Monads as Functions

How does a Leibnizian monad (which, viewed as active, or as clearly and distinctly perceiving, possesses substantial form, and which, viewed as passive, or as obscurely and confusedly perceiving, possesses prime matter) relate to its body? The monad/body distinction maps onto the distinction between primitive and derivative force, and Leibniz sometimes also says that derivative force (what physics studies) is the momentary value of the primitive force which gives rise to it, in the sense in which a point on a line is a given value for a mathematical function. This analogy provides a helpful way of making sense of Leibniz’s interest in substantial forms over and above the well-founded phenomena of bodies: what God creates is a spatio-temporal manifold populated with existents that extend in space and time, and whose states at time accounts for (provides reasons for) their states at time t+1; the substantial form is the intelligible structure that unifies these states.

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