A New Metaphysical Explication of Infinitesimals
By Lu Chen (UMass, Philosophy)
Date: Tuesday 18th February, 2020
Time: 1640-1800
Place: H-232
Abstract: Infinitesimals are widely used in physics and mathematics, but are considered merely heuristic due to a lack of rigorous understanding. Smooth Infinitesimal Analysis (SIA), alternatively known as Synthetic Differential Geometry, is the most developed mathematical system for regimenting reasoning that involves infinitesimals. But to have a realistic interpretation of SIA as a foundation of physics, we face a significant obstacle: SIA is formulated in intuitionistic logic and is classically inconsistent. Furthermore, various authors have argued that there can be no classical reconstructions of SIA. If this is true, then infinitesimals will remain merely heuristic for classical logicians. Against this, I argue that there is a realistic interpretation of SIA as a novel theory of space that allows for infinitesimal regions. To argue for this claim, I advance a realistic understanding of the models for SIA proposed by Moerdijk and Reyes (1991), which augment manifolds with infinitesimal ones.
About the speaker: Lu Chen is a philosophy Ph.D. candidate at the University of Massachusetts, Amherst. She specializes in metaphysics, philosophy of science, and logic. Her primary research interest is in the metaphysical foundation of physical geometry. Her work has been published in Journal of Philosophical Logic and Synthese.
