Shows
MCMP – Mathematical Philosophy (Archive 2011/12)Modality and CategoriesSteve Awodey (CMU/MCMP) gives a talk at the MCMP Workshop on Modality titled "Modality and Categories".2019-04-221h 01MCMP – Mathematical Philosophy (Archive 2011/12)On an occasionally heard objection to Carnap's conception of logical truthSteve Awodey (CMU/MCMP) gives a talk at the MCMP Workshop on Carnap titled "On an occasionally heard objection to Carnap's conception of logical truth".2019-04-2031 min
MCMP – Philosophy of MathematicsThe Univalence AxiomSteve Awodey (CMU) gives a talk at the MCMP Colloquium (16 July, 2014) titled "The Univalence Axiom". Abstract: In homotopy type theory, the Univalence Axiom is a new principle of reasoning which implies that isomorphic structures can be identified. I will explain this axiom and consider its background and consequences, both mathematical and philosophical.2019-04-1800 minMCMP – Mathematical Philosophy (Archive 2011/12)Homotopy Type Theory and Univalent Foundations of MathematicsSteve Awodey (CMU/MCMP) gives a talk at the MCMP Colloquium (13 June, 2012) titled "Homotopy Type Theory and Univalent Foundations of Mathematics". Abstract: Recent advances in foundations of mathematics have led to some developments that are significant for the philosophy of mathematics, particularly structuralism. The discovery of an interpretation of constructive type theory into homotopy theory suggests a new approach to the foundations of mathematics with both intrinsic geometric content and a computational implementation. In this setting, leading homotopy theorist Vladimir Voevodsky has proposed new axiom for foundations with both geometric and logical significance: the Univalence Axiom. It captures the familiar...2012-09-191h 03