This won’t be at all original, but it’s an interesting issue. And topical now, since it came up over at the “Fake Country”:http://www.brown.edu/Departments/Philosophy/Blog/Archives/002792.html blog. Often, if not always, the explanation of the truth of one proposition is the truth of another proposition. We’re going to focus on those kinds of explanations here. The first question is

bq. If both p and q explain r, and p entails q, which of p and q is the better explanation? If the answer is “It depends”, say what it depends on and why.

David Lewis, in his paper on explanation in “Philosophical Papers volume 2”:http://www.amazon.com/exec/obidos/ASIN/0195036468/ref=nosim/caoineorg-20 suggests that it’s p. The aim of explanations is to give information about causal history, and p is more informative.

Many others have suggested the answer is q. Frank Jackson and Philip Pettit say this in their original paper on Program Explanations, but there’s plenty of people who agree. (For instance Michael Smith in the paper Jonathan cites, though Jonathan is critical on just this point.) Here’s an example from Putnam that many find persuasive.

bq. _Peg and Hole_
I’m trying to fit a square peg of diameter 5 into a round hole of diameter 4. I fail. (That’s proposition r.) Let p be the complete microphysical description of the setup and my attempt, with conjuncts referring to where the peg hit the edges of the hole and was repelled and so on. Let q be the proposition that I’m trying to fit a square peg into a round hole. I take it that p entails q.

bq. Each of p and q explains r, but q is a better explanation. For one thing it is more illuminating. For another, and this is the point Jackson and Pettit stress, it correctly indicates that the failure is modally resilient in a certain direction. A slightly different attempt, with a slightly different microphysical description p’, would also have failed as long as it was an attempt to fit a square peg into a round hole.

Let’s run with that, and say that our answer to the the original question is q. (Or maybe “it depends” with the answer being q as long as the explanation holds across all nearby q-worlds.) Now the puzzle. Disjunctive explanations are bad. None of the following would be a good explanation.

q₁: I was trying to fit a square peg into a round hole or I was prevented by a God from doing what I was trying to do.
q₂: I was trying to fit a square peg into a round hole or I was trying to fit a round peg into a square hole.

I think q is clearly a better explanation that q₁ or q₂. Why should this be? It is certainly less more illuminating, but that’s just restating the puzzle as much as answering it. The fact that I fail is resilient across all nearby q₁ and q₂ worlds, so resilience can’t be the issue. I know of three answers, though I’m not satisfied with any of them. (Thanks to Jonathan Ichikawa for the small correction in this paragraph.)

“Michael Strevens suggests”:http://www.stanford.edu/~strevens/research/expln/expln101/index.html the answer is that weaker explanations are better than stronger explanations only if they are “cohesive”. The explanation is cohesive only if the same kinds of causal processes lead to r all (nearby) worlds in which the explanans is true. (I’m summarising a lot here – read his paper for more details.) I think cohesion is neither necessary nor sufficient for a weaker explanation to be preferable to a stronger explanation.

The counterexample to sufficiency is q₂. The same kinds of processes matter in all the worlds where q₂ is true, but that doesn’t make q₂ a better explanation than q.

Some counterexamples to necessity are generated by explanations that involve AIDS. I’ll simplify a lot here to make the case easiest. Let’s say the way AIDS works is that it kills off many different parts of the body’s defence mechanisms, so any kind of disease could be deadly. (That’s not really true of actual AIDS, I think.) So there’s very little in common in the causal processes that lead to death in nearby worlds where an AIDS patient dies. There’s a similarity at the start where they acquire the AIDS virus, but that’s it. Still, that the patient had AIDS is often a better explanation of their death than the very detailed account of just how they died, i.e. of which routine illness they weren’t able to fight off.

A second answer is that disjunctive propositions like that are simply not suitable to be explanations. I think that’s the position implicit in Woodward and Hitchcock’s paper in _No{u^}s_ last year, and I think it’s basically on the right track. But we need a substantive theory of why this is true, and such a theory will need some heavy-duty metaphysics, and I’m not really sure how such a theory will be built. (Or defended.)

Is there a third answer, or a way of filling out the second answer so it resolves this problem? I don’t know – that’s why it’s a puzzle!