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The Prehistory of Mathematical Structuralism最新文献

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Introduction and Overview 简介与概述
The Prehistory of Mathematical Structuralism Pub Date : 2020-04-30 DOI: 10.1093/oso/9780190641221.003.0001
E. Reck, G. Schiemer
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引用次数: 0
Explication as Elimination: W. V. Quine and Mathematical Structuralism 解释即消除:奎因与数学结构主义
The Prehistory of Mathematical Structuralism Pub Date : 2020-04-30 DOI: 10.1093/oso/9780190641221.003.0016
S. Morris
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引用次数: 1
Cassirer’s Reception of Dedekind and the Structuralist Transformation of Mathematics 卡西尔对戴德金德的接受与数学的结构主义转变
The Prehistory of Mathematical Structuralism Pub Date : 2020-04-30 DOI: 10.1093/oso/9780190641221.003.0013
E. Reck
{"title":"Cassirer’s Reception of Dedekind and the Structuralist Transformation of Mathematics","authors":"E. Reck","doi":"10.1093/oso/9780190641221.003.0013","DOIUrl":"https://doi.org/10.1093/oso/9780190641221.003.0013","url":null,"abstract":"Ernst Cassirer was a keen observer of development in the mathematical sciences, especially in the 19th and early 20th centuries. In this essay, the focus is on his reception of Dedekind’s contributions to the foundations of mathematics, and with it, on Dedekind’s mathematical structuralism. Cassirer adopts that structuralism early on, defends it against a number of criticisms, and embeds it into a rich historical account of the structuralist transformation of modern mathematical science. He also adds some original elements to our understanding of structuralism, e.g., by relating it to the Kantian notion of the “construction of concepts” in mathematics, by introducing a basic distinction between “substance concepts” and “function concepts”, and by tracing the “unfolding” of structuralist aspects far back in the history of thought. Overall, Cassirer’s approach is guided by the conviction that the metaphysics of modern mathematics should be approached by way of its distinctive methodology.","PeriodicalId":332231,"journal":{"name":"The Prehistory of Mathematical Structuralism","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126739983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
“If Numbers Are to Be Anything At All, They Must Be Intrinsically Something”: Bertrand Russell and Mathematical Structuralism “如果数字是任何东西，它们本质上必须是某种东西”:伯特兰·罗素和数学结构主义
The Prehistory of Mathematical Structuralism Pub Date : 2020-04-30 DOI: 10.1093/oso/9780190641221.003.0012
J. Heis
{"title":"“If Numbers Are to Be Anything At All, They Must Be Intrinsically Something”: Bertrand Russell and Mathematical Structuralism","authors":"J. Heis","doi":"10.1093/oso/9780190641221.003.0012","DOIUrl":"https://doi.org/10.1093/oso/9780190641221.003.0012","url":null,"abstract":"Bertrand Russell was one of the first philosophers to recognize clearly the philosophically innovative nature of Richard Dedekind’s philosophy of arithmetic: a position we now describe as non-eliminative structuralism. But Russell’s response was deeply negative: “If [numbers] are to be anything at all, they must be intrinsically something” (Principles of Mathematics, §242). Nevertheless, Russell also played a significant positive role in making possible the emergence of structuralist philosophy of mathematics. This chapter explains Russell’s double role, identifying three positive contributions to structuralism, while laying out Russell’s objections to Dedekind’s non-eliminative structuralism.","PeriodicalId":332231,"journal":{"name":"The Prehistory of Mathematical Structuralism","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132390842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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