Leibniz and inter-monadic causation

Along with my graduate students, I was trying yesterday to figure out how Leibniz’s argument against inter-monadic causation works. There are two constrants on figuring this out:

1. Leibniz thinks intra-monadic causation happens.

2. Leibniz thinks God can exercise causation on monads.

Here is a somewhat a moderately interesting Aristotelian argument that may or may not be what Leibniz had in mind:

3. Inter-monadic causation is the causation of an accident of one substance by another substance.

4. Accidents are grounded in their substances.

5. If y is grounded in x, and z causes y, then either z causes x or z = x.

6. So, if substance z causes accident y of substance x, then either z causes x or z = x. (by 4, 5)

7. So, a distinct substance can only cause an accident in another substance if it causes that substance. (by 6)

Leibniz thinks that only God causes monads. Given this, it would follow from (7) that only God can cause an accident in a distinct substance.

One controversial premise in the argument is (5). But it seems to me to have some intuitive force. An official’s being elected is grounded in her getting a majority of the votes, say. But then the only way you can cause the official to be elected is by causing her to get a majority of the votes: i.e., you cause the grounded event (election) by causing the ground (majority vote).

Perhaps the big weakness in the argument is that (5) is most plausible for full grounding, while accidents seem to be only partly grounded in their substances. But the best argument that accidents are only partly grounded in their substances seems to be that full grounding necessitates: if x fully grounds y, then x’s existence or occurrence necessitates y’s; but accidents are not in general necessitated to exist by the existence of their substance. However, Leibniz does think that accidents are in general necessitate to exist by the existence of their substance—that is part of the “complete individual concept” idea. So Leibniz may think (4) is true even for full grounding. (Spinoza almost certainly does.)