Lenses and Waves

132 CHAPTER 4
in terms of analogies and explicitly said these did not reflect the true nature
of light. Restricting in this way his account to the behavior of rays, he
methodologically tied in with tradition. Still, mechanistic thinking was at the
heart of La Dioptrique. Assuming a proportionality between density and
motion is almost unthinkable outside a corpuscular framework. Indeed, at
the close of the second discourse Descartes showed his hand. The
comparisons had a much higher content of realism than suggested by his
circumspect introduction of them.
“For finally I dare to say that the three comparisons which I have just used are so
correct, that all the particularities that that can be noted in them correspond to certain
others which are found to be very similar in light; …” 86
If the mechanisms Descartes employed in the analogies and to which he
ascribed a fair degree of realism do little to persuade our post-Galilean
minds, one ought to remember that they were modeled on an understanding
of motion that was rooted in a hydrostatics of pressures rather than a
kinematics of velocities. Probably this was also one of the reasons the
analogies did not convince his seventeenth-century readers either. 87
Descartes’ intricate employment of mechanical analogies brings us to the
third level of inference in his account of refraction, where the physical nature
is involved in the analysis. Although he did not elaborate his theory of light
and circumspectly presented the mechanics of deflected motion as analogy,
Descartes’ line of reasoning strongly suggests that the laws of optics to be
derived from his mechanistic understanding of light. In Sabra’s words: “As
repeatedly asserted by Descartes, the ‘suppositions’ at the beginning of the
Dioptric belong to this [domain of a priori truth]”. 88 This is substantiated by
the fact that Descartes deviated from perspectivist tradition in a second
important respect as well. In La Dioptrique he did not explicitly call for an
empirical foundation of the sine law. In this way, Descartes’ derivation of the
sine law was intended as a derivation from the true nature of light.
Historian’s assessment of Descartes’ optics
The question whether or not Descartes actually succeeded in deriving the
sine law from his mechanistic theory of light has been a matter of incessant
debate among historians of science. Although few seventeenth-century
students of optics were convinced by Descartes argument, I think it
appropriate to digress somewhat to contemporary evaluations because these
are illuminating as regard the exact purport of his account.
Many have argued that Descartes’ claim, that a tendency to move is
subject to the same laws as motion itself, was mere rhetoric. Schuster, on the
other hand, argues that Descartes’ theory of light did provide the basis of the
86 “Car enfin j’ose dire que les trois comparaisons, dont je viens de me servir, sont si propres, que toutes
les particularités que s’y peuvent remarquer, se raportent a quelques autres qui se trouvent toutes
semblables en la lumiere; …” AT6, 104.
87 Except Clerselier who expressly defended Descartes’ mechanistic models; Sabra, Theories, 116-135.
88 Sabra, Theories, 44.