I’m working on a short paper arguing that Armstrong’s account of causation fails. The argument seems so simple that I’m worried I’ve missed something obvious. Any suggestions are much appreciated.
Armstrong identifies singular causal relations with instantiations of a law—with instances of the necessitation relation. Let N(P, Q) represent P’s necessitation of Q. In the case of determinism, N(P, Q) is something like P probabilifies Q to degree x.
I claim that Armstrong’s theory fails in indeterministic contexts. Whenever N(P, Q) holds, every instance of P is related by N to Q. After all, instances of universals are, according to Armstrong, nothing other than the universal itself. But then in cases where P occurs but does not cause Q, the instance of P is still related by N to Q. The law is instantiated, but causation does not occur. Hence, causation is not the instantiation of a law.
Here’s a slightly different way of putting the same problem: Assume indeterminism. Let it be an indeterministic law that N(P, Q). Assume there is an instance of P that is not followed by an instance of Q. (This is possible, given the assumption of indeterminism.) Either the instance of P is related by an instance of N to Q or it is not. Suppose it is. Then P caused Q, contrary to our assumption. On the other hand, suppose P is not related by N to Q. Then there is an instance of P not related by N to Q. But, then it can’t be a law that N(P, Q), contrary to our assumption.
It seems to me that Armstrong needs singular causal relations in addition to laws, so that in indeterministic contexts, the law can be instantiated without the singular causal relation holding.