The definition of space as body also affords Descartes the opportunity to deny the very anti-naturalistic Scholastic view that the earth and the heavens are composed of different sorts of matter. The Scholastics believed that earthly substances were composed of the four elements (terrestrial matter) while the heavens were made up of the perfect fifth element or celestial matter. This view obviously made a unified science very difficult, since it required that heavenly bodies have completely different properties from terrestrial bodies.

Descartes' argument against this position has two stages. First he proves that the extension of the world is indefinite. No matter where we imagine the limit of physical substance to be, he claims, we can always conceive that there is some space beyond that. Since all space is filled with physical substance, this space too must be filled with physical substance. So there is no limit to the extension of physical substance. Now that he has proved that the extension of our world is indefinite, he can prove that there is no such thing as celestial matter. Matter whose nature consists in being an extended substance already occupies all the imaginable space in the world. Therefore, there is no room for any other kind of substance. (Mental substance and God, of course, do not take up any physical space, so there does not need to be any room left for them.)