Anti-Realism and Anti-Revisionism in Wittgenstein’s Philosophy of Mathematics

A. Nakano
{"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":" October","pages":"451-474"},"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.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
维特根斯坦数学哲学中的反现实主义与反修正主义
自《数学基础论》出版以来,维特根斯坦的阐释者们一直在努力调和他对数学的普遍建构主义/反现实主义态度与他公认的反修正主义哲学。在这篇文章中,作者重新审视了这个问题,并提出了一个解决方案。基本思想在于探索这样一个事实,即所谓的“非建设性结果”可以被解释为使它们看起来根本不具有建设性。作者通过展示逻辑之间翻译的可能性所给出的数学结果的翻译,可以被视为部分实现维特根斯坦所设想的解决方案的工具,来证实这个解决方案。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
1.40
自引率
0.00%
发文量
11
期刊最新文献
When is a Belief Formed in an Epistemically Circular Way? The Epistemology of Reading and Interpretation, written by René van Woudenberg Rational Belief, Reflection, and Undercutting Defeat Warum sich doch sinnvoll über Geschmack streiten lässt Das intentionale Objekt als Unding
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1