158 Dear
had no ideas on such questions, but simply that he could not prove them
conclusively using mathematical- experimental means. He was careful,
too, not to rule out the possibility of such causal discoveries in the future,
of a sort broadly resembling Beeckman’s original corpuscular “physico-
mathematics”; the methodological caution of Newton’s “experimental
philosophy” was not rooted in skeptical principles.
In his introductory “Ode” to the Principia, Edmond Halley described
the work as a “mathematico- physical treatise.”^29 An earlier expression
that one of the founders of the Royal Society, John Wilkins, once used to
describe the charge of the nascent Society was “Physico- Mathematicall-
Experimentall Learning.”^30 Wilkins’s combination of such apparently
disparate categories in that elaborate label captures well the relationship
between “physico- mathematics” and “experimental philosophy” subse-
quently sought by Isaac Newton.MATHEMATICS, MECHANICAL CAUSES, AND NATURAL PHILOSOPHY
As John Heilbron observes in his contribution to this volume, the label
of physico- mathematics, like that of mixed mathematics, continued to
be used throughout the eighteenth century. This continuation seems to
have merged with the specifi cally Newtonian sense of the term as the
century progressed, but never displaced, or even truly rivaled, “mixed
mathematics” as the more commonly used expression. D’Alembert’s use
of “mixed mathematics” in his taxonomy of the sciences in the Ency-
clopédie certainly chimed with his admiration for Francis Bacon and the
latter’s own inventory in the Advancement of Learning, but, as we have
seen, it had long since become usual and uncontroversial. As d’Alembert
himself remarked, “Some divisions, such as those of mathematics into
pure and mixed mathematics, that we have in common with Bacon, are
found everywhere, and consequently belong to everyone.”^31 The relation-
ship between mixed mathematics and natural philosophy that the term
“physico- mathematics” could be used to assert remained ambiguous
nonetheless; it all turned on the crucial traditional claims of “physics”
to identify causes. Were physical causes as understood in the later seven-
teenth or eighteenth centuries in any sense continuous with the older,
Aristotelian sorts of causes that had underpinned the old demarcation of
mathematics from physics? Or did “causal” explanation now mean some-
thing fundamentally different?
Newton’s own pronouncements on this matter are important not just
because they relate to his own scientifi c work but also because of the in-