Substances, Attributes, and Modes – Substantial Structures in Descartes, Spinoza and Leibniz

Aristotle introduced the concept of substance in philosophy. Thus, we find reflections on substance in different works of Aristotle. In the Categories, he introduces the so-called ontological square, containing individual substances, universal or second substances, individual accidents and universal accidents. Individual substances are characterized by the fact that they are the final point (end-point) both of inherence and predication, i.e. they are neither contained (in subiecto esse) in another entity nor can they be said or predicated (de subiecto dici) of another entity. Another well-known characterization of substance, also from Aristotle in the Categories, is the fact that substances are able to receive contrary accidents, i.e. a white substance can become red and vice versa. Concerning the inherence of an individual accident in an individual substance the Scholastics formulated the so-called non-migration principle: an individual can inhere in only one individual substance, and it cannot migrate from one substance to another. Leibniz formulates this principle in different texts, and he uses it even in his Monadology, where he says in §7 that accidents can neither be detached from substances, nor wander around outside of substances. And so, neither substances nor accidents can enter a monad from without.