Since so much of life both inside and outside the study is concerned with finding explanations of things, it would be desirable to have a concept of what counts as a good explanation, and what distinguishes good from bad. Under the influence of logical positivist approaches to the structure of science, it was felt that the criterion ought to be found in a definite logical relationship between the explanans (that which does the explaining) and the explanandum (that which is to be explained). This approach culminated in the covering law model of explanation, or the view that an event is explained when it is subsumed under a law of nature, that is, its occurrence is deducible from the law plus a set of initial conditions. A law would itself be explained by being deduced from a higher-order or covering law, in the way that Kepler’s laws of planetary motion are deducible from Newton’s laws of motion. The covering law model may be adapted to include explanation by showing that something is probable, given a statistical law. Questions for the covering law model include querying whether laws are necessary to explanation (we explain everyday events without overtly citing laws); querying whether they are sufficient (it may not explain an event just to say that it is an example of the kind of thing that always happens); and querying whether a purely logical relationship is adapted to capturing the requirements we make of explanations. These may include, for instance, that we have a ‘feel’ for what is happening, or that the explanation proceeds in terms of things that are familiar to us or unsurprising, or that we can give a model of what is going on, and none of these notions is captured in a purely logical approach. Recent work, therefore, has tended to stress the contextual and pragmatic elements in requirements for explanation, so that what counts as a good explanation given one set of concerns may not do so given another.

The inference to the best explanation is the view that once we can select the best of any competing explanations of an event, then we are justified in accepting it, or even believing it. The principle needs qualification, since sometimes it is unwise to ignore the antecedent improbability of a hypothesis which would explain the data better than others: e.g. the best explanation of a coin falling heads 530 times in 1,000 tosses might be that it is biased to give a probability of heads of 0·53, but it might be more sensible to suppose that it is fair, or to suspend judgement.