Title: Ampliative Deductive Proof in Mathematical Practice--Lessons from Kant and Frege
Speaker: Danielle Macbeth (Haverford College)
Time: 15:10-18:00 (Oct. 31st)
Location: Room 108, Geology Building (地学楼), Peking University

Abstract: Mathematicians in their practice appear to establish fully contentful, non-trivial truths that extend our knowledge. And in some cases, they do so through a course of deductive reasoning from the contents of concepts, from definitions. Building on the work of Kant and Frege I aim to clarify how this works, how it is that by deductive reasoning on the basis of definitions of mathematical concepts one can discover substantial and novel mathematical truths.

Bio: Danielle Macbeth is T. Wistar Brown Professor and Professor of Philosophy at Haverford College in Pennsylvania, USA. She is the author of Frege's Logic (Harvard University Press, 2005) and Realizing Reason: A Narrative of Truth and Knowing (Oxford University Press, 2014), and has published as well essays on issues in metaphysics, epistemology, philosophy of language, philosophy of mind, history and philosophy of mathematics, and history and philosophy of logic. Macbeth has been a National Endowment for the Humanities (NEH) Fellow, an American Council of Learned Societies (ACLS) Burkhardt Fellow, and a Fellow at the Center for Advanced Study in the Behavioral Sciences.