Miracle Worlds in David Lewis’ Account of Counterfactuals

In a previous post, we considered Bennett (1974) and Fine’s (1975) objection to David Lewis’ theory that counterfactual truth is based on similarities between possible worlds. According to their objection, Lewis’ theory cannot handle “miracle” worlds because they generate the wrong truth-values for counterfactuals.

In a seminal article entitled Counterfactual Dependence and Time’s Arrow (1979), Lewis responded to the above objection by arguing that certain features of possible worlds are more or less relevant to determining similarities between worlds. He maintained that the absence of large-scale exceptions to natural laws matters more to similarity than the presence of large-scale agreement on matters of particular fact. Stated conversely, discrepancies pertaining to laws of nature make a bigger difference when comparing worlds than discrepancies in how particular details unfold.

How does Lewis’ standard of comparison apply to the previous objection? Well, it means that “miracle” worlds may not generate the wrong truth-values for counterfactuals after all! To see why, consider the chart (below) which compares the worlds most relevant to the truth of counterfactual S*: “if Tom had ignited the gunpowder, a global holocaust would have ensued.”

Chart of worlds (672 width)

In the actual world, Tom refrains from igniting the pile of gunpowder, and life goes on as usual; in W1, Tom ignites the powder with a match, and the powder is so potent that the explosion causes a global holocaust that extinguishes all life on planet earth; in W2, the powder is mostly damp, which means that when Tom ignites the dry particles, the explosion fails to occur, and life goes on normally; in W3, Tom lights the powder, but an exception to the laws of combustion happens immediately after the ignition, leaving the planet unscathed by a holocaust.

Now, Bennett and Fine argue that W3 is closer to the actual world than W1 because life goes on in W3 much like in the actual world; the only difference is the occurrence of a miracle. But if Lewis’ standard of comparison is correct, this point is mistaken. The miracle creates a bigger disparity than originally supposed.

What’s worse, there is reason to believe that multiple miracles (not just one) are needed to align W3’s future with ours. Why? Because Tom’s actions in W3 have had multiple effects on its future. For example, that future contains Tom’s memories of lighting the gunpowder; Tom’s surprise at the failed explosion; additional quantities of unused gunpowder; and less atmospheric oxygen. Thus, extra miracles would be needed to blot out Tom’s memories, erase his surprise, annihilate the extra powder, and redistribute the oxygen. As you can see, the effects of Tom’s activity in W3 generate a future that deviates quite a bit from the one in which Tom simply refrains from lighting the powder.

But the occurrence of extra miracles entails large-scale exceptions to the laws of nature operating in W3. Thus, by Lewis’ standards of comparison, W3 ends up being less similar to our world than the “holocaust” world in which these laws haven’t been tampered with. So it seems that Lewis has evaded Bennett and Fine’s objection.

However, Lewis’ evasion can be challenged on two points. First, instead of ironing out every discrepancy between W3’s future and our own, why not simply accept them as they are? A slightly different future with one miracle seems trivial in comparison to a global holocaust without a miracle!

Second, even if my first point fails, why should we assume (as Lewis does) that multiple miracles would be needed to iron out the differences? Michael Tooley (2014) has questioned this assumption in his book entitled Causation: Fundamental Issues, so I will be addressing Tooley’s arguments in my next post.

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