{"title":"数学符号从何而来","authors":"Dirk Schlimm","doi":"10.1111/tops.12786","DOIUrl":null,"url":null,"abstract":"<p><p>There is a sense in which the symbols used in mathematical expressions and formulas are arbitrary. After all, arithmetic would be no different if we would replace the symbols ' <math><semantics><mo>+</mo> <annotation>$+$</annotation></semantics> </math> ' or '8' by different symbols. Nevertheless, the shape of many mathematical symbols is in fact well motivated in practice. In the case of symbols that were introduced a long time ago, the original motivations remain mostly inaccessible to us. Accordingly, motivations that are discussed in the literature are only ascribed retrospectively and should be considered as post-hoc rationalizations. For more recent introductions of new symbols (e.g., in symbolic logic), however, we sometimes do have first-hand accounts by the authors that inform us of the reasons behind their notational choices. In this paper, I present a systematic overview of possible motivations for the design of mathematical symbols, which include practical (such as ease of writing and reuse of previously used symbols) as well as cognitive aspects (such as indicating relations to other symbols or to their intended meanings).</p>","PeriodicalId":47822,"journal":{"name":"Topics in Cognitive Science","volume":" ","pages":""},"PeriodicalIF":3.0000,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Where Mathematical Symbols Come From.\",\"authors\":\"Dirk Schlimm\",\"doi\":\"10.1111/tops.12786\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>There is a sense in which the symbols used in mathematical expressions and formulas are arbitrary. After all, arithmetic would be no different if we would replace the symbols ' <math><semantics><mo>+</mo> <annotation>$+$</annotation></semantics> </math> ' or '8' by different symbols. Nevertheless, the shape of many mathematical symbols is in fact well motivated in practice. In the case of symbols that were introduced a long time ago, the original motivations remain mostly inaccessible to us. Accordingly, motivations that are discussed in the literature are only ascribed retrospectively and should be considered as post-hoc rationalizations. For more recent introductions of new symbols (e.g., in symbolic logic), however, we sometimes do have first-hand accounts by the authors that inform us of the reasons behind their notational choices. In this paper, I present a systematic overview of possible motivations for the design of mathematical symbols, which include practical (such as ease of writing and reuse of previously used symbols) as well as cognitive aspects (such as indicating relations to other symbols or to their intended meanings).</p>\",\"PeriodicalId\":47822,\"journal\":{\"name\":\"Topics in Cognitive Science\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2025-02-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topics in Cognitive Science\",\"FirstCategoryId\":\"102\",\"ListUrlMain\":\"https://doi.org/10.1111/tops.12786\",\"RegionNum\":2,\"RegionCategory\":\"心理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PSYCHOLOGY, EXPERIMENTAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topics in Cognitive Science","FirstCategoryId":"102","ListUrlMain":"https://doi.org/10.1111/tops.12786","RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PSYCHOLOGY, EXPERIMENTAL","Score":null,"Total":0}
There is a sense in which the symbols used in mathematical expressions and formulas are arbitrary. After all, arithmetic would be no different if we would replace the symbols ' ' or '8' by different symbols. Nevertheless, the shape of many mathematical symbols is in fact well motivated in practice. In the case of symbols that were introduced a long time ago, the original motivations remain mostly inaccessible to us. Accordingly, motivations that are discussed in the literature are only ascribed retrospectively and should be considered as post-hoc rationalizations. For more recent introductions of new symbols (e.g., in symbolic logic), however, we sometimes do have first-hand accounts by the authors that inform us of the reasons behind their notational choices. In this paper, I present a systematic overview of possible motivations for the design of mathematical symbols, which include practical (such as ease of writing and reuse of previously used symbols) as well as cognitive aspects (such as indicating relations to other symbols or to their intended meanings).
期刊介绍:
Topics in Cognitive Science (topiCS) is an innovative new journal that covers all areas of cognitive science including cognitive modeling, cognitive neuroscience, cognitive anthropology, and cognitive science and philosophy. topiCS aims to provide a forum for: -New communities of researchers- New controversies in established areas- Debates and commentaries- Reflections and integration The publication features multiple scholarly papers dedicated to a single topic. Some of these topics will appear together in one issue, but others may appear across several issues or develop into a regular feature. Controversies or debates started in one issue may be followed up by commentaries in a later issue, etc. However, the format and origin of the topics will vary greatly.