Thursday 16 June 2016

Modal Realism and Counterpossibles: A Tension in Lewis

David Lewis held that possible worlds are worlds as concrete as our own (cf. Lewis (1986)). He also held, in his work on counterfactuals (cf. Lewis (1973)), that all counterfactuals with impossible antecedents - 'counterpossibles' - are vacuously true. These two views do not fit together well. Embracing modal realism leads to especially compelling counterexamples - counterexamples given modal realism, that is - to the thesis that counterpossibles are all true. These take the form of conditionals whose antecedents are not intuitively impossible, but which are impossible given modal realism.

These arise because, according to modal realism, reality as a whole – that is, the totality of the posited worlds – is necessarily the way it is. Lewis is very upfront about this. Witness:

There is but one totality of worlds; it is not a world; it could not have been different. (Lewis 1986: 80.)

So, for example:

'If there had been two fewer men in reality as a whole than there actually are, there would have been fewer women.'

There is no reason to think this is true. And yet Lewis's thesis about counterpossibles, together with modal realism, implies that it is vacuously true.

Perhaps worse:

'If there had been fewer men in reality as a whole than there actually are, there would have been just as many men in reality as a whole as there actually are.'

This seems positively false.


Thanks to Quentin Ruyant for pointing out that the last counterfactual, given modal realism and the thesis that there are infinitely many worlds with men in them, actually seems to come out true in a funny way: if there had been two fewer men, there still would have been infinitely many. So this was a bad example. Consider instead:

'If there had been no Model-T Fords in reality as a whole, there still would have been some Model-T Fords in reality as a whole'.


Lewis, David K. (1973). Counterfactuals. Blackwell Publishers.

Lewis, David K. (1986). On the Plurality of Worlds. Blackwell Publishers.


  1. So if one wanted to maintain Modal Realism could they just say: "well yea, these counterpossibles aren't true"? Does the Modal Realist have to make any sacrifices that he or she might not want to?

    1. I think that would be a fine response for the modal realist, yes. The point is that it is hard to be, like Lewis, both a modal realist and someone who holds that all counterpossibles are true. Giving up the latter in response to my argument is a perfectly respectable response, putting aside modal realism's general implausibility.

  2. If there is an infinite number of possible worlds, then if there had been two fewer men, there would still be an infinite number of men in reality as a whole, so the second sentence is true.

    In any case as Lewis suggests that modal talk reduce to talk about possible worlds I'm not sure the sentences provided make sense at all. You're taking about other possible "realities at a whole" but there's no such thing. We expect his theory to account for modal discourse in common talk, or maybe in scientific discourse, but here, you're not providing examples from science or every day usage. I'd say your examples are just meaningless sentences, once we're clear about what "reality as a whole"is.

    1. 'If there is an infinite number of possible worlds, then if there had been two fewer men, there would still be an infinite number of men in reality as a whole, so the second sentence is true'

      Good point! Updating the post now with a new example which doesn't have this problem.

      Regarding the second point: intuitively, the counterfactuals involved do not - I think - suggest that there are somehow 'other realities as a whole' which exist. They are just about what would be the case if the one and only reality as a whole were different in certain ways.

      Now, I take it that the suggestion is that, *from a Lewisian point of view*, these sentences may just be meaningless. I have a two-pronged response to this.

      First prong: that's a hard sell. How exactly is the modal realist story about their meaninglessness supposed to go? Applying modal realism and the Lewisian analysis of counterfactuals to these, it doesn't seem like they wind up being about other realities as a whole. Rather, it seems like they amount to something like: at the closest possible world where (reality as a whole is different in some way), (some other claim about reality as a whole holds). And since, by modal realist lights, the antecedent of such a counterfactual won't be true at *any* possible world, it comes out vacuously true given Lewis's thesis about counterpossibles.

      Secondly, even if the modal realist can somehow argue that from inside their way of looking at things, these sentences are not vacuously true after all, but meaningless, then the question arises:

      Do these supposedly meaningless sentences still count as counterpossibles? If so, then you have to agree that your modal realism fits badly with the vacuous-truth thesis about counterpossibles!

      Furthermore, and whether or not they count as counterpossibles on your view, you still have a problem, since intuitively these conditionals do make sense (and non-vacuously have truth-values).

      (NB: that 'you' and 'your' here refer to hypothetical-Lewis, or any hypothetical philosophers who holds modal realism and also holds the vacuous-truth thesis about - not you Quentin.)

  3. Thank you for your answer. Intuitively I would say that when we talk about "reality as a whole" (the set of all possible worlds), we are in some kind of meta-language whose role is to reduce the modal discourse of an object language to possible worlds. That's why I was tempted to analyse your statements in a "meta-meta-language" (=other possible "realities as a whole"). Then your point would be either that reducing modal discourse within the object-language is problematic, or that producing modal statements *in* the meta-language is problematic. But one could grant that modalities can only be reduced from a meta-language, and stipulate that modalities should not be part of the meta-language, because the point was to reduce modal talk! That's a way of making sense of the meaninglessness of these examples. This answers to your second point too: such sentences do not count as counterpossible, because only object-language sentences can be counterpossible, and we should resist the intuition that they make sense, because we're actually mixing two different levels of language.

    Now that's the kind of intuition I had and I am not sure that it's what Lewis would say (indeed I'm not a lewisian) but it looks like a good way to solve the problem.

    1. By your reference to 'the problem' I take it that my work is done here! At least in the first instance: the point was to show that there is a difficulty in combining modal realism with the thesis that counterpossibles are vacuously true - not that there is no possible answer to the difficulty.

      Regarding your answer, one thing I'm not clear on is: isn't the "object language" here ordinary discourse? And so doesn't this language allow for the conditionals in my examples? Is there any principled reason to exclude them?

    2. I agree that your post raises an interesting issue. No problem! :-)
      Regarding your second point: precisely, I would say that talking about "reality as a whole" as "the set of all possible worlds" is not part of ordinary discourse, but a metaphysical machinery whose role is to clarify ordinary discourse. That was my point, in my very first comment, that your examples do not seem to correspond to something we would say in ordinary discourse. Also, I think I read somewhere that Kripke, who reintroduced possible world semantic for modalities, was well aware that this should be conceived of as a meta-language analysis (but I have no precise reference on this, sorry...).

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