Tuesday, January 26, 2010

Armstrong on Lewis on causation

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?


  1. Suppose A counterfactually depends on B--the nearest not-B world is a not-A world. Perhaps the idea is that the truthmakers for that counterfactual are the features of THIS world in virtue of which the not-B world that's most similar to this world is also a not-A world.

  2. Hi Jonathan,

    maybe a simplified example helps to make the point (this is from my Lewis book): let's say that world w1 counts as _more similar_ to w0 than w2 iff w1 has the same laws as w0, and w2 doesn't. On a simple counterfactual analysis, A then causes C (in the actual world) iff among worlds with the actual laws, there is at least one world with A and C and none with ~A and C. In other words, A causes C iff A is nomologically sufficient for C. The worlds talk cancels out.

    The general point is that similarity is an internal relation: how similar one world is to another is determined by their intrinsic nature. Moreover, for Lewis the extent of logical space is neither contingent nor a posteriori. So whenever it is true that the closest A worlds are C worlds, this must be due entirely to intrinsic (non-modal) features of the actual world: not only do counterfactual truths supervene on these non-modal facts, they are also a priori entailed by them. For Lewis, the relevant facts concern the laws of nature and the distribution of local properties through spacetime. The worlds talk is just a convient way to pick them out.


  3. Thanks, Daniel and wo.

    Grant that similarity is an internal relation. But since the similarity relation used when giving a semantics of counterfactuals is *comparative similarity of worlds*, then on the assumption that there are no worlds, this can't be what grounds the counterfactuals, even if the relation is internal, since you still need the other worlds for the similarity relation to hold. You need both relata. So the similarity relation is also part of the calculational device. What should be said is that what grounds the counterfactuals is simply the intrinsic nature of this world, which, as it happens, is such that were there to be any other worlds, the comparative similarity relation would hold in thus-and-so a manner. (I think you'll both agree. Am I right?)

    Here's one thing that now puzzles me. If Lewis thought all actually true counterfactuals (the not counter-nomic ones) were grounded in the intrinsic nature of the actual world in this manner—did he?—then it looks like the truthmakers for a great deal of modal truths are this-worldly as well. We can, after all, define necessity and possibility in terms of the counterfactual. So if the laws were necessary, Lewis wouldn't need possible worlds. (That must be the point of Armstrong's parenthetical.)

    Can that be right? If Lewis could have been convinced that the laws were necessary, he would thereby have a reason to give up on the plurality of worlds?

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  6. Hi Jonathan,

    On the last point---I'm not sure Lewis would buy the Armstrongian project of looking to "what's needed to ground the truth" of a theory for one's ontological commitments of that theory. (I'm taking it that something like that is needed for the step you make from "the truhtmakers for a great deal of modal truths are this-worldly" to "if laws were necessary, Lewis wouldn't need possible worlds".)

    If you're more Quinean, then the fact that you need to quantify over possibilia in the canonical paraphrase of some de re modal truth, will commit you to those possibilia, even if there's also a sense in which the modal truth is *grounded in* actuality alone.

    But others know far more about this than me... so I offer this a bit tentatively.

    (@wo, when are we going to see an English translation of your book? It's either that or I have to learn German :)

  7. I agree with Robbie. On Lewis's view, all modal truths (at least all interesting modal truths) follow a priori and necessarily from non-modal truths about the actual world. So the other worlds aren't needed to "ground" modal truths, if grounding is a matter of necessitation or a priori entailment. The argument for the plurality of worlds is more like the indispensability argument for numbers.

    Jonathan, you're right that Lewis's analysis makes causal facts depend on both 1) the intrinsic nature of our world, and 2) the extent of logical space: what other worlds there are. This is why it is important for Armstrong's point that (2) is not a variable. It is neither metaphysically nor epistemically possible that there be fewer (or more, or different) worlds than there are. So (2) is fixed, and the only thing that can vary is (1). In this sense, the truth of a causal statement depends only on the intrinsic nature of our world.