Hempel's Ravens

Suppose an ornithologist wishes to determine whether or not all ravens are black. The reasonable thing for him to do is to go outside and look for ravens. If he finds even one that isn't black, that proves that not all ravens are black. If, on the other hand, he sees thousands of ravens and every single one of them is black, then that offers support for the proposition that they are all in fact black. Although no amount of observations can ever conclusively prove the hypothesis, each new black raven found provides additional evidence for it.

But now suppose that our ornithologist, after seeing thousands of ravens, becomes tired of looking for them, and decides to try a different method. He reasons as follows:

The statement "all ravens are black" is logically equivalent to the statement "all nonblack objects are nonravens". When you see a blue sky, a yellow submarine, or any other nonblack nonraven, that supports the proposition that all nonblack objects are nonravens. But in that case, it also supports the proposition that all ravens are black. So all one has to do is look around at ordinary objects to acquire evidence that all ravens are black! No need to go out in the woods in search of ravens, since each nonblack nonraven is also evidence for that hypothesis. This is the paradox known as Hempel's ravens, named after Carl Hempel, who discovered it in 1946.

But how can seeing a green thumb or a pink panther add to the evidence that all ravens are black? Perhaps the answer is that it does add to the evidence, but only by a very tiny amount. Since there are many more nonblack nonravens in the universe than there are black ravens, it is a bad idea to attempt to confirm the hypothesis that all ravens are black by investigating nonblack things. In principle, however, it could be done. The evidence that each nonblack nonraven adds to the proposition may be infinitessimal, but is nevertheless real.

Unfortunately, our difficulties do not end here. What our ornithologist didn't notice is that a yellow submarine is not merely an example of a nonblack nonraven. It is also an example of (among other things) a nonwhite nonraven. Thus, a yellow submarine provides evidence not only for the proposition "all ravens are black", but also for the proposition "all ravens are white". But how can it be possible for one fact to support two contradictory claims?