Lewis’s counterfactual theory of causation is right, goddamnit.

Now that I’m ending my blog hiatus (abracadabra, whoof, wham, it’s ended), it’s time to lure my various blogospheric constituencies (that is, all three people who read this thing) back to the fold.  And I think first stop is the philosophers.

Perhaps the title is a little strong (but I’m an extrovert, or so I’m told by a reliable source, so I’ll call that an excuse), but I definitely think that there are some really bad objections to Lewis’s theory out there.  And one of the most annoying shows up in Woodward’s Making Things Happen, so I’d like to try and shoot some holes in it.  Ok?  Thanks. 

First, a quick and highly dirty overview (meant for people who are totally unfamiliar with it, and in a couple sentences, so please don’t gripe at me for oversimplification) of Lewis’s theory of causation.  The basic idea is that we say that A caused B if, following the white rabbit into modal-land and considering the closest possible world where A is absent, B is not present.  How do we determine what the closest possible world is?  By making use of Lewis’s criteria for proximity of possible worlds, which basically counsel avoiding big violations of physical law (miracles — the idea being that some miracle would be necessary to get us to a possible world anyway, but we should evaluate them by smallness of miracles) and maximizing the amount of match of fact.  Gah, just go read the link.  ANYWAY:

Right. (What follows is a modified excerpt from a seminar paper that I’ll never do anything with, a.k.a. perfect blog fodder.)  So… Woodward (among other objections) presents several examples where Lewis’s similarity criteria for possible worlds (particularly the criterion barring unnecessary multiplication of miracles) supposedly cause us to evaluate the relevant counterfactuals in such a way that we get the wrong answer about causation.  But slight modifications to Lewis’s similarity criteria, fully in the spirit of the original project, can easily handle the cases where avoiding the multiplication of miracles supposedly gets the wrong answer.

Woodward’s most convincing counterexample to Lewis’s theory involves the sort of complicated cases where the first similarity criterion – avoiding big, widespread, diverse violations of law – causes us to evaluate the counterfactuals the wrong way.  Thus, he offers a case (Making Things Happen pg. 139-142) where C causes E, as well as (renamed for clarity) D1-Dn (for arbitrarily large n), but D1-Dn do not cause E.  He asks us to consider the contention (intuitively false) that D1-Dn caused E, using Lewis’s theory.  That is, we’re to evaluate the closest possible world where D1-Dn are not the case, and see if E is also not the case. If that’s so, we’ll say that D1-Dn cause E.

Because Lewis’s first criterion generally advises minimizing the number of miracles,  Woodward argues that it declares that a world where a miracle is directed against C is closer than one where miracles are directed at each individual D.  Consequently, the counterfactual is evaluated incorrectly as true: in that closest world where the D variables are all false, the E variable is also false (because C, the actual cause of E, was removed).

I find that interpretation extremely uncharitable.  Lewis constructed his similarity conditions on the basis of counterfactuals with one term in the antecedent, but the point of the first similarity condition is obviously to minimize the violations of law in the process of cleanly removing the antecedent from the picture.  And where we have a big, diverse, widespread antecedent, we’ll obviously need a big, diverse, widespread miracle to remove it. 

Instead, a small emendation to Lewis’s first criterion for similarity of possible worlds just dissolves the objection.  I’m going to call my emendation M-CONS, because it ripples off the tongue so delightfully.

M-CONS Big, widespread, diverse miracles are to be avoided.  We test for whether a big, widespread, diverse miracle has occurred only after the number of discrete miracles has reached M.  M is defined over the entire set of possible worlds, as follows: M is the smallest number of miracles found in any possible world that meets the following two conditions: 1) each term in the antecedent of the counterfactual under examination is false, and 2) no possible world meeting 1) can be found in which there is a larger spatiotemporal region of perfect match of particular fact.  The examination for perfect match of particular fact  is conducted only in the temporal region corresponding to the time before the last antecedent occurred in the actual world.   Ordinarily, M will equal the number of terms in the antecedent of the counterfactual under examination.

M-CONS seems to be a fairly obvious change to Lewis’s theory, one that expands its scope of applicability from counterfactuals with a single term in the antecedent to those with many terms in the antecedent.  As such, it ought not to greatly offend the original theory: in the cases Lewis considered with one term in the antecedent, M will ordinarily equal 1, and thus we will check for big, widespread, diverse miracles in all cases as under the original theory.

But look what it does to Woodward’s “counterexample!”  Now, the first condition permits exactly n miracles before we worry about big, widespread, diverse violations of law.  So a world with a set of miracles that eliminates each D variable is just as close, under the first criterion, as the miracle that eliminates C.  And that world is closer, under the second criterion, because the region of perfect match of particular fact is increased to include a perfect match with respect to C (and E!).  The counterexample has just collapsed.

Mad-dog modal realism will rise again!


4 Responses to “Lewis’s counterfactual theory of causation is right, goddamnit.”

  1. Inner City Trendy Says:

    Interesting post… I think Woodward is a bit fast with a few of his objections to other theories. Nevertheless, I’m very sympathetic to his approach.

    I think the problem with the Lewis approach is that it leaves it rather mysterious why we would have a concept of causation. Why would it be so useful to have a concept involving events in ‘real’ but ‘non-acutal’ worlds?

    The advantage of interventionism is that it gives us a naturalistically respectable way of understanding why humans (and other creatures) would have a concept of causation.

    Nice blog btw.

  2. Paul Gowder Says:


    I confess, I don’t fully understand why the property to which you refer (which Woodward calls “practicality”) is a virtue. Intuitively, it feels like it is, but I don’t know any argument for why our account of a concept needs to also give us an account of why we have the concept. Isn’t that a job for psychology?

    Unrelatedly, I find it interesting that Woodward argues that his theory can be extended to cases where no intervention is possible – that the interventionist approach explains how we can coherently make causal claims about what would happen if the moon were in a different place, even though we can’t move the moon and may not ever be able to move the moon. Obviously, when we ask what the moon’s position causes, we’re not doing so because we want to know how to manipulate the moon! The extension of Woodward’s theory to non-manipulable events partially demotivates the theory, I think, if it gets its motivation from that kind of practicality — especially if we think there are lots of non-manipulable phenomena.

  3. Uncommon Priors » I have too much fun with seminar papers. Says:

    [...] wrote for a philosophy of science class had the following example in the course of a discussion of counterfactual theories of causation: Here I must identify another weakness in my argument, however. Woodward might offer an amended [...]

  4. Uncommon Priors » Sleep-deprivation roundup Says:

    [...] Or a marvelous (as usual) Legal Theory Lexicon on causation. The correct theory of causation is [...]

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