Leibnizian explanations

Say that p is a Leibnizian explanation of why q rather than r provided that p explains why q and not r and it is not possible for p to explain r.

I am inclined to think that a Leibnizian explanation of why q rather than r is a contrastive explanation of why q rather than r. But does the converse hold? Are contrastive explanations always Leibnizian?

The answer may depend on what we do about background assumptions in explanations—whether we count them as part of the explanation. I ask why you are wearing a watch on your right wrist rather than your left. You say:

1. I didn't want to be like everyone else.

But in a country where watches are normally worn on the right wrist, this could explain why the watch was worn on the left. So if we count (1) as a bona fide case of contrastive explanation, not all contrastive explanations are Leibnizian.

But perhaps we should take the background assumptions to be tacitly a part of the explanans in (1). Thus, maybe the real explanans is:

2. I didn't want to be like everyone else, and everyone else was wearing watches on their left wrist.

The problem with this move, however, is that the game can go on. Suppose that it's Lent and we're in a community where everybody tries to frustrate their minor preferences during Lent. Then (2) could explain why one was wearing the watch on the left wrist. So it's still not a Leibnizian explanation. But maybe, once again, we should take the explanans as tacitly including information from the background, like:

3. I didn't want to be like everyone else, and everyone else was wearing watches on their left wrist, and I had no reason to frustrate my minor preferences.

But the game doesn't stop here. Imagine a world where aliens frustrate people's minor preferences when and only when the people have no reason to frustrate them. Then (3) could explain wearing a watch on the left wrist, because the aliens would ensure that it's there. We can say that there was more tacit stuff in the explanans that rules this out. But can we ever stop? Do we really want to insist that explanations are always implicitly infinite?

So it looks like it's hard to defend the claim that contrastive explanations are Leibnizian. But perhaps we can defend the claim that contrastive explanations are weakly Leibnizian, where p is a weakly Leibnizian explanation of why q rather than r provided p explains q and not r, but p does not explain r in close worlds where it is true that r. I like the context-sensitivity of the "in close worlds". But if one doesn't like it, one could instead go for:

4. p is a weakly Leibnizian explanation of why q rather than r if and only if p explains why q and not r, and were r to hold, it would be false that p explains r.

It is now fairly plausible that contrastive explanations are weakly Leibnizian. Is it plausible that weakly Leibnizian explanations are contrastive? I think so.