Intuition, Iteration, Induction

IF 0.8 1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Philosophia Mathematica Pub Date : 2023-11-11 DOI:10.1093/philmat/nkad017
Mark van Atten
{"title":"Intuition, Iteration, Induction","authors":"Mark van Atten","doi":"10.1093/philmat/nkad017","DOIUrl":null,"url":null,"abstract":"Brouwer’s view on induction has relatively recently been characterised as one on which it is not only intuitive (as expected) but functional, by van Dalen. He claims that Brouwer’s ‘Ur-intuition’ also yields the recursor. Appealing to Husserl’s phenomenology, I offer an analysis of Brouwer’s view that supports this characterisation and claim, even if assigning the primary role to the iterator instead. Contrasts are drawn to accounts of induction by Poincaré, Heyting, and Kreisel. On the phenomenological side, the analysis provides an alternative to that in Tieszen’s Mathematical Intuition, and confirms a view of Gödel on his Dialectica Interpretation.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Philosophia Mathematica","FirstCategoryId":"98","ListUrlMain":"https://doi.org/10.1093/philmat/nkad017","RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
引用次数: 0

Abstract

Brouwer’s view on induction has relatively recently been characterised as one on which it is not only intuitive (as expected) but functional, by van Dalen. He claims that Brouwer’s ‘Ur-intuition’ also yields the recursor. Appealing to Husserl’s phenomenology, I offer an analysis of Brouwer’s view that supports this characterisation and claim, even if assigning the primary role to the iterator instead. Contrasts are drawn to accounts of induction by Poincaré, Heyting, and Kreisel. On the phenomenological side, the analysis provides an alternative to that in Tieszen’s Mathematical Intuition, and confirms a view of Gödel on his Dialectica Interpretation.
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
直觉,迭代,归纳法
布劳威尔的归纳法观点最近被范达伦描述为不仅是直观的(正如预期的那样),而且是功能性的。他声称,布劳威尔的“原始直觉”也产生了递归。诉诸于胡塞尔的现象学,我对布劳威尔的观点进行了分析,以支持这一特征和主张,即使将主要角色分配给迭代器。与庞卡洛、海廷和克瑞塞尔对归纳法的描述形成对比。在现象学方面,这一分析提供了一种对铁生《数学直觉》的替代,并证实了Gödel对其《辩证法解释》的观点。
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
Philosophia Mathematica
Philosophia Mathematica HISTORY & PHILOSOPHY OF SCIENCE-
CiteScore
1.70
自引率
9.10%
发文量
26
审稿时长
>12 weeks
期刊介绍: Philosophia Mathematica is the only journal in the world devoted specifically to philosophy of mathematics. The journal publishes peer-reviewed new work in philosophy of mathematics, the application of mathematics, and computing. In addition to main articles, sometimes grouped on a single theme, there are shorter discussion notes, letters, and book reviews. The journal is published online-only, with three issues published per year.
期刊最新文献
Is Iteration an Object of Intuition? A Taxonomy for Set-Theoretic Potentialism Up with Categories, Down with Sets; Out with Categories, In with Sets! Chris Pincock.  Mathematics and Explanation Donald Gillies.Lakatos and the Historical Approach to Philosophy of Mathematics
×
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