If space were the primary substance for Descartes, the vacuum would be metaphysically possible, yet he argues its impossibility precisely because extension cannot exist without corporeal substance (Pr II 16-18).

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Descartes: # Descartes René Descartes was a French philosopher and mathematician from the 1600s who fundamentally changed how people think about knowledge and the mind. He's famous for the idea "I think, therefore I am" (cogito ergo sum), which means that the very fact that you can think proves you exist—a foundation for modern philosophy. He also invented the coordinate system used in mathematics (the x and y axes on a graph), which connects geometry and algebra in practical ways we still use today.
Pr II 16-18(citation showing where Descartes makes this argument): A reference to specific numbered sections in Descartes' book 'Principles of Philosophy' (Part 2, sections 16-18) where he discusses these ideas.
corporeal substance(Leibnizian metaphysics of living matter): A body endowed with a basic entelechy or vital principle, of which it may be said in general that it is living.
extension(Semantics and philosophy of language): Another term for reference, i.e., the object or set of objects a term picks out

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