philosophers and present the philosophical arguments in Frege's late essays. These arguments were included in the neo-Kantian context of discussions about the philosophy of mathematics. This fact is an important cause for Frege's having disregarded the contemporary discussion of the paradoxes of set theory.