Hempel's paradox

The principle of induction by enumeration allows a suitable generalization to be confirmed by its instances. Thus observation of black ravens should confirm the generalization that all ravens are black. It is also clear that if evidence confirms a hypothesis, it should confirm any hypothesis logically equivalent to it. Now ‘all non-black things are non-ravens’ is logically equivalent to ‘all ravens are black’. Its instances are things like white shoes. So observation of a white shoe should confirm that all non-black things are non-ravens, and hence that all ravens are black. But intuitively the observation is entirely irrelevant to this hypothesis. The paradox depends upon (i) Nicod's criterion and (ii) the principle that whatever confirms an hypothesis confirms any logically equivalent hypothesis. Solutions include restricting the kinds of generalization that can be confirmed by their instances, denying the principle that if evidence confirms a hypothesis it confirms any logically equivalent hypothesis, and accepting the conclusion that the observation is, in fact, relevant, although very weakly so. This last solution (Hempel's own) points out that if the numbers of things involved, or the background information, were different we might well allow something that was neither A nor B to confirm that all As are B. Nevertheless the paradox forces further investigation of the rationale behind Nicod's criterion.