Mixed Mathematics 157seventeenth century. However, the “physical” claims made by the latter
necessarily also served to weaken, or alter, the strict causal “Aristotelian”
meaning of physics itself. And here another ambiguity arises: where the
older grounds for separating physics from mathematics had been that
mathematics did not participate in the causal explanatory mission of
physics, so by the late seventeenth century a reason for combining them
was now, not that mathematics really was causal after all (the argument
of early seventeenth- century Jesuit mathematicians, among others), but
that physics itself no longer needed to be strictly causal. In effect, this was
Newton’s mature position, as laid out in the Philosophiae naturalis principia
mathematica (Principia) of 1687 and its subsequent defenses, as well as in
his optical work.
The “mathematical principles of natural philosophy” rode roughshod
over Aristotelian metabasis; natural philosophy, physics, should not have
been able to rest on “mathematical” principles—this had been the very
predicament that had led Aristotle to invent subordinate sciences. But
Newton’s natural philosophy was not presented as any kind of subordi-
nate science. Indeed, the natural philosophy, whose mathematical prin-
ciples were presented in the Principia, was by no means the entirety of
Newton’s philosophy of nature. He considered much more widely qualita-
tive and matter- theoretical aspects of nature that did not fi gure (or fi gure
signifi cantly) in the Principia and yet that he took as seriously as the math-
ematical aspects. Some of these elements of his “speculative” philosophy
appeared later in the “Queries” appended to successive editions of his
Opticks from 1704 onwards, as well as in the General Scholium added to
the Principia’s second edition of 1713. But Newton represented the mode
of philosophizing found in the Principia itself, as well in the main text of
the Opticks, as the results of “experimental philosophy.”^28 Experimental
philosophy, an expression familiar in work by other early fellows of the
Royal Society besides Newton, especially Robert Boyle, implied in New-
ton’s hands also an intimate integration with mathematics. Thus, for ex-
ample, Newton calibrated and measured gravitational force in relation
to mechanical forces such as centrifugal force by conducting measuring
experiments with conical pendulums. He insisted that he could demon-
strate phenomena of nature, typically associated with forces of various
kinds, through conclusive experimental and observational means, but
that he could not—as yet—determine the causes of those phenomena.
Most famously, he explained that he was unable to demonstrate the cause
of gravitational attraction; he also proclaimed nescience in his optical
studies concerning the nature of light, similarly restricted to demonstra-
tions of properties and measurable phenomena. This did not mean that he