{"title":"大卫·阿姆斯特朗论数学的形而上学","authors":"Thomas Donaldson","doi":"10.48106/dial.v74.i4.05","DOIUrl":null,"url":null,"abstract":"This paper has two components. The first, longer component (sec. 1-6) is a critical exposition of Armstrong's views about the metaphysics of mathematics, as they are presented in Truth and Truthmakers and Sketch for a Systematic Metaphysics. In particular, I discuss Armstrong's views about the nature of the cardinal numbers, and his account of how modal truths are made true. In the second component of the paper (sec. 7), which is shorter and more tentative, I sketch an alternative account of the metaphysics of mathematics. I suggest we insist that mathematical truths have physical truthmakers, without insisting that mathematical objects themselves are part of the physical world.","PeriodicalId":46676,"journal":{"name":"DIALECTICA","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"David Armstrong on the Metaphysics of Mathematics\",\"authors\":\"Thomas Donaldson\",\"doi\":\"10.48106/dial.v74.i4.05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper has two components. The first, longer component (sec. 1-6) is a critical exposition of Armstrong's views about the metaphysics of mathematics, as they are presented in Truth and Truthmakers and Sketch for a Systematic Metaphysics. In particular, I discuss Armstrong's views about the nature of the cardinal numbers, and his account of how modal truths are made true. In the second component of the paper (sec. 7), which is shorter and more tentative, I sketch an alternative account of the metaphysics of mathematics. I suggest we insist that mathematical truths have physical truthmakers, without insisting that mathematical objects themselves are part of the physical world.\",\"PeriodicalId\":46676,\"journal\":{\"name\":\"DIALECTICA\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"DIALECTICA\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48106/dial.v74.i4.05\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"DIALECTICA","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48106/dial.v74.i4.05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Arts and Humanities","Score":null,"Total":0}
This paper has two components. The first, longer component (sec. 1-6) is a critical exposition of Armstrong's views about the metaphysics of mathematics, as they are presented in Truth and Truthmakers and Sketch for a Systematic Metaphysics. In particular, I discuss Armstrong's views about the nature of the cardinal numbers, and his account of how modal truths are made true. In the second component of the paper (sec. 7), which is shorter and more tentative, I sketch an alternative account of the metaphysics of mathematics. I suggest we insist that mathematical truths have physical truthmakers, without insisting that mathematical objects themselves are part of the physical world.
期刊介绍：
Dialectica publishes first-rate articles predominantly in theoretical and systematic philosophy. It is edited in Switzerland and has a focus on analytical philosophy undertaken on the continent. Continuing the work of its founding members, dialectica seeks a better understanding of the mutual support between science and philosophy that both disciplines need and enjoy in their common search for understanding.
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