I am re-reading the chapters devoted to causal explanation of Woodward's Making Things Happen: A theory of causal explanation.  The book is very interesting and ambitious and probably Woodward is offering there one of the most complete and attractive theories of causal explanation available today.  I am sympathetic to some of the main ideas.  The purpose of this note is to indicate some potential problems with the general account defended by Woodward.

Some background first.  Woodward proposes necessary and sufficient conditions for a generalization to represent a causal or explanatory relationship.  The idea is that the generalization should be invariant under some testing interventions on variables occurring in the relationship (page 253).  This simple formulation presupposes a lot.  For example, it presupposes that the generalization is expressible in a functional form . The technical term “testing intervention” needs to be explained as well. Consider an intervention (meeting the conditions specified by Woodward in chapter 3 of his book) that changes the value of , say , that presently holds to some other value , where is claimed by the generalization to be associated with a value of that is different from the value associated with . So, if abbreviates our generalization we have that is different from and is also different from  . Such interventions are called “testing interventions.”

Invariance is a rich notion but for our purposes it suffices to take into account that invariance is determined in terms of the truth of counterfactuals of the form:

If the value assigned by the variable to were to be changed via an intervention (e.g. from to ) then the value assigned by to would change in some way predicted by the generalization.

The theory works well in various crucial cases related to the usual counterexamples to the DN account (asymmetries, irrelevance, etc). But it seems that the necessary and sufficient conditions in terms of interventions rule out as explanatory some simple causal generalizations. Consider for example:

(G) Every person who ingests a high dosage of arsenic dies.

It seems that one can explain the cause of death of Jones, who ingested the appropriate dosage of arsenic at time , by invoking (G).

But (G) does not fit in Woodward's account very well. (G) has similar logical form than:

(S) Latent syphilis causes paresis.

This kind of generalization is what Woodward calls “possible-cause” generalizations. Notice first that these type of generalizations might not even be “change-related” in the sense that they can be expressed in the functional form presented above to motivate Woodward's ideas. Woodward makes some efforts to interpret this kind of generalizations as if they had functional form. Part of these efforts consist in proposing that there are readings of (G) that entail that every person who does not ingest a hight dosage of arsenic remains alive. I do not see any way in which (G) can be reasonably interpreted in this way. Assume that the current value assigned by the variable to in is , that is if is dead, apparently there is simply no testing intervention that one can perform in this case. In general possible-cause generalizations are problematic for Woodward. A rather different interventionist interpretation for them is offered at the end of chapter 6 (section 6.15). But it seems that this interpretation does not coincide with the main idea of the rest of the book, namely considering questions of the form “what if things had been different” or w-questions.

Paradoxically Woodward's theory has a response regarding the single-causal explanation that might correspond to (G):

(GS) Jones' ingestion of a high dosage of arsenic caused his death.

In this case Woodward proposes various counterfactuals that play the closest role that he can find to the idea of considering w-questions for functional generalizations. In particular he proposes the not-not counterfactual: ”Had Jones not ingested a high quantity of arsenic he would not have died.” At this point Woodward's theory gets close to other counterfactual theories of causality like Lewis'. But it seems that this proposal is a poor substitute for a truly interventionist theory of causal explanation. Notice that the non-not counterfactuals could perfectly be Lewis' counterfactuals. Apparently one does not need a general theory of intervention to evaluate these conditionals. Moreover it seems that this type of conditionals can go beyond an interventionist account of conditionals. Consider for example:

(GS) Jones' ingestion of a high dosage of arsenic and the antidote's failure caused his death.

One can use imaging in order to deal with the not-not  counterfactuals related to (GS) but if one wants to evaluate P(not-D| do(not-A or not-F)) things are more complicated. This constitutes an ambiguous intervention. Spirtes and Scheines have investigated this type of interventions but it seems that imaging has a greater degree of generality than what one can do via interventions in this case.

So, in a nutshell, it seems that the necessary and sufficient conditionals given by Woodward for a generalization to be causal or explanatory seem to exclude generalizations like (G) above, which intuitively seem both causal and explanatory. Efforts to domesticate this kind of generalizations into Woodward's account seem to be tantamount to a change of theme. It would be nice to have an unified account of causal generalizations in the context of a broad causal theory. Perhaps one has to adopt a theory that does not use intervention as a primitive to do so. The notion of intervention is quite useful but it seems to have some limitations, especially when it comes to interpret counterfactuals. But this is in part a different story. Perhaps I am misunderstanding something in Woodward's account. And this is a quick note to cover a large topic. But I hope that the main ideas are clear.