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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
Mathematical Explanations: An Analysis Via Formal Proofs and Conceptual Complexity 数学解释：通过形式证明和概念复杂性进行分析
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-12-07 DOI: 10.1093/philmat/nkad023
Francesca Poggiolesi
{"title":"Mathematical Explanations: An Analysis Via Formal Proofs and Conceptual Complexity","authors":"Francesca Poggiolesi","doi":"10.1093/philmat/nkad023","DOIUrl":"https://doi.org/10.1093/philmat/nkad023","url":null,"abstract":"This paper studies internal (or intra-)mathematical explanations, namely those proofs of mathematical theorems that seem to explain the theorem they prove. The goal of the paper is a rigorous analysis of these explanations. This will be done in two steps. First, we will show how to move from informal proofs of mathematical theorems to a formal presentation that involves proof trees, together with a decomposition of their elements; secondly we will show that those mathematical proofs that are regarded as having explanatory power all display an increase of conceptual complexity from the assumptions to the conclusion.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138559460","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
Luciano Boi and Carlos Lobo, eds. When Form Becomes Substance: Power of Gestures, Diagrammatical Intuition and Phenomenology of Space Luciano Boi 和 Carlos Lobo 编辑。当形式成为实质：手势的力量、图解直觉和空间现象学
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-12-06 DOI: 10.1093/philmat/nkad024
{"title":"Luciano Boi and Carlos Lobo, eds. When Form Becomes Substance: Power of Gestures, Diagrammatical Intuition and Phenomenology of Space","authors":"","doi":"10.1093/philmat/nkad024","DOIUrl":"https://doi.org/10.1093/philmat/nkad024","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138598119","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
Joel D. Hamkins.Lectures on the Philosophy of Mathematics Joel D. Hamkins.数学哲学讲座
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-12-06 DOI: 10.1093/philmat/nkad022
J. Ferreirós
{"title":"Joel D. Hamkins.Lectures on the Philosophy of Mathematics","authors":"J. Ferreirós","doi":"10.1093/philmat/nkad022","DOIUrl":"https://doi.org/10.1093/philmat/nkad022","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138595463","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
Intuition, Iteration, Induction 直觉，迭代，归纳法
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-11-11 DOI: 10.1093/philmat/nkad017
Mark van Atten
{"title":"Intuition, Iteration, Induction","authors":"Mark van Atten","doi":"10.1093/philmat/nkad017","DOIUrl":"https://doi.org/10.1093/philmat/nkad017","url":null,"abstract":"Brouwer’s view on induction has relatively recently been characterised as one on which it is not only intuitive (as expected) but functional, by van Dalen. He claims that Brouwer’s ‘Ur-intuition’ also yields the recursor. Appealing to Husserl’s phenomenology, I offer an analysis of Brouwer’s view that supports this characterisation and claim, even if assigning the primary role to the iterator instead. Contrasts are drawn to accounts of induction by Poincaré, Heyting, and Kreisel. On the phenomenological side, the analysis provides an alternative to that in Tieszen’s Mathematical Intuition, and confirms a view of Gödel on his Dialectica Interpretation.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"110423257","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
Dominique Pradelle.Être et genèse des idéalités. Un ciel sans éternité 多米尼克Pradelle。理想的存在和起源。没有永恒的天空
1区 哲学
Philosophia Mathematica Pub Date : 2023-11-08 DOI: 10.1093/philmat/nkad020
Bruno Leclercq
{"title":"Dominique Pradelle.<i>Être et genèse des idéalités. Un ciel sans éternité</i>","authors":"Bruno Leclercq","doi":"10.1093/philmat/nkad020","DOIUrl":"https://doi.org/10.1093/philmat/nkad020","url":null,"abstract":"Journal Article Dominique Pradelle.Être et genèse des idéalités. Un ciel sans éternité Get access Dominique Pradelle.*Être et genèse des idéalités. Un ciel sans éternité, [Being and genesis of ideal elements: A heaven without eternity.] Collection Épiméthée. Paris: PUF [Presses universitaires de France], 2023. Pp. 544. ISBN: 978-2-13-083587-5 (pbk); 978-2-13-083588-2 (epub); 978-2-13-085194-3 (pdf). Bruno Leclercq Bruno Leclercq Philosophy Department, Université de Liège, 4000 Liège, Belgium E-mail: b.leclercq@uliege.be https://orcid.org/0000-0002-3322-943X Search for other works by this author on: Oxford Academic Google Scholar Philosophia Mathematica, nkad020, https://doi.org/10.1093/philmat/nkad020 Published: 08 November 2023","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135430051","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
Internal Applications and Puzzles of the Applicability of Mathematics 数学适用性的内部应用和困惑
1区 哲学
Philosophia Mathematica Pub Date : 2023-10-25 DOI: 10.1093/philmat/nkad019
Douglas Bertrand Marshall
{"title":"Internal Applications and Puzzles of the Applicability of Mathematics","authors":"Douglas Bertrand Marshall","doi":"10.1093/philmat/nkad019","DOIUrl":"https://doi.org/10.1093/philmat/nkad019","url":null,"abstract":"Abstract Just as mathematics helps us to represent and reason about the natural world, in its internal applications one branch of mathematics helps us to represent and reason about the subject matter of another. Recognition of the close analogy between internal and external applications of mathematics can help resolve two persistent philosophical puzzles concerning its applicability: a platonist puzzle arising from the abstractness of mathematical objects; and an empiricist puzzle arising from mathematical propositions’ lack of empirical factual content. In order to see how this is the case, we will examine what it is to apply mathematics internally and describe examples.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135168582","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
Sorin Bangu, Emiliano Ippoliti, and Marianna Antonutti Marfori, eds. Explanatory and Heuristic Power of Mathematics Sorin Bangu, Emiliano Ippoliti和Marianna Antonutti Marfori主编。数学的解释力和启发式力量
1区 哲学
Philosophia Mathematica Pub Date : 2023-10-16 DOI: 10.1093/philmat/nkad018
{"title":"Sorin Bangu, Emiliano Ippoliti, and Marianna Antonutti Marfori, eds. <i>Explanatory and Heuristic Power of Mathematics</i>","authors":"","doi":"10.1093/philmat/nkad018","DOIUrl":"https://doi.org/10.1093/philmat/nkad018","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136079969","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
Are Large Cardinal Axioms Restrictive? 大基数公理是限制性的吗?
1区 哲学
Philosophia Mathematica Pub Date : 2023-09-24 DOI: 10.1093/philmat/nkad014
Neil Barton
{"title":"Are Large Cardinal Axioms Restrictive?","authors":"Neil Barton","doi":"10.1093/philmat/nkad014","DOIUrl":"https://doi.org/10.1093/philmat/nkad014","url":null,"abstract":"Abstract The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper I question this claim. I show that there is a kind of maximality (namely absoluteness) on which large cardinal axioms come out as restrictive relative to a formal notion of restrictiveness. Within this framework, I argue that large cardinal axioms can still play many of their usual foundational roles.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135925160","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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