Here's my current position: modal notions (i.e. possibility versus necessity) cannot be applied simpliciter. Instead, they need to be assessed against some background framework of stipulated limitations. Some examples would be:
- Epistemic possibility - Whether a state of affairs is consistent with our current state of knowledge.
- Physical possibility - Whether something contradicts our actual (practical) physical capabilities and such. E.g. it is physically impossible for a human to run a mile in ten seconds.
- Natural possibility - Whether something contradicts the 'natural laws' (or laws of physics) that govern our universe. E.g. travelling faster than light is impossible in this sense.
- Logical possibility - Whether something is logically consistent. E.g. it is logically impossible for my cat to be both alive and not alive (at the same time).
One might also extend this template to interpret deontic possibility (or rather, permissibility) in terms of what is consistent with (or allowed by) some particular set of rules - e.g. a moral or legal code.
But what about metaphysical possibility? What's really possible? What could have existed? I don't think we can answer this question. I'm not even sure if it's asking anything meaningful.
Some might equate metaphysical possibility with what people can imagine or conceive of. But conceivability merely tells us about the limits of human cognition, and doesn't necessarily imply anything deeper about the possible nature of reality. I have difficulty conceiving that time and simultaneity could be relative, not absolute. Yet this is not only possible, but indeed true!
Others might simply equate metaphysical with logical possibility. But I'm not sure that this is justified either. After all, what reason is there to think that logical impossibilities are metaphysically impossible? We cannot conceive of them, sure, they seem "absurd". But, as suggested above, this cannot be reason enough.
Besides, it might (this is an epistemic 'might') be the case that some logical contradictions are in fact true. [Update: I reconsider and indeed retract this claim, here.] Quantum physics is the most serious contender here (did the photon go through the left slot or the right? Is Schrodinger's cat dead or alive?). Some also argue that the Liar's Paradox is best understood as being both true and false. If we adopt a paraconsistent (rather than classical) logic, then this is not a disastrous result.
And this then brings up another reason for doubt: namely, that there are many different logics! "Logical possibility" is (I think?) bound by classical logic. But there's no reason to think that reality is, when there are so many alternatives to choose from. For those who think it "obvious", and the alternatives "absurd", the fall of Euclidean geometry provides a handy precedent. For centuries, mathematicians and philosophers thought that Euclidean geometry was "absolute truth". But in actual fact, it merely applies to flat planar surfaces, and if we instead consider curved surfaces, then non-Euclidean geometries (complete with different laws and a priori 'truths') result. So although people in the past took it as a necessary truth that exactly one line can be drawn through a point, such that this new line is parallel to some other given line, in actual fact this axiom isn't even always contingently true!
Don't get me wrong, I think the idea of "possible worlds" can be a useful heuristic. But if they're merely defined by logical possibility, rather than metaphysical possibility, then we should be clear on that. For example, the usually-sharp Maverick Philosopher attempted to refute the idea that laws of logic are empirical generalisations (and hence only contingently true), by equating contingency with logical contingency. But of course this is quite blatantly question-begging. Of course if you assume that metaphysical possibility simply is (or implies) logical possibility, then the laws of logic are necessary and not merely contingent. He reached the conclusion by (implicitly) assuming it as a premise, which is a rather cheap (and unconvincing) move. [Update: see here and here for more detail.]
To change tack slightly, I was also struck by the problem of (categorical) possibility when writing my essay on Van Inwagen & Free Will. For if determinism is true, then given the current state of affairs and the laws of nature, there is only one categorically possible future. And that seems to be an awfully limited understanding of possibility! Indeed, even if we ignore determinism, the fatalist's "argument from truth" would seem to establish this categorical uniqueness.
The Fatalist's Argument From Truth:
1) Let E be any event that occurs in the future
2) Then, the proposition that E will occur is true.
3) So, nobody can bring it about that E does not occur.
4) That is, E is inevitable.
In my essay above, I argued that adopting a categorical notion of 'could' (i.e. possibility) commits one to the soundness of this absurd fatalist argument. After all, one presumably could not (categorically) bring about a logically inconsistent state of affairs.
I conclude, then, that categorical possibility is so empty as to be effectively meaningless - we are better off adopting a hypothetical understanding of choice and modality.
Modal notions seem to arise from a certain sort of counter-factual thinking. We establish some particular limitations, and then we consider what states of affairs are allowed within our chosen framework. But divorced of any such framework, modal notions strike me as meaningless. If you take away the limitations, then we're stuck with the empty truism: "anything is possible".
Am I missing something here?