Carl Hempel's idea of explanation (D.N. model) in the sciences is that you should be able to make some deductive argument by which the fact you're trying to explain is the conclusion. I.e. you form an argument by which the fact you're trying to explain is either made certain by your premises or is, statistically speaking, expected (the latter being a case of I.S. explanation).
There's a famous counter-example given to this model of explanation by which is used to generally attack these criteria:
- Law: All males who use birth control fail to become pregnant.
- Conditions: John is a male who has been taking birth control.
- Explanandum: John failed to get pregnant
Obviously we don't have a proper explanation of events here but they seem to fit the D.N. structure.
Is it not possible to 'combine' Salmon's conditions for what counts as an explanation with Hempel's? Specifically, the statistical relevance condition.
We can see that the explanans law and condition don't actually increase the probability that John failed to get pregnant in any way beyond the knowledge we already have that John is a man and men already cannot get pregnant (which is itself a successful explanation which includes a law and condition).
Perhaps we could then 'compare' the statistical relevance of different explanations to compare their 'strength' as explanations (which is a kind of Bayesian way of looking at things, I suppose).
Is there a problem with this approach to altering Hempel's original conditions? Since I haven't seen this approach discussed or really any approaches that involve marrying some of the aspects of different models of explanation. Thanks.