For all events e1 and e2: if e1 occurred and e2 occurred after e1, then e1 was a cause of e2 only if there are kinds k1 and k2 such that: e1 is of kind k1, e2 is of kind k2, and it is a law that events of kind k1 are followed by events of kind k2. (Let's say that in this case the law covers e1 and e2.)
Well, almost: there are no laws covering intentional mental events (believings, desirings, hopings, intendings) and physical events.
This is Davidson's anomolism of the mental. We'll look at his argument soon.
Suppose your desiring to drink water (a mental event) caused your turning on of the tap (a physical event). If Davidson is right, this is only because the first event falls under some physical kind (in addition to a mental kind); that is, because it has some physical property (in addition to a mental property). So it seems that the only properties of the first event that are causally relevant are its physical properties - whatever mental properties it happens to have are causally irrelevant. But then in what sense have we saved mental causation?
We should reject the nomological theory of causation.
One alternative is a counterfactual theory of causation. Here is a starting version: Event c was a cause of event e iff (a) c and e occurred, and (b) if c had not occurred then e would not have occurred.
We will not discuss this here (see Kim).
If a physical event e has a cause, then it has a physical cause, and moreover it has a sufficient physical cause: there is a physical event e' which occurs and causally necessitates the occurrence of e.
(Note that the biological domain is not causally closed: radiation causes cells to mutate.)
Unless an event e is causally overdetermined it cannot have more than one sufficient cause.
Cases of overdetermination: two bullets hitting a victim; a short circuit and a lightning strike both causing a house fire.
For all x and m: if m is a mental property and x has m then there is a p (a supervenience base for m) such that: p is a physical property and x has p and necessarily: for all y: if y has p then y has m.
But this response relies on the possibility of mental-to-physical causation, and according to the exclusion argument mental-to-physical causation is not possible.