Article ID: CBB808807913

Hobbes’s model of refraction and derivation of the sine law (2021)


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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Authors & Contributors
Goulding, Robert
Dijksterhuis, Fokko Jan
Malet, Antoni
Alexandrescu, Vlad
Alvarez Jimenez, Carlos
Baldin, Gregorio
Studies in History and Philosophy of Science
Annals of Science: The History of Science and Technology
Archive for History of Exact Sciences
British Journal for the History of Philosophy
Foundations of Science
Fabrizio Serra Editore
Hackett Publishing Company
Motion (physical)
Philosophy of science
Descartes, René
Hobbes, Thomas
Harriot, Thomas
Galilei, Galileo
Newton, Isaac
Fermat, Pierre de
Time Periods
17th century
16th century
19th century
Early modern
Great Britain

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