“Leibniz's Constructivism and Infinitely Folded Matter” This essay examines Leibniz's account of the structure of matter and its relation to his views of the infinite. Leibniz interprets the actually infinite division of matter into finite parts on the model of infinite convergent series, but that model admits of different ontological interpretations; and the one Leibniz adopts appears to be in conflict with his metaphysical analysis of matter as a discrete rather than continuous quantity. I identify a constructivist strand of thought in Leibniz's philosophy of mathematics, revealing two...

“Leibniz's Constructivism and Infinitely Folded Matter” This essay examines Leibniz's account of the structure of matter and its relation to his views of the infinite. Leibniz interprets the actually infinite division of matter into finite parts on the model of infinite convergent series, but that model admits of different ontological interpretations; and the one Leibniz adopts appears to be in conflict with his metaphysical analysis of matter as a discrete rather than continuous quantity. I identify a constructivist strand of thought in Leibniz's philosophy of mathematics, revealing two competing conceptions of the infinite in his philosophy. Leibniz's constructivism, I suggest, obscures from his view the difficulties with his own model of the structure of matter, yet his eventual recognition of some of those difficulties prepares the ground for his later doctrine of incorporeal substance. Thus, Leibniz's constructivism appears to play an instrumental role in the emergence of that doctrine.