Conceptualism and contextualism in the recent historiography of Newton's \textit{Principia}.
type: Item
instance of: scholarly article
title: Conceptualism and contextualism in the recent historiography of Newton's \textit{Principia}.
zbMATH Open document ID: 1053.01010
DOI: 10.1016/S0315-0860(03)00051-X
published in: Historia Mathematica
publication date: 2004-02-03T00:00:00Z
review text: Observing that recently the \textit{Principia} has been the object of renewed interest among mathematicians and physicists, and referring to a lot of such publications, the author notices that several interesting and fruitful questions have emerged concerning Newton's mathematization of motion. The philosophical views on the nature of mathematics orient historical research along different lines, which are called by the author \textit{conceptualism} and \textit{contextualism}. The former can lead to cumulative, linear history, and the latter to a history where ramifications and perhaps even revolutionary changes are possible. The author would like to advocate an approach to the study of the mathematical methods of Newton's \textit{Principia} in which both these aspects are taken into consideration. Newton was a thinker who did not draw a clear-cut distinction between natural philosophy, theology, mathematics, and alchemy. In the publication policy he followed the dualism between public and private, mostly in theology, alchemy, and optics, but also in the case of mathematics. His mathematical discoveries in the late 1660s and early 1670s were printed decades later, especially those concerning infinite series and the calculus, which were rendered available to the mathematical community through letters and manuscript circulation. He found it convenient to avoid print publication of his fluxional method that appeared to him not well-founded from a logical point of view and distant from the rigor attained by the ancient geometrical synthesis. In the case of \textit{Principia} Newton affirmed to have made use of the modern analysis as a heuristic tool and to have retranslated a pristine analytical text into geometrical form in order to conform his work to the style of the ancient geometers. He viewed himself as a heir of an ancient mathematical tradition. The interrelation between a mechanically based geometry and natural motion allows Newton to defend the superiority of h…
Mathematics Subject Classification ID: 01A45
Mathematics Subject Classification ID: 01A50
zbMATH DE Number: 2037200
zbMATH Keywords: Newton
zbMATH Keywords: historiography of mathematics
zbMATH Keywords: Principia
zbMATH Keywords: fluxional method
author: Niccolò Guicciardini
reviewed by: Ülo Lumiste
MaRDI profile type: Publication
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full work available at URL: s0315-0860(03)00051-x
OpenAlex ID: W2010786829
description: scientific article; zbMATH DE number 2037200