For several decades in the twentieth century there was a dominant answer to this question, that was an outgrowth of the tradition of logical positivism and examples from the natural sciences. This theory of explanation focused on the idea of subsumption of an event or regularity under a higher-level set of laws. The deductive-nomological theory of explanation specified that an outcome is explained when we have produced a deductively valid argument with premises that include at least one general law and that lead to a description of the event as conclusion. Carl Hempel was the most prominent advocate for this theory (Aspects of Scientific Explanation), but it was widely accepted throughout the philosophy of science in the 1950s and 1960s. The "covering law" model was a core dogma for the philosophy of science for several decades.
The D-N theory was subject to many kinds of criticisms, including the obvious point that much explanation involves phenomena that are probabilistic rather than deterministic. Hempel introduced the inductive version of the D-N model to cover probabilistic-statistical explanation, along these lines. An argument provides a scientific explanation of E if it provides at least one probabilistic law and a set of background conditions such that, given the law and conditions, E is highly probable. This model was described as the "Inductive-Statistical" model (I-S model). Wesley Salmon's Scientific Explanation and the Causal Structure of the World falls within this tradition but offers important refinements, including his formal definition of causal relevance.
In each case the motivation for the theory of explanation is a plausible one: we explain an event when we show how it was necessary [or highly probable] in the circumstances, given existing conditions and relevant laws of nature. On the logical positivist approach, an explanation is an answer to a "why necessary" question: why did this event occur? In this conception of explanation the idea of necessity or probability is replaced with the idea of deductive or inductive derivability -- a syntactic relationship among sets of sentences.
A different approach to explanation turns to the idea of causation. We provide an explanation of an event or pattern when we succeed in identifying the causal conditions and events that brought it about. This approach can be tied to the D-N approach, if we believe that all causal relations are the manifestation of strict or probabilistic causal regularities. But not all D-N explanations are causal, and not all causal explanations invoke regularities. Derivability is no longer the criterion of explanatory success, and explanation is no longer primarily a syntactic relation between sets of sentences. Instead, substantive theories of causal powers and properties are the foundation of scientific explanation. A leading exponent of this view is Rom Harré in Harré and Madden, Causal Powers: Theory of Natural Necessity. Nancy Cartwright's Nature's Capacities and Their Measurements is also an important contribution to this view. And J. L. Mackie's The Cement of the Universe: A Study of Causation is an important contribution as well. The causal approach retains the idea that explanation involves showing why an event is necessary or probable, but it turns from derivability from statements of laws of nature, to theories of causal powers and properties.
The causal mechanisms approach to explanation continues the insight that explanations involve demonstrating why an event occurred; but this approach moves even farther away from the idea of a causal law, replacing it with the idea of a discrete causal mechanism. On this approach, we explain an event when we identify a series of causal interactions that lead from some antecedent condition to the outcome of interest. Hedstrom and Swedborg's Social Mechanisms: An Analytical Approach to Social Theory presents aspects of this theory of explanation in application to the social sciences. One benefit of the social mechanisms approach is that it also provides a basis for answering "how possible" questions: if our puzzlement is that an outcome has occurred that seems inherently unlikely, we can provide an account of a set of causal mechanisms that transpired to bring it about.
The chief line of dispute in the traditions mentioned so far is between the "general laws" camp and the "causal powers" camp. Both are committed to the idea that explanation involves showing how an outcome fits into the ways the world works; but the general laws approach presumes that law-like regularities are fundamental, whereas the causal approach presumes that causal powers and mechanisms are fundamental.
So what has developed in the theory of explanation in the past twenty years? Quite a bit. A recent collection of essays coming largely from the Scandinavian tradition of the philosophy of science is quite helpful in orienting readers to recent developments. This is Johannes Persson and Petri Ylikoski's 2007 Rethinking Explanation. Quite a number of the contributions are worth reading carefully. But Jan Faye's "Pragmatic-Rhetorical Theory of Explanation" is a good place to start. Faye distinguishes among three basic approaches to the theory of explanation: formal-logical, ontological, and pragmatic. The formal-logical approach is essentially the H-D and I-S approaches described above. The ontological approach is the causal-powers approach described above. The pragmatic approach is in a sense the most important recent contribution to the theory of explanation, and represents a significant re-focusing of the debates in post-empiricist philosophy of science. Here is how Faye describes the pragmatic approach to explanation-theory:
The pragmatic view sees scientific explanations to be basically similar to explanations in everyday life. It regards every explanation as an appropriate answer to an explanation-seeking question, emphasising that the context of the discourse, including the explainer’s interest and background knowledge, determines the appropriate answer. (44)And why should we consider a pragmatic approach? Faye offers eight reasons:
First, we have to recognise that even within the natural sciences there exist many different types of accounts, which scientists regard as explanatory. (46)
Second, if one is looking for a prescriptive treatment of explanation, I see no reason why the social sciences and the humanities should be excluded from such a prescription. If they are included, the prescriptive account must include intentional and interpretive explanations, i.e., accounts providing information about either motives or meanings. (47)
Third, the meaning of a why-question alone does not determine whether the answer is relevant or not. (47)
Fourth, John Searle has correctly argued that the meaning of every indicative sentence is context-dependent. He does not deny that many sentences have literal meaning, which is traditionally seen as the semantic content a sentence has independently of any context. (49)
Fifth, many explanations take the form of stories. Arthur Danto has argued that what we want to explain is always a change of some sort. When a change occurs, we have one situation before and another situation after, and the explanation is what connects these two situations. This is the story. (50)
Sixth, a change always takes place in a complex causal field of circumstances each of which is necessary for its occurrence. Writers like P.W. Bridgman, Norwood Russell Hanson, John Mackie, and Bas van Fraassen have all correctly argued that events are enmeshed in a causal network and that it is the salient factors mentioned in an explanation that constitute the causes of that events. (50)Faye then goes on to analyze scientific explanation as a speech act. We need to understand the presuppositions and purposes that the explainer and the listener have, before we can say much about how the explanation works.
Seventh, the level of explanation depends also on our interest of communication. In science an appropriate nomic or causal account can be given on the basis of different explanatory levels, and which of these levels one selects as informative depends very much on the rhetorical purposes. (51)
Eight, scientific theories are empirically underdetermined by data. It is always possible to develop competing theories that explain things differently and, therefore, it is impossible to set up a crucial experiment that shows which of these theories that yields the correct account of the data available. (52)
Petri Ylikoski's contribution to the volume, "The Idea of Contrastive Explanandum," picks up on one particular but pervasively important feature of the rhetorical situation of explanation, the idea of contrast. When we ask for an explanation of an outcome, often we are not asking simply why it occurred, but rather why it occurred instead of something else. And the contrastive condition is crucial. If we ask "why did the Prussian army win the Franco-Prussian War?", the answer we give will be very different depending on whether we understand the question as:
"Why did the Prussian army [rather than the French army] win the Franco-Prussian War?"or:
"Why did the Prussian army win [rather than fighting to stalemate] the Franco-Prussian War?"So scientific explanation is context-dependent in at least this important respect: we need to understand what the question-asker has in mind before we can provide an adequate explanation from his/her point of view. As Henrik Hallsten puts it in his contribution, "What to Ask of an Explanation-Theory",
To summarize: Any explanation-theory must [do] justice to the distinction between objective explanatory relevance and context dependent explanatory relevance or provide good arguments as to why this distinction should not be upheld. (16)So perhaps the most important recent developments in the theory of scientific explanation fall in a few categories. First, there has been substantial work on refining the idea of causal explanation (link). Second, philosophers have reinforced the idea that explanation has pragmatic and rhetorical aspects that cannot be put aside in favor of syntactic and substantive features of explanation. And third, there is more recognition and acceptance of the idea that explanatory models and standards may reasonably differ across disciplines and research areas. In particular, the social and historical sciences are entitled to offer explanatory frameworks that are well adapted to the particular kinds of why and how questions that are posed in these fields. In each case the philosophy of science has made a very great deal of progress since the state of the debates about explanation that transpired in the 1960s.