On The Source of Incompossibility in Leibniz's Paris Notes and some Remarks on Time and Space as Packing Constraints

The aim of this paper is to trace the source of incompossibility relations in Leibniz’s modal system as it takes shape during his formative years in Paris (1672–1676). I present the problem of incompossibility against Leibniz’s attempt to amend the Cartesian proof of God’s existence. Leibniz argues that the notion of the most perfect being must be shown to be possible. Leibniz’s reasoning is this: if the most perfect being could be shown to be possible, it would follow that it necessarily exists. To prove this, Leibniz argues that the notion of a subject that entails all positive and simple attributes is possible or does not involve a contradiction. However, if all attributes are compatible, and all things are composed of such attributes, how could any conflicts among them come about? If there were no internal conflicts and no negations, there would result, it seems, only one large individual. If so, there would be no diversity and no multiplicity of possible individuals. It would follow that there would be no multiplicity of possible worlds. A single possible world would imply that everything possible would be actual and thus nothing which is merely possible. And this would imply a Spinoza-like picture, which Leibniz seeks to avoid precisely by developing the notion of incompossibility, so that one could account for possibilities that are not actualized.