霍布斯折射模型及正弦定律的推导

IF 0.7 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Hao Dong
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I argue that, first, Hobbes’s criticisms do expose certain shortcomings of Descartes’ optics which presupposes a twofold distinction between real motion and inclination to motion, and between motion itself and determination of motion; second, Hobbes’s optical theory presented in <i>Tractatus Opticus I</i> constitutes a more economical alternative, which eliminates the twofold distinction and only admits actual local motion, and Hobbes’s derivation of the sine law presented therein, which I call “the early model” and which was retained in <i>Tractatus Opticus II</i> and <i>First Draught</i>, is mathematically consistent and physically meaningful. These two points give Hobbes’s early optics some theoretical advantage over that of Descartes. However, an issue that has baffled commentators is that, in <i>De Corpore</i> Hobbes’s derivation of the sine law seems to be completely different from that presented in his earlier works, furthermore, it does not make any intuitive sense. 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引用次数: 2

摘要

本文旨在解决解读霍布斯对正弦折射定律推导的技术问题,并为霍布斯的机械哲学这一更广泛的问题提供一些启示。我首先要重述一下霍布斯和笛卡尔之间关于笛卡尔光学的争论。我认为,首先,霍布斯的批评确实暴露了笛卡尔光学的某些缺点,笛卡尔光学预设了真实运动和运动倾向之间以及运动本身和运动决定之间的双重区别;第二,Hobbes在Tractatus Opticus I中提出的光学理论构成了一个更经济的替代方案,它消除了双重区别,只允许实际的局部运动,以及Hobbes对其中提出的正弦定律的推导,我称之为“早期模型”,并保留在Tractatu Opticus II和First Draught中,在数学上是一致的,在物理上是有意义的。这两点使霍布斯早期的光学在理论上优于笛卡尔。然而,一个让评论家感到困惑的问题是,在德·科尔波雷的著作中,霍布斯对正弦定律的推导似乎与他早期作品中的推导完全不同,而且,它没有任何直观的意义。我认为,如果我们把De Corpore中正弦定律的推导理解为早期模型的简化,那么它在数学上确实是有意义的,而霍布斯在Tractatus Opticus I的最后一个命题中已经暗示了这一点,似乎是在乞求问题,却没有给出之前的所有结果?我的推测是,从早期模型到晚期模型的转变是霍布斯对物理学和数学关系的看法发生变化的症状。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Hobbes’s model of refraction and derivation of the sine law

Hobbes’s model of refraction and derivation of the sine law

This paper aims both to tackle the technical issue of deciphering Hobbes’s derivation of the sine law of refraction and to throw some light to the broader issue of Hobbes’s mechanical philosophy. I start by recapitulating the polemics between Hobbes and Descartes concerning Descartes’ optics. I argue that, first, Hobbes’s criticisms do expose certain shortcomings of Descartes’ optics which presupposes a twofold distinction between real motion and inclination to motion, and between motion itself and determination of motion; second, Hobbes’s optical theory presented in Tractatus Opticus I constitutes a more economical alternative, which eliminates the twofold distinction and only admits actual local motion, and Hobbes’s derivation of the sine law presented therein, which I call “the early model” and which was retained in Tractatus Opticus II and First Draught, is mathematically consistent and physically meaningful. These two points give Hobbes’s early optics some theoretical advantage over that of Descartes. However, an issue that has baffled commentators is that, in De Corpore Hobbes’s derivation of the sine law seems to be completely different from that presented in his earlier works, furthermore, it does not make any intuitive sense. I argue that the derivation of the sine law in De Corpore does make sense mathematically if we read it as a simplification of the early model, and Hobbes has already hinted toward it in the last proposition of Tractatus Opticus I. But now the question becomes, why does Hobbes take himself to be entitled to present this simplified, seemingly question-begging form without having presented all the previous results? My conjecture is that the switch from the early model to the late model is symptomatic of Hobbes’s changing views on the relation between physics and mathematics.

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来源期刊
Archive for History of Exact Sciences
Archive for History of Exact Sciences 管理科学-科学史与科学哲学
CiteScore
1.30
自引率
20.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.
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