  In the preface to the Foundations, Du Châtelet writes: “It is certain that there are a number of points in metaphysics which lend themselves to demonstrations just as rigorous as the demonstrations of geometry, even if they are different in kind” (Avant-propos, XII). Du Châtelet's first epistemological principles thus help to establish what she takes to be the certain truth of some metaphysical claims. At least two of these claims, she believes, are necessarily true (see below for the kind of necessity at work here). So, for example, and echoing Leibniz, because of the infinite divisibility of extension, and because atoms are extended, atoms cannot be the ultimate beings of nature; simple substances (or monads) must be such beings, and the PC establishes this necessary (in Du Châtelet's mind) metaphysical fact (IP §121). The argument for this runs as follows. Atoms, defined as indivisible, extended particles of matter are actually divisible, and thus their very definition, taken together with the fact of their divisibility, implies a contradiction. So atoms cannot be the necessary beings out of which matter is composed; indeed, they are by definition impossible. How does Du Châtelet justify the claim to atoms' divisibility? She justifies this claim based upon the PC: ‘there is no contradiction in the divisibility of extended things,’ and atoms are extended thing (IP §121). Notice here, she must be relying upon a conceptual divisibility rather than a physical divisibility (for atoms are defined as physically indivisible), though one could bolster this argument by claiming that if an atom is conceptually divisible by us, then it is physically divisible by an omnipotence God, and therefore is in neither way indivisible. Indeed, the divisibility of anything—atoms or something else—that is extended indicates that extension is composed and not simple; it is composed out of the parts into which it can be divided (IP §120). So nothing extended—neither atoms nor any other piece of extension—can serve as the simple beings out of which composed beings are made. Only things that are unextended can serve as those simple beings (IP §122). Since this conclusion follows from the PC, it is a conclusion about the necessary constitution of the simple beings of our universe.