2022 WINTER MEETING OF THE ASSOCIATION FOR SYMBOLIC LOGIC WITH THE APA Palmer House, Chicago, IL Central APA Meeting February 24, 2022

Abstract

s of invited plenary lectures ROY COOK, Notes towards a Kripke model of smooth infinitesimal analysis. Department of Philosophy, University of Minnesota, Minneapolis, MN 55455, USA. E-mail: cookx432@umn.edu. Smooth infinitesimal analysis (SIA) is an axiomatization of real analysis which includes axioms that guarantee the existence of nilsquares: infinitesimals so “small” that, although they fail to be identical to zero, their squares are identical to zero. These axioms of are inconsistent if one works within classical logic, but SIA has been shown to be consistent within an intuitionistic setting via category-theoretic constructions. Unfortunately, the categorytheoretic methods do not provide a good intuitive picture of what the SIA continuum “looks like”. Thus, in this talk I will construct Kripke models for SIA (as well as a number of subtheories of full SIA)—models which make apparent the dynamic character of the SIA domain. The models in question, viewed from the (classical) metatheory, display both indeterminacy of identity and non-constancy of domain. Further, I will argue that the “intended” model of SIA (again, as seen from the classical metatheory), is, in a certain sense, countably infinite. SEAN EBELS DUGGAN, Vagueness, specificity, and mathematical structure. Department of Philosophy, Northwestern University, Evanston, IL 60208, USA. E-mail: s-ebelsduggan@u.northwestern.edu. Color predicates, to take a well-worn example, are vague. This patch of blue is more purple than the second patch, but it is still blue. Keep this up and you’ll call purple things blue, which © The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic 1079-8986/22/2803-0007 DOI :10.1017/bsl.2022.26