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No Easy Road to Impredicative Definabilism 通往令人印象深刻的挑战之路并不容易
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-09-10 DOI: 10.1093/philmat/nkad013
Øystein Linnebo, Sam Roberts
{"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":null,"pages":null},"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}
引用次数: 0
On Algorithms, Effective Procedures, and Their Definitions 论算法、有效程序及其定义
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-07-29 DOI: 10.1093/philmat/nkad011
Philippos Papayannopoulos
{"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":null,"pages":null},"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}
引用次数: 0
Carl Posy and Yemima Ben-Menahem, eds. Mathematical Objects, Knowledge and Applications: Essays in Memory of Mark Steiner 卡尔·波西和叶玛·本·梅纳赫姆编。数学对象、知识与应用:纪念马克·斯坦纳论文
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-06-23 DOI: 10.1093/philmat/nkad012
{"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":null,"pages":null},"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}
引用次数: 0
Paola Cantù and Italo Testa, guest editors. Mathematical Practice and Social Ontology 保拉Cantù和伊塔洛·泰斯塔，客座编辑。数学实践与社会本体论
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-06-01 DOI: 10.1093/philmat/nkad010
{"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":null,"pages":null},"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}
引用次数: 0
A Critique of Yablo’s If-thenism 对雅布洛的If-thenism的批判
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-05-26 DOI: 10.1093/philmat/nkad009
Bradley Armour-Garb, F. Kroon
{"title":"A Critique of Yablo’s If-thenism","authors":"Bradley Armour-Garb, F. Kroon","doi":"10.1093/philmat/nkad009","DOIUrl":"https://doi.org/10.1093/philmat/nkad009","url":null,"abstract":"\u0000 Using ideas proposed in Aboutness and developed in ‘If-thenism’, Stephen Yablo has tried to improve on classical if-thenism in mathematics, a view initially put forward by Bertrand Russell in his Principles of Mathematics. Yablo’s stated goal is to provide a reading of a sentence like ‘The number of planets is eight’ with a sort of content on which it fails to imply ‘Numbers exist’. After presenting Yablo’s framework, our paper raises a problem with his view that has gone virtually unnoticed in the literature. If we are right, then Yablo’s version of if-thenism cannot succeed.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44222472","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
Justified Epistemic Exclusions in Mathematics 数学中合理的认识论排除
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-04-18 DOI: 10.1093/philmat/nkad008
C. Rittberg
{"title":"Justified Epistemic Exclusions in Mathematics","authors":"C. Rittberg","doi":"10.1093/philmat/nkad008","DOIUrl":"https://doi.org/10.1093/philmat/nkad008","url":null,"abstract":"\u0000 Who gets to contribute to knowledge production of an epistemic community? Scholarship has focussed on unjustified forms of exclusion. Here I study justified forms of exclusion by investigating the phenomenon of so-called ‘cranks’ in mathematics. I argue that workload-management concerns justify the exclusion of these outsiders from mathematical knowledge-making practices. My discussion reveals three insights. There are reasons other than incorrect mathematical argument that justify exclusions from mathematical practices. There are instances in which mathematicians are justified in rejecting even correct mathematical arguments. Finally, the way mathematicians spot mathematical crankery does not support the pejorative connotations of the ‘crank’ terminology.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45722292","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 Caesar Problem — A Piecemeal Solution 凯撒问题——一个零敲碎打的解决方案
1区 哲学
Philosophia Mathematica Pub Date : 2023-04-12 DOI: 10.1093/philmat/nkad006
J P Studd
{"title":"The Caesar Problem — A Piecemeal Solution","authors":"J P Studd","doi":"10.1093/philmat/nkad006","DOIUrl":"https://doi.org/10.1093/philmat/nkad006","url":null,"abstract":"Abstract The Caesar problem arises for abstractionist views, which seek to secure reference for terms such as ‘the number of $X$s’ or $#X$ by stipulating the content of ‘unmixed’ identity contexts like ‘$#X = #Y$’. Frege objects that this stipulation says nothing about ‘mixed’ contexts such as ‘$# X = text{Julius Caesar}$’. This article defends a neglected response to the Caesar problem: the content of mixed contexts is just as open to stipulation as that of unmixed contexts.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135290162","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 Note on von Neumann Ordinals and Dependence 关于冯·诺伊曼序数及其依赖性的注记
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-03-24 DOI: 10.1093/philmat/nkad007
Jonas Werner
{"title":"A Note on von Neumann Ordinals and Dependence","authors":"Jonas Werner","doi":"10.1093/philmat/nkad007","DOIUrl":"https://doi.org/10.1093/philmat/nkad007","url":null,"abstract":"\u0000 This note defends the reduction of ordinals to pure sets against an argument put forward by Beau Madison Mount. In the first part I will defend the claim that dependence simpliciter can be reduced to immediate dependence and define a notion of predecessor dependence. In the second part I will provide and defend a way to model the dependence profile of ordinals akin to Mount’s proposal in terms of immediate dependence and predecessor dependence. I furthermore show that my alternative dependence profile allows us to single out the reduction of ordinals to von Neumann ordinals as the only viable set-theoretic reduction.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46461402","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
Paola Cantù, Brice Halimi, Gerhard Heinzmann, Frédéric Patras, eds. Objectivity in mathematics/L’objectivité en mathématiques = =地理= =根据美国人口普查，这个县的土地面积为。数学中的客观性/数学中的客观性
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-02-28 DOI: 10.1093/philmat/nkad002
{"title":"Paola Cantù, Brice Halimi, Gerhard Heinzmann, Frédéric Patras, eds. Objectivity in mathematics/L’objectivité en mathématiques","authors":"","doi":"10.1093/philmat/nkad002","DOIUrl":"https://doi.org/10.1093/philmat/nkad002","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46591158","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
Francesca Boccuni and Andrea Sereni, eds. Origins and Varieties of Logicism: On the Logico-Philosophical Foundations of Mathematics 博库尼、塞雷尼主编：《逻辑学的起源与变化：论数学的逻辑哲学基础》
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2023-02-25 DOI: 10.1093/philmat/nkad001
{"title":"Francesca Boccuni and Andrea Sereni, eds. Origins and Varieties of Logicism: On the Logico-Philosophical Foundations of Mathematics","authors":"","doi":"10.1093/philmat/nkad001","DOIUrl":"https://doi.org/10.1093/philmat/nkad001","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43461025","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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