Matter, unity and infinity in early Leibniz

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




Jonathan Bennett


Leibniz, Gottfried Wilhelm

Subject Categories



This essay discusses Leibniz's theory of matter, his analysis of continuity, his philosophy of mathematics and his philosophy of the infinite. I focus on the early writings, those of c. 1676, in which his views of matter, continuity, mathematics and infinity take shape together. The overarching theme of the essay is that the interplay between metaphysics and mathematics documented by Leibniz's early writings--as he broaches the labyrinth of the composition of the continuum--is central to his metaphysical thought, and actually generates the core of his mature metaphysics.

I argue that in his inquiries into the metaphysics of matter, Leibniz looks to mathematics for light, and that in the process he is forced to rewrite his mathematics (indeed, mathematics itself) at the foundations. In particular, he appeals to the concept of the infinite convergent numerical series to solve a puzzle about how a finite portion of matter could actually divide into an infinity of finite parts. To use this mathematical structure as a model for the infinite division of matter he has to clarify the concept of the infinite convergent series and the concept of infinity, and to revise some facets of the related mathematics.

Still, even once the mathematics is secured, Leibniz's resulting theory of matter is defective. His account of the way matter is divided into its parts is incompatible with his own analysis of its metaphysical nature as a discrete (rather than continuous) quantity. I attribute that defect to a subtle constructivist strand in Leibniz's thought about mathematical entities and infinity. While an actualist about the infinity of material things, Leibniz is a constructivist about the infinity of numbers; and, I argue, his constructivism leads him to adopt the wrong ontological model of the division of matter into an infinity of parts.

Leibniz comes later to recognize a key difficulty facing his theory of matter and responds not by revising his account of matter's division, but rather by positing new metaphysical foundations for matter, consisting of simple immaterial substances that are elements of matter but not its parts: and thus emerges the theory of monads.


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