{"title":"On the relativity of magnitudes","authors":"Jonathan Fay","doi":"10.1016/j.shpsa.2024.06.004","DOIUrl":null,"url":null,"abstract":"<div><p>Faced with the mathematical possibility of non-Euclidean geometries, 19th Century geometers were tasked with the problem of determining which among the possible geometries corresponds to that of our space. In this context, the contribution of the Belgian philosopher-mathematician, Joseph Delboeuf, has been unduly neglected. The aim of this essay is to situate Delboeuf’s ideas within the context of the philosophies of geometry of his contemporaries, such as Helmholtz, Russell and Poincaré. We elucidate the central thesis, according to which Euclidean geometry is given special status on the basis of the relativity of magnitudes, we uncover its hidden history and show that it is defensible within the context of the philosophies of geometry of the epoch. Through this discussion, we also develop various ideas that have some relevance to present-day methods in gravitational physics and cosmology.</p></div>","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":"106 ","pages":"Pages 165-176"},"PeriodicalIF":1.4000,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0039368124001031/pdfft?md5=67a8f2c2707efe4e07094c8900a5d3fa&pid=1-s2.0-S0039368124001031-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in History and Philosophy of Science","FirstCategoryId":"98","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0039368124001031","RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
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Abstract
Faced with the mathematical possibility of non-Euclidean geometries, 19th Century geometers were tasked with the problem of determining which among the possible geometries corresponds to that of our space. In this context, the contribution of the Belgian philosopher-mathematician, Joseph Delboeuf, has been unduly neglected. The aim of this essay is to situate Delboeuf’s ideas within the context of the philosophies of geometry of his contemporaries, such as Helmholtz, Russell and Poincaré. We elucidate the central thesis, according to which Euclidean geometry is given special status on the basis of the relativity of magnitudes, we uncover its hidden history and show that it is defensible within the context of the philosophies of geometry of the epoch. Through this discussion, we also develop various ideas that have some relevance to present-day methods in gravitational physics and cosmology.
期刊介绍：
Studies in History and Philosophy of Science is devoted to the integrated study of the history, philosophy and sociology of the sciences. The editors encourage contributions both in the long-established areas of the history of the sciences and the philosophy of the sciences and in the topical areas of historiography of the sciences, the sciences in relation to gender, culture and society and the sciences in relation to arts. The Journal is international in scope and content and publishes papers from a wide range of countries and cultural traditions.
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