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Philosophia Mathematica最新文献

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Dominique Pradelle. Intuition et idéalités. Phénoménologie des objets mathématiques [Intuition and idealities: Phenomenology of mathematical objects.] Collection Épiméthée 多米尼克·普拉德尔。直觉和理想。数学对象的现象学[直觉和理想：数学对象的现象学]。
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab014
Bruno Leclercq
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引用次数: 0
Bob Hale. Essence and Existence: Selected Essays 鲍勃·黑尔。本质与存在：散文选集
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab015
Øystein Linnebo
{"title":"Bob Hale. Essence and Existence: Selected Essays","authors":"Øystein Linnebo","doi":"10.1093/philmat/nkab015","DOIUrl":"https://doi.org/10.1093/philmat/nkab015","url":null,"abstract":"","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 3","pages":"420-427"},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016814/9623708/09623716.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70607977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Domain Extension and Ideal Elements in Mathematics 领域扩展与数学中的理想元素
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab018
Anna Bellomo
{"title":"Domain Extension and Ideal Elements in Mathematics","authors":"Anna Bellomo","doi":"10.1093/philmat/nkab018","DOIUrl":"https://doi.org/10.1093/philmat/nkab018","url":null,"abstract":"Domain extension in mathematics occurs whenever a given mathematical domain is augmented so as to include new elements. Manders argues that the advantages of important cases of domain extension are captured by the model-theoretic notions of existential closure and model completion. In the specific case of domain extension via ideal elements, I argue, Manders's proposed explanation does not suffice. I then develop and formalize a different approach to domain extension based on Dedekind's Habilitationsrede, to which Manders's account is compared. I conclude with an examination of three possible stances towards extensions via ideal elements.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 3","pages":"366-391"},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016814/9623708/09623712.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70607954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Measurable Selections: A Bridge Between Large Cardinals and Scientific Applications? 可衡量的选择：大型红雀和科学应用之间的桥梁？
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab016
John P Burgess
{"title":"Measurable Selections: A Bridge Between Large Cardinals and Scientific Applications?","authors":"John P Burgess","doi":"10.1093/philmat/nkab016","DOIUrl":"https://doi.org/10.1093/philmat/nkab016","url":null,"abstract":"There is no prospect of discovering measurable cardinals by radio astronomy, but this does not mean that higher set theory is entirely irrelevant to applied mathematics broadly construed. By way of example, the bearing of some celebrated descriptive-set-theoretic consequences of large cardinals on measurable-selection theory, a body of results originating with a key lemma in von Neumann's work on the mathematical foundations of quantum theory, and further developed in connection with problems of mathematical economics, will be considered from a philosophical point of view.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 3","pages":"353-365"},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70607972","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
Physical Possibility and Determinate Number Theory 物理可能性与行列式数论
IF 1.1 1区 哲学
Philosophia Mathematica Pub Date : 2021-07-01 DOI: 10.1093/philmat/nkab013
Sharon Berry
{"title":"Physical Possibility and Determinate Number Theory","authors":"Sharon Berry","doi":"10.1093/philmat/nkab013","DOIUrl":"https://doi.org/10.1093/philmat/nkab013","url":null,"abstract":"It is currently fashionable to take Putnamian model-theoretic worries seriously for mathematics, but not for discussions of ordinary physical objects and the sciences. However, I will argue that (under certain mild assumptions) merely securing determinate reference to physical possibility suffices to rule out the kind of nonstandard interpretations of our number talk Putnam invokes. So, anyone who accepts determinate reference to physical possibility should not reject determinate reference to the natural numbers on Putnamian model-theoretic grounds.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 3","pages":"299-317"},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70607961","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
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
{"title":"Objectivity in Mathematics, Without Mathematical Objects","authors":"Markus Pantsar","doi":"10.1093/philmat/nkab010","DOIUrl":"https://doi.org/10.1093/philmat/nkab010","url":null,"abstract":"I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"29 3","pages":"318-352"},"PeriodicalIF":1.1,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/philmat/nkab010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70607962","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
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":"29 3","pages":"445-448"},"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":"29 1","pages":"195-213"},"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":"29 1","pages":"296-297"},"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
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":"29 1","pages":"214-233"},"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
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