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.

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.

Frege’s Philosophy of Geometry

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.
The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.
Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists. The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws. Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

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Frege’s Philosophy of Geometry

Frege’s Philosophy of Geometry

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