Philosophy of mathematics in the early works of Moritz Schlick

Jendrik Stelling

Moritz-Schlick-Forschungsstelle, Rostock

Moritz Schlick never published any text specifically about the philosophy of mathematics. Nonetheless, his views on this topic influenced many of his other positions and the status of the subject was centrally important to the philosophical stances of many members of the Vienna Circle. Up to 1926, however, he regularly lectured on the philosophy of mathematics. These lectures are all based on one text, originally written in 1913, that was amended and corrected over the years, but remained substantially the same in content. In it, Schlick explicates his views on the status of both geometry and arithmetic, including the Cantorian transfinite numbers that had made their way into mathematics only recently and were still hotly debated. In this presentation I will reconstruct the central features of Schlick’s early philosophy of mathematics, based for the most part on unpublished materials. A central focus will be on Schlick’s self-identification as a formalist in the sense of Hilbert, which he retained until he converted to Wittgenstein’s position around 1927. Yet in his early writings, as we will see, it is not at all clear whether the formalist label really fits. I will argue that in many ways his philosophical stance was much more closely aligned with Poincaré, and an attempt will be made to explain this misidentification.