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Mark Jay Steiner May 6, 1942 – April 6, 2020 Mark Jay Steiner 1942年5月6日- 2020年4月6日
1区 哲学 Q1 Arts and Humanities Pub Date : 2023-09-16 DOI: 10.1093/philmat/nkad015
Yemima Ben-Menahem, Carl Posy
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
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引用次数: 0
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 Q1 Arts and Humanities Pub Date : 2023-09-10 DOI: 10.1093/philmat/nkad013
Øystein Linnebo, Sam Roberts
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。
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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 Q1 Arts and Humanities Pub Date : 2023-07-29 DOI: 10.1093/philmat/nkad011
Philippos Papayannopoulos
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’.
我研究了“算法”作为一个顺序的、循序渐进的、确定性的过程的经典思想(即20世纪30年代已经使用的“算法”思想),涉及三个主题,它与“有效过程”概念的关系,它在逻辑、计算机科学和数学(侧重于数值分析)中的不同作用和用途,以及这些领域从业者提出的不同形式的定义。我认为,“算法”在上述领域已经以不同的方式被概念化和使用,并讨论了采用(经典)“算法”的最终基础理论的挑战和前景。
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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 Q1 Arts and Humanities Pub Date : 2023-06-23 DOI: 10.1093/philmat/nkad012
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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 Q1 Arts and Humanities Pub Date : 2023-06-01 DOI: 10.1093/philmat/nkad010
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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 Q1 Arts and Humanities Pub Date : 2023-05-26 DOI: 10.1093/philmat/nkad009
Bradley Armour-Garb, F. Kroon
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.
利用《关于》一书中提出并在《If-thenism》中发展起来的思想,斯蒂芬·亚布罗试图改进数学中的经典If-thenism,这一观点最初是由伯特兰·罗素在他的《数学原理》中提出的。Yablo宣称的目标是提供一个句子的阅读,比如“行星的数量是8个”,在某种内容上它不能暗示“数字存在”。在提出Yablo的框架之后,我们的论文提出了一个在文献中几乎没有被注意到的问题。如果我们是对的,那么亚布罗的“如果论”就不可能成功。
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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 Q1 Arts and Humanities 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 Q1 Arts and Humanities 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 Q1 Arts and Humanities 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 Q1 Arts and Humanities Pub Date : 2023-02-28 DOI: 10.1093/philmat/nkad002
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引用次数: 0
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Philosophia Mathematica
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