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Huygens’s Criticism of Descartes’ La Dioptrique

In order to understand Spinoza’s dissatisfaction with and objection to Descartes’ La Dioptrique  (found in letters 39 and 40 linked below), one has to understand the opinions of those contemporary to Spinoza. Below I post a selection from Fokko Jan Dijksterhuis comprehensive book on Christian Huygens, who is well-noted for having been Spinoza’s neighbor in Voorburg.  

La Dioptrique was written, Descartes said in the opening discourse, for the benefit of craftsmen who would have to grind and apply his elliptic and hyperbolic lenses. Therefore the mathematical content was kept to a minimum. Apparently this implied that Descartes need not elaborate a theory of the dioptrical properties of lenses. Descartes adopted the term Kepler had coined for the mathematical study of lenses. He had not, however, adopted the spirit of Kepler’s study. Dioptrice and La Dioptrique approached the telescope from opposite directions. Kepler had discussed actual telescopes and drudged on properties of lenses that did not fit mathematics so neatly. Descartes prescribed what the telescope should be according to mathematical theory. The telescope, having been invented and thus far cultivated by experience and fortune, could not reach a state of perfection by explaining its difficulties. Huygens was harsh in his judgement of La Dioptrique. In 1693, he wrote:

“Monsieur Descartes did not know what would be the effect of his hyperbolic telescopes, and assumed incomparably more about it than he should have. He did not understand sufficiently the theory of dioptrics, as his poor build-up demonstration of the telescope reveals” (OC10 402-403)

We can say that Descartes, according the Huygens, had failed to develop a theory of the telescope. He had ignored the questions that really mattered according the Huygens: an exact theory of the dioptrical properties of lenses and their configurations. La Dioptrique glanced over the telescope that existed only in ideal world of mathematics (37).

Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century, Fokko Jan Dijksterhuis

Here we get a sense of Spinoza’s complaint that Descartes may have avoided certain questions due to mathematical complexity, and that Descartes is not dealing with actual telescopes. It is significant to follow that indeed the analogical form of arguments in the La Dioptrique was designed to be in favor of the craftsmen and artisans who were meant to grind Descartes’ miraculous hyperbolic lens, while in life (and theory), it was the great tension with this human and technical reality that that produced the Cartesian telescope failure.

A line by line interpretation of Spinoza’s Optical letters: Deciphering Spinoza’s Optical Letters

Jerry Rothman’s website dedicated to Kepler’s Dioptrice: here



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