Hempel’s paradox of confirmation can be formulated as the following argument:
Nicod’s Condition (NC): For any object x and any properties F and G, the
proposition that x has both F and G confirms the hypothesis that every F
has G (Nicod 219).
Equivalence Condition (EC): If hypotheses H1 and H2 are logically
equivalent, then any evidence E that confirms H1 also confirms H2.
Together, these two principles entail the following conclusion:
Paradoxical Conclusion (PC): an object a, which is a non-black non-raven
(~Ba & ~Ra) confirms the hypothesis (H) that all ravens are black.
This argument is valid. From NC, it follows that ~Ba & ~Ra confirms the
hypothesis that all non-black things are non-ravens. This hypothesis is the
contrapositive of H and therefore logically equivalent to H. So by EC, ~Ba & ~Ra
confirms H. But this seems counterintuitive—a white shoe seems irrelevant to
whether all ravens are black. Thus, we have an argument that starts from apparently
obvious premises and proceeds through valid reasoning to an apparently
unacceptable conclusion—a paradox.
