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
{"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":"28 10","pages":"0"},"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}
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.
{"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":"198 2","pages":"0"},"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}
{"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":"73 4 1","pages":"0"},"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}
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.
{"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":"81 1","pages":"0"},"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}
Journal Article Elaine Landry.Plato Was Not a Mathematical Platonist Get access Elaine Landry*Plato Was Not a Mathematical Platonist. Cambridge Elements in the Philosophy of Mathematics. Cambridge University Press, 2023. Pp. 48. ISBN: 978-0-19-966262-3 (online). Colin McLarty Colin McLarty Departments of Philosophy and of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106, U.S.A colin.mclarty@case.edu https://orcid.org/0000-0002-3181-7537 Search for other works by this author on: Oxford Academic Google Scholar Philosophia Mathematica, nkad016, https://doi.org/10.1093/philmat/nkad016 Published: 16 September 2023
{"title":"Elaine Landry.<i>Plato Was Not a Mathematical Platonist</i>","authors":"Colin McLarty","doi":"10.1093/philmat/nkad016","DOIUrl":"https://doi.org/10.1093/philmat/nkad016","url":null,"abstract":"Journal Article Elaine Landry.Plato Was Not a Mathematical Platonist Get access Elaine Landry*Plato Was Not a Mathematical Platonist. Cambridge Elements in the Philosophy of Mathematics. Cambridge University Press, 2023. Pp. 48. ISBN: 978-0-19-966262-3 (online). Colin McLarty Colin McLarty Departments of Philosophy and of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106, U.S.A colin.mclarty@case.edu https://orcid.org/0000-0002-3181-7537 Search for other works by this author on: Oxford Academic Google Scholar Philosophia Mathematica, nkad016, https://doi.org/10.1093/philmat/nkad016 Published: 16 September 2023","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135306043","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}
Journal Article Mark Jay Steiner May 6, 1942 – April 6, 2020 Get access Yemima Ben-Menahem, Yemima Ben-Menahem The Hebrew University of Jerusalem E-mail: yemima.ben-menahem@mail.huji.ac.il. https://orcid.org/0009-0007-3632-3820 Search for other works by this author on: Oxford Academic Google Scholar Carl Posy Carl Posy The Hebrew University of Jerusalem E-mail: carl.posy@mail.huji.ac.il. https://orcid.org/0000-0002-8047-8527 Search for other works by this author on: Oxford Academic Google Scholar Philosophia Mathematica, nkad015, https://doi.org/10.1093/philmat/nkad015 Published: 16 September 2023
期刊文章Mark Jay Steiner 1942年5月6日- 2020年4月6日访问耶路撒冷希伯来大学Yemima Ben-Menahem, Yemima Ben-Menahem电子邮件:yemima.ben-menahem@mail.huji.ac.il。https://orcid.org/0009-0007-3632-3820搜索作者的其他作品:牛津学术谷歌学者卡尔·波西卡尔·波西耶路撒冷希伯来大学电子邮件:carl.posy@mail.huji.ac.il。https://orcid.org/0000-0002-8047-8527搜索作者的其他作品:牛津学术谷歌学者数学哲学，nkad015, https://doi.org/10.1093/philmat/nkad015出版日期:2023年9月16日
{"title":"Mark Jay Steiner May 6, 1942 – April 6, 2020","authors":"Yemima Ben-Menahem, Carl Posy","doi":"10.1093/philmat/nkad015","DOIUrl":"https://doi.org/10.1093/philmat/nkad015","url":null,"abstract":"Journal Article Mark Jay Steiner May 6, 1942 – April 6, 2020 Get access Yemima Ben-Menahem, Yemima Ben-Menahem The Hebrew University of Jerusalem E-mail: yemima.ben-menahem@mail.huji.ac.il. https://orcid.org/0009-0007-3632-3820 Search for other works by this author on: Oxford Academic Google Scholar Carl Posy Carl Posy The Hebrew University of Jerusalem E-mail: carl.posy@mail.huji.ac.il. https://orcid.org/0000-0002-8047-8527 Search for other works by this author on: Oxford Academic Google Scholar Philosophia Mathematica, nkad015, https://doi.org/10.1093/philmat/nkad015 Published: 16 September 2023","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135306040","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}
Bob Hale has defended a new conception of properties that is broadly Fregean in two key respects. First, like Frege, Hale insists that every property can be defined by an open formula. Second, like Frege, but unlike later definabilists, Hale seeks to justify full impredicative property comprehension. The most innovative part of his defense, we think, is a “definability constraint” that can serve as an implicit definition of the domain of properties. We make this constraint formally precise and prove that it fails to characterize the domain uniquely. Thus, we conclude, there is no easy road to impredicative definabilism.
Bob Hale为一种新的财产概念进行了辩护，这种概念在两个关键方面都是Fregean的。首先，像弗雷格一样，黑尔坚持认为每个性质都可以用一个开放公式来定义。第二，像弗雷格一样，但与后来的定义主义者不同，黑尔试图证明完全的不确定性理解是合理的。我们认为，他的辩护中最具创新性的部分是“可定义性约束”，它可以作为属性域的隐含定义。我们使这个约束形式上精确，并证明它不能唯一地刻画域。因此，我们得出的结论是，没有一条通往不可定义性的简单道路。
{"title":"No Easy Road to Impredicative Definabilism","authors":"Øystein Linnebo, Sam Roberts","doi":"10.1093/philmat/nkad013","DOIUrl":"https://doi.org/10.1093/philmat/nkad013","url":null,"abstract":"Bob Hale has defended a new conception of properties that is broadly Fregean in two key respects. First, like Frege, Hale insists that every property can be defined by an open formula. Second, like Frege, but unlike later definabilists, Hale seeks to justify full impredicative property comprehension. The most innovative part of his defense, we think, is a “definability constraint” that can serve as an implicit definition of the domain of properties. We make this constraint formally precise and prove that it fails to characterize the domain uniquely. Thus, we conclude, there is no easy road to impredicative definabilism.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"5 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71435176","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}
I examine the classical idea of ‘algorithm’ as a sequential, step-by-step, deterministic procedure (i.e., the idea of ‘algorithm’ that was already in use by the 1930s), with respect to three themes, its relation to the notion of an ‘effective procedure’, its different roles and uses in logic, computer science, and mathematics (focused on numerical analysis), and its different formal definitions proposed by practitioners in these areas. I argue that ‘algorithm’ has been conceptualized and used in contrasting ways in the above areas, and discuss challenges and prospects for adopting a final foundational theory of (classical) ‘algorithms’.
{"title":"On Algorithms, Effective Procedures, and Their Definitions","authors":"Philippos Papayannopoulos","doi":"10.1093/philmat/nkad011","DOIUrl":"https://doi.org/10.1093/philmat/nkad011","url":null,"abstract":"\u0000 I examine the classical idea of ‘algorithm’ as a sequential, step-by-step, deterministic procedure (i.e., the idea of ‘algorithm’ that was already in use by the 1930s), with respect to three themes, its relation to the notion of an ‘effective procedure’, its different roles and uses in logic, computer science, and mathematics (focused on numerical analysis), and its different formal definitions proposed by practitioners in these areas. I argue that ‘algorithm’ has been conceptualized and used in contrasting ways in the above areas, and discuss challenges and prospects for adopting a final foundational theory of (classical) ‘algorithms’.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49635820","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}
{"title":"Carl Posy and Yemima Ben-Menahem, eds. Mathematical Objects, Knowledge and Applications: Essays in Memory of Mark Steiner","authors":"","doi":"10.1093/philmat/nkad012","DOIUrl":"https://doi.org/10.1093/philmat/nkad012","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43472816","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}
{"title":"Paola Cantù and Italo Testa, guest editors. Mathematical Practice and Social Ontology","authors":"","doi":"10.1093/philmat/nkad010","DOIUrl":"https://doi.org/10.1093/philmat/nkad010","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47005865","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}
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