Routledge History of Philosophy Volume IV

DESCARTES: METHODOLOGY 165
commitment to a mathematical physics was an extremely potent one, and
Descartes was the first to offer such a combination to any significant extent.
This question must be seen in a broad context. The theoretical justification for
the use of mathematical theorems and techniques in the treatment of problems in
physical theory is not obvious. To many natural philosophers it was far from
clear that such an approach was necessary, justified, or even possible. Aristotle
had provided a highly elaborate conception of physical explanation which
absolutely precluded the use of mathematics in physical enquiry and it was this
conception that dominated physical enquiry until the seventeenth century.
Briefly, Aristotle defines physics and mathematics in terms of their subject
genera: physics is concerned with those things that change and have an
independent existence, mathematics with those things that do not change and
have dependent existence (i.e. they are mere abstractions). The aim of scientific
enquiry is to determine what kind of thing the subject matter of the science is by
establishing its general properties. To explain something is to demonstrate it
syllogistically starting from first principles which are expressions of essences,
and what one is seeking in a physical explanation is a statement of the essential
characteristics of a physical phenomenon—those characteristics which it must
possess if it is to be the kind of thing it is. Such a statement can only be derived
from principles that are appropriate to the subject genus of the science; in the
case of physics, this means principles appropriate to explaining what is changing
and has an independent existence. Mathematical principles are not of this kind.
They are appropriate to a completely different kind of subject matter, and
because of this mathematics is inappropriate to syllogistic demonstrations of
physical phenomena, and it is alien to physical explanation. This approach
benefited from a well-developed metaphysical account of the different natures of
physical and mathematical entities, and it resulted in a physical theory that was
not only in close agreement with observation and common sense, but which
formed part of a large-scale theory of change which covered organic and
inorganic phenomena alike.
By the beginning of the seventeenth century, the Aristotelian approach was
being challenged on a number of fronts, and Archimedean statics, in particular,
was seen by many as the model for a physical theory, with its rigorously
geometrical demonstrations of novel and fundamental physical theorems. But
there was no straightforward way of extending this approach in statics (where it
was often possible to translate the problem into mathematical terms in an
intuitive and unproblematic way), to kinematics (where one had to deal with
motion, i.e. continuous change of place) and in dynamics (where one had
somehow to quantify the forces responsible for changes in motion). Moreover,
statics involved a number of simplifying assumptions, such as the Earth’s surface
being a true geometrical plane and its being a parallel force field. These
simplifying assumptions generate all kinds of problems once one leaves the
domain of statics, and the kinds of conceptual problems faced by natural