Mixed Mathematics 161a central part of natural philosophy. Causes were not what they used to be.
Newton’s exploitation of what amounted to a failure of strict mechanism
in physics enabled the elevation of the phenomenological demonstra-
tions of mixed mathematics to a primary role in natural philosophy.^37
This was not always Newton’s position; his eschewal of causes in de-
fending his mathematical work was tactical as much as it was principled.
In his early optical work (1672), later presented in the Opticks as a similar
sort of mathematical- experimental demonstration to that of the Principia,
he tried to make inferences from conclusions about colors and white
light to the determination of the ontological nature of colors themselves:
“These things being so, it can be no longer disputed, whether there be
colours in the dark, nor whether they be the qualities of the objects we
see, no nor perhaps, whether Light be a Body. For since Colours are the
qualities of Light, having its Rays for their intire and immediate subject,
how can we think those Rays qualities also, unless one quality may be the
subject of and sustain another; which in effect is to call it Substance.”^38
Newton thus attempted to extend into the realm of natural philoso-
phy the inferences that could be drawn from work in optics, a branch
of mixed mathematics. His remarks were immediately and appropriately
understood to support a view of light as material, in contrast to the wave
theories of his optical critics Huygens and Robert Hooke. “I suppose,” he
wrote in a reply to Hooke, “the Science of Colours will be granted Math-
ematicall & as certain as any part of Optiques.”^39 The argument about the
substantiality of light was a signifi cant claim, therefore, in the context of
mechanical natural philosophy—even though Newton’s argument about
“qualities” and “substance” was couched in scholastic Aristotelian termi-
nology, and would perhaps not have been possible in a strictly mechani-
cal idiom.
Another, and much more consequential, of Newton’s attempts to in-
trude the procedures of mixed mathematics into natural philosophy con-
cerns his assault on Cartesian physics in Book II of the Principia. Again,
a mechanical idiom set the ground rules. Descartes had tried to explain
celestial motions in terms of vortices of subtle matter or ether that would
sweep planets and other objects around in their orbits. Like all matter for
Descartes, that comprising the vortices admitted of no void space: spa-
tial extension and matter were identical. Newton made it his business to
demonstrate the nonexistence of this ether by showing that it exerted no
resistance to bodies supposedly moving through it, and thereby to dem-
onstrate the existence of the vacuum. He did this through mathemati-
cal arguments about resistance to motion through a medium that were
in large part predicated on precise experimental work with pendulums.^40