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Philosophia Mathematica最新文献

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Mirja HartimoHusserl and Mathematics Mirja HartimoHussell与数学
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2022-09-05 DOI: 10.1093/philmat/nkac020
Jairo José da Silva
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引用次数: 0
Penelope Rush.Ontology and the Foundations of Mathematics: Talking Past Each Other. 佩内洛普·拉什。本体论与数学的基础:各执一词。
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2022-08-13 DOI: 10.1093/philmat/nkac018
G. Hellman
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引用次数: 0
The Role of Imagination and Anticipation in the Acceptance of Computability Proofs: A Challenge to the Standard Account of Rigor 想象和预期在可计算性证明的接受中的作用:对标准严谨性描述的挑战
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2022-07-30 DOI: 10.1093/philmat/nkac015
Keith Weber
{"title":"The Role of Imagination and Anticipation in the Acceptance of Computability Proofs: A Challenge to the Standard Account of Rigor","authors":"Keith Weber","doi":"10.1093/philmat/nkac015","DOIUrl":"https://doi.org/10.1093/philmat/nkac015","url":null,"abstract":"\u0000 In a 2022 paper, Hamami claimed that the orthodox view in mathematics is that a proof is rigorous if it can be translated into a derivation. Hamami then developed a descriptive account that explains how mathematicians check proofs for rigor in this sense and how they develop the capacity to do so. By exploring introductory texts in computability theory, we demonstrate that Hamami’s descriptive account does not accord with actual mathematical practice with respect to computability theory. We argue instead for an alternative account in which imagination, anticipation, and interpretations of natural language play roles in establishing mathematical rigor.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44476200","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: 1
Thomas Macaulay Ferguson and Graham Priest, eds. Robert Meyer and Relevant Arithmetic 托马斯·麦考利·弗格森和格雷厄姆·普里斯特主编。罗伯特·迈耶和相关算术
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2022-07-15 DOI: 10.1093/philmat/nkac017
{"title":"Thomas Macaulay Ferguson and Graham Priest, eds. Robert Meyer and Relevant Arithmetic","authors":"","doi":"10.1093/philmat/nkac017","DOIUrl":"https://doi.org/10.1093/philmat/nkac017","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43105150","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
Gödel’s Disjunctive Argument 哥德尔的虚拟论证
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2022-07-09 DOI: 10.1093/philmat/nkac013
Wesley Wrigley
{"title":"Gödel’s Disjunctive Argument","authors":"Wesley Wrigley","doi":"10.1093/philmat/nkac013","DOIUrl":"https://doi.org/10.1093/philmat/nkac013","url":null,"abstract":"\u0000 Gödel argued that the incompleteness theorems entail that the mind is not a machine, or that certain arithmetical propositions are absolutely undecidable. His view was that the mind is not a machine, and that no arithmetical propositions are absolutely undecidable. I argue that his position presupposes that the idealized mathematician has an ability which I call the recursive-ordinal recognition ability. I show that we have this ability if, and only if, there are no absolutely undecidable arithmetical propositions. I argue that there are such propositions, but that no recognizable example of one can be identified, even in principle.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48118638","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
Frederick Kroon, Jonathan McKeown-Green, and Stuart Brock. A Critical Introduction to Fictionalism 弗雷德里克·克鲁恩，乔纳森·麦基翁-格林和斯图尔特·布洛克。小说主义批判导论
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2022-06-30 DOI: 10.1093/philmat/nkac012
M. Leng
{"title":"Frederick Kroon, Jonathan McKeown-Green, and Stuart Brock. A Critical Introduction to Fictionalism","authors":"M. Leng","doi":"10.1093/philmat/nkac012","DOIUrl":"https://doi.org/10.1093/philmat/nkac012","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45409091","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
Salvatore Florio and Øystein Linnebo. The Many and the One. A Philosophical Study of Plural Logic Salvatore Florio和Öystein Linnebo。The Many and The One。多元逻辑的哲学研究
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2022-06-25 DOI: 10.1093/philmat/nkac009
F. Boccuni
{"title":"Salvatore Florio and Øystein Linnebo. The Many and the One. A Philosophical Study of Plural Logic","authors":"F. Boccuni","doi":"10.1093/philmat/nkac009","DOIUrl":"https://doi.org/10.1093/philmat/nkac009","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49451448","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
Bradley Armour-Garb and Frederick Kroon, eds. Fictionalism in Philosophy 布拉德利·阿玛尔-加尔布和弗雷德里克·克鲁恩编。哲学中的虚构主义
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2022-06-14 DOI: 10.1093/philmat/nkac010
F. Kroon
{"title":"Bradley Armour-Garb and Frederick Kroon, eds. Fictionalism in Philosophy","authors":"F. Kroon","doi":"10.1093/philmat/nkac010","DOIUrl":"https://doi.org/10.1093/philmat/nkac010","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45344363","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
Breaking the Tie: Benacerraf's Identification Argument Revisited 打破平局：对贝纳瑟拉夫身份认同论的再认识
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2022-04-01 DOI: 10.1093/philmat/nkac022
Arnon Avron;Balthasar Grabmayr
{"title":"Breaking the Tie: Benacerraf's Identification Argument Revisited","authors":"Arnon Avron;Balthasar Grabmayr","doi":"10.1093/philmat/nkac022","DOIUrl":"10.1093/philmat/nkac022","url":null,"abstract":"Most philosophers take Benacerraf's argument in ‘What numbers could not be’ to rebut successfully the reductionist view that numbers are sets. This philosophical consensus jars with mathematical practice, in which reductionism continues to thrive. In this note, we develop a new challenge to Benacerraf's argument by contesting a central premise which is almost unanimously accepted in the literature. Namely, we argue that — contra orthodoxy — there are metaphysically relevant reasons to prefer von Neumann ordinals over other set-theoretic reductions of arithmetic. In doing so, we provide set-theoretical facts which, we believe, are crucial for informed assessment of reductionism.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"31 1","pages":"81-103"},"PeriodicalIF":1.1,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46615070","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: 1
Penelope Maddy. A Plea for Natural Philosophy: And Other Essays 佩内洛普·马迪。为自然哲学辩护：及其他随笔
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2022-04-01 DOI: 10.1093/philmat/nkac030
{"title":"Penelope Maddy. A Plea for Natural Philosophy: And Other Essays","authors":"","doi":"10.1093/philmat/nkac030","DOIUrl":"10.1093/philmat/nkac030","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"31 1","pages":"143-143"},"PeriodicalIF":1.1,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44021473","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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