Armstrong claims that truthmakers for causal claims, for Lewis, are entirely this-worldly:
"Lewis's talk of possible worlds here is to a degree miselading. It is important to realize, as I did not originally realize, and I think many others have not realized, that these counterfactuals are supposed to hold solely in virtue of features of the world in which the causal relation holds. As I would put it, the truthmaker for causal truths is to be found solely in the world in which the relation holds. (I think this follows straight from the contingency of the causal relation, a contingency that Lewis does not doubt.) In his theory of causation the possible worlds enter as mere calculational devices. He has given me as an example the way that we might say with truth that a person is a Montague rather than a Capulet, without being being committed to the view that these families are actual. The fictional families are used as no more than a calculational device." ("Going through the Open Door Again: Counterfactual versus Singularist Theories of Causation," p. 445)
I must confess that I don't understand, so perhaps you all can help me understand. If the possible worlds are merely a calculational device, then there should be some way to make the calculation with a different device. (I could explain what was meant by a person being a Montague rather than a Capulet with different concepts if you had never read Shakespeare.) Assume, then that there are no possible worlds. What is it, in this world, that makes causal counterfactuals—had c not occurred, e would not have occurred—true (when they are)? It must have something to do with laws, but I'm not sure how that would go.
(I assume that Armstrong does not mean merely that the possible worlds don't need to be Lewisian worlds, that they might be linguistic constructions or sets of abstract states of affairs. The claim is not that the truthmakers don't have to be other-worldly; it's that they are entirely this-worldy.)
I'm also puzzled by Armstrong's parenthetical remark, that the this-worldy nature of truthmakers for causal claims follows directly from the contingency of causation. How is that argument supposed to go?