Matter, unity and infinity in early Leibniz

TL;DRAbstract

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

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