文章基本信息

标题：Relevant Arithmetic and Mathematical Pluralism
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作者：Zach Weber
期刊名称：Australasian Journal of Logic
印刷版ISSN：1448-5052
电子版ISSN：1448-5052
出版年度：2021
卷号：18
期号：5
DOI：10.26686/ajl.v18i5.6926
语种：English
出版社：Philosophy Department, University of Melbourne
摘要：In The Consistency of Arithmetic and elsewhere, Meyer claims to “repeal” Goedel’s second incompleteness theorem. In this paper, I review his argument, and then consider two ways of understanding it: from the perspective of mathematical pluralism and monism, respectively. Is relevant arithmetic just another legitimate practice among many, or is it a rival of its classical counterpart—a corrective to Goedel, setting us back on the path to the (One) True Arithmetic? To help answer, I sketch a few worked examples from relevant mathematics, to see what a non-classical (re)formulation of mathematics might look like in practice. I conclude that, while it is unlikely that relevant arithmetic describes past and present mathematical practice, and so might be most acceptable as a pluralist enterprise, it may yet prescribe a more monistic future venture.