Explanation in Science: Covering Law and Causal Models

Carl Gustav Hempel and Paul Oppenheim, in their landmark 1948 article "Studies in the Logic of Explanation" (Philosophy of Science), proposed what became known as the covering-law model, or deductive-nomological (D-N) model, of scientific explanation: an explanation of a particular event consists in a valid deductive argument whose conclusion states that the event occurred, and whose premises include at least one universal law of nature (the "covering law") together with statements of the relevant initial or antecedent conditions — to explain why a given quantity of gas expanded, for instance, is to deduce that fact from the ideal gas law together with statements about the gas's initial pressure, volume, and temperature. Hempel later extended the model, in Aspects of Scientific Explanation (1965), to statistical explanation via the inductive-statistical (I-S) model, in which the covering "law" is a statistical rather than universal generalization and the explanandum is rendered highly probable, rather than logically certain, by the explanans.