Lewis's Account of Counterfactual Asymmetry

Contents 1 Lewis's Original Formulation 2 The Similarity Objection 3 Lewis's Theory of Similarity 4 Objections to Lewis's Theory of Similarity

Lewis's Original Formulation

David Lewis (Counterfactuals, 1973) defended a logic and semantics of counterfactuals closely tied to his theory of possible worlds.

Here is an overview of the analysis:

"If it were that A, then it would be that C" (symbolized here as A > C) is true iff some world where both A and C are true is more similar to our actual world than any world where A is true but C is false.

Of course, this analysis depends heavily on the notion of similarity. Similarity, of course, can apply to many different respects. If we imagine an orange circle, an orange square, and a blue circle, it will not be at all clear which objects are the most similar. In Counterfactuals, Lewis argues that the similarity relation is a primitive that he takes to have the logical properties of transitivity (for any three worlds and a target world, i, whenever j is more similar to i than k, and k is more similar to i than h, j is more similar to i than h), and connectedness (for any two worlds and a target world i, either j is more similar to i than k, k is more similar to i than j or they are equisimilar). Lewis defends his use of similarity as a primitive by claiming that, though vague, the notion is not ill-understood. Perhaps the vagueness is appropriate, since, as Lewis himself states, "Counterfactuals are notoriously vague."

The Similarity Objection

Shortly after the 1973 publication of Counterfactuals, several philosophers, notably, Kit Fine and Jonathan Bennett, pointed out a problem with Lewis's original formulation. Consider the following counterfactual:

If Nixon had pressed the button, there would have been a nuclear war.

This counterfactual is intuitively true, but on the Lewis analysis it looks as though it is going to come out false. It seems as though a world at which the consequent is false (because the signal died on the wire or some malfunction caused the missile to fail to deploy) is closer than any world in which the nuclear war takes place. After all, a nuclear war would change things drastically. It seems like any counterfactual of the form A > Big-difference, is going to be false on Lewis theory.

This objection demonstrates that the similarity relation cannot be based on intuitive judgments about overall similarity. The theory needs to be narrowed in order to consider the relevant respects of similarity that will generate the correct results for counterfactuals.

Lewis's Theory of Similarity

In "Counterfactual Dependence and Time's Arrow," Lewis responded to these criticisms. First, Lewis argued that similarity with respect to adherence to the actual laws of nature is intuitively more important than similarity with respect to matters of particular fact. But, this ought not to be held invariably, says Lewis. If actual laws are deterministic, then any counterfactual will have a different history and a different future from that of the actual world. So, we may have to admit tiny "miracles," inconspicuous isolated violations of the laws of nature, to secure match with respect to particular matters of fact.

It is important to note that counterfactual dependence of the past on the present, or backtracking, presents a special problem for Lewis. Conditionals like, "If I jumped out the window, there would have to be a trampoline below (since I'm not suicidal)," have to come out false. Though most philosophers look for a principled method of ruling out backtracking conditionals, the issue is especially pressing for Lewis because he gives a counterfactual account of causation. If backtracking conditionals can be true, causes can precede their effects.

[Need to make distinction between backward directed countefactuals and backtracking ones.]

Bearing this idea in mind, Lewis argued that instead of fixing on what the similarity relation is, and using that idea to test his analysis, we should determine the nature of the relation by extrapolating from our intuitions about cases.

In comparing candidate worlds for the most similar, Lewis settled upon the following four claims about the similarity relation:

1) It is of first importance to avoid big, widespread, diverse violations of law.

2) It is of second importance to maximize the spatio-temporal region throughout which perfect match of particular fact prevails.

3) It is of third importance to avoid even small, localized, simple violations of law.

4) It is of little or no importance to secure approximate similarity of particular fact, even in matters that concern us greatly.

Given these principles, the future similarity conditionals come out true, and, Lewis asserts, the backtracking conditionals come out false. Why? Lewis assumes that diverging from the actual world (sharing the same history and separating via a tiny isolated violation in the laws of nature) is easy. He thinks converging (having a different past but, through some breach in the laws, sharing an identical future) to the actual world is difficult. It seems as though converging to the actual world would involve miracles that create faux causal traces of past events that didn't occur, and miracles in people's memory of events that never transpired. Lewis argues that this can't be accomplished though a tiny miracle. Hence, the asymmetry of counterfactual dependence. The past is not counterfactually dependent on the present, and the backtracking conditionals are ruled out.

Objections to Lewis's Theory of Similarity

Due to arguments by Bennett, Elga, and Loewer (which I will not recreate in detail here), many are persuaded that Lewis was incorrect in his assumption that convergence to the actual world via a tiny miracle is impossible. These examples consider worlds in which highly improbable processes that involve decreases in entropy occur. These worlds are, nonetheless, lawful. (See Elga, "Statistical Mechanics and the Asymmetry of Counterfactual Dependence," 2000)

Lewis responded to these examples by stating that, "worlds that converge onto worlds like ours are worlds with counter-entropic funny-business. I think "the remedy--which doesn't undercut what I'm trying to do--is to say that such funny business, though not miraculous, makes for dissimilarity in the same way miracles do."

Many have suggested that this approach raises the question of whether fixing the similarity relation in this way is not just gerrymandering.

Douglas Kutach has suggested that the challenge that Elga's and Loewer's counterexamples presents has nothing to do with the problems of entropy (see Kutach, "Similarity is a Bad Guide for Counterfactual Truth, 2006). Rather it has to with a specific reading of the negation in the antecedent. Consider the following conditional: "If I hadn't dropped an egg into a heated pan, there wouldn't be a fried egg in the pan." There are two possible readings of the antecedent: ¬(I dropped the egg in the pan), I ¬(dropped the egg in the pan). Reading the antecedent differently draws our attention to different worlds as candidates for the most similar. In the first case, we might consider worlds in which I didn't exist, for instance. In the second case we may not. Due to the fact that reading of the antecedent ought to be context-sensitive, there is no way to codify a simple similarity relation that is likely to rule out problematic cases. In other words, the vagueness of counterfactuals undercuts Lewis's ability to come up with a unified theory of similarity.

If we drop the assumption of determinism, a plethora of problems are raised for Lewis's account. This is significant, since a good theory of counterfactuals should not depend on the truth of determinism.

Some of these problems center on Lewis's fourth criterion for similarity, that is, in assessing the closeness of a possible world to the actual world, little or no weight should be given to approximate match in matters of fact. To see the force of the objection, consider the following case due to Dorothy Edgington (see Edgington's "On Conditionals"):

In the actual world, at time t, a tree falls over and destroys the roof of a house. The counterfactual, "If the tree had not fallen, the roof would not have been destroyed," seems straightforwardly true. On Lewis's analysis, the closest possible will be one in which the past is the same as our past up slightly before t, at which point a tiny miracle ensures that the tree did not blow over. The consequent of the conditional, "the roof was not destroyed," is true at that world. But suppose, in the actual world, there was a tiny chance of lightning striking the roof of the house at t. It did not strike. Now consider a further world at which the tree does not blow over, but through an indeterministic branching, the lightning does strike.

The first thing to note is that the future of that world is fairly similar to the actual future. The family are homeless, people are injured, etc. And at that world, the consequent of the original conditional, is, of course, false. Since both worlds have the same stretch of match with regard to particular matters of fact, and both world have the same tiny miracle, the worlds are equally close, if we do not take any approximate match with regard to particular matters of fact into consideration. If we do take such matters into account, the world at which lightning struck must be counted as more similar, and the original conditional, "If the tree had not fallen, the roof would not have been destroyed," comes out false.

Additional worries arise from dropping deterministic assumptions. Laws of quantum mechanics tell us that in most ordinary situations, there is some small probability of an extremely bizarre event's occurring. So, if I drop a plate, there is some non-zero probability that it will fly off sideways instead of falling to the floor without any violation of the actual law. This threatens to make most ordinary counterfactuals, like, "If I drop a plate, it would fall to the ground," false. Lewis attempts to add to his similarity relation in order to fix the problem. He labels remarkable events with very low probabilities (like the sideways-flying plate) as "quasi-miracles." He then states claims that worlds with at witch quasi miracles occur are, ceteris paribus, less similar to the actual world than worlds at which they do not occur. Counterexamples presented by John Hawthorne (see "Chance and Counterfactuals") demonstrate that this strategy fails. I will not construct all of Hawthorne's cases in detail, but, I will rehash one to demonstrate the thrust of his argument:

Remarkable events sometimes have reasonably high probabilities. Consider a genius with a %20 chance of making some staggering scientific discovery. The genius dies in infancy. The counterfactual, "If the genius hadn't died, he wouldn't have made the discovery," seems false. But high probability outcomes, observes Hawthorne, divide into low probability subcases (series of events which lead the genius to make his discovery). So any world in which each of the remarkable, low probability subcases occurs will be father from the actual word, ceteris paribus, than any in which none of those processes occurred. By Lewis's lights, the counterfactual comes out true.

The plethora of counterexamples that have been launched against the Lewis analysis, in addition to these observations, have persuaded many philosophers that there is no way to patch up the Lewis's similarity relation so that it can do the theoretical work that he would like.