Leibniz’s Monadology (1714) is anything but a cosy, Sunday-afternoon read. We know Bertrand Russell was an avid reader of Leibniz’s work and its exegesis. Russell even wrote a book on it, A Critical Exposition of the Philosophy of Leibniz (1900). We know that. We know that and we cannot understand why. Leibniz's writing is callous and it is frustrating.
Nevertheless, here and there we find a piece of argumentation. And argumentation in those days was a hot bowl full of spaghetti with more geometrico, thank you. For instance, in order to prove that the world is made out of teeny-tiny souls – “monads” – which receive unique and infinite understanding from God, he went as follows.
First, two postulates:
I. Every substance is either simple or compound.
II. A compound substance is composed of simple substances.
Nice. But let one not be fooled by simplicity. These be starting points treacherous and deluding! Anyway, a conclusion certainly follows.
III. Every substance is either simple or composed of simple substances.
We then lay down two additional postulates:
IV. Each material substance has a divisible extension.
Has a what? An extension of a substance is, in Descartes’ terminology, is the amount of space matter occupies. Let it be said that, by borrowing this scholastic concept, Descartes was perfectly mudded in an old medieval metaphysics as to the distinction between mind and matter (intension and extension). But be it. The next postulate is:
V. Nothing that has a divisible extension is a simple substance.
Exactly, right? Because it is a divisible extension. But take III, IV & V, and state it clearly so that Russell can hear you:
VI. No simple substance is a material substance.
And, if not material, we know what’s left:
VII. Every substance is either material or spiritual
VIII. Each simple substance is spiritual.
PS: For those sufficiently sadistisch, check the Monadology for why every monad is a perceiving being!