I tremendously admire Leibniz, but have always been very puzzled by his notion of “substance”. Clearly it is different from that of Aristotle, which I still ought to develop more carefully, based on the hints in my various comments on Aristotle’s very distinctive approaches to “dialectic” and “being”. (See also Form, Substance.)
Leibniz compounds a criterion of simplicity — much emphasized in the neoplatonic and scholastic traditions — with his own very original notion of the complete concept of a thing, which is supposed to notionally encompass every possible detail of its description. He also emphasizes that every substance is “active”. Leibniz’ famous monads are identified by him with substances.
A substance is supposed to be simple. He explicitly says this means it has no parts. In part, he seems to have posited substances as a sort of spiritual atoms, with the idea that it is these that fundamentally make up the universe. The true atoms, Leibniz says, are fundamentally spiritual rather than material, though he also had great interest in science, and wanted to vindicate both mathematical and Aristotelian physics. Leibniz’ notion of spiritual atoms seems to combine traditional attributes of the scholastic “intellectual soul” (which, unlike anything in Aristotle, was explicitly said by its advocates to be a simple substance) with something like Berkeley’s thesis that what can truly be said to exist are just minds.
On the other hand, a substance is supposed to be the real correlate of a “complete” concept. The complete concept of a thing for Leibniz comprises absolutely everything that is, was, or will be true of the thing. This is related to his idea that predicates truly asserted of a grammatical subject must be somehow “contained” within the subject. Leibniz also famously claimed that all apparent interaction between substances is only an appearance. The details of apparent interaction are to be explained by the details contained within the complete concept of each thing. This is also related to his notions of pre-established harmony and possible worlds, according to which God implicitly coordinates all the details of all the complete concepts of things in a world, and makes judgments of what is good at the level of the infinite detail of entire worlds. One of Kant’s early writings was a defense of real interaction against Leibniz.
Finally, every monad is said by Leibniz to contain both a complete microcosm of the world as expressed from its distinctive point of view, and an infinite series of monads-within-monads within it. Every monad has or is a different point of view from every other, but they all reflect each other.
At least in most of his writings, Leibniz accordingly wanted to reduce all notions of relation to explanations in terms of substances. In late correspondence with the Jesuit theologian Bartholomew Des Bosses, he sketched an alternate view that accepted the reality of relations. But generally, Leibniz made the logically valid argument that it is far simpler to explain the universe in terms of each substance’s unique relation to God, rather than in terms of infinities of infinities of relations between relations. For Leibniz all those infinities of infinities are still present, but only in the mind of God, and in reflection in the interior of each monad.
Leibniz’ logically simpler account of relations seems like an extravagant theological fancy, but however we may regard that, and however much we may ultimately sympathize with Kant over Leibniz on the reality of interaction and relations, Leibniz had very advanced intuitions of logical-mathematical structure, and he is fundamentally right that from a formal point of view, extensional properties of things can all be interpreted in an “intensional” way. Intension in logic refers to internal content of a concept, and to necessary and sufficient conditions that constitute its formal definition. This is independent of whatever views we may have about minds. (See also Form as a Unique Thing.)
So, there is much of interest here, but I don’t see how these ultra-rich notional descriptions can be true of what are also supposed to be logical atoms with no parts. In general, I don’t see how having a rich description could be compatible with being logically atomic. I think the notion of logical atomicity is only arrived at through abstraction, and doesn’t apply to real things.