Frege’s Philosophy of Geometry

Matthias Schirn (LMU) gives a talk at the MCMP Colloquium (18 Jan, 2012) titled "Frege’s Philosophy of Geometry". Abstract: My talk tonight is in five sections. I begin with introductory remarks. In the second section, I cast a glance at Frege’s early views on geometry and arithmetic, while in the third I comment on the relationship between Frege’s and Kant’s views of geometrical knowledge. In the fourth section, I examine, in a critical way, Frege’s remarks on space, spatial intuition, and geometrical axioms in a key passage of his book The Foundations of Arithmetic of 1884. I conclude with critical remarks on the topic “Frege and non-Euclidean geometry” and a succinct overall assessment of Frege’s philosophy of geometry.