  If a finite substance is to have a CIC, as Leibniz claims in §8 of the Discourse on Metaphysics, what is its ontological status? That is, what kind of thing could have such a CIC or such a nature? Leibniz's answer to this question brings to the fore another paradigm of substancehood: unity. While it is the nature of an individual substance to have a CIC, only a genuine unity can qualify as a substance. Leibniz expresses his position in a letter to Arnauld in a very clear and forceful manner: “To put it briefly, I hold this identical proposition, differentiated only by the emphasis, to be an axiom, namely, that what is not truly one being is not truly one being either.” (G II 97/AG 86) In the period of the Discourse on Metaphysics and Correspondence with Arnauld, Leibniz appeals to certain Scholastic notions, chief among them, the notion of a substantial form. In later years, the Scholastic way of speaking fades away, but the fundamental idea remains the same: there must be something that guarantees or makes possible the unity of a substance, and this is the substantial form or the soul. The point Leibniz wants to make is that only a soul or a substantial form is the kind of thing that can be said to have or underlie a complete individual concept, for only a soul or substantial form is by its nature an imperishable unity. Leibniz makes this point very clear in another letter to Arnauld: “A substantial unity requires a thoroughly indivisible and naturally indestructible being, since its notion includes everything that will happen to it, something which can be found neither in shape nor in motion (both of which involve something imaginary, as I could demonstrate), but which can be found in a soul or substantial form, on the model of what is called me” (G II 76/AG 79). Thus, unity is the hallmark of a genuine substance, but equally important is Leibniz's paradigm case of a substance: the self. This thought underlies much of Leibniz's reflections on the nature of substance and has important consequences. For, following not only Descartes but also the entire Augustinian tradition, the “I” is essentially immaterial, a mind or a soul. Similarly, he writes in Primary Truths, “Something lacking extension is required for the substance of bodies, otherwise there would be no source [principium] for the reality of phenomena or for true unity… But since atoms are excluded, what remains is something lacking extension, analogous to the soul, which they once called form or species” (A VI iv 1648/AG 34). (Material atoms, as advocated by Democritus in the classical period and by Gassendi and others in the seventeenth century, are excluded, Leibniz thinks, because they violate PII; that is, two purely material atoms would seem to be qualitatively identical and yet distinct, which is impossible if one accepts PC, PSR, and the derivation of PII.)