Abstract

This paper develops an explicit, pragmatic solution to the problem of deciding when an explanans which only approximately "covers" a desired event-explanandum E is acceptable as an adequate explanation. It shows in detail how comparisons made by the explanation's audience with the numerical value in E are what determine how closely E must be approximated for success. With the aid of several physics examples, it spells out the principles that govern these explanandum-comparisons, the conditions under which those principles hold, and the audience traits that influence which comparisons they take seriously.