There are many ways of defining the doctrine of determinism, but here's one that seems fairly straightforward, taken from the beginning of John Earman's book A Primer on Determinism:
World W1 is deterministic just in case for any physically possible world W2, if W2 agrees with W1 at any time as far as relevant physical properties are concerned, then W2 agrees with W1 at all times. [p. 13]
If we understand the notion of a physically possible world to be any world that shares the same laws of nature, then it is a consequence of this definition that if the actual world is deterministic, there is no physically possible world (except the actual world itself, of course) that agrees at any time with the actual world as far as relevant physical properties are concerned. Or, in other words, if determinism is true, then every physically possible world must have a completely different past, present, and future.
So far so good. But what I'm wondering about is what effect determinism in this sense might have on the proper analysis of counterfactual conditionals. According to the (perhaps) most promising approach to counterfactuals, in order to determine whether the conditional, "If A were the case, then B would be the case" is true, one needs to look at those possible worlds which are closest to the actual world where A obtains to see if B also obtains. If so, then the counterfactual is true. Of course, figuring out which worlds are closest to the actual world is a vexed question. But it seems to me that if determinism is true, the question becomes a lot more vexed than usual.
If determinism is true, which worlds are closest to the actual world? Surely none of the physically possible worlds are that close to the actual world, since as we saw above, all of those worlds have a completely different past, present, and future. But that means that the worlds closest to the actual world must have different laws of nature than the actual world. But that would be quite odd, too, because there is a strong intuition to think that worlds which are not physically possible are actually irrelevant to the truth or falsity of a counterfactual conditional. For instance, if I want to know what would have been the case if I hadn't gone to graduate school, I don't think I would be satisfied with finding out what happens in some world that doesn't share the actual laws of nature. I want to know what would have happened to me, in this world, if I hadn't gone to graduate school. But that's not the answer I get.
So I guess the problem might be put in the form of a dilemma. Assume that the correct analysis of counterfactuals is the one sketched above. Now, either the worlds closest to the actual world are the physically possible worlds or they're not. But all the physically possible worlds have a completely different past, present, and future, so those worlds can't be closest to the actual world. So, the worlds closest to the actual world are not the physically possible worlds. But the non-physically possible worlds don't seem relevant to the truth or falsity of certain counterfactual statements. So -- should we reject this analysis of counterfactuals? What other options sound better?
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