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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
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引用次数: 1
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":"29 1","pages":"234-255"},"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
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":"29 1","pages":"298-298"},"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":"29 1","pages":"292-293"},"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":"29 1","pages":"153-194"},"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
Rainer Stuhlmann-Laeisz. Gottlob Freges Grundgesetze der Arithmetik: Ein Kommentar des Vorworts, des Nachworts und der einleitenden Paragraphen. [Gottlob Frege's Basic Laws of Arithmetic: A Commentary on the Foreword, the Afterword and the Introductory Paragraphs] Rainer Stuhlmann Laeisz。戈特洛布·弗雷格的算术基本定律：序言、后记和引言段落评述。[戈特洛布·弗雷格的《算术基本定律：前、后和引言段落述评》]
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-02-01 DOI: 10.1093/philmat/nkab011
Matthias Wille
{"title":"Rainer Stuhlmann-Laeisz. Gottlob Freges Grundgesetze der Arithmetik: Ein Kommentar des Vorworts, des Nachworts und der einleitenden Paragraphen. [Gottlob Frege's Basic Laws of Arithmetic: A Commentary on the Foreword, the Afterword and the Introductory Paragraphs]","authors":"Matthias Wille","doi":"10.1093/philmat/nkab011","DOIUrl":"10.1093/philmat/nkab011","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 1","pages":"288-291"},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/philmat/nkab011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42276960","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
Internality, transfer, and infinitesimal modeling of infinite processes 无穷过程的内在性、传递和无穷小建模†
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-02-01 DOI: 10.1093/philmat/nkaa033
Emanuele Bottazzi;Mikhail G Katz
{"title":"Internality, transfer, and infinitesimal modeling of infinite processes","authors":"Emanuele Bottazzi;Mikhail G Katz","doi":"10.1093/philmat/nkaa033","DOIUrl":"10.1093/philmat/nkaa033","url":null,"abstract":"A probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal probabilities are underdetermined. The claim is based upon external hyperreal-valued measures. We show that internal hyperfinite measures are not underdetermined. The importance of internality stems from the fact that Robinson's transfer principle only applies to internal entities. We also evaluate the claim that transferless ordered fields (surreals, Levi-Civita field, Laurent series) may have advantages over hyperreals in probabilistic modeling. We show that probabilities developed over such fields are less expressive than hyperreal probabilities.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 1","pages":"256-277"},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/philmat/nkaa033","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46761265","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: 7
There May Be Many Arithmetical Gödel Sentences 可能有很多算术句子Gödel
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-02-01 DOI: 10.1093/philmat/nkaa041
Kaave Lajevardi;Saeed Salehi
{"title":"There May Be Many Arithmetical Gödel Sentences","authors":"Kaave Lajevardi;Saeed Salehi","doi":"10.1093/philmat/nkaa041","DOIUrl":"10.1093/philmat/nkaa041","url":null,"abstract":"We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel's First Incompleteness Theorem, one cannot, without impropriety, talk about the Gödel sentence of the theory. The reason is that, without violating the requirements of Gödel's theorem, there could be a true sentence and a false one each of which is provably equivalent to its own unprovability in the theory if the theory is unsound.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 1","pages":"278-287"},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/philmat/nkaa041","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47318243","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
OUP accepted manuscript OUP接受稿件
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-01-01 DOI: 10.1093/philmat/nkab015
{"title":"OUP accepted manuscript","authors":"","doi":"10.1093/philmat/nkab015","DOIUrl":"https://doi.org/10.1093/philmat/nkab015","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61635006","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
OUP accepted manuscript OUP接受稿件
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-01-01 DOI: 10.1093/philmat/nkab018
{"title":"OUP accepted manuscript","authors":"","doi":"10.1093/philmat/nkab018","DOIUrl":"https://doi.org/10.1093/philmat/nkab018","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61635694","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
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