数学适用性的内部应用和困惑

IF 0.8 1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Douglas Bertrand Marshall
{"title":"数学适用性的内部应用和困惑","authors":"Douglas Bertrand Marshall","doi":"10.1093/philmat/nkad019","DOIUrl":null,"url":null,"abstract":"Abstract Just as mathematics helps us to represent and reason about the natural world, in its internal applications one branch of mathematics helps us to represent and reason about the subject matter of another. Recognition of the close analogy between internal and external applications of mathematics can help resolve two persistent philosophical puzzles concerning its applicability: a platonist puzzle arising from the abstractness of mathematical objects; and an empiricist puzzle arising from mathematical propositions’ lack of empirical factual content. In order to see how this is the case, we will examine what it is to apply mathematics internally and describe examples.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Internal Applications and Puzzles of the Applicability of Mathematics\",\"authors\":\"Douglas Bertrand Marshall\",\"doi\":\"10.1093/philmat/nkad019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Just as mathematics helps us to represent and reason about the natural world, in its internal applications one branch of mathematics helps us to represent and reason about the subject matter of another. Recognition of the close analogy between internal and external applications of mathematics can help resolve two persistent philosophical puzzles concerning its applicability: a platonist puzzle arising from the abstractness of mathematical objects; and an empiricist puzzle arising from mathematical propositions’ lack of empirical factual content. In order to see how this is the case, we will examine what it is to apply mathematics internally and describe examples.\",\"PeriodicalId\":49004,\"journal\":{\"name\":\"Philosophia Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Philosophia Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/philmat/nkad019\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Philosophia Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/philmat/nkad019","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

摘要

正如数学帮助我们对自然世界进行表征和推理一样,在其内部应用中,数学的一个分支帮助我们对另一个分支的主题进行表征和推理。认识到数学的内部和外部应用之间的密切相似,有助于解决关于数学适用性的两个长期存在的哲学难题:数学对象的抽象性引起的柏拉图主义难题;以及由于数学命题缺乏经验事实内容而产生的经验主义困惑。为了了解这是怎么回事,我们将研究一下什么是内部应用数学并描述一些例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Internal Applications and Puzzles of the Applicability of Mathematics
Abstract Just as mathematics helps us to represent and reason about the natural world, in its internal applications one branch of mathematics helps us to represent and reason about the subject matter of another. Recognition of the close analogy between internal and external applications of mathematics can help resolve two persistent philosophical puzzles concerning its applicability: a platonist puzzle arising from the abstractness of mathematical objects; and an empiricist puzzle arising from mathematical propositions’ lack of empirical factual content. In order to see how this is the case, we will examine what it is to apply mathematics internally and describe examples.
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
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.
×
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