A further projection problem arises from a puzzle invented by Hempel. Inductive reasoning is also thought to include probabilistic reasoning. It is said that an inference is justified if it conforms to the theorems of the probability calculus. Against this, it is objected that, if true, a 'computational explosion' would ensue. Even so, Harman does seem to concede that the rules of the probability calculus might be thought of as normatively correct, that is, as rules which a human inferrer should use to the extent that he satisfies appropriate assumptions on computationally ideal reasons.
Abduction is recognized in two varieties.
In one sense, it is 'inference to the best explanation' , which is a means of justifying the postulation of unobservable phenomena on the strength of explanations they afford of observable phenomena. In its other variety, abduction is the process of forming generic beliefs from known data. Attractive though it is, the idea of inference to the best explanation awaits an adequate generalized specification of what 'best' consists of. And the idea of generic inference requires a satisfactory account of when negative instances do and do not falsify generic claims. Nelson Goodman, Fact, Fiction, and Forecast , 4th edn.