{"title":"\"什么线不能用尺子量？数学与美学中的谜语与概念形成","authors":"Samuel Wheeler, William Brenner","doi":"10.15845/nwr.v13.3691","DOIUrl":null,"url":null,"abstract":"We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is to bring out and elucidate the essentially riddle-like character of these problems.","PeriodicalId":31828,"journal":{"name":"Nordic Wittgenstein Review","volume":"68 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"“What Line Can’t Be Measured With a Ruler?”: Riddles and Concept-Formation in Mathematics and Aesthetics\",\"authors\":\"Samuel Wheeler, William Brenner\",\"doi\":\"10.15845/nwr.v13.3691\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is to bring out and elucidate the essentially riddle-like character of these problems.\",\"PeriodicalId\":31828,\"journal\":{\"name\":\"Nordic Wittgenstein Review\",\"volume\":\"68 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nordic Wittgenstein Review\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15845/nwr.v13.3691\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nordic Wittgenstein Review","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15845/nwr.v13.3691","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Arts and Humanities","Score":null,"Total":0}
“What Line Can’t Be Measured With a Ruler?”: Riddles and Concept-Formation in Mathematics and Aesthetics
We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is to bring out and elucidate the essentially riddle-like character of these problems.
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