{"title":"Poincare on Mathematics, Intuition and the Foundations of Science","authors":"Janet Folina","doi":"10.1086/psaprocbienmeetp.1994.2.192931","DOIUrl":null,"url":null,"abstract":"In his first philosophy book, Science and Hypothesis, Poincare provides a picture in which the different sciences are arranged in a hierarchy. Arithmetic is the most general of all the sciences because it is presupposed by all the others. Next comes mathematical magnitude, or the analysis of the continuum, which presupposes arithmetic; and so on. Poincare's basic view was that experiment in science depends on fixing other concepts first. More generally, certain concepts must be fixed before others: hence the hierarchy. This paper attempts to dissolve some potential problems regarding Poincare's hierarchy. One is an apparent epistemological circularity in the hierarchy. A more serious problem regarding the epistemology of analysis is also addressed.","PeriodicalId":288090,"journal":{"name":"PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association","volume":"262 1-2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1994-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1086/psaprocbienmeetp.1994.2.192931","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
In his first philosophy book, Science and Hypothesis, Poincare provides a picture in which the different sciences are arranged in a hierarchy. Arithmetic is the most general of all the sciences because it is presupposed by all the others. Next comes mathematical magnitude, or the analysis of the continuum, which presupposes arithmetic; and so on. Poincare's basic view was that experiment in science depends on fixing other concepts first. More generally, certain concepts must be fixed before others: hence the hierarchy. This paper attempts to dissolve some potential problems regarding Poincare's hierarchy. One is an apparent epistemological circularity in the hierarchy. A more serious problem regarding the epistemology of analysis is also addressed.
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