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Philosophia Mathematica最新文献

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Critical Studies/Book Reviews 批判性研究/书评
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-09-22 DOI: 10.1093/philmat/nkab025
Sandra Lapointe
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引用次数: 0
Challenges Facing Counterfactual Accounts of Explanation in Mathematics 数学中反事实解释面临的挑战
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-09-21 DOI: 10.1093/philmat/nkab023
Lange M.
{"title":"Challenges Facing Counterfactual Accounts of Explanation in Mathematics","authors":"Lange M.","doi":"10.1093/philmat/nkab023","DOIUrl":"https://doi.org/10.1093/philmat/nkab023","url":null,"abstract":"<span><div>ABSTRACT</div>Some mathematical proofs explain why the theorems they prove hold. This paper identifies several challenges for any counterfactual account of explanation in mathematics (that is, any account according to which an explanatory proof reveals how the explanandum would have been different, had facts in the explanans been different). The paper presumes that countermathematicals can be nontrivial. It argues that nevertheless, a counterfactual account portrays explanatory power as too easy to achieve, does not capture explanatory asymmetry, and fails to specify why certain proofs are explanatory and others are not. Greater informativeness about counterfactual dependence can even yield less explanatory power. </span>","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"54 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138534220","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
Critical Studies/Book Reviews 批判性研究/书评
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-09-21 DOI: 10.1093/philmat/nkab024
R. Cook
{"title":"Critical Studies/Book Reviews","authors":"R. Cook","doi":"10.1093/philmat/nkab024","DOIUrl":"https://doi.org/10.1093/philmat/nkab024","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45324998","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
J.E. Fenstad. Structures and Algorithms: Mathematics and the Nature of Knowledge J.E. Fenstad。结构与算法:数学与知识的本质
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-09-21 DOI: 10.1093/philmat/nkab021
{"title":"J.E. Fenstad. Structures and Algorithms: Mathematics and the Nature of Knowledge","authors":"","doi":"10.1093/philmat/nkab021","DOIUrl":"https://doi.org/10.1093/philmat/nkab021","url":null,"abstract":"<span>FenstadJ.E.. <strong><span style=\"font-style:italic;\">Structures and Algorithms: Mathematics and the Nature of Knowledge</span></strong>. Logic, Argumentation &amp; Reasoning; 15. Springer, 2018. Pp. x + 134. ISBN 978-3-319-72973-2 (hbk); 978-3-030-10294-4 (pbk); 978-3-319-72974-9 (e-book). doi.org/10.1007/978-3-319-72974-9.</span>","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"35 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138534222","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 Price of Mathematical Scepticism 数学怀疑论的代价
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-27 DOI: 10.1093/philmat/nkac011
P. Levy
{"title":"The Price of Mathematical Scepticism","authors":"P. Levy","doi":"10.1093/philmat/nkac011","DOIUrl":"https://doi.org/10.1093/philmat/nkac011","url":null,"abstract":"\u0000 This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions.\u0000 Underlying this argument is the following philosophical view. Mathematical belief springs from certain intuitions, each of which can be either accepted or doubted in its entirety, but not half-accepted. Therefore, our beliefs about reality, bivalence, choice and consistency should all be aligned.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43980663","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
Taking Stock: Hale, Heck, and Wright on Neo-Logicism and Higher-Order Logic Hale、Heck和Wright对新逻辑学和高阶逻辑的评价
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab017
Crispin Wright
{"title":"Taking Stock: Hale, Heck, and Wright on Neo-Logicism and Higher-Order Logic","authors":"Crispin Wright","doi":"10.1093/philmat/nkab017","DOIUrl":"https://doi.org/10.1093/philmat/nkab017","url":null,"abstract":"Four philosophical concerns about higher-order logic in general and the specific demands placed on it by the neo-logicist project are distinguished. The paper critically reviews recent responses to these concerns by, respectively, the late Bob Hale, Richard Kimberly Heck, and myself. It is argued that these score some successes. The main aim of the paper, however, is to argue that the most serious objection to the applications of higher-order logic required by the neo-logicist project has not been properly understood. The paper concludes by outlining a strategy, prefigured in recent work of Øystein Linnebo, for meeting this objection.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 3","pages":"392-416"},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70607957","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
Bob Hale. Essence and Existence 鲍勃·黑尔。本质与存在
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab004
{"title":"Bob Hale. Essence and Existence","authors":"","doi":"10.1093/philmat/nkab004","DOIUrl":"https://doi.org/10.1093/philmat/nkab004","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 3","pages":"417-418"},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70607959","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
Juliette Kennedy. Gödel, Tarski and the Lure of Natural Language: Logical Entanglement, Formalism Freeness 朱丽叶·肯尼迪。哥德尔、塔斯基与自然语言的诱惑：逻辑纠缠、形式主义自由
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab012
Penelope J Maddy
{"title":"Juliette Kennedy. Gödel, Tarski and the Lure of Natural Language: Logical Entanglement, Formalism Freeness","authors":"Penelope J Maddy","doi":"10.1093/philmat/nkab012","DOIUrl":"https://doi.org/10.1093/philmat/nkab012","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 3","pages":"428-438"},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70607993","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
Mojtaba Mojtahedi, Shahid Rahman, and Mohammad Saleh Zarepour, eds. Mathematics, Logic, and their Philosophies: Essays in Honour of Mohammad Ardeshir Mojtaba Mojtahedi、Shahid Rahman和Mohammad Saleh Zarepour编辑。数学、逻辑及其哲学：纪念Mohammad Ardeshir的文章
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab002
{"title":"Mojtaba Mojtahedi, Shahid Rahman, and Mohammad Saleh Zarepour, eds. Mathematics, Logic, and their Philosophies: Essays in Honour of Mohammad Ardeshir","authors":"","doi":"10.1093/philmat/nkab002","DOIUrl":"https://doi.org/10.1093/philmat/nkab002","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 3","pages":"451-452"},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70607965","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
Paul Ernest, ed. The Philosophy of Mathematics Education Today 保罗·欧内斯特主编《今日数学教育哲学》
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab005
{"title":"Paul Ernest, ed. The Philosophy of Mathematics Education Today","authors":"","doi":"10.1093/philmat/nkab005","DOIUrl":"https://doi.org/10.1093/philmat/nkab005","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 3","pages":"449-450"},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70607967","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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