Archive for History of Exact Sciences最新文献_第10页

On Peirce’s 1878 article ‘The probability of induction’: a conceptualistic appraisal 论皮尔斯1878年的文章《归纳的可能性》：一种概念性的评价

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-07-28 DOI: 10.1007/s00407-020-00256-x

G. A. Kyriazis

{"title":"On Peirce’s 1878 article ‘The probability of induction’: a conceptualistic appraisal","authors":"G. A. Kyriazis","doi":"10.1007/s00407-020-00256-x","DOIUrl":"10.1007/s00407-020-00256-x","url":null,"abstract":"<div><p>Charles Sanders Peirce wrote the article ‘The probability of induction’ in 1878. It was the fourth article of the series ‘Illustrations of the Logic of Science’ which comprised a total of six articles. According to Peirce, to get a clear idea of the conception of probability, one has ‘to consider what real and sensible difference there is between one degree of probability and another.’ He endorsed what John Venn had called the ‘materialistic view’ of the subject, namely that probability is the proportion of times in which an occurrence of one kind is accompanied by an occurrence of another kind. On the other hand, Peirce recognized the existence of a different interpretation of probability, which was termed by Venn the ‘conceptualistic view,’ namely the degree of belief that ought to be attached to a proposition. Peirce’s intent on writing this article seems to be to inquire about the claims of the conceptualists concerning the problem of induction. After reasoning on some examples, he concluded on the impossibility of assigning probability for induction. We show here that the arguments advanced in his article are not sufficient to support such conclusion. Peirce’s thoughts on the probability of induction surely may have influenced statisticians and research scientists of the twentieth century in shaping data analysis.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 1","pages":"1 - 20"},"PeriodicalIF":0.5,"publicationDate":"2020-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00256-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50521218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Peirce’s 1878 article ‘The probability of induction’: a conceptualistic appraisal 论皮尔斯1878年的文章《归纳法的概率》:一个概念主义的评价

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-07-28 DOI: 10.1007/s00407-020-00256-x

G. Kyriazis

引用次数: 0

Pascal’s mystic hexagram, and a conjectural restoration of his lost treatise on conic sections 帕斯卡神秘的六进制，以及他遗失的圆锥曲线论文的推测性恢复

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-07-08 DOI: 10.1007/s00407-020-00251-2

Andrea Del Centina

引用次数: 8

Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics Petrović和Fine的多边形、代数常微分方程和当代数学

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-06-29 DOI: 10.1007/s00407-020-00250-3

Vladimir Dragović, Irina Goryuchkina

引用次数: 3

Mathématiques et architecture: le tracé de l’entasis par Nicolas-François Blondel 数学与建筑：Nicolas François Blondel的图

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-04-23 DOI: 10.1007/s00407-020-00248-x

Dominique Raynaud

{"title":"Mathématiques et architecture: le tracé de l’entasis par Nicolas-François Blondel","authors":"Dominique Raynaud","doi":"10.1007/s00407-020-00248-x","DOIUrl":"10.1007/s00407-020-00248-x","url":null,"abstract":"<div><p>In <i>Résolution des quatre principaux problèmes d’architecture</i> (1673) then in <i>Cours d’architecture</i> (1683), the architect–mathematician Nicolas-François Blondel addresses one of the most famous architectural problems of all times, that of the reduction in columns (<i>entasis</i>). The interest of the text lies in the variety of subjects that are linked to this issue. (1) The text is a response to the challenge launched by Curabelle in 1664 under the name <i>Étrenne à tous les architectes</i>; (2) Blondel mathematicizes the problem in the “style of the Ancients”; (3) The problem is reformulated and solved through the continuous drawing of the curve; (4) Blondel refutes the uniqueness of the curve by enumerating a variety of solutions (conchoid, spiral, parabola, ellipse, circle, hyperbola). This exuberance responds to an intention that does not coincide with the state of the art of mathematics at the end of the seventeenth century, nor with the taste for geometry of the Ancients, nor with any pedagogical project. This feature is explained by Blondel’s plan to found architecture on scientific bases. The reasons for his failure are analysed.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"74 5","pages":"445 - 468"},"PeriodicalIF":0.5,"publicationDate":"2020-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00248-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41707604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Leibniz’s syncategorematic infinitesimals II: their existence, their use and their role in the justification of the differential calculus 莱布尼茨的合范畴无穷小Ⅱ：它们的存在、使用及其在微分学论证中的作用

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-04-06 DOI: 10.1007/s00407-020-00249-w

David Rabouin, Richard T. W. Arthur

{"title":"Leibniz’s syncategorematic infinitesimals II: their existence, their use and their role in the justification of the differential calculus","authors":"David Rabouin, Richard T. W. Arthur","doi":"10.1007/s00407-020-00249-w","DOIUrl":"10.1007/s00407-020-00249-w","url":null,"abstract":"<div><p>In this paper, we endeavour to give a historically accurate presentation of how Leibniz understood his infinitesimals, and how he justified their use. Some authors claim that when Leibniz called them “fictions” in response to the criticisms of the calculus by Rolle and others at the turn of the century, he had in mind a different meaning of “fiction” than in his earlier work, involving a commitment to their existence as non-Archimedean elements of the continuum. Against this, we show that by 1676 Leibniz had already developed an interpretation from which he never wavered, according to which infinitesimals, like infinite wholes, cannot be regarded as existing because their concepts entail contradictions, even though they may be used as if they exist under certain specified conditions—a conception he later characterized as “syncategorematic”. Thus, one cannot infer the <i>existence</i> of infinitesimals from their successful <i>use</i>. By a detailed analysis of Leibniz’s arguments in his <i>De quadratura</i> of 1675–1676, we show that Leibniz had already presented there two strategies for presenting infinitesimalist methods, one in which one uses finite quantities that can be made as small as necessary in order for the error to be smaller than can be assigned, and thus zero; and another “direct” method in which the infinite and infinitely small are introduced by a fiction analogous to imaginary roots in algebra, and to points at infinity in projective geometry. We then show how in his mature papers the latter strategy, now articulated as based on the Law of Continuity, is presented to critics of the calculus as being equally constitutive for the foundations of algebra and geometry and also as being provably rigorous according to the accepted standards in keeping with the Archimedean axiom.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"74 5","pages":"401 - 443"},"PeriodicalIF":0.5,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00249-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45467689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 11

Poincaré’s stated motivations for topology Poincaré关于拓扑的既定动机

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-03-04 DOI: 10.1007/s00407-020-00247-y

Lizhen Ji, Chang Wang

引用次数: 1

Borelli’s edition of books V–VII of Apollonius’s Conics, and Lemma 12 in Newton’s Principia 波雷利版本的阿波罗尼乌斯的《圆锥定理》的第v - 7卷，以及牛顿的《原理》的引理12

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-01-10 DOI: 10.1007/s00407-019-00244-w

Andrea Del Centina, Alessandra Fiocca

引用次数: 2

On Qin Jiushao’s writing system 论秦九韶的写作体系

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-01-04 DOI: 10.1007/s00407-019-00243-x

Zhu Yiwen

引用次数: 3

A proto-Normal Star Almanac dating to the reign of Artaxerxes III: BM 65156 阿尔塔薛西斯三世统治时期的原始恒星年鉴：BM 65156

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-01-02 DOI: 10.1007/s00407-019-00246-8

John Steele

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引用次数: 0