Friday, 20 January 2017

'Close Enough' Closer to the Truth About Counterfactuals

Lewis would have liked to be able to say that a counterfactual A > C is true iff the corresponding material conditional is true at all closest worlds. But his example of the inch long line seemed to show that sometimes there are no closest worlds - you can get closer and closer without limit to being one inch long while still not becoming one inch long. Wanting to avoid the Limit Assumption - the assumption that you do hit a limit as you get closer to actuality, after which you cannot get closer except by reaching actuality - he plumped for a clever, but complicated and costly solution; requiring that no A & ~C world is closer to actuality than any A & C world. (In his (1981) he admitted that this is costly in terms of simplicity and intuitiveness.)

I think Lewis here was too hung up on the idea of minimal change to the actual world. Proposing instead that a counterfactual A > C is true iff the corresponding material conditional is true at all close enough, or relevantly similar, worlds is a better way to avoid the Limit Assumption. (This theory might work for indicatives, too, but that's an especially vexed issue.) Why is this better?

(1) It lets you have a simpler, more intuitive form of account, with a set of worlds which are relevant.

(2) This also lets you have nice things like these results about when it's OK to use certain inference patterns.

(3) It better handles what might be called 'categorical' or 'no matter what' conditionals like 'If you had seen a cat then you would have seen an animal', where this is intended in such a way that you could add 'definitely' or 'no matter what' after the 'then' without changing the truth-condition, and is generally a more flexible and hence powerful account.

(4) It lets you straightforwardly explain why 'If this person had been taller, they would have been only a tiny bit taller' and the like are not true. Lewis can do this at the cost of saying that here close similarity in height just isn't important, but this is a little awkward given his case against the Limit Assumption.

(Donald Nute long ago proposed a 'close enough' account as better than Lewis's (see references below), but it seems few people listened. Also, some of his reasons can be diffused by being clever and flexible about what matters for similarity, and he didn't have (2) above to offer, and maybe not (3) either.)

Why wouldn't you go this way? One reason I can think of is that it may seem like a regrettable move to a less definite, less informative form of account. After all, if I am told 'the tallest people will be given a prize' this seems more informative than 'everyone tall enough will be given a prize'. But in the present context, this is illusory. You need to build in so much contextual flexibility into Lewis's account to make it at all plausible that the indefiniteness there swallows up the apparent difference in informativeness. Either that, or you keep the edge in definiteness but at the cost of implausible truth-value verdicts. Minimal change, I suspect, is a good way of thinking about lots of counterfactuals, and maybe those were the ones on Lewis's mind - but I see no reason why the change would ever have to be so minimal that you need to abandon having a set of relevant worlds and move to Lewis's official 'no A & ~C world closer than any A & C world' account. For other counterfactuals, minimality seems not to the point at all. So it's good to have a more flexible 'close enough' style account for your general theory of counterfactuals (or conditionals in general).


Lewis, David (1981). Ordering semantics and premise semantics for counterfactuals. Journal of Philosophical Logic 10 (2):217-234.

Nute, Donald (1975). Counterfactuals and the similarity of words. Journal of Philosophy 72 (21):773-778. (Title [sic]. As far as I know it's just a very unfortunate typo and it should be 'worlds'.)