causally independent. This means that each individual essence reflects others
from its own perspective; extending links onward, each reflects the whole
universe.
Leibniz is conservatively reinstating the doctrine of essences which Galileo
and his movement had overthrown in physics in favor of mathematical de-
scription of matter in motion. But contemporary science is part of Leibniz’s
armament as well. His calculus alerted him to another dimension beyond the
conventional representations of matter in motion. When he says that each
substance contains traces of all its past and future states, he can visualize a
point moving along mathematical coordinates. Geometrically a moving body
is indistinguishable from one at rest; hence there must be an additional quality,
“living force”—later called “kinetic energy” (Broad, 1975: 65)—which implies
its past and future. A similar line of thought connects his calculus to the
controversy over atoms and infinite divisibility. Descartes’s extended substance
was being criticized by Foucher as infinitely divisible, and hence not really a
substance at all, while atoms were rejected as incapable of making up a
continuum (Brown, 1984: 42). These problems were reinforced by recent
discoveries by microscope of microorganisms, which led Leibniz and others to
suppose that there are infinite arrays of infinitesimals within each order of size.
Leibniz’s calculus made it familiar for him to invoke a transcendent order of
reality, rather than the physical dichotomy of atoms versus infinitesimality.
Leibniz reformulated all mathematical and metaphysical distinctions as quali-
ties of a continuum. Rest may be conceptualized as infinitely slow motion,
equality as infinitely small differences.^11
Borrowing from Spinoza and Malebranche, Leibniz proposed a coherent
explanatory system. The world is composed of an infinity of substances; each
is unique, each having an essence which contains logically and causally all that
it ever is. Leibniz accommodates atomism and microscopic biology by suppos-
ing that visible bodies are made up of many such monads; he accommodates
living organisms and the human soul by supposing that they too are monads
on their own scale. He accepts Spinoza’s solution to the mind-body problem
by positing that each substance is simultaneously mind and matter. But these
ultimate entities are not bare atoms, interchangeable except for their positions
in time and space; each has its individual essence, the equivalent of Duns
Scotus’s haecceitas, the principle of individuation. They cannot be interchange-
able in time and space, because time and space are not independently existing
containers but are internal characteristics of the monads themselves, their
modes of relating to one another.^12 The relations among these self-subsistent
monads seem paradoxical, a mark of Leibniz’s inability to force through a
complete synthesis of his disparate materials. Nevertheless, the underlying
thrust of his argument may be interpreted as holding that the essence of
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