Raven paradox

The Raven paradox is a paradox first presented by the German logician Carl Gustav Hempel in the 1940s.  The paradox stems from two intuitive principles for inductive reasoning: (i) logically-equivalent claims are interchangeable and (ii) particular instances confirm the corresponding universal generalization.  Hempel showed that (i) and (ii) together entail the unintuitive conclusion that claims of the form "All As are Bs" can be confirmed by observing non-A, non-B objects.

The paradox
Saying:
 (1) All ravens are black.

is logically equivalent to saying:
 (2) If something is not black then it is not a raven.

Whenever (2) is true, (1) is too; likewise in all circumstances where (2) is false (i.e. if a world with white ravens is imagined), (1) is also false.  Accordingly, (1) and (2) can be safely interchanged with one another.

Next, a particular object which is both A and B intuitively constitutes evidence for the claim "All As are Bs".  Thus,

 (3) Nevermore, my pet raven, is black.

is evidence supporting the hypothesis that 

 (4) All ravens are black.

Following the same reasoning, a green apple (a non-black and non-raven object) is evidence supporting the hypothesis that all non-black things are non-ravens.    

The paradox appears when these two principles are combined.  If a green apple is evidence for "all non-black things are non-ravens" and "all non-black things are non-ravens" is equivalent to "all ravens are black", then green apples are also evidence for the hypothesis that "all ravens are black"!  This conclusion is highly unintuitive despite the appeal of both starting principles.  

References

Category:Logical paradoxes