logic science

 [where] the premisses of demonstrated knowledge must be true, primary, immediate, better known than and prior to the conclusion, which is further related to them as effect to cause. (Posterior Analytics 1.71–2, as quoted in Jeffrey 1969: 104)

In his semi-formal explication of the requirements for adequate scientific explanations, Hempel specified four conditions of adequacy (CA) that have to be satisfied, namely:

(CA-1)

The explanandum must be a deductive consequence of the explanans;

(CA-2)

The explanans must contain general laws, which are required to satisfy (CA-1);

(CA-3)

The explanans must have empirical content and must be capable of test; and,

(CA-4)

The sentences of the explanans must be true. (Hempel & Oppenheim 1948)

Hempel’s endorsement of Goodman’s approach to select generalizations that support subjunctive conditionals, therefore, was not only consistent with the tradition of Hume—who believed that attributions of natural necessity in causal relations are merely “habits of mind”, psychologically irresistible, perhaps, but logically unwarranted—but circumvented a disconcerting consequence of his explication.

Students of Hempel have found it very difficult to avoid the impression that Hempel was not only defending the position that every adequate scientific explanation is potentially predictive but also the position that every adequate scientific prediction is potentially explanatory. This impression is powerfully reinforced in “The Theoretician’s Dilemma” (Hempel 1958), where, in the course of demonstrating that the function of theories goes beyond merely establishing connections between observables, he offers this passage:

Scientific explanations, predictions, and postdictions all have the same logical character: they show that the fact under consideration can be inferred from certain other facts by means of specified general laws. In the simplest case, the type of argument may be schematized as a deductive inference of the following form [here substituting the “simplest case” for the abstract schemata presented in the original]:

$\left(x\right)(Rx\supset Bx)$	Explanans
$Rc$
$Bc$	Explanandum

Figure 4. A Covering-Law Explanation

… While explanation, prediction, and postdiction are alike in their logical structure, they differ in certain other respects. For example, an argument [like Figure 4 above] will qualify as a prediction only if [its explanandum] refers to an occurrence at a time later than that at which the argument is offered; in the case of postdiction, the event must occur before the presentation of the argument. These differences, however, require no further study here, for the purpose of the preceding discussion was simply to point out the role of general laws in scientific explanation, prediction, and postdiction (Hempel 1958: 37–38).

What is the Hempel covering law model?

'Explanation in science' begins with Carl Hempel's covering law model of explanation, which says that to explain a phenomenon is to show that its occurrence follows deductively from a general law, perhaps supplemented by other laws and/or particular facts, all of which must be true.