2022年符号逻辑协会冬季会议与美国心理学协会帕尔默之家,芝加哥,伊利诺斯州

Palmer House, G. Sher, Eileen S. Nutting
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引用次数: 0

摘要

ROY COOK,光滑无穷小分析的Kripke模型注释。美国明尼苏达大学哲学系,明尼阿波利斯,MN 55455电子邮件:cookx432@umn.edu。平滑无穷小分析(SIA)是实分析的一种公理化,它包括保证零平方存在的公理:无穷小如此“小”,尽管它们不能等于零,但它们的平方等于零。如果一个人在经典逻辑中工作,这些公理是不一致的,但SIA已被证明在直觉主义背景下通过范畴论结构是一致的。不幸的是,范畴论的方法并没有提供一个很好的直观的图像,什么是SIA连续体“看起来像”。因此,在这次演讲中,我将构建SIA的Kripke模型(以及完整SIA的一些子理论)-这些模型使SIA领域的动态特征变得明显。从(经典)元理论的角度来看,所讨论的模型既表现出同一性的不确定性,又表现出域的非恒定性。此外,我将论证SIA的“预期”模型(再次从经典元理论来看)在某种意义上是可数无限的。SEAN EBELS DUGGAN,模糊性,特殊性和数学结构。美国西北大学哲学系,伊利诺伊州埃文斯顿60208电子邮件:s-ebelsduggan@u.northwestern.edu。举一个老生常谈的例子,颜色谓词是模糊的。这块蓝色比第二块更紫,但它仍然是蓝色的。坚持下去,你会把紫色的东西称为蓝色,这是©The Author(s), 2022。由剑桥大学出版社代表符号逻辑协会出版1079-8986/22/2803-0007 DOI:10.1017/bsl.2022.26
本文章由计算机程序翻译,如有差异,请以英文原文为准。
2022 WINTER MEETING OF THE ASSOCIATION FOR SYMBOLIC LOGIC WITH THE APA Palmer House, Chicago, IL Central APA Meeting February 24, 2022
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
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