## Contrastive explanation and the PSR

Perhaps, though, we can formulate the dissatisfaction with statistical quantum mechanical and libertarian explanations as follows. Suppose we are dealing with an electron in a mixed |up> + |down> state, which in an appropriate magnetic field will either go up or down, with equal probability. Suppose it goes up. Why did it go up? Because of its state, the experimental setup, and the laws of nature. Maybe this is a fine explanation, but it does not seem to be a contrastive explanation. It does not explain why the electron went up rather than down.

The simplest move at this point is just to deny this intuition, and say that the same facts can explain why it went up rather than down, as would have explained why it went down rather than up. Alternatively, one might distinguish the quantum mechanical and libertarian cases. Perhaps one can take a deterministic interpretation of quantum mechanics, and in libertarian cases give contrastive explanations in terms of different sets of reasons, as in Section 2.3.2.3, above.

Another move available to the defender of the PSR is to admit the failure of contrastive explanations. But the PSR says that every contingently true proposition p has an explanation, not that for every pair of propositions p and q where p is contingently true and q is a relevant alternative to p, there is an explanation of why p rather than q holds. There may well be such a notion of explanation that would make explanation be a ternary relation, but there is also a perfectly fine notion of explanation that makes explanation a binary relation, and it is the latter that the PSR concerns.

Some do, however, believe that all explanation is contrastive (cf. Dretske 1972; van Fraassen 1980). The standard example is something like this. George ate a banana rather than eating an orange because he liked bananas. George ate a banana rather than putting it in his backpack because he was hungry. Without specifying a contrast, we cannot tell which explanation we are after.

Arguments like this do not, however, establish that explanation is always contrastive. If we do not specify a contrast, we can give an explanation along either set of lines. George ate a banana because he liked bananas and chose to eat. George ate a banana because he was hungry and chose a banana. Neither explanation tells the whole story. But we can elicit more of the story by applying the PSR again. Why did George like bananas and choose to eat? Granted, we might say that this is because he likes nonjuicy sweet fruit and chose to eat, leaving that second conjunct as yet unexplained. But if explanation comes to an end in an ultimate explanation, we cannot just keep on furthering the explanation of the first conjunct - eventually, we will be done with that side, and a further demand for explanation will force us to tackle the question why George chose to eat.

A different move is that on its own terms the PSR that I am defending requires contras-tive explanation. After all, it requires an explanation of every contingent proposition and that the electron went up rather than going down, or that George ate a banana rather than eating an orange, is a perfectly good proposition.

There is room to be quite unsure here, though. For it might be argued that when we make a contrastive claim, we are doing two things. We are asserting a proposition with an "and . . . not" truth-functional connective, for example, that the electron went up and did not go down, and drawing the listener's attention to the contrast between the two claims joined by the truth-functional connective. The proposition asserted, however, is not con-trastive in nature and can be explained straightforwardly. We can just give the statistical explanation of why the electron went up and explain that if it went up, it could not have gone down at the same time, so it went up and did not go down.

There is reason to think this is the right way to understand contrastive claims. First, note that whatever proposition is asserted by saying "p rather than q holds," necessarily, it is a proposition that is true if and only if p is true and q is false. To see this, begin by observing that if p is not true or q is not false, then whatever "p rather than q holds" expresses must be false.

The converse is more difficult to establish. There certainly are cases where the sentence "p rather than q holds" is not assertible even though "p holds" and "q does not hold" are assertible. These will be cases when there is no relevant contrast between p and q. Thus, in typical contexts, "The moon is spherical rather than Jupiter being cubical" is not assertible. However, the failure of assertibility is not due to facts about the objective situation being talked about, but due to one's concerns, interests, and epistemic position. There will be epistemic contexts involving no mistakes but where "The moon is spherical rather than Jupiter being cubical" is assertible. For instance, suppose that George has seen neither the moon or Jupiter, and nobody has told him anything about them, except that an epistemic authority testified to him that the moon is spherical or Jupiter is cubical. One day, George learns that Jupiter is spherical. He then correctly sums up his conclusions: "The moon is spherical rather than Jupiter being cubical!" Given knowledge that p and that not-q, the assertibility of "p rather than q holds" depends on nonalethic matters, and hence all we need for truth is p and not q.

One might object that "p rather than q holds" asserts something about the state of mind of the speaker - that it is a mind-dependent proposition. But that is completely mistaken, since, then, every "rather than" claim would entail the existence of a speaker saying that claim, but that the moon is spherical rather than Jupiter being cubical entails nothing about a speaker who is saying that the moon is spherical rather than Jupiter being cubical.

So if proposition r is expressed by "p rather than q holds," then, necessarily, r holds if and only if p&~q. I think it is simplest to suppose that r is actually the same proposition as p&~q.

But suppose this is denied, and it is said that there is "something more" in the proposition that p rather than q holds than in p&~q (for surely there is nothing less). Nonetheless, the contrastive explanation argument can be questioned. It is no coincidence that p rather than q holds if and only if p&~q holds - it is a necessary truth, in light of the said argument, that this is always the case. In fact, it seems right to say that what makes it be true that p rather than q holds is simply that p holds and q does not hold. The fact that p&~q seems to be the more basic, the more primitive, since the fact that p rather than q holds contains it and that mysterious "something more." But then, this provides a conceptual explanation of why it is the case that p holds rather than q: p holds rather than q because p&~q holds, and p&~q is more ontologically basic, and necessarily whenever a&~b holds, a rather than b holds. Granted, this is not a contrastive explanation; but that only shows that the attempt to assimilate contrastive explanations to explanations of contrastive propositions failed.