- This article deals with explanatory power in the context of the philosophy of science. For a statistical measure of explanatory power, see Coefficient of determination or Mean squared prediction error.
In the past, various criteria or measures for explanatory power have been proposed. In particular, one hypothesis, theory or explanation can be said to have more explanatory power than another about the same subject matter
- if more facts or observations are accounted for;
- if it changes more "surprising facts" into "a matter of course" (following Peirce);
- if more details of causal relations are provided, leading to a high accuracy and precision of the description;
- if it offers greater predictive power, i.e., if it offers more details about what we should expect to see, and what we should not;
- if it depends less on authorities and more on observations;
- if it makes fewer assumptions;
Recently, David Deutsch proposed that the correct hypothesis or theory, the one that stands out among all possible explanations, is that specific explanation that
- is hard to vary.
By this expression he intends to state that the correct theory, i.e., the true explanation, provides specific details which fit together so tightly that it is impossible to change any one detail without affecting the whole theory.
Philosopher and 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.
Relation to other criteria
It can be argued that the criterion hard to vary is closely related to Occam's razor: both imply logical consistency and a minimum of assumptions.