 Solution

The covering-law model captures one important feature of scientific explanation: a result should follow from general principles together with the relevant circumstances. In its deductive-nomological model, laws and conditions entail the phenomenon, the laws are needed in the derivation, and the premises must be true and empirically substantive. That is stronger than merely redescribing the event.^[ref]

For example, the ideal gas law, a specified amount of gas and a fixed-volume condition explain why changing its temperature changes its pressure in the model's regime. The derivation identifies a systematic dependence rather than an isolated coincidence. It also makes assumptions visible: a calculation using a law outside its domain is not repaired simply by being logically valid.

Nevertheless, valid subsumption does not by itself determine explanatory direction. A vertical pole of height $h$, a solar elevation $\alpha$ and a shadow of length $l$ satisfy $h=l\tan \alpha$ under suitable geometric assumptions. The same relation allows one to deduce the height from the shadow. In an ordinary intervention on the pole, changing its height changes its shadow; shortening the shadow with a screen does not shorten the pole. The reverse calculation can be excellent evidence for the height without providing the same causal explanation. This is explanatory asymmetry.

Relevance is another difficulty. One can append an irrelevant fact to a sound derivation without invalidating the deduction, but the added fact need not explain anything. Requiring an essential law prevents some vacuous derivations, yet still does not identify which features make a physical difference. A useful explanation should reveal the dependence the question is asking about, not merely contain enough true premises to reach its conclusion.

Nor are all explanations deterministic. A particular radioactive decay can have a good account in terms of a physical decay mechanism and a probability distribution without being entailed by initial conditions. An inductive-statistical model extends the covering-law idea, but requiring a high probability would exclude the explanation of some rare outcomes. Conversely, a high conditional probability produced by irrelevant correlations need not explain a mechanism.

The model is therefore a valuable discipline for organizing some explanations, rather than a sufficient universal analysis. It clarifies derivational structure and testable commitments. An adequate broader account must also address causal relevance, the question's contrast, statistical events and explanations by constraints or unification that are not straightforward causal histories.