Lenses and Waves

262 CHAPTER 7
matters – or, more properly speaking, to Descartes’ dealings with
mathematics.
Descartes set Huygens’ agenda as he did for seventeenth-century science
in general, but in this case it was a mathematical agenda instead of a natural
philosophical one. He was no builder of a system of natural philosophy,
neither in the Cartesian sense, nor in the way Newton was. Leibniz criticized
him for failing to draw philosophical conclusions from his laws of impact.
“He had no taste for metaphysics”. 9 Huygens did not pursue questions raised
by Descartes’ natural philosophical program, he responded to his
contributions to the various branches of mathematics. He firmly criticized
these and even his whole approach. In Huygens’ view, Descartes had
corrupted mathematical science and he would do better.
The point I want to make here is that the historical significance of Traité
de la Lumière has blown up Huygens’ alleged Cartesianism and distorted our
view of the whole of his optics – and his science in general. Sabra offers an
example of the pitfall created by presuming Huygens to be pursuing
Cartesian science. He discusses the wave theory prior to the dispute on
colors with Newton, which is historically incorrect, thus making him more
mechanistic than he actually was at that time. 10 Huygens did not have some
kind of research program aimed at unraveling the mechanistic nature of
things, not even a program aimed at establishing the mathematical nature of
things.
The small Archimedes
For Huygens, applying mathematics to real things (large and small) went
without saying. He investigated the mathematical aspects of phenomena and
one suspects that he did not have explicit ideas about the ultimate
mathematical nature of nature like Galileo had. Huygens seems to have
lacked “…a personal conviction about access to deep secrets of nature.” 11 I
regard his revolutionary conception of the probable nature of explanatory
knowledge not as an outcome of some philosophical or epistemological
conviction, but rather as a reflection of the cumulative character of his
Archimedean mathematics. I do not think that the preface of Traité de la
Lumière reflects some scepticist attitude. Colors or polarization were simply
additional parameters not yet fathomed, but for Huygens this did not detract
from the validity of his wave theory.
Huygens has been called a problem solver, and this he was, marking
himself off by solving problems his contemporaries passed over. He was
perfectly happy with brilliantly solving sophisticated problems of
9
Heinekamp, “Huygens vu par Leibniz”, 106. Leibniz, Philosophische Schriften III, 611. “Il n’avoit point de
goust pour la Metaphysique.”
10
Sabra, Theories of Light: chapter VI “Huygens’ Cartesianism and his theory of conjectural explanation”,
chapter VIII “Huygens’ wave theory”, chapter X “Three critics of Newton’s theory: Hooke, Pardies,
Huygens”
11
Hall, “Summary”, 307.