A Priori Metaphysical Possibility (by guest blogger Jonathan Ichikawa)
Some philosophers think that we can't know any propositions to be possible a priori. One way to argue that we can't do this might go something like this: at best, you can only know something to be conceptually possible a priori; but conceptual possibility doesn't entail real (metaphysical) possibility, for which armchair investigation isn't enough. This is because, as Kripke demonstrated, some conceptual possibilities are metaphysically impossible.
(Hesperus is not Phosphorus is metaphysically impossible because 'Hesperus' and 'Phosphorus' refer rigidly to the same object something that requires empirical investigation to establish. But it seems in some sense conceivable. We might call this a mere conceptual possibility.)
I agree that not all conceptual possibilities are metaphysical possibilities. But I think that, given a priori access to conceptual possibility and conceptual impossibility, we can get some a priori access to metaphysical possibility. Because I think there is an a priori link between conceptual and metaphysical possibility.
Here's a principle that might be true and a priori:
For any proposition q, if q is conceptually possible but metaphysically impossible, then there is some conceptually possible proposition p such that p -> []~q is conceptually necessary. (That's a material conditional and the box of metaphysical necessity.)
Why believe this principle? For one thing, for any such q, ~q is an a posteriori necessity, and a posteriori necessities follow a priori from empirical facts and concept possession. Since all empirical facts are conceptually possible, this is sufficient to prove the principle.
This principle gives us an a priori test for metaphysical possibility. (I'm assuming a priori conceptual modality.) Take some conceptually possible proposition q. If it is conceptually impossible that some conceptually possible proposition p is such that p conceptually entails necessarily not-q, then q is genuinely metaphysically possible.
For instance, it is conceptually possible for the Bears to have won the 2007 Super Bowl. Furthermore, there is no conceivable proposition p such that it is a priori that if p, then it is metaphysically impossible for the Bears to have won the 2007 Super Bowl. Therefore, it is metaphysically possible for the Bears to have won the 2007 Super Bowl.
If this is right, then one upshot is that it's worth getting clear on what conceptual possibility amounts to, and how it works.
I'd like to thank Eric for the opportunity to guest-blog for the past few weeks, and to thank everyone who's read and offered valuable comments. I hope and believe that this has helped get me back into the habit of philosophical blogging I'll be continuing back at my own blog, There is Some Truth in That. I hope to see some of you there.
[And from Eric: Thanks so much, Jonathan, for your thought-provoking posts!]