发布求助
文献互助 智能选刊 最新文献

Philosophia Mathematica最新文献

筛选
英文 中文
Fregean Metasemantics Fregean Metasemantics
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2025-05-23 DOI: 10.1093/philmat/nkaf003
Ori Simchen
{"title":"Fregean Metasemantics","authors":"Ori Simchen","doi":"10.1093/philmat/nkaf003","DOIUrl":"https://doi.org/10.1093/philmat/nkaf003","url":null,"abstract":"How the semantic significance of numerical discourse gets determined is a metasemantic issue par excellence. At the sub-sentential level, the issue is riddled with difficulties on account of the contested metaphysical status of the subject matter of numerical discourse, i.e., numbers and numerical properties and relations. Setting those difficulties aside, I focus instead on the sentential level, specifically, on obvious affinities between whole numerical and non-numerical sentences and how their significance is determined. From such a perspective, Frege’s 1884 construction of number, while famously mathematically untenable, fares better metasemantically than extant alternatives in the philosophy of mathematics.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"24 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144133725","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
Intrinsic Justification for Large Cardinals and Structural Reflection 大基数和结构反射的内在理由
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2025-05-13 DOI: 10.1093/philmat/nkaf006
Joan Bagaria, Claudio Ternullo
{"title":"Intrinsic Justification for Large Cardinals and Structural Reflection","authors":"Joan Bagaria, Claudio Ternullo","doi":"10.1093/philmat/nkaf006","DOIUrl":"https://doi.org/10.1093/philmat/nkaf006","url":null,"abstract":"We deal with the issue of whether large cardinals are intrinsically justified set-theoretic principles (Intrinsicness Issue). To this end, we review, in a systematic fashion, the abstract principles that have been formulated to motivate them and their mathematical expressions, and assess their intrinsic justifiability. A parallel, but closely linked, issue is whether there exist mathematical principles that yield all large cardinals (Universality Issue), and we also test principles for their ability to respond to this issue. Finally, we discuss Structural Reflection Principles and their responses to Intrinsicness and Universality, and also make some further considerations on their general justifiability.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"27 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143945668","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
Neologicism Meets Fiction 新词与小说相遇
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2025-05-12 DOI: 10.1093/philmat/nkaf009
Geoffrey Hellman
{"title":"Neologicism Meets Fiction","authors":"Geoffrey Hellman","doi":"10.1093/philmat/nkaf009","DOIUrl":"https://doi.org/10.1093/philmat/nkaf009","url":null,"abstract":"Neologicism (NL) invokes a “syntactic-priority thesis” (SPT) to derive existence of numbers, etc., from abstraction principles. Innumerable counterexamples to the SPT, however, are seen to arise from fiction, e.g., “Pegasus is (entirely) fictive”. Examination of possible defenses of the SPT leads to just one viable option, based on quasi-modal “in-fiction” operators. This, however, applies just as well to abstraction principles themselves, thereby undermining NL’s case for countenancing mathematical abstracta. Appeal to the linguistics principle of compositionality is seen not to help NL.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"38 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143940197","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 Triptych on Empirical Philosophy of Mathematics. Part III: How? 实证数学哲学三联画。第三部分：怎么做？
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2025-05-07 DOI: 10.1093/philmat/nkaf004
Deborah Kant, Benedikt Löwe
{"title":"A Triptych on Empirical Philosophy of Mathematics. Part III: How?","authors":"Deborah Kant, Benedikt Löwe","doi":"10.1093/philmat/nkaf004","DOIUrl":"https://doi.org/10.1093/philmat/nkaf004","url":null,"abstract":"The International Humanities Council has established a new international research network Diversity of Mathematical Research Cultures & Practices (DMRCP) at the Universität Hamburg. In a tripartite contribution, we outline and discuss the specific philosophical approach that DMRCP seeks to promote for which we use the term ‘empirical philosophy of mathematics’: the contribution is therefore programmatic and methodological, rather than a contribution to a specific philosophical research question. This article forms Part III of the triptych.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"119 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143920101","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
How Should We Understand the Modal Potentialist’s Modality? 我们应该如何理解情态潜在者的情态？
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2025-04-13 DOI: 10.1093/philmat/nkaf007
Boaz D Laan
{"title":"How Should We Understand the Modal Potentialist’s Modality?","authors":"Boaz D Laan","doi":"10.1093/philmat/nkaf007","DOIUrl":"https://doi.org/10.1093/philmat/nkaf007","url":null,"abstract":"Modal potentialism argues that mathematics has a generative nature, and aims to formalise mathematics accordingly using quantified modal logic. This paper shows that Øystein Linnebo’s approach to modal potentialism in his book Thin Objects is incoherent. In particular, he is committed to the legitimacy of introducing a primitive modal predicate of formulae. However, as with the semantic paradoxes, natural principles for such a predicate are inconsistent; no such predicate can underpin an account of modal potentialism. Hence, Linnebo’s intended interpretation of the primitive modality and his formal framework do not match up.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"13 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143827659","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
Inference to the Best Explanation as a Form of Non-Deductive Reasoning in Mathematics 作为数学非演绎推理形式的最佳解释推理
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2025-04-02 DOI: 10.1093/philmat/nkae024
Marc Lange
{"title":"Inference to the Best Explanation as a Form of Non-Deductive Reasoning in Mathematics","authors":"Marc Lange","doi":"10.1093/philmat/nkae024","DOIUrl":"https://doi.org/10.1093/philmat/nkae024","url":null,"abstract":"This paper proposes that mathematicians routinely use inference to the best explanation (IBE) to confirm their conjectures. Mathematicians can justly reason that the ‘best explanation’ of some mathematical evidence they possess would be a proof of it that likewise proves a given conjecture. By IBE, the evidence thereby confirms that such an as-yet-undiscovered proof exists and that the conjecture holds. This reasoning can be expressed in Bayesian terms once Bayesianism’s logical omniscience has been circumvented. A Bayesian analysis identifies considerations affecting a mathematical IBE’s strength and helps to unify mathematical IBEs with scientific IBEs.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"3 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143775500","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 Potentialist Perspective on Intuitionistic Analysis 直觉分析的潜在主义视角
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2025-03-31 DOI: 10.1093/philmat/nkae025
Ethan Brauer
{"title":"A Potentialist Perspective on Intuitionistic Analysis","authors":"Ethan Brauer","doi":"10.1093/philmat/nkae025","DOIUrl":"https://doi.org/10.1093/philmat/nkae025","url":null,"abstract":"Free choice sequences play a key role in the Brouwerian continuum. Using recent modal analysis of potential infinity, we can make sense of free choice sequences as potentially infinite sequences of natural numbers without adopting Brouwer’s distinctive idealistic metaphysics. This provides classicists with a means to make sense of intuitionistic ideas from their own classical perspective. I develop a modal-potentialist theory of real numbers that suffices to capture the most distinctive features of intuitionistic analysis, such as Brouwer’s continuity theorem, the existence of a sequence that is monotone, bounded, and non-convergent, and the inability to decompose the continuum non-trivially.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"75 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143744947","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 Problem 凯撒问题
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2025-03-04 DOI: 10.1093/philmat/nkaf002
Francesca Boccuni, Luca Zanetti
{"title":"The Caesar-problem Problem","authors":"Francesca Boccuni, Luca Zanetti","doi":"10.1093/philmat/nkaf002","DOIUrl":"https://doi.org/10.1093/philmat/nkaf002","url":null,"abstract":"Hume’s Principle (HP) does not determine the truth values of ‘mixed’ identity statements like ‘$ #F $ = Caesar’. This is the Caesar Problem (CP). Still, neologicists such as Hale and Wright argue that (1) HP is a priori, and (2) HP introduces the pure sortal concept Number. We argue that Neologicism faces a Caesar-problem Problem (CPP): if neologicists solve CP by establishing that ‘$ #Fneq $ Caesar’ is true, (1) and (2) cannot be retained simultaneously. We examine various responses neologicists might provide and show that they do not address CPP. We conclude that CP uncovers a fatal tension in Neologicism.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"28 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143546334","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 Logic of Potential Infinity 潜在无限的逻辑
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-12-15 DOI: 10.1093/philmat/nkae022
Roy T Cook
{"title":"The Logic of Potential Infinity","authors":"Roy T Cook","doi":"10.1093/philmat/nkae022","DOIUrl":"https://doi.org/10.1093/philmat/nkae022","url":null,"abstract":"Michael Dummett argues that acceptance of potentially infinite collections requires that we abandon classical logic and restrict ourselves to intuitionistic logic. In this paper we examine whether Dummett is correct. After developing two detailed accounts of what, exactly, it means for a concept to be potentially infinite (based on ideas due to Charles McCarty and Øystein Linnebo, respectively), we construct a Kripke structure that contains a natural number structure that satisfies both accounts. This model supports a logic much stronger than intuitionistic logic, demonstrating that Dummett was wrong. We conclude by briefly examining ways to extend the account(s) in question to indefinitely extensible concepts such as Cardinal, Ordinal, and Set.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"116 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142825480","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
Predicative Classes and Strict Potentialism 谓词类和严格的潜在论
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2024-11-12 DOI: 10.1093/philmat/nkae020
Øystein Linnebo, Stewart Shapiro
{"title":"Predicative Classes and Strict Potentialism","authors":"Øystein Linnebo, Stewart Shapiro","doi":"10.1093/philmat/nkae020","DOIUrl":"https://doi.org/10.1093/philmat/nkae020","url":null,"abstract":"While sets are combinatorial collections, defined by their elements, classes are logical collections, defined by their membership conditions. We develop, in a potentialist setting, a predicative approach to (logical) classes of (combinatorial) sets. Some reasons emerge to adopt a stricter form of potentialism, which insists, not only that each object is generated at some stage of an incompletable process, but also that each truth is “made true” at some such stage. The natural logic of this strict form of potentialism is semi-intuitionistic: where each set-sized domain is classical, the domain of all sets or all classes is intuitionistic.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"40 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142601934","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
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信