## Wednesday, January 27, 2010

### Againt Armstrong on Causation

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.

1. If I recall correctly, Armstrong's earlier work mentions the necessitation relation, but he's agnostic about whether this is causation or not. It is in later replies to his work (by van Fraasen, for example) that he says that the necessitation relation is causation (though I don't know why he doesn't just say that causation is a truthmaker for laws of this form).

My guess would be that Armstrong would deny that there is such indeterministic causation. Cases that seem like indeterministic causation would either be 1) underspecified, or 2) cases where an unknown defeater was present. (Again, though, this is guessing).

Do you know of a passage where Armstrong commits himself to indeterminisitc causation? If so, then its much more likely that his views are inconsistent.

2. I'd like to know a more about what you take the "N" relation to mean in an indeterministic universe. Here are two options.

- N(P,Q) might mean: "P necessitates Q in all possible worlds." But then we can say P causes Q in all possible worlds, and there's no problem.

- N(P,Q) might mean: "P necessitates Q in some possible world." Then we can say P causes Q in some possible worlds, and there's no problem.

Anyone with the view you're attacking would clearly want "necessitates" and "causes" to have the same domain -- either both apply to all worlds, or both apply to some worlds. But your objection seems to assume they don't: "necessitates" applies to some worlds, while "causes" applies to all worlds. Why would you assume that?

3. @Brandon: See World of States of Affairs, pp.74-75, where Armstrong says that probabilistic causality should be thought of as objective probability of causing. See also chapters 14 and 15 for discussion of these issues.

Let N(P, Q) hold, and be so interpreted: "There is an objective probability, x, that P will cause Q." Let P be instantiated but not Q. The law is instanced, since there still is an objective probability of x that this instance of P will cause an instance of Q, but there is no singular causation.

4. @Bryan: For Armstrong, N is a genuine piece of his ontology, a bit of the world. It is a second-order universal, linking universals. So N(P, Q) doesn't mean anything about any world but this one. When N(P, Q) holds, that means there is a genuine state of affairs or fact, the universal P bearing the relation N to the universal Q.

So I'm not clear on what you mean by "have the same domain" or "apply to all worlds" or "apply to some worlds".

Armstrong does think that when N(P, Q) holds, it holds contingently, so while it may be true in this world that P bears N to Q, it is not true in all worlds.

But nothing about my argument took us to alternative worlds, even worlds with the same laws.

It may help to remember that Armstrong thinks causation is, in the first instance, singular. It holds between particular events.

Suppose N(P, Q) in this world. According to Armstrong, in indeterministic contexts, this means P gives an objective probability that an instance of Q will be caused to exist in suitable relation to P (A World of States of Affairs, 237). That is consistent with P occurring and Q not occurring. So, in this world, let an instance of P occur, but where an instance of Q suitably related to P does not occur, even though in this world N(P, Q). P does not cause Q, since Q does not occur. Does P still give an objective probability that an instance of Q will be caused to exist in suitable relation to P? If yes, then causation is not the instantiation of law. If no, then N(P, Q) does not hold after all.

Is that more clear?

5. How about this crazy idea? When ordinary folks would say that A has a probability 0.5 of causing B, what actually happens is this. When A occurs, by law, there is a probability 0.5 of C occurring. This law is not a causal law (on pain of regress). It is a law grounded in the nature of A, a law that always obtains, whether or not C happens. Next, there is a law that C always causes B. This is a causal law.

6. Jonathan,

Just to note where I think Armstrong would take issue with the argument: he does claim that “Probabilistic laws are universals which are instantiated only in the cases where the probability is realized,”( on P. 129 of What is a Law of Nature). So it looks like Armstrong is going to deny that there is an instantiation of the law N(F,G) when F occurs without the occurrence of G.

Furthermore, Armstrong remarks that, “If the relation between F and G is (N:1) then there logically must be necessitation in each singular case. If the relations is (N:P) where P is less than 1, then we have a certain objective probability of necessitation in each singular case” (on p.132 of What is a Law of Nature).

So I’m struggling to understand why Armstrong should think that it can’t be a law that ((N:P)(F,G)), where P is less than 1, if there is an occurrence of F without an occurrence of G since the law just means there is a probability of degree P that F will necessitate G.

7. Jeremy,

Thanks for the references. You're exactly right that that's what he would take issue with. He's going to claim (and has claimed, as you've pointed out) that the law is not instantiated in cases where F occurs but G does not. I think there are reasons to think he shouldn't say that. When I've got them in more presentable form, I post them as comments here.