Explanation modulo a fact

A notion that I find rather natural is the idea of explanation modulo a fact. This notion can do some of the work that contrastive explanation can.

1. Why did you eat a banana?

can be precisified contrastively in ways like:

2. Why did you eat a banana rather than something else?
3. Why did you eat a banana rather than doing something else with it?
4. Why did you eat a banana rather than not eating anything?

But one can also accomplish the same thing this with requests for explanation modulo a fact. Doing the work of 2 and 3 is easy:

5. Given that you ate, why did you eat a banana?
6. Given that you did something with a banana, why did you eat it?

Doing the work of 4 is a bit harder, but maybe this works:

7. Given that you ate a banana if you ate anything, why did you eat a banana?

When we ask for explanation why p given q, we are asking for something that isn't just an explanation why q, and that gives us a further explanation why p when added to the fact taht q. The question presupposes there is such an additional truth. If the fact that q is the one and only complete explanation why p, then the question has a false presupposition.

It seems, however, that any request for explanation modulo a fact can be rephrased as a request for contrastive explanation. For instead of asking:

8. Given q, why p?

one can ask:

9. Why p and q rather than not-p and q?

This makes explanation modulo a fact not very useful, it seems. However, one can also formulate contrastive questions as requests for explanation modulo a fact. Thus the contrastive question:

10. Why p₁ rather than p₂, p₃, ... or p_n?

can be replaced with:

11. Given p₁, p₂, p₃, ... or p_n, why p₁?

So which is more fundamental? Explanation-modulo or contrastive explanation? I don't know. The literature prefers contrastive explanation, but that may be a historical accident.

In any case, I think all this makes an important fact about contrastive explanation clearer, a fact that I learned from conversation with Dan Johnson: When you make a request for a contrastive explanation, you are also indicating a refusal to accept certain kinds of answers. In the explanation-modulo case, these are answers that merely go through the given fact. But then the defender of the Principle of Sufficient Reason should feel no embarrassment about being unable to give answers to all requests for contrastive explanation—after all, that every fact has an explanation does not make for any kind of guarantee that the explanation will be of the sort we want. Once we start ruling out certain kinds of explanations, we might well be left with none.