Lenses and Waves

136 CHAPTER 4
his own demonstration. Right after the publication of La Dioptrique he had
severely criticized Descartes’ derivation, and maintained his objections when
supporters of Descartes reopened the debate in 1657. 101 Employing the
principle of natural economy, previously used by Hero and Witelo for
reflection, Fermat deduced the law of sines in 1662, thus strengthening his
conviction that Descartes’ mechanistic line of reasoning had been false. To
know that the law was independent of Descartes’ mechanistic reasoning may
have facilitated its acceptance, although it may well be that the ostensible
non-acceptance was simply a matter of inactivity on the front of optics
during the 1640s and 1650s.
The reception of La Dioptrique makes clear that the treatise is hard to
situate in the development of seventeenth-century optics. It formed the
starting-point of most subsequent investigations in optics, and has therefore
been the focus of many historical studies. 102 La Dioptrique showed how the
properties of light could be discussed in corpuscular terms and its readers
got this message. Although few agreed with the details of Descartes’
derivation of the sine law, nor with his system of mechanistic philosophy in
full, he set the idiom for the all-prevailing thinking on light in corpuscular
terms. As a consequence, the traditional analogies between light and motion
implied a potential claim about the true nature of light and could not be used
as informally as before. Descartes had intended to found the laws of optics
in the mechanistic nature of light, but his derivation was not free from
ambiguities and obscurities. A mathematician like Barrow adopted the
corpuscular understanding of nature but not Descartes’ approach to
explanation. We now turn to him, to see how he dealt with questions
regarding the status of the corpuscular nature of light and how it ought to
explain the laws of optics.
Barrow’s causal account of refraction
Barrow was a mathematician with a clear awareness of the epistemological
intricacies of mathematics and its applications to nature. The lectures on
mathematics which he delivered at Cambridge between 1664 and 1666 dealt
at great length with the status of mathematical concepts and methods and
their relevance for the study of nature. 103 His subsequent lectures on optics
are likewise riddled with epistemic statements. Lectiones XVIII of 1669 is
illuminating with respect to Huygens’ ‘Projet’ as it assigns a similar role to
explanations of the causes of the laws of optics. The subject of the lectures
was ‘Optics’, one of the fields that are “… bright with the flowers of Physics
and sown with the harvest of Mechanics,…” 104 The core of this science
101
The debate is listed in Smith, Descartes’s theory of light and refraction, 81-82 and discussed in detail in Sabra,
Theories of Light, 116-135.
102
Sabra, Theories, 12.
103
Published in 1666 as Lectiones mathematicae XXIII. They were translated by John Kirkby and published in
1734 under the title The usefulness of mathematical learning etc. It is cited in Shapiro, Fits providing improved
translations.
104
Barrow, Lectiones, [10].