Posted by: Justin | February 18, 2010


I’m interested in looking at the plausibility of using counterpossibles – subjunctive conditionals with impossible antecedents – in philosophy for a few different reasons. I think we do, in fact, use them (or at least use what we should think are counterpossibles) pretty often. Suppose you’re an eternalist who thinks that eternalism is a necessary truth. If you want to offer an argument against presentism, you may run a quick modus tollens argument like this:

(1) If presentism were true, then some truths would lack truthmakers.
(2) But no truth can lack a truthmaker.
(3) Therefore, presentism cannot be true.

Now you may think this is a bad argument against presentism, but, of course, that’s not important for my point. Another worry is that the first premise of an argument like this isn’t usually put as a subjunctive conditional. But I don’t really know enough about the issue to know how important that is (hence the post).

Anyway, the point of this is to show that, if you’re an eternalist who thinks that eternalism is a necessary truth, then you should think that (1) is a counterpossible. The standard treatment of counterpossibles (following along with the standard Lewisian treatment for counterfactuals) is that they are vacuously true: “If it were the case that p, then it would have been the case that q” is true just in case the closest p-world is also a q-world (there are counterexamples to this as stated, but it will do for now). But if you want to run the above argument against presentism, then you shouldn’t think that (1) is vacuously true – you should think it makes a substantive claim. So if you want to use arguments like the one above in metaphysics (or any other discipline where many of the theories are taken to be necessary truths), then you should think that counterpossibles aren’t vacuously true.

From the little bit that I’ve read, I’ve also seen people make this point (Brogaard and Salerno cite Nolan). There seems to be a significant difference between (a) and (b):

(a) If Goedel had proved that arithmetic is complete, then Hilbert’s program may have been successful.
(b) If Goedel had proved that arithmetic is complete, then Goedel wouldn’t have proved that arithmetic is complete.

(a) sounds true, while (b) sounds false. But if counterpossibles are vacuously true, then (a) and (b) are both (vacuously) true, since the antecedent is impossible.

I think that there may be interesting applications for counterpossibles in philosophy, even beyond running modus tollens arguments against our opponents, as long as we do not treat them as vacuously true. I know that Brogaard and Salerno have a couple of papers on them, and Nolan has written something as well. I suppose I should also have a look at Lewis’s Counterfactuals. Any other suggestions?



  1. Trenton Merricks makes substantive use of counterpossibles in his book Objects and Persons. He says that it is not just false but impossible that chairs exist, but affirms that there are such things as atoms arranged chair-wise. He then defines the predicate “arranged chair-wise” as “arranged in such a way that, if (per impossibile) folk ontology were correct, they would compose a chair.” (I’m paraphrasing from memory here – that’s not exactly how he words it.) He also considers a fictionalist formulation (“atoms which, according to the fiction of folk ontology, compose a chair”), but prefers the counterpossible one.

    This particular use of counterpossibles seems pretty problematic to me (and, I think, to most people).

  2. Daniel Nolan’s paper “Impossible Worlds: A Modest Approach” can be found in a special issue of the Notre Dame Journal of Formal Logic edited by Graham Priest, on the topic of impossible worlds. There are a bunch of nifty papers in it, and the whole thing is available online here:
    Let me know if you decide to read through it! I’d be quite interested in discussing it.

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