Explanatory power is the ability of a hypothesis to effectively explain the subject matter it pertains to. One theory is sometimes said to have more explanatory power than another theory about the same subject matter if it offers greater predictive power. That is, if it offers more details about what we should expect to see, and what we should not.
Explanatory power may also suggest that more details of causal relations are provided, or that more facts are accounted for. Scientist David Deutsch adds that a good theory is not just predictive and falsifiable (i.e. testable); a good explanation also provides specific details which fit together so tightly that it is difficult to change one detail without affecting the whole theory. The opposite of explanatory power is explanatory impotence.
Physicist David Deutsch offers a criterion for a good explanation that he says may be just as important to scientific progress as learning to reject appeals to authority, and adopting formal empiricism and falsifiability. To Deutsch, these aspects of a good explanation, and more, are contained in any theory that is specific and "hard to vary". He believes that this criterion helps eliminate "bad explanations" which continuously add justifications, and can otherwise avoid ever being truly falsified.
Deutsch takes examples from Greek mythology. He describes how very specific, and even somewhat falsifiable theories were provided to explain how the gods' sadness caused the seasons. Alternatively, Deutsch points out, one could have just as easily explained the seasons as resulting from the gods' happiness - making it a bad explanation, because it is so easy to arbitrarily change details. Without Deutsch's criterion, the 'Greek gods explanation' could have just kept adding justifications. This same criterion, of being "hard to vary", may be what makes the modern explanation for the seasons a good one: none of the details - about the earth rotating around the sun at a certain angle in a certain orbit - can be easily modified without changing the theory's coherence.
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