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An explanandum (a Latin term) is a sentence describing a phenomenon that is to be explained, and the explanans are the sentences adduced as explanations of that phenomenon. For example, one person may pose an explanandum by asking "Why is there smoke?", and another may provide an explanans by responding "Because there is a fire". In this example, "smoke" is the explanandum, and "fire" is the explanans.
Carl Gustav Hempel and Paul Oppenheim (1948), in their deductive-nomological model of scientific explanation, motivated the distinction between explanans and explanandum in order to answer why-questions, rather than simply what-questions:
"the event under discussion is explained by subsuming it under general laws, i.e., by showing that it occurred in accordance with those laws, by virtue of the realization of certain specified antecedent conditions"-- Hempel & Oppenheim, 1948, (p.152)
Specifically, they define the concepts as follows:
"By the explanandum, we understand the sentence describing the phenomenon to be explained (not that phenomenon itself); by the explanans, the class of those sentences which are adduced to account for the phenomenon"-- Hempel & Oppenheim, 1948, (p.152)
The crucial comment, with respect to the scientific method, is given as follows:
"It may be said... that an explanation is not fully adequate unless its explanans, if taken account of in time, could have served as a basis for predicting the phenomenon under consideration.... It is this potential predictive force which gives scientific explanation its importance: Only to the extent that we are able to explain empirical facts can we attain the major objective of scientific research, namely not merely to record the phenomena of our experience, but to learn from them, by basing upon them theoretical generalizations which enable us to anticipate new occurrences and to control, at least to some extent, the changes in our environment"-- Hempel & Oppenheim, 1948, (p.154)