Pub Date : 2024-01-01Epub Date: 2023-07-03DOI: 10.1007/s11098-023-01968-w
Salim Hirèche
Grounding necessitarianism (GN) is the view that full grounds necessitate what they ground. Although GN has been rather popular among philosophers, it faces important counterexamples: For instance, A = [Socrates died] fully grounds C = [Xanthippe became a widow]. However, A fails to necessitate C: A could have obtained together with B = [Socrates and Xanthippe were never married], without C obtaining. In many cases, the debate essentially reduces to whether A indeed fully grounds C-as the contingentist claims-or if instead C is fully grounded in A+, namely A plus some supplementary fact S (e.g. [Xanthippe was married to Socrates])-as the necessitarian claims. Both sides typically agree that A+ necessitates C, while A does not; they disagree on whether A or A+ fully grounds C. This paper offers a novel defence of the claim that, in these typical cases, unlike A+, A fails to fully ground C-thereby bringing further support to GN. First and foremost, unlike A+, A fails to fully ground C because it fails to contain just what is relevant to do so, in two distinct senses-explanatory and generative relevance. Second, going for A, rather than A+, as a full ground undermines not just grounding necessitarianism, but modally weaker views which even contingentists may want to preserve.
基础必然论（GN）认为，充分的基础必然是它们所基础的东西。尽管 GN 在哲学家中颇受欢迎，但它也面临着重要的反例：例如，A = [苏格拉底死了] 完全成立 C = [桑西佩成了寡妇]。然而，A并不必然导致C：A本可以与B = [苏格拉底和桑西佩从未结婚]一起得到，而不会导致C。在许多情况下，争论实质上归结为 A 是否真的完全基于 C--如偶然论者所言--或者 C 是否完全基于 A+，即 A 加上一些补充事实 S（如[赞西佩嫁给了苏格拉底]）--如必然论者所言。双方通常都同意 A+ 是 C 的必要条件，而 A 却不是；他们在 A 或 A+ 是否完全基于 C 的问题上存在分歧。本文为这一主张提供了新颖的辩护，即在这些典型案例中，与 A+ 不同，A 未能完全基于 C--从而为 GN 带来了进一步的支持。首先，与 A+ 不同的是，A 未能充分支持 C，因为它未能包含与充分支持 C 相关的内容，这体现在两个不同的意义上--解释性相关和生成性相关。其次，选择 A 而非 A+ 作为充分根据不仅破坏了根据必要性论，而且破坏了模态上较弱的观点，而这些观点即使是或然论者也可能想要保留。
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Pub Date : 2023-11-01DOI: 10.1016/j.hm.2023.08.001
J. Marshall Unger
Late 18th and early 19th century Japanese mathematicians (wasanka) found solutions of two problems concerning the incircles of the quarter-triangles and skewed sectors of cyclic quadrilaterals. There is a modern proof of the first solution, but it makes extensive use of trigonometry and is therefore unlikely to be what a wasanka would have written. As for the second solution, Aida Yasuaki (1747–1817) gave two proofs for it, the second of which has been summarized in Japanese, but not the first. All three proofs are presented here together with commentary on their mathematical and historical significance.
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Pub Date : 2023-11-01DOI: 10.1016/j.hm.2023.09.002
Viktor Blåsjö
Newton was critical of Descartes's constructivist vision of the foundations of geometry organised around certain curve-tracing principles. In unpublished work, Newton outlined a constructivist program of his own, based on his “organic” method of curve tracing, which subsumes Descartes's emblematic turning-ruler-and-moving-curve construction method as a special case, but does not suffer from the latter's flaw of being unable to trace all conics. This Newtonian program has been little studied and is more thoughtful and technically substantive than is commonly recognised. It also clashes with, and arguably supersedes and improves upon, Newton's perhaps better known earlier statements on the subject.
{"title":"Newton on constructions in geometry","authors":"Viktor Blåsjö","doi":"10.1016/j.hm.2023.09.002","DOIUrl":"10.1016/j.hm.2023.09.002","url":null,"abstract":"<div><p>Newton was critical of Descartes's constructivist vision of the foundations of geometry organised around certain curve-tracing principles. In unpublished work, Newton outlined a constructivist program of his own, based on his “organic” method of curve tracing, which subsumes Descartes's emblematic turning-ruler-and-moving-curve construction method as a special case, but does not suffer from the latter's flaw of being unable to trace all conics. This Newtonian program has been little studied and is more thoughtful and technically substantive than is commonly recognised. It also clashes with, and arguably supersedes and improves upon, Newton's perhaps better known earlier statements on the subject.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"65 ","pages":"Pages 14-29"},"PeriodicalIF":0.5,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086023000666/pdfft?md5=cfffb05a2f2f6ca7ed57de11fa0b2c09&pid=1-s2.0-S0315086023000666-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135614706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.1016/j.hm.2023.07.002
Alessandro Belcastro, Giuseppina Fenaroli
We discuss the probabilistic question faced by the Italian scholar Giovanni Rizzetti (1675–1751) and suggest this is a variant of what we refer to today as the “ballot sequences”, variant to which Catalan numbers offer a solution.
Rizzetti's search for a solution led him to produce an iterative rule which involved the consideration of Catalan numbers. Although coming up with these were not his final goal, the rule he elaborated allowed him to carry on calculating them as long as he wanted. As such, it is possible this was the first time such numbers were determined.
{"title":"A determination of Catalan numbers in 18th century Italy by Giovanni Rizzetti (1675–1751)","authors":"Alessandro Belcastro, Giuseppina Fenaroli","doi":"10.1016/j.hm.2023.07.002","DOIUrl":"https://doi.org/10.1016/j.hm.2023.07.002","url":null,"abstract":"<div><p>We discuss the probabilistic question faced by the Italian scholar Giovanni Rizzetti (1675–1751) and suggest this is a variant of what we refer to today as the “<em>ballot sequences</em>”, variant to which Catalan numbers offer a solution.</p><p>Rizzetti's search for a solution led him to produce an iterative rule which involved the consideration of Catalan numbers. Although coming up with these were not his final goal, the rule he elaborated allowed him to carry on calculating them as long as he wanted. As such, it is possible this was the first time such numbers were determined.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"64 ","pages":"Pages 34-47"},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50190797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.1016/j.hm.2023.06.001
Dominique Raynaud
This article aims at identifying the sources of fols. 395r and 686r-686v of the Codex Atlanticus. These anonymous folios, inserted in Leonardo da Vinci's notebooks, do not deal with the duplication of the cube proper, nor do they derive from Giorgio Valla's De expetendis et fugiendis rebus (1501), as has been claimed. They deal specifically with the extraction of the cube root by geometric methods. The analysis of the sources by the tracer method reveals that these fragments are taken from the Practica geometrie by Leonardo Fibonacci (1220) and, more precisely, from a volgarizzamento that appears in the Praticha d'arismetrica by Benedetto da Firenze (1463). Leonardo could have consulted this text in one of his two Florentine periods, around 1463-1482 or around 1503-1506.
本文旨在确定fols的来源。395r和686r-686v。这些匿名的对开本插入了达的笔记本中，并没有处理立方体本身的复制，也没有像人们所说的那样源自乔治·瓦拉的《De expetendis et fugiendis rebus》（1501）。它们专门处理通过几何方法提取立方根的问题。通过示踪法对来源的分析表明，这些碎片取自莱昂纳多·斐波那契（1220）的《几何实践》，更准确地说，取自贝内代托·达·弗伦泽（1463）的《阿里斯特里卡实践》中出现的一个volgarizzamento。莱昂纳多可能在他的两个佛罗伦萨时期中的一个时期，即1463-1482年左右或1503-1506年左右查阅了这篇文章。
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Pub Date : 2023-08-01DOI: 10.1016/j.hm.2023.06.002
Michael Wiescher
This paper evaluates possible reasons and motivations for 19th century geometer Julius Plücker's change in direction from his purely mathematical work to experimental physics. The author argues that this change did not happen suddenly in 1846 as is frequently suggested but rather, was a gradual change. This move took more than a decade and was triggered by Plücker's idea to apply his mathematical formalism to physical objects and phenomena, such as crystals and the trajectories of light in crystalline materials, a move which eventually led him to the newly discovered phenomena of diamagnetism.
{"title":"Julius Plücker – A path from geometry to optics","authors":"Michael Wiescher","doi":"10.1016/j.hm.2023.06.002","DOIUrl":"10.1016/j.hm.2023.06.002","url":null,"abstract":"<div><p>This paper evaluates possible reasons and motivations for 19<sup>th</sup><span> century geometer Julius Plücker's change in direction from his purely mathematical work to experimental physics. The author argues that this change did not happen suddenly in 1846 as is frequently suggested but rather, was a gradual change. This move took more than a decade and was triggered by Plücker's idea to apply his mathematical formalism to physical objects and phenomena, such as crystals and the trajectories of light in crystalline materials, a move which eventually led him to the newly discovered phenomena of diamagnetism.</span></p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"64 ","pages":"Pages 19-33"},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42901203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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