Descartes accepted the Aristotelian concept of a plenum, that is, that there are no spaces empty of matter, a view that was also popular among the Scholastics and various other early modern natural philosophers (e.g., Hobbes). Nevertheless, the rationale for Descartes’ acceptance of the plenum is based on his unique metaphysical conception of matter. As he states in the Principles of Philosophy (1644), his most ambitious and important philosophical work: “That a vacuum in the philosophical sense of the term (that is, a space in which there is absolutely no substance) cannot exist is evident from the fact that the extension of space … does not differ from the extension of body” (AT VIIIA 49, MM 46–47). Given Descartes’ view that corporeal substance is only conceptually distinct from three-dimensional extension (AT VIIIA 46), it thus follows that space is a plenum and that there can be no spaces entirely empty of matter, or vacuum.

The traditional substance-property scheme would seem to form the basis of Descartes’ unique concept of matter, moreover, since extension alone would be an accident or attribute without an underlying substance, which is metaphysically impossible: “From the sole fact that a body is extended in length, breadth, and depth; we rightly conclude that it is a substance: because it is entirely contradictory for that which is nothing to possess extension” (AT VIIIA 68, MM 47). While this reasoning leads to the conclusion that there can be no vacuum within the material world, if the corporeal world was finite in extent, then a nonextended vacuum outside of the world could be envisioned, as many earlier thinkers had believed. Yet Descartes rejects this possibility, arguing instead “that this world, or the universe of material substance, has no limits to its extension,” since “wherever we may imagine these limits to be, we are always able, not merely to imagine other indefinitely extended spaces beyond them; but also to clearly perceive that these are as we conceive them to be, and, consequently, that they contain an indefinitely extended material substance” (AT VIIIA 52, MM 49).

The conjunction of Descartes’ plenum and metaphysics of corporeal substance raised a number of difficulties for his natural philosophy and prompted various unique responses.