Now my worry is this: Swinburne’s god seems metaphysically possible, and yet this possibility seems incompatible with PSR. But if so, then why shouldn’t I conclude, “so much the worse for PSR”?

Myself, I think the intuitions behind (2) come from non-circular finite cases where (2) does in fact hold. (If circular explanation is impossible, then I can drop the “non-circular” in the previous sentence.) I can occasionally get myself into a mood (mainly by reading and thinking about Aquinas) where I find denying (1) plausible. But generally I find (1) fairly plausible, and the conjunction of (1) and (2) very implausible, and so I tend to deny (2).

I wonder if we’re mislocating the clash of intuitions here. I think the cannonball’s flight is explicable because every part of it is explicable. More precisely, I think the following argument is sound.

1) Every part of the cannonball’s flight is explicable.
2) If every part of the cannonball’s flight is explicable, then the flight is explicable.
3) So, the cannonball’s flight is explicable.

I take it the cannonball is an interesting example because it’s meant to be a challenge to (2), which is an instance of a more general principle (the Hume-Edwards principle).

But to the extent I can see any intuitive force here, it’s to reject (3). And, if I try to put myself in the frame of mind to reject (3), what I find is that (2) still seems plausible, but I start to doubt (1). I start to think, that is, that an ‘ungrounded’ explanation, such as the explanation of the cannonball’s later trajectory in terms of its earlier trajectory, is no explanation at all.

That would be independently interesting for debates about regresses. But now I’m interested if there’s any positive reason to think (2) is the culprit in this argument rather than (1)? (Assuming, of course, that there is a culprit. I think on reflection the argument is sound, and the force of the arguments for (1) and (2) is stronger than any intuitive implausibility of (3).)

Even if you don’t have the intuition that E3+E4 fails to be an explanation for (5), do you think there’s a theory of explanation that says it is an explanation?

I don’t think E3+E4 unifies, in any interesting way, the relevant facts, so I don’t think it counts as an explanation on a unification approach.

And I think (5) is the wrong kind of thing to be caused, it doesn’t report the occurrence of an event after all, so it can’t have an explanation on a causal account.

And, unsurprisingly, it fails to be an explanation on a prominent hybrid account like Strevens’.

So even if you think intuitively E3+E4 is an explanation for (5), do you think there’s a theory of explanation on which this is true?

First of all, it wouldn’t do justice to our intuitions about the PSR if the flight of cannonball counted as explicable. For then bricks popping into existence ex nihilo and all that would be explicable, as long as they did so on time intervals open at the lower end.

Suppose I first hear of the flight of the cannonball, but don’t hear of the cannon being fired. I then hear of the cannot being fired. It seems that only when I’ve heard of the firing of the cannon that “it makes sense”, that it becomes explicable. (It doesn’t seem to me that this is like the case of a coincidence where when there is no further explanation of the conjunction, we shrug our shoulders and say: “I guess it was just a coincidence”, but when we find a further explanation, we say: “Ah, so it’s not just a coincidence.” Chains of causes aren’t the same sort of thing as coincidences.)

I suppose you’d have the same intuition about circularity? If I learn how to make the time machine from my future self, and then go and make it and tell my past self how to do that, do you have the intuition that this is all explicable?

It’s true that there isn’t, as far as I can tell, an explanation for the flight. But I think that’s a very different question.