Truth-conditions of counterfactuals
In a previous post, I described David Lewis’ (1973) counterfactual analysis of causation and his claim that the truth of counterfactuals is rooted in similarities between this actual world and other possible worlds. That is to say, a counterfactual statement S is true (in our world) if and only if its antecedent and consequent are true in a nearby world, and that world is more similar to ours than any other world in which its antecedent is true but its consequent false. For instance, let S represent the following true counterfactual:
S: had Tom ignited the gunpowder with the match, it would have exploded
According to Lewis, S is true if and only if (1) there is a nearby world (W1) where Tom ignites the powder with the match and it explodes; and (2) W1 is more similar to our world than any other world in which the gunpowder fails to explode when ignited. These two conditions are jointly necessary and sufficient for the truth of S.
Objections from Bennett and Fine
As it would happen, philosophers like Jonathan Bennett (1974) and Kit Fine (1975) have criticized Lewis’ second condition on the grounds that its appeal to similarity ends up generating the wrong truth-values for counterfactuals like S. To see why, let’s amend our example by imagining that the pile of gunpowder is so potent that an explosion would cause a global holocaust and extinguish all life on planet earth. Thus, the following counterfactual S* is true:
S*: had Tom ignited the gunpowder, a global holocaust would have ensued
With this amendment in place, Lewis would have us believe that (1*) there is a world (W1) in which Tom lights the gunpowder with the match and a holocaust happens; and (2*) W1 more like ours than any world in which the ignition is not followed by a holocaust.
But is that reasonable to believe? It seems not, because we can conceive of a world (W2) in which Tom lights the powder without an ensuing holocaust and that world is more like our world in the all relevant respects. Suppose that in W2, the pile of gunpowder is partially damp so that the explosion is stayed when Tom lights it. In that scenario, the antecedent of S* is true, but life goes on in much the same way as it does in our world. Surely W2 is more like our world than W1 where all planetary life ends up being destroyed! But if W2 is closer than W1, then on Lewis’ account S* is turns out to be false – which is the wrong truth-value.
Lewis (1979) has a good response to this objection, however. He can point out that the antecedent conditions in W1 and W2 are not precisely the same. Tom applies the flame to the powder in both worlds, but in W2 the pile is partly damp whereas in W1 it is not. These differences are relevant because Lewis’ theory of counterfactuals requires that the antecedents in both worlds be the same before they get compared to the actual world.
Moreover, when all the historical details in W1 (leading up to and including Tom’s ignition of the dry gunpowder) are fixed as part of the antecedent of S*, we see that the powder can’t be damp. It has to be dry because otherwise we’d be dealing with an antecedent different from the one specified by S*! Thus, Lewis can argue that when all the relevant details are fixed beforehand, the holocaust follows inevitably.
Unfortunately for Lewis, Bennett and Fine’s objection can be modified to apply to counterfactuals with fixed antecedents. To see why, imagine a world (W3) where Tom ignites the dry pile but due to a miraculous exception to the laws of nature (at that moment) the powder does not explode. The antecedent of S* is true in W3 but the consequent of S* is false because a holocaust has been averted.
Now, here is the rub. W3’s future proceeds in much the same way as it does in ours. In both worlds, creatures on earth continue to thrive and go about their usual business. The only discrepancy is a minor miracle that occurs in W3 but not in ours. However, W1’s future is vastly different from ours! The holocaust has destroyed the earth’s biosphere and events proceed along a very different course. If so, then W3 (the “minor miracle” world) is more similar to ours than W1 (the “holocaust” world), and so by condition 2* of Lewis’ theory, S* turns out to be false – which is the wrong truth-value.
How might Lewis undercut the claim that W3 is closer to our world than W1? What if (contrary to Bennett and Fine) many large-scale miracles were needed to make W3’s future coincide with ours? Would W3 then be a problem for Lewis’ theory?
 This modification is more fantasy than fact, but bear with me. The reader can easily substitute a different example in which Tom detonates a fission bomb, causing a nuclear holocaust!