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Objectivity in Mathematics, Without Mathematical Objects 数学的客观性，没有数学对象
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab010
Markus Pantsar
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引用次数: 7
Mark Wilson. Innovation and Certainty 马克·威尔逊。创新与确定性
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab019
Donald Gillies
{"title":"Mark Wilson. Innovation and Certainty","authors":"Donald Gillies","doi":"10.1093/philmat/nkab019","DOIUrl":"https://doi.org/10.1093/philmat/nkab019","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70607970","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: 1
Intrinsic Justifications for Large-Cardinal Axioms 大基数公理的内在证明
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-02-01 DOI: 10.1093/philmat/nkaa038
Rupert McCallum
{"title":"Intrinsic Justifications for Large-Cardinal Axioms","authors":"Rupert McCallum","doi":"10.1093/philmat/nkaa038","DOIUrl":"https://doi.org/10.1093/philmat/nkaa038","url":null,"abstract":"We shall defend three philosophical theses about the extent of intrinsic justification based on various technical results. We shall present a set of theorems which indicate intriguing structural similarities between a family of “weak” reflection principles roughly at the level of those considered by Tait and Koellner and a family of “strong” reflection principles roughly at the level of those of Welch and Roberts, which we claim to lend support to the view that the stronger reflection principles are intrinsically justified as well as the weaker ones. We consider connections with earlier work of Marshall.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/philmat/nkaa038","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68176532","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: 1
Geoffrey Hellman. Mathematics and Its Logics: Philosophical Essays 杰弗里·赫尔曼。数学及其逻辑:哲学论文集
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-02-01 DOI: 10.1093/philmat/nkab006
{"title":"Geoffrey Hellman. Mathematics and Its Logics: Philosophical Essays","authors":"","doi":"10.1093/philmat/nkab006","DOIUrl":"10.1093/philmat/nkab006","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43141776","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
On the Buck-Stopping Identification of Numbers 关于数字的Buck Stopping识别†
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-02-01 DOI: 10.1093/philmat/nkab009
Dongwoo Kim
{"title":"On the Buck-Stopping Identification of Numbers","authors":"Dongwoo Kim","doi":"10.1093/philmat/nkab009","DOIUrl":"10.1093/philmat/nkab009","url":null,"abstract":"Kripke observes that the decimal numerals have the buck-stopping property: when a number is given in decimal notation, there is no further question of what number it is. What makes them special in this way? According to Kripke, it is because of structural revelation: each decimal numeral represents the structure of the corresponding number. Though insightful, I argue, this account has some counterintuitive consequences. Then I sketch an alternative account of the buck-stopping property in terms of how we specify the positions of numbers in the progression.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/philmat/nkab009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44847446","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: 1
How Do We Semantically Individuate Natural Numbers? 我们如何在语义上个性化自然数?__
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-02-01 DOI: 10.1093/philmat/nkab001
Stefan Buijsman
{"title":"How Do We Semantically Individuate Natural Numbers?","authors":"Stefan Buijsman","doi":"10.1093/philmat/nkab001","DOIUrl":"10.1093/philmat/nkab001","url":null,"abstract":"How do non-experts single out numbers for reference? Linnebo has argued that they do so using a criterion of identity based on the ordinal properties of numerals. Neo-logicists, on the other hand, claim that cardinal properties are the basis of individuation, when they invoke Hume's Principle. I discuss empirical data from cognitive science and linguistics to answer how non-experts individuate numbers better in practice. I use those findings to develop an alternative account that mixes ordinal and cardinal properties to provide a detailed (though not conclusively proven) answer to the question: how do we in fact semantically individuate numbers?","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/philmat/nkab001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49268017","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: 2
Stewart Shapiro and Geoffrey Hellman, eds. The History of Continua: Philosophical and Mathematical Perspectives Stewart Shapiro和Geoffrey Hellman主编：连续体的历史：哲学和数学视角
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-02-01 DOI: 10.1093/philmat/nkab003
{"title":"Stewart Shapiro and Geoffrey Hellman, eds. The History of Continua: Philosophical and Mathematical Perspectives","authors":"","doi":"10.1093/philmat/nkab003","DOIUrl":"10.1093/philmat/nkab003","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45161747","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: 1
Carl Posy and Ofra Rechter, eds. Kant's Philosophy of Mathematics. Volume 1: The Critical Philosophy and its Roots Carl Posy和Ofra Rechter主编，《康德数学哲学》。第一卷：批判哲学及其根源
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-02-01 DOI: 10.1093/philmat/nkaa037
{"title":"Carl Posy and Ofra Rechter, eds. Kant's Philosophy of Mathematics. Volume 1: The Critical Philosophy and its Roots","authors":"","doi":"10.1093/philmat/nkaa037","DOIUrl":"https://doi.org/10.1093/philmat/nkaa037","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68176535","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
William Boos. Metamathematics and the Philosophical Tradition William Boos。元数学与哲学传统
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-02-01 DOI: 10.1093/philmat/nkab008
Brendan Larvor
{"title":"William Boos. Metamathematics and the Philosophical Tradition","authors":"Brendan Larvor","doi":"10.1093/philmat/nkab008","DOIUrl":"10.1093/philmat/nkab008","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/philmat/nkab008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46713901","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 Equivalence of Definitions of Algorithmic Randomness 算法随机性定义的等价性†
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-02-01 DOI: 10.1093/philmat/nkaa039
Christopher Porter
{"title":"The Equivalence of Definitions of Algorithmic Randomness","authors":"Christopher Porter","doi":"10.1093/philmat/nkaa039","DOIUrl":"10.1093/philmat/nkaa039","url":null,"abstract":"In this paper, I evaluate the claim that the equivalence of multiple intensionally distinct definitions of random sequence provides evidence for the claim that these definitions capture the intuitive conception of randomness, concluding that the former claim is false. I then develop an alternative account of the significance of randomness-theoretic equivalence results, arguing that they are instances of a phenomenon I refer to as schematic equivalence. On my account, this alternative approach has the virtue of providing the plurality of definitions of randomness with conceptual unity and a rationale for certain investigations that are carried out in the field.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/philmat/nkaa039","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49566434","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: 2
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