90 Kant: A Biographycare whether this principle was called "form," "entelechy," or "force," he
claimed that it was central for understanding motion. The Cartesians were
wrong in equating a body's moving force with the (scalar) momentum, the
product that results from multiplying the quantity of motion (speed) with
the weight of the body. He argued that there was an important difference
between speed and force, and that more than twice the force must be pres¬
ent to give something twice the speed, and that living force actually equals
mv^2 (where m = mass and v = velocity). This theory of how force is meas¬
ured thus has deep roots within Leibnizian metaphysics, and some of the
arguments Leibniz adduces are more metaphysical than empirical in nature.
The Newtonians, who were not interested in such hypotheses, also opted
for an account of moving force in terms of "momentum" rather than "liv¬
ing force." The dispute between the Leibnizians and the Cartesians was
fierce. What was the true measure of force? Was it Descartes's momentum
or Leibniz's "living force?" Newton, whose position about the activity of
matter was intermediate between the positions of Descartes and Leibniz,
made the problem more difficult.^132 Like Leibniz, he criticized the Car¬
tesian concept of inert matter and included forces in his conception of
matter, but Newton emphasized what he called the vis impressa, which cor¬
responded to Leibniz's vis mortua, and he tried to exclude vis viva entirely
from physics. On the other hand, both Leibniz and Newton thought that
there was a "force of resistance" proportional to the quantity of matter,
resident in every body, and this fitted "neatly into Leibniz' general account
of matter as dynamic."^133
Kant began his discussion explicitly with some "metaphysical con¬
cepts."^134 He wanted to mediate between the parties, arguing that both
parties were wrong and that neither of them could describe all of nature.
He thought the Leibnizians had perhaps the most severe problems. Math¬
ematics proved them wrong, because it "allows no other measure of force
than the old Cartesian one."^135 The mathematical definition of "body" al¬
lows only external relations between bodies as far as mechanics is concerned.
Most of the book is concerned with showing that the Leibnizian arguments
against this position are insufficient.
In a somewhat surprising turn of argument, Kant goes on to argue in
the third part of his book that the mathematical definition of "body" is not
necessarily the only or the correct definition of physical bodies. He now
"presents a new estimation of the living forces as the true measure of force
in nature."^136 Arguing that the axioms of mathematics may exclude cer¬
tain characteristics that physical or natural bodies may nevertheless really