数学推导过程中的实用考虑因素在数学应用性中的作用

IF 0.4 4区 哲学 0 PHILOSOPHY
José Antonio Pérez-Escobar
{"title":"数学推导过程中的实用考虑因素在数学应用性中的作用","authors":"José Antonio Pérez-Escobar","doi":"10.1111/phin.12412","DOIUrl":null,"url":null,"abstract":"The conditions involved in the applicability of mathematics in science are the subject of ongoing debates. One of the best-received approaches is the inferential account, which involves structural mappings and pragmatic considerations in a three-step model. According to the inferential account, these pragmatic considerations happen in the immersion and interpretation stages, but not during derivation (symbol-pushing in a mathematical formalism). In this work, I draw inspiration from the later Wittgenstein and make the case that the applicability of mathematics also rests on pragmatic considerations at the mathematical derivation level. I make the further case that pragmatic considerations at the mathematical derivation level may substitute pragmatic considerations in the other two stages, thus showing how they are holistically interrelated. I illustrate these two points with the solution of a simple geometrical problem.","PeriodicalId":47112,"journal":{"name":"PHILOSOPHICAL INVESTIGATIONS","volume":"96 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The role of pragmatic considerations during mathematical derivation in the applicability of mathematics\",\"authors\":\"José Antonio Pérez-Escobar\",\"doi\":\"10.1111/phin.12412\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The conditions involved in the applicability of mathematics in science are the subject of ongoing debates. One of the best-received approaches is the inferential account, which involves structural mappings and pragmatic considerations in a three-step model. According to the inferential account, these pragmatic considerations happen in the immersion and interpretation stages, but not during derivation (symbol-pushing in a mathematical formalism). In this work, I draw inspiration from the later Wittgenstein and make the case that the applicability of mathematics also rests on pragmatic considerations at the mathematical derivation level. I make the further case that pragmatic considerations at the mathematical derivation level may substitute pragmatic considerations in the other two stages, thus showing how they are holistically interrelated. I illustrate these two points with the solution of a simple geometrical problem.\",\"PeriodicalId\":47112,\"journal\":{\"name\":\"PHILOSOPHICAL INVESTIGATIONS\",\"volume\":\"96 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-12-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"PHILOSOPHICAL INVESTIGATIONS\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1111/phin.12412\",\"RegionNum\":4,\"RegionCategory\":\"哲学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"0\",\"JCRName\":\"PHILOSOPHY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"PHILOSOPHICAL INVESTIGATIONS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1111/phin.12412","RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"0","JCRName":"PHILOSOPHY","Score":null,"Total":0}
引用次数: 0

摘要

数学在科学中的应用所涉及的条件一直是争论的主题。其中一种最受欢迎的方法是推论说,它在一个三步模型中涉及结构映射和实用考虑。根据推论说,这些实用性考虑发生在浸入和解释阶段,但不发生在推导阶段(数学形式主义中的符号推导)。在这项工作中,我从后来的维特根斯坦那里得到启发,提出数学的适用性也依赖于数学推导层面的语用考虑。我还进一步提出,数学推导层面的实用性考虑可以替代其他两个阶段的实用性考虑,从而说明它们是如何整体地相互关联的。我用一个简单几何问题的解答来说明这两点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The role of pragmatic considerations during mathematical derivation in the applicability of mathematics
The conditions involved in the applicability of mathematics in science are the subject of ongoing debates. One of the best-received approaches is the inferential account, which involves structural mappings and pragmatic considerations in a three-step model. According to the inferential account, these pragmatic considerations happen in the immersion and interpretation stages, but not during derivation (symbol-pushing in a mathematical formalism). In this work, I draw inspiration from the later Wittgenstein and make the case that the applicability of mathematics also rests on pragmatic considerations at the mathematical derivation level. I make the further case that pragmatic considerations at the mathematical derivation level may substitute pragmatic considerations in the other two stages, thus showing how they are holistically interrelated. I illustrate these two points with the solution of a simple geometrical problem.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
0.70
自引率
66.70%
发文量
46
审稿时长
45 weeks
期刊介绍: Philosophical Investigations features articles in every branch of philosophy. Whether focusing on traditional or on new aspects of the subject, it offers thought-provoking articles and maintains a lively readership with an acclaimed discussion section and wide-ranging book reviews. Special issues are published on topics of current philosophical interest.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信