Mixed Mathematics 159fl uential role they played thereafter. Besides eighteenth- century self- styled
followers of Newton, the nineteenth century too took notice of the great
man’s metaphysical and methodological assertions. In that later period,
for example, British physicists such as Faraday and Maxwell used New-
ton’s words to lend additional legitimacy to their own arguments, besides
the generally unquestioned admiration for Newton’s theoretical achieve-
ments among nineteenth- century physical scientists. Newton famously
received severe criticisms of his work in the Principia from the great math-
ematical philosophers Christiaan Huygens and Gottfried Wilhelm Leibniz,
as well as from lesser lights, and their objections were certainly not due
in those cases to a dislike of the mathematical sciences as philosophical
tools.^32 The difference between Newton and these critics was simply that
Newton explicitly eschewed in the Principia any claims to explain, in his
mathematical demonstrations, the cause, or true nature, of gravitational
attraction. He could demonstrate mathematically and experimentally the
properties and characteristics of gravitational behavior, but not, he ar-
gued, its causes; on those he could only speculate. Here is an important
point to note: Newton never claimed that natural philosophy was nothing
more than its mathematically demonstrable aspects. His book was entitled
Mathematical Principles of Natural Philosophy to signal that it dealt only
with the mathematical principles, not to suggest that natural philosophy’s
principles were exclusively mathematical. In his preface to the fi rst edi-
tion, Newton remarked that “since the moderns... have undertaken to
reduce the phenomena of nature to mathematical laws, it has seemed best
in this treatise to concentrate on mathematics as it relates to natural phi-
losophy.”^33 Demonstrability, always the trump card of the mathematical
sciences, was central to Newton’s accomplishments in his own eyes.
Among the responses directed at Newton’s critics after the appearance
of the Principia was a particularly pointed passage in Roger Cotes’s edito-
rial introduction to the second edition in 1713. The passage responds to
complaints by Huygens and others that, while Newton had demonstrated
that motions in the solar system could be accounted for on the supposi-
tion that they were brought about by an inverse- square force law quan-
titatively identifi able with gravitational attraction, he had not provided
an explanation of the underlying cause of that force. Because he had not
addressed the causes involved, Newton’s work was not, in Huygens’s view,
natural philosophy. Cotes replied:
But will gravity be called an occult cause and be cast out of natural phi-
losophy on the grounds that the cause of gravity itself is occult and not yet
found? Let those who so believe take care lest they believe in an absurdity