{"title":"有数学铰链吗?","authors":"A. Coliva","doi":"10.1163/22105700-bja10013","DOIUrl":null,"url":null,"abstract":"\nIn this paper I argue that, contrary to what several prominent scholars of On Certainty have claimed, Wittgenstein did not maintain that simple mathematical propositions like “2 × 2 = 4” or “12 × 12 = 144,” much like G. E. Moore’s truisms, could be examples of hinge propositions. In particular, given his overall conception of mathematics, it was impossible for him to single out these simpler mathematical propositions from the rest of mathematical statements, to reserve only to them a normative function. I then maintain that these mathematical examples were introduced merely as objects of comparison to bring out some peculiar features of the only hinges he countenanced in On Certainty, which were all outside the realm of mathematics. I then close by gesturing at how the distinction between mathematical hinges and non-hinges could be exemplified and by exploring its consequences with respect to (Wittgenstein’s) philosophy of mathematics.","PeriodicalId":41464,"journal":{"name":"International Journal for the Study of Skepticism","volume":"10 1","pages":"346-366"},"PeriodicalIF":0.1000,"publicationDate":"2020-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Are There Mathematical Hinges?\",\"authors\":\"A. Coliva\",\"doi\":\"10.1163/22105700-bja10013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\nIn this paper I argue that, contrary to what several prominent scholars of On Certainty have claimed, Wittgenstein did not maintain that simple mathematical propositions like “2 × 2 = 4” or “12 × 12 = 144,” much like G. E. Moore’s truisms, could be examples of hinge propositions. In particular, given his overall conception of mathematics, it was impossible for him to single out these simpler mathematical propositions from the rest of mathematical statements, to reserve only to them a normative function. I then maintain that these mathematical examples were introduced merely as objects of comparison to bring out some peculiar features of the only hinges he countenanced in On Certainty, which were all outside the realm of mathematics. I then close by gesturing at how the distinction between mathematical hinges and non-hinges could be exemplified and by exploring its consequences with respect to (Wittgenstein’s) philosophy of mathematics.\",\"PeriodicalId\":41464,\"journal\":{\"name\":\"International Journal for the Study of Skepticism\",\"volume\":\"10 1\",\"pages\":\"346-366\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2020-11-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal for the Study of Skepticism\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1163/22105700-bja10013\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"0\",\"JCRName\":\"PHILOSOPHY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for the Study of Skepticism","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1163/22105700-bja10013","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"0","JCRName":"PHILOSOPHY","Score":null,"Total":0}
In this paper I argue that, contrary to what several prominent scholars of On Certainty have claimed, Wittgenstein did not maintain that simple mathematical propositions like “2 × 2 = 4” or “12 × 12 = 144,” much like G. E. Moore’s truisms, could be examples of hinge propositions. In particular, given his overall conception of mathematics, it was impossible for him to single out these simpler mathematical propositions from the rest of mathematical statements, to reserve only to them a normative function. I then maintain that these mathematical examples were introduced merely as objects of comparison to bring out some peculiar features of the only hinges he countenanced in On Certainty, which were all outside the realm of mathematics. I then close by gesturing at how the distinction between mathematical hinges and non-hinges could be exemplified and by exploring its consequences with respect to (Wittgenstein’s) philosophy of mathematics.
期刊介绍:
As the first international journal entirely devoted to philosophical skepticism, the International Journal for the Study of Skepticism publishes high-quality articles and discussion notes on any field of research relevant to the study of skeptical thought. The journal also contains critical notices and reviews of major books on skepticism, and organizes book symposia on recent ground-breaking works. On occasion, it publishes special issues devoted to current lively debates on specific topics or authors. The wide range of areas covered includes the history and significance of ancient, medieval, modern, and contemporary skepticism as well as discussions of current specific skeptical problems and arguments in epistemology, metaethics, ontology, philosophy of religion, philosophy of mind, and philosophy of language.