Article ID: CBB808807913

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

unapi

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
Malet, Antoni
Dijksterhuis, Fokko Jan
Descartes, René
Olscamp, Paul J.
Schmaltz, Tad M.
Journals
Studies in History and Philosophy of Science
Historia Scientiarum: International Journal of the History of Science Society of Japan
Foundations of Science
Synthese
Monist: An International Quarterly Journal of General Philosophical Inquiry
Nuncius: Annali di Storia della Scienza
Publishers
Hackett Publishing Company
Springer
Fabrizio Serra Editore
Concepts
Physics
Optics
Mathematics
Motion (physical)
Refraction
Philosophy of science
People
Descartes, René
Hobbes, Thomas
Harriot, Thomas
Fermat, Pierre de
Galilei, Galileo
Newton, Isaac
Time Periods
17th century
16th century
Early modern
19th century
Renaissance
Places
Germany
England
France
Wales
Great Britain
Europe
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