{"title":"Anti-Realism and Anti-Revisionism in Wittgenstein’s Philosophy of Mathematics","authors":"A. Nakano","doi":"10.1163/18756735-000109","DOIUrl":null,"url":null,"abstract":"\nSince the publication of the Remarks on the Foundations of Mathematics, Wittgenstein’s interpreters have endeavored to reconcile his general constructivist/anti-realist attitude towards mathematics with his confessed anti-revisionary philosophy. In this article, the author revisits the issue and presents a solution. The basic idea consists in exploring the fact that the so-called “non-constructive results” could be interpreted so that they do not appear non-constructive at all. The author substantiates this solution by showing how the translation of mathematical results, given by the possibility of translation between logics, can be seen as a tool for partially implementing the solution Wittgenstein had in mind.","PeriodicalId":43873,"journal":{"name":"Grazer Philosophische Studien-International Journal for Analytic Philosophy","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2020-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1163/18756735-000109","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Grazer Philosophische Studien-International Journal for Analytic Philosophy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1163/18756735-000109","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"0","JCRName":"PHILOSOPHY","Score":null,"Total":0}
引用次数: 2
Abstract
Since the publication of the Remarks on the Foundations of Mathematics, Wittgenstein’s interpreters have endeavored to reconcile his general constructivist/anti-realist attitude towards mathematics with his confessed anti-revisionary philosophy. In this article, the author revisits the issue and presents a solution. The basic idea consists in exploring the fact that the so-called “non-constructive results” could be interpreted so that they do not appear non-constructive at all. The author substantiates this solution by showing how the translation of mathematical results, given by the possibility of translation between logics, can be seen as a tool for partially implementing the solution Wittgenstein had in mind.
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