Can a crocodile and a rooster mate and get a young? Disappointingly, they cannot. It’s impossible. Of course this impossibility has to be established empirically, either by trying to get a rooster and a crocodile to mate; or, more plausibly, by developing an understanding of reproductive processes and genetics that allows us to say with high confidence that species as unalike as these cannot generate live offspring.

These are answers given by science, not answers given by metaphysics. Does metaphysics also tell us that the child of a crocodile and a rooster is impossible? It depends. Certain metaphysical systems — those based on a liberal Humean principle of recombination, for instance — imply that it is possible for a crocodile to conceive after having intercourse with a rooster; and that much wilder things are possible too. According to the Humean, anything can follow anything else. But this seems to put metaphysics on a collision course with science. If science tells us that something is impossible, and philosophy tells us that it is possible… what are we to do? Isn’t the Humean guilty of terrible a priori biology?

The Humean does not take herself to be contradicting science. And the most common opponent of the Humean, while disagreeing with the Humean about what is possible, does agree with the Humean that there is a philosophical dispute here that science simply cannot adjudicate. Both the Humean and her opponents work with a distinction between different types of possibility. There is, first of all, physical possibility, which is possibility according to the actual laws of nature. This is what the natural sciences tell us about. Then there is metaphysical possibility, which is the domain of (unsurprisingly) metaphysics. The idea is that it is possible for the laws of nature to be different than they actually are; and so there ‘are’ ‘possible worlds’ in which things happen that are not physically possible, but which are metaphysically possible. Then, beyond metaphysical possibility, there is logical possibility. To be logically possible is simply to not be a contradiction. Certain things are supposed to be logically possible but not metaphysically possible, e.g., an object being both red all over and green all over.

We can thus create a kind of hierarchy:

1. This crocodile is green and it is not the case that this crocodile is green. (Logically impossible.)
2. This crocodile is green all over and this crocodile is red all over. (Logically possible, metaphysically impossible.)
3. This crocodile has been impregnated by a rooster. (Metaphysically possible, physically impossible.)
4. This crocodile is hungry. (Physically possible.)

And now it is extremely easy to fall into the following trap: to think, namely, that the different levels of this hierarchy are gradations of (im)possibility. It is very temping to think that while a crocodile being impregnated by a rooster is impossible, yet it is somehow more possible than a crocodile being red all over and green all over; which in turn is somehow more possible than it being the case that the crocodile is green and it not being the case that it is green. In order to have the crocodile conceive after intercourse with a rooster, we only have to break the laws of physics, whereas for the other items, we must do something that is even more impossible, namely, break the laws of metaphysics or even logic.

This is a trap and we must not fall into it. It is impossible for a crocodile to get pregnant from a rooster. End of story. The levels of the hierarchy are not gradations of impossibility; rather, they express what we need to show that something is false. A proposition p is logically impossible in case we can show its falsity using only formal logic. It is metaphysically impossible in case we can show its falsity using only principles of abstract metaphysics. It is physically impossible if we can show its falsity using the laws of physics. And it is not impossible in any of these senses, but simply contingently false, if we can show its falsity using particular empirical observations.

This hierarchy, then, is a hierarchy that makes sense only in the context of certain human practices. “This crocodile is green and it is not the case that this crocodile is green” is called logically impossible because standard propositional logic is strong enough to prove its falsity. If we only had propositional logic, then “This crocodile is green and it is not the case that any crocodile is green” would have to be called logically possible, and its impossibility would probably be called metaphysical, based on metaphysical principles about all-ness and particularity. But of course we do have a standard logic that formalises principles about all-ness and particularity, first order predicate logic, and so “This crocodile is green and it is not the case that any crocodile is green” is deemed logically impossible. But this is a fact, not about crocodiles and not about possibility, but about the classifications that follow from our practices. If we standardly used a logic built around the idea of compatible and incompatible predicates, then “This crocodile is green all over and this crocodile is red all over” would be logically impossible. But we don’t, and so we classify the impossibility as metaphysical. Of course, if we didn’t talk about predicates and compatibility even in our metaphysics, then this claim would be considered false on the basis of a scientific theory of colours.

Once we understand that this is how the different kinds of possibility function, it’s hard to see what the interesting issue is between the Humean and her opponent. The Humean says “a crocodile and a rooster can mate and have a child together.” If this is meant to be a piece of biology, that is, if we are allowed to use all our scientific knowledge in order to evaluate it, then it is straightforwardly and uncontroversially false. But now it is supposed to be a piece of metaphysics; we are supposed to find out whether it is metaphysically possible that these two animals have offspring. What this means is that we are not allowed to use our scientific knowledge. We are supposed to abstract away from anything we know about crocodiles and roosters, conceive of them in purely ‘metaphysical’ terms, and see if the falsity of the claim follows. Why would we want to do this? Surely only to test the strength of our metaphysical theory, so to speak.

The Humean tells us that in purely metaphysical terms, the claim to be evaluated is “an A and a B are contiguous for a while, and then are followed by a C.” Of course we can’t see anything wrong with that. The dispositionalist will say that the claim to be evaluated is something like “an object A with the disposition to be followed by a C only after it has been contiguous with a D, has been contiguous with a B but not with a D, and is then followed by a C.” Clearly, if we encode enough information about crocodiles and their causal powers in our metaphysics, then we’ll end up with enough information in that metaphysics to judge that crocodiles and roosters cannot have kids together. But none of this should be controversial. The Humean and the dispositionalist cannot disagree about these conditional claims about metaphysical possibility; they can only disagree about the conditions themselves, about how metaphysics should abstract from the world. But what is the relevance of that dispute? After all, crocodiles and roosters cannot have kids together. Whether we can reproduce that fact in certain of our more abstract modes of thinking seems, if not entirely uninteresting, at least not a question about reality.

And that’s the crucial point. Questions about metaphysical possibility are not questions about reality, at least not in any straightforward way. At best they are indirect questions about which metaphysical theories are to be preferred. If pressed, I would be willing to say “it is impossible for a world to be just like ours, except that the future is cut off and time just stops now.” But all that I mean with that is that a good theory about the nature of time is a theory that understands the future in terms of causal properties of the present; and that therefore no good story about temporality, at whatever level of abstraction, should allow for causally active objects without a future. To claim that worlds with a certain kind of temporal structure are impossible is really just a picturesque way of claiming that in philosophy we need to tell certain stories about time. Those stories about time are not a way in which we get a grip on a realm of real things, the metaphysical temporal possibilities.

Incalculable damage has been done to analytic metaphysics by the idea that one of the aims of metaphysics is to get a grip on what is metaphysically possible and what is metaphysically impossible; that metaphysical modality is a special subject matter for philosophy. But it’s not a subject matter at all. Given a certain theory of time, perhaps some temporal scenarios will be implied by that theory to be false, and then those are called metaphysically impossible. Given a certain theory of properties, perhaps some arrangements of things will be implied by that theory not to occur, and then those are called metaphysically impossible. But without the theories, there is nothing left. There is no realm of facts, there are no intuitions, there is nothing to investigate. And the theories are not made to get the realm of possibilities right. The theories are made to get time right, or properties, or value, or the mind, or whatever it is we are investigating. Those are the real topics.