Shows
MCMP – Mathematical Philosophy (Archive 2011/12)Frege’s Philosophy of GeometryMatthias 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 criti...
2019-04-201h 19MCMP – Mathematical Philosophy (Archive 2011/12)Logical abstractions and logical objects in Frege: a critical approachMatthias Schirn (LMU) gives a talk at the MCMP Colloquium (26 Jan, 2012) titled "Logical abstractions and logical objects in Frege: a critical approach". Abstract: In this talk, I shall critically discuss some key issues related to Frege’s notion of logical object, his paradigms of second-order abstraction principles (Hume’s Principle and Axiom V; see my handout), his logicism and, if time allows, the position which has come to be known as neo-logicism. Although the notion of logical object plays a key role in Frege’s foundational project, it has hardly been analyzed in depth so far. I shall begin by explai...
2019-04-201h 33
MCMP – History of PhilosophyHilbert's metamathematics, finitist consistency proofs and the concept of infinityMatthias Schirn (LMU) gives a talk at the MCMP Colloquium (20 November, 2013) titled "Hilbert's metamathematics, finitist consistency proofs and the concept of infinity". Abstract: The main focus of my talk is on a critical analysis of some aspects of Hilbert’s proof-theoretic programme in the 1920s. During this period, Hilbert developed his metamathematics or proof theory to defend classical mathematics by carrying out, in a purely finitist fashion, consistency proofs for formalized mathematical theories T. The key idea underlying metamathematical proofs was to establish the consistency of T by means of weaker, but at the same time more reliable methods than th...
2014-02-181h 15