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A Taxonomy for Set-Theoretic Potentialism 集合论潜在论的分类标准
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-08-28 DOI: 10.1093/philmat/nkae016
Davide Sutto
{"title":"A Taxonomy for Set-Theoretic Potentialism","authors":"Davide Sutto","doi":"10.1093/philmat/nkae016","DOIUrl":"https://doi.org/10.1093/philmat/nkae016","url":null,"abstract":"Set-theoretic potentialism is one of the most lively trends in the philosophy of mathematics. Modal accounts of sets have been developed in two different ways. The first, initiated by Charles Parsons, focuses on sets as objects. The second, dating back to Hilary Putnam and Geoffrey Hellman, investigates set-theoretic structures. The paper identifies two strands of open issues, technical and conceptual, to clarify these two different, yet often conflated, views and categorize the potentialist approaches that have emerged in the contemporary debate. The final outcome is a taxonomy that should help researchers navigate the rich landscape of modal set theories.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Up with Categories, Down with Sets; Out with Categories, In with Sets! 分类向上，集合向下；分类向外，集合向内！
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-04-13 DOI: 10.1093/philmat/nkae010
Jonathan Kirby
{"title":"Up with Categories, Down with Sets; Out with Categories, In with Sets!","authors":"Jonathan Kirby","doi":"10.1093/philmat/nkae010","DOIUrl":"https://doi.org/10.1093/philmat/nkae010","url":null,"abstract":"Practical approaches to the notions of subsets and extension sets are compared, coming from broadly set-theoretic and category-theoretic traditions of mathematics. I argue that the set-theoretic approach is the most practical for ‘looking down’ or ‘in’ at subsets and the category-theoretic approach is the most practical for ‘looking up’ or ‘out’ at extensions, and suggest some guiding principles for using these approaches without recourse to either category theory or axiomatic set theory.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140551916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Chris Pincock.  Mathematics and Explanation 克里斯-品科克 数学与解释
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-04-12 DOI: 10.1093/philmat/nkae007
Alan Baker
{"title":"Chris Pincock.  Mathematics and Explanation","authors":"Alan Baker","doi":"10.1093/philmat/nkae007","DOIUrl":"https://doi.org/10.1093/philmat/nkae007","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140709072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Donald Gillies.Lakatos and the Historical Approach to Philosophy of Mathematics 唐纳德-吉利斯.拉卡托斯与数学哲学的历史方法
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-04-01 DOI: 10.1093/philmat/nkae008
B. Larvor
{"title":"Donald Gillies.Lakatos and the Historical Approach to Philosophy of Mathematics","authors":"B. Larvor","doi":"10.1093/philmat/nkae008","DOIUrl":"https://doi.org/10.1093/philmat/nkae008","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140763127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Felix Lev.Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory 费利克斯-列夫.有限数学是经典数学和量子理论的基础
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-03-30 DOI: 10.1093/philmat/nkae006
J. P. Van Bendegem
{"title":"Felix Lev.Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory","authors":"J. P. Van Bendegem","doi":"10.1093/philmat/nkae006","DOIUrl":"https://doi.org/10.1093/philmat/nkae006","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140363570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Logic for Mathematics without Ex Falso Quodlibet 没有 Ex Falso Quodlibet 的数学逻辑学
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-03-11 DOI: 10.1093/philmat/nkae001
Neil Tennant
{"title":"The Logic for Mathematics without Ex Falso Quodlibet","authors":"Neil Tennant","doi":"10.1093/philmat/nkae001","DOIUrl":"https://doi.org/10.1093/philmat/nkae001","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140252558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A.C. Paseau and Alan Baker.Indispensability A.C. Paseau 和 Alan Baker.不可或缺性
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-02-21 DOI: 10.1093/philmat/nkae003
Christian Alafaci
{"title":"A.C. Paseau and Alan Baker.Indispensability","authors":"Christian Alafaci","doi":"10.1093/philmat/nkae003","DOIUrl":"https://doi.org/10.1093/philmat/nkae003","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140443641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Jean W. Rioux. Thomas Aquinas’ Mathematical Realism 让-W-里奥托马斯-阿奎那的数学现实主义
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-02-20 DOI: 10.1093/philmat/nkae004
Daniel Eduardo Usma Gómez
{"title":"Jean W. Rioux. Thomas Aquinas’ Mathematical Realism","authors":"Daniel Eduardo Usma Gómez","doi":"10.1093/philmat/nkae004","DOIUrl":"https://doi.org/10.1093/philmat/nkae004","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140445823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Identity and Extensionality in Boffa Set Theory 波法集合论中的同一性和扩展性
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-02-08 DOI: 10.1093/philmat/nkad025
Nuno Maia, Matteo Nizzardo
{"title":"Identity and Extensionality in Boffa Set Theory","authors":"Nuno Maia, Matteo Nizzardo","doi":"10.1093/philmat/nkad025","DOIUrl":"https://doi.org/10.1093/philmat/nkad025","url":null,"abstract":"Boffa non-well-founded set theory allows for several distinct sets equal to their respective singletons, the so-called ‘Quine atoms’. Rieger contends that this theory cannot be a faithful description of set-theoretic reality. He argues that, even after granting that there are non-well-founded sets, ‘the extensional nature of sets’ precludes numerically distinct Quine atoms. In this paper we uncover important similarities between Rieger’s argument and how non-rigid structures are conceived within mathematical structuralism. This opens the way for an objection against Rieger, whilst affording the theoretical resources for a defence of Boffa set theory as a faithful description of set-theoretic reality.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139750353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Interest of Philosophy of Mathematics (Education) 数学哲学（教育）的趣味性
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-01-11 DOI: 10.1093/philmat/nkad026
Karen François
{"title":"The Interest of Philosophy of Mathematics (Education)","authors":"Karen François","doi":"10.1093/philmat/nkad026","DOIUrl":"https://doi.org/10.1093/philmat/nkad026","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139625803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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