Counterfactuals and Causal Explanation

Abstract

This article defends the use of interventionist counterfactuals to elucidate causal and explanatory claims against criticisms advanced by James Bogen and Peter Machamer. Against Bogen, I argue that counterfactual claims concerning what would happen under interventions are meaningful and have determinate truth values, even in a deterministic world. I also argue, against both Machamer and Bogen, that we need to appeal to counterfactuals to capture the notions like causal relevance and causal mechanism. Contrary to what both authors suppose, counterfactuals are not “unscientific”—a substantial tradition within statistics and the causal modelling literature makes heavy use of them.

Notes

Correspondence: Division of Humanities and Social Sciences, 101‐40, California Institute of Technology, Pasadena, CA 91125, USA. E‐mail: [email protected]

Or at least this is what Bogen (2004) says in the main body of his paper. In a footnote (fn. 13), he allows for the possibility that “depending on your logical preferences” all such counterfactuals may “have a third truth value or be truth‐valueless or false”. I take it, however, that as long as all counterfactuals with false antecedents have the same truth value (or none) they will be useless for elucidating causal claims, so that there is no loss of generality if we take Bogen to be claiming that all such counterfactuals are vacuously true.

When Bogen (2004) says that the world is indeterministic, I take it that what he means is not just that there are some outcomes that are undetermined since this is compatible with most outcomes being determined and deterministic counterfactuals about them being true. Instead, Bogen must mean that determinism fails quite generally for most or all outcomes. It is unclear to me how Bogen's claim that under indeterminism, deterministic counterfactuals are false is supposed to fit with his earlier contention that under determinism all counterfactuals with false antecedents are vacuously true. Both claims can't be right.

For details, see Woodward (2003). Recall that it is built into the notion of an intervention on X with respect to Y, that any change in Y results only from the intervention on X. This means that the causal characteristics of the intervention process itself must have no independent influence on Y other than any influence they may have through the value of X. So in assessing the counterfactual “If X were the case, then Y would be the case” where X is realized by an intervention, all that matters is what the value of X is (and what the value of Y would be for that value of X)—the additional details of how X came to have that value don't matter.

Suppose that I claim regarding some particular match, that if struck it would light. The truth of this counterfactual claim will depend on the characteristics of the match (whether it is dry, appropriately constructed, etc.) and the characteristics of the striking. It reflects a misunderstanding to respond to this claim by saying, “Wait a minute. How did it come about that the match was struck?” For similar reasons, it would be a mistake to respond to the counterfactual described in the example from Halliday and Resnik below by demanding an account of how the tunnel through the earth came to be built and whether the process that built it was indeterministic.

Part of Bogen's motivation for this claim seems to be the following: under determinism, it is “impossible” for anything to happen other than what actually happens—impossible because inconsistent with the laws and the actual initial conditions. If counterfactuals with impossible antecedents are vacuously true, it follows that under determinism any counterfactual with a contrary to fact antecedent is vacuously true. But even if one agrees that, for some sense of “impossible”, counterfactuals with impossible antecedents are vacuously true, why assume that the relevant sense of impossible is given by inconsistency with the laws and actual initial conditions? There is nothing that requires this assumption and most standard accounts of counterfactuals don't make it, again for the obvious reason that it trivializes the use of counterfactuals under determinism. If one wishes to take the view that counterfactuals with impossible antecedents are vacuously true, there are many alternative construals of “impossible” that seem more plausible and appropriate. One such construal takes “impossible” to mean “logically impossible”. Another possible construal takes the antecedent of a counterfactual to be impossible if and only if it is inconsistent with the laws alone and possible as long as it is consistent with some (not necessarily actual) initial conditions and the laws. As long as laws (or other causal generalizations) are stable under changes in initial conditions, then, as argued above, both construals will yield non‐trivial truth values for many counterfactuals under determinism, even if it is accepted that counterfactuals with impossible antecedents have trivial truth values.

This is a generalization of the screening off conditions proposed by Reichenbach (1956). A set of variables and an associated probability distribution satisfy the Causal Markov condition if conditional on its direct causes every variable is independent of every other except for its effects. See Spirtes, Glymour, and Scheines (2000) and Hausman and Woodward (1999) for additional discussion.

Indeed we now have in Spirtes, Glymour, and Scheines (2000) and Pearl (2000) a series of theorems specifying when such undetermination exists and its extent.

For an analysis along these lines, see Hitchcock (2001) and Woodward (2003).

Here is one issue that merits such additional attention: Machamer (2004) writes, in the context of a discussion in which he denies that causation is transitive, that “what one wants to do in establishing and displaying [a] mechanism is to show how one stage produces the next, and so on”. This seems to suggest that he is committed to something like the following claim: if c ₁ produces c ₂ which produces c ₃, then c ₁ produces c ₃ (or there is a mechanism connecting c ₁ to c ₃ or c ₁ causes c ₃). But this is just to claim that production or causation or “there is a mechanism connecting X and Y” is transitive, contrary to what Machamer has just said and contrary to what the dog bite example seems to show. Put slightly differently, it seems to me that the mechanist who wants to dispense with counterfactuals faces a dilemma concerning such cases. On the one hand, we clearly want to infer in many cases in which there are relationships of “production” between successive stages in the operation of a mechanism to the conclusion that there is an overall relationship of “production” between the beginning and ending stages of the mechanism. On the other hand, we know from the dog bite example that such inferences are not always reliable. The counterfactual account has a ready account of when such an inference is reliable and when it is not. What is the mechanist's account?

It is perhaps worth underscoring what the temporal stability assumption says. It does not say that if the switch had been flipped up at times other than t, this would be followed by the light going on. Instead the assumption says that what follows from the switch not being flipped up at times other than t is the same as what would follow if the switch had not been flipped up at t. In effect, what is assumed is that the light does not go on spontaneously, even when the switch is down.

A very similar objection is also raised by Stathis Psillos (forthcoming).

Of course it is true that Lashley's experimental manipulations are actual and not merely hypothetical. However, it is a mistake to infer from this that Lashley's inference to the causal role of the visual cortex in the blinded rats is based purely on correlational evidence, concerning what actually happens. The causal features of Lashley's experimental manipulations are crucial to the logic of his inference. For example, it is crucial that his manipulations not be a common cause of the cortical damage and of the rat's maze running performance. For reasons that have been made clear by a number of writers (e.g. Cartwright 1979) these causal features cannot be characterized in purely correlational terms.

In other words, consider a non‐counterfactual claim of the general form: the objective chance of random variable X taking value x = p; Pr(X = x) = p. In an indeterministic system some claims of this form must be true, by definition. Whatever the interpretation of objective chance is according to which such claims are true, we can also consider counterfactuals of the form: If q were the case, then the objective chance of X = x is p. Such counterfactuals will have determinate, non‐trivial truth values.

For more details see Woodward (2003).

But for more in defence of the claim, see Woodward and Cowie (2003).