Explanation

In plain terms

A statement can be perfectly true and explain nothing. The height of a flagpole and the length of its shadow are related by a law, and you can derive either from the other - but the pole explains the shadow and the shadow does not explain the pole.

So explanation is not just correct derivation. Something asymmetric is going on, and the obvious candidate is causation: the pole makes the shadow, and shadows make nothing.

But that cannot be the whole story either, because some good explanations cite no causes at all. Why can nobody cross the seven bridges of Königsberg exactly once? Because of a fact about the graph, not because of anything that happened.

Which leaves the question of what the different kinds have in common, and whether anything does.

As a philosopher would put it

Hempel's deductive-nomological model makes an explanation a valid deduction of the explanandum from laws plus initial conditions. Its counterexamples are famous: the flagpole shows the asymmetry problem, the barometer and the storm show that correlation is not enough, and the man who takes birth control pills and does not become pregnant shows that irrelevant premises can satisfy the schema.

Salmon's causal-mechanical model locates explanation in exhibiting the causal processes involved, which fixes the asymmetry and struggles with explanations that are not causal.

Van Fraassen's pragmatic account makes explanation relative to a contrast class and a context: why did Adam eat the apple, rather than why did Adam eat it. Kitcher's unification account makes it a matter of deriving many phenomena from few argument patterns. Woodward's interventionist account is now the most widely used: an explanation shows what the explanandum depends on, in the sense of what would change it under intervention.

What is actually disputed

Whether explanation is one thing.

Monists hold that all genuine explanation is causal, or unifying, or dependence-tracking, and that apparent exceptions are either not explanations or reduce to the favoured kind. Pluralists hold that mathematical, structural, causal and functional explanations are genuinely different and share only a role.

The non-causal cases are the pressure point. A proof that a task is impossible explains why nobody has managed it, and cites no events.

A second question is whether explanation is objective. Van Fraassen's pragmatic account makes it relative to interests and context, so there is no such thing as the explanation of an event - only answers to particular why-questions. Critics regard this as giving up on the notion that some accounts are better than others; his reply is that the standard is set by the question, and that pretending otherwise conceals which question was asked.