{"title":"数学结构主义和束论","authors":"Bahram Assadian","doi":"10.1111/rati.12397","DOIUrl":null,"url":null,"abstract":"According to the realist rendering of mathematical structuralism, mathematical structures are ontologically prior to individual mathematical objects such as numbers and sets. Mathematical objects are merely positions in structures: their nature entirely consists in having the properties arising from the structure to which they belong. In this paper, I offer a bundle-theoretic account of this structuralist conception of mathematical objects: what we normally describe as an individual mathematical object is the mereological bundle of its structural properties. An emerging picture is a version of mereological essentialism: the structural properties of a mathematical object, as a bundle, are the mereological parts of the bundle, which are possessed by it essentially.","PeriodicalId":46553,"journal":{"name":"Ratio","volume":"8 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mathematical structuralism and bundle theory\",\"authors\":\"Bahram Assadian\",\"doi\":\"10.1111/rati.12397\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"According to the realist rendering of mathematical structuralism, mathematical structures are ontologically prior to individual mathematical objects such as numbers and sets. Mathematical objects are merely positions in structures: their nature entirely consists in having the properties arising from the structure to which they belong. In this paper, I offer a bundle-theoretic account of this structuralist conception of mathematical objects: what we normally describe as an individual mathematical object is the mereological bundle of its structural properties. An emerging picture is a version of mereological essentialism: the structural properties of a mathematical object, as a bundle, are the mereological parts of the bundle, which are possessed by it essentially.\",\"PeriodicalId\":46553,\"journal\":{\"name\":\"Ratio\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-02-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ratio\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1111/rati.12397\",\"RegionNum\":4,\"RegionCategory\":\"哲学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"0\",\"JCRName\":\"PHILOSOPHY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ratio","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1111/rati.12397","RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"0","JCRName":"PHILOSOPHY","Score":null,"Total":0}
According to the realist rendering of mathematical structuralism, mathematical structures are ontologically prior to individual mathematical objects such as numbers and sets. Mathematical objects are merely positions in structures: their nature entirely consists in having the properties arising from the structure to which they belong. In this paper, I offer a bundle-theoretic account of this structuralist conception of mathematical objects: what we normally describe as an individual mathematical object is the mereological bundle of its structural properties. An emerging picture is a version of mereological essentialism: the structural properties of a mathematical object, as a bundle, are the mereological parts of the bundle, which are possessed by it essentially.
期刊介绍：
Ratio publishes work of a high quality on a wide variety of topics. It encourages articles which meet the highest standards of philosophical expertise, while at the same time remaining accessible to readers from a broad range of philosophical disciplines. The journal"s main emphasis is on analytic philosophy, but it also includes work from other traditions.
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