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Justified Epistemic Exclusions in Mathematics 数学中合理的认识论排除
IF 1.1 1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2023-04-18 DOI: 10.1093/philmat/nkad008
C. Rittberg
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.
谁能为认知共同体的知识生产做出贡献?学术界关注的是不合理的排斥形式。在这里,我通过研究数学中所谓的“怪人”现象来研究合理的排除形式。我认为,工作量管理方面的考虑证明了将这些外部人员排除在数学知识制造实践之外是合理的。我的讨论揭示了三点见解。除了不正确的数学论证之外,还有其他原因可以证明排除在数学实践之外。在某些情况下,数学家甚至有理由拒绝正确的数学论点。最后,数学家发现数学怪癖的方式并不支持“怪癖”术语的贬义含义。
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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2023-04-12 DOI: 10.1093/philmat/nkad006
J P Studd
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.
凯撒问题出现在抽象主义的观点中,它试图通过规定“未混合”的身份上下文的内容,如“$#X = #Y$”,来确保对诸如“$X$s的数量”或“$#X$”等术语的引用。弗雷格反对说,这一规定没有提到“混合”上下文,如“$# X = text{Julius Caesar}$”。本文为对凯撒问题的一种被忽视的回应进行了辩护:混合上下文的内容与非混合上下文的内容一样可以规定。
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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2023-03-24 DOI: 10.1093/philmat/nkad007
Jonas Werner
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.
本文针对博·麦迪逊·芒特提出的一个论点,为序数归约为纯集辩护。在第一部分中,我将捍卫简单依赖可以简化为直接依赖的主张,并定义了前驱依赖的概念。在第二部分中,我将提供并捍卫一种方法来对序数的依赖性进行建模,这种方法类似于Mount在直接依赖性和前体依赖性方面的建议。我进一步表明,我的替代依赖概况允许我们挑出序数到冯·诺伊曼序数的约简作为唯一可行的集合论约简。
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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2023-02-28 DOI: 10.1093/philmat/nkad002
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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2023-02-25 DOI: 10.1093/philmat/nkad001
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引用次数: 0
Refocusing Frege’s Other Puzzle: A Response to Snyder, Samuels, and Shapiro 重新聚焦弗雷格的另一个困惑:对斯奈德、塞缪尔和夏皮罗的回应
IF 1.1 1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2023-02-20 DOI: 10.1093/philmat/nkad005
Thomas Hofweber
In their recent article ‘Resolving Frege’s other Puzzle’ Eric Snyder, Richard Samuels, and Stewart Shapiro defend a semantic type-shifting solution to Frege’s other Puzzle and criticize my own cognitive type-shifting solution. In this article I respond to their criticism and in turn point to several problems with their preferred solution. In particular, I argue that they conflate semantic function and semantic value, and that their proposal is neither based on general semantic type-shifting principles nor adequate to the data.
Eric Snyder、Richard Samuels和Stewart Shapiro在他们最近的文章《解决Frege的另一个谜题》中为Frege的其他谜题的语义类型转换解决方案辩护,并批评了我自己的认知类型转换解决方法。在这篇文章中,我回应了他们的批评,并指出了他们首选解决方案的几个问题。特别是,我认为他们将语义功能和语义价值混为一谈,他们的建议既不基于一般的语义类型转换原则,也不适合数据。
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引用次数: 0
Sharon Berry.  A Logical Foundation for Potentialist Set Theory 莎朗·贝瑞。潜能集合论的逻辑基础
IF 1.1 1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2023-02-20 DOI: 10.1093/philmat/nkad004
Chris Scambler
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引用次数: 0
Matthew Handelman.The Mathematical Imagination: On the Origins and Promise of Critical Theory 马太福音Handelman。数学想象:论批判理论的起源和前景
1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2023-01-05 DOI: 10.1093/philmat/nkac033
Mirna Džamonja
Journal Article Matthew Handelman.The Mathematical Imagination: On the Origins and Promise of Critical Theory Get access Matthew Handelman.*The Mathematical Imagination: On the Origins and Promise of Critical Theory. Philosophy & Theory; 11. New York: Fordham University Press, 2019. Pp. 256. ISBN: 978-0-823283835. DOI: https://research.library.fordham.edu/philos/11. Mirna Džamonja Mirna Džamonja Institut de Recherche en Informatique Fondamentale (CNRS and Université de Paris Cité), 75205 Paris Cedex 13, France E-mail: mdzamonja@irif.fr https://orcid.org/0000-0002-6771-3975 Search for other works by this author on: Oxford Academic Google Scholar Philosophia Mathematica, Volume 31, Issue 2, June 2023, Pages 283–285, https://doi.org/10.1093/philmat/nkac033 Published: 05 January 2023
期刊文章马修·汉德尔曼。数学想象:论批判理论的起源和前景数学想象:论批判理论的起源和前景。哲学与理论;11. 纽约:福特汉姆大学出版社,2019。256页。ISBN: 978-0-823283835。DOI: https://research.library.fordham.edu/philos/11。Mirna Džamonja Mirna Džamonja信息基础研究所(CNRS和巴黎城市大学),75205 Paris Cedex 13, France E-mail: mdzamonja@irif.fr https://orcid.org/0000-0002-6771-3975搜索作者的其他作品:牛津学术谷歌学者数学哲学,第31卷,第2期,2023年6月,283-285页,https://doi.org/10.1093/philmat/nkac033出版日期:2023年1月5日
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引用次数: 0
Justin Clarke-Doane.  Mathematics and Metaphilosophy 贾斯汀Clarke-Doane。数学与哲学
IF 1.1 1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2022-09-06 DOI: 10.1093/philmat/nkac021
S. Pollard
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引用次数: 0
Mirja HartimoHusserl and Mathematics Mirja HartimoHussell与数学
IF 1.1 1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2022-09-05 DOI: 10.1093/philmat/nkac020
Jairo José da Silva
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引用次数: 0
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Philosophia Mathematica
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