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| Program > Themes in the Philosophy of Science |
| Programme > Thèmes en philosophie des sciences |
| Zvi
Biener
& Chris Smeenk (University
of Pittsburgh) Is Gravity at the Heart of the Matter? Mathematics and Philosophy in the Newton-Cotes Correspondence |
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At
the heart of Newton’s achievement in the Principia lies an
innovative conception of matter and matter’s relation to
gravitation. Modern readers are tempted to see this conception as the
familiar idea of mass. In fact, Newton uses “quantity of matter”
throughout the Principia as a measure of a body's response to
impressed forces. However, this dynamical conception of matter
exists alongside a geometrical
conception that is often ignored due to its apparently less important
role in the Principia itself and its neglect by subsequent
developers of Newtonian theory. On this conception, introduced in De
Gravitatione, the quantity of matter is to be measured by the amount
of space filled by a body. We argue that this forgotten conception
is essential for understanding Newton’s broad theory of matter and
its philosophical foundations. The
relation of these two conceptions of matter to the philosophical
foundations of Newtonian theory will be articulated through an
analysis of the correspondence between Newton and Roger Cotes, editor
of the Principia’s second edition. Cotes shows that
Newton’s use of the two conceptions in the Argument for Universal
Gravitation is inappropriate since the two conceptions are at odds
with one another both philosophically and mathematically.
Mathematically, the two conceptions lead to conflicting ways of
quantifying the proportionality between matter and gravitation and
thus Newton must make strong and unjustified assumptions regarding
their equivalence in order to salvage the main argument of Book III.
Philosophically, the two conceptions reveal the precarious
methodological role the Third Rule of Philosophizing plays in
Newton’s experimental philosophy, particularly in ascertaining the
essential properties of matter.
Dept. of History and Philosophy of Science
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