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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE
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 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Philosophia Mathematica
Pub Date : 2021-09-21 DOI: 10.1093/philmat/nkab023
Lange M.
ABSTRACT
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.
一些数学证明解释了为什么它们所证明的定理成立。本文确定了数学中任何反事实解释的几个挑战(也就是说，任何根据解释性证明揭示解释如何不同的解释，如果解释中的事实不同)。这篇论文假定反数学可以是非平凡的。它认为，尽管如此，反事实的解释将解释力描绘得太容易实现，没有捕捉到解释的不对称性，也没有说明为什么某些证据是解释性的，而其他证据不是。关于反事实依赖的更多信息甚至可能产生更少的解释力。
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引用次数: 0
Critical Studies/Book Reviews 批判性研究/书评
IF 1.1 1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Philosophia Mathematica
Pub Date : 2021-09-21 DOI: 10.1093/philmat/nkab024
R. Cook
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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Philosophia Mathematica
Pub Date : 2021-09-21 DOI: 10.1093/philmat/nkab021
FenstadJ.E.. Structures and Algorithms: Mathematics and the Nature of Knowledge. Logic, Argumentation & 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.
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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Philosophia Mathematica
Pub Date : 2021-07-27 DOI: 10.1093/philmat/nkac011
P. Levy
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. 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.
本文认为，只要我们怀疑连续统假设的二价性或选择公理的真实性，我们也应该怀疑三阶算术的一致性，无论是经典的还是直觉的版本。这一论点的基础是以下哲学观点。数学信仰源于某些直觉，每一个直觉都可以完全接受或怀疑，但不能只接受一半。因此，我们对现实、二元性、选择和一致性的信念应该是一致的。
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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Philosophia Mathematica
Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab017
Crispin Wright
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.
区分了对高阶逻辑的四种哲学关注，以及新逻辑学家项目对其提出的具体要求。本文批判性地回顾了已故的鲍勃·黑尔、理查德·金伯利·赫克和我本人最近对这些问题的回应。有人认为，这些措施取得了一些成功。然而，本文的主要目的是认为，对新逻辑学家项目所要求的高阶逻辑应用的最严重的反对意见还没有得到正确的理解。论文最后概述了一项战略，该战略在最近的工作中已经预见到，以满足这一反对意见。
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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Philosophia Mathematica
Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab004
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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Philosophia Mathematica
Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab012
Penelope J Maddy
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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Philosophia Mathematica
Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab002
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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 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Philosophia Mathematica
Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab005
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引用次数: 0
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