"论通过非标准分析解读莱布尼茨无穷小的不可行性

IF 0.5 3区哲学 Q3 HISTORY & PHILOSOPHY OF SCIENCE

Historia Mathematica Pub Date : 2024-03-01 DOI:10.1016/j.hm.2023.12.001

Richard Arthur , David Rabouin

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引用次数: 0

摘要

非标准分析常常被认为是严格表达莱布尼茨无穷小概念的适当框架。本文打算从历史的角度来研究这一解释，并消除它所依据的一系列误解。为此，我们建议回到莱布尼茨关于量、数和大小的概念上来，而这一方法在文献中尚未得到发展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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“On the Unviability of Interpreting Leibniz's Infinitesimals through Non-standard analysis”

Non-standard analysis has often been presented as the proper framework for expressing rigorously Leibniz's conception of infinitesimals. This paper intends to study this interpretation from an historical point of view and to dispel a series of misunderstandings on which it rests. In order to do so, we propose to go back to Leibniz's conception of quantity, number and magnitude, an approach which has not been developed yet in the literature.

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来源期刊

Historia Mathematica 数学-科学史与科学哲学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

72 days

期刊介绍： Historia Mathematica publishes historical scholarship on mathematics and its development in all cultures and time periods. In particular, the journal encourages informed studies on mathematicians and their work in historical context, on the histories of institutions and organizations supportive of the mathematical endeavor, on historiographical topics in the history of mathematics, and on the interrelations between mathematical ideas, science, and the broader culture.