(S1) All ravens are black.
(S2) All non-black things are non-ravens.
(S3) Everything is either black or non-raven (or both).
Since the statements are all equivalent, they must be confirmed (or not) by the same evidence. (In particular, each statement is disconfirmed by finding a non-black raven.) But generalizing the sort of logic used in our intuitive claim above, we can say that observing non-black non-ravens is evidence for (S2), and therefore (S1). So observing a red herring is evidence that all ravens are black! But this seems absurd.
I think the "paradox" can be resolved once we recognize why it is that observing black ravens supports the claim that all ravens are black. Hempel claims:
R1: Whenever an object has two attributes C1, C2, it constitutes confirming evidence for the hypothesis that every object which has the attribute C1 also has the attribute C2.
But this, I claim, is mistaken. It makes a difference how you came by the observation. If you go searching solely for black things, and bring me back a sample of them, the observation of black ravens in this collection will not provide any evidence whatsoever that all ravens are black.
Why not? Well, recall that a non-black (henceforth, 'coloured') raven is what would falsify our statements S1-S3 (which from now on I will just call 'S'). The perfect test of S would be to exhaustively search the world for coloured ravens. If we found one, S would be shown to be false, but otherwise we would have established its truth. But we can also do imperfect tests, which merely sample the population of worldly objects, rather than doing an exhaustive census.
Suppose we took a random sample of objects from the world. Every sampled object that was not a coloured raven would count as (weak) evidence that there are no such creatures. For if there were coloured ravens then we should expect them to turn up occasionally in random samples. The fact that they don't, counts against them.
But this evidential justification requires that the sample be drawn from a population that would include coloured ravens were any to exist. For suppose that you go and collect a bucket of herrings for me. There is no chance that there are any coloured ravens populating this bucket. So their absence from my observations cannot count against them. My observations of nothing but herrings in the bucket is precisely what we should expect even if there are coloured ravens in the world. (Granted, each red herring we sample is evidence that there are no coloured ravens in our sample population - i.e. the bucket - but we already knew that!) Similarly for populations of black objects. If we purposefully sample only black things, then there is no chance of finding coloured ravens even if they exist. So, again, our failure to find any does not count against them. (It just tells us the trivial result that there are no coloured ravens among the black population.) So observing black ravens in such a sample does not at all count as evidence that all ravens are black! Hempel is simply mistaken about the nature of confirming evidence.
Now suppose instead that we took a random sampling from the population of ravens. If any coloured ravens exist, they would have some chance of turning up in the sample. So the failure to find any coloured ravens in such a sample would count as evidence against them, and in favour of S. Moreover, the same can be said of a random sample of coloured (non-black) objects -- or even a random sample of all the objects in the world. Every time our randomly chosen sample object turns out not to be a coloured raven (say it is a red herring instead), this offers some very slight evidence that there are no coloured ravens to be found in the broader population from which the sample was taken. So it helps confirm S.
There are pragmatic reasons why black ravens could count more heavily than red herrings in confirming S. This is because the population of ravens is much smaller than the population of coloured things. So, if any coloured ravens exist, they will form a much higher proportion of the raven population than they will the coloured population. Since they should be easier to find in the raven population, the failure to find them there will count more heavily against them. It's just a whole lot more practical to sample the raven population than it is the coloured (or even universal) population. But this difference is merely one of degree, not kind.
Indeed, if we are taking a random sample from the entire population of worldly objects, then there is no evidential difference between finding a black raven or a red herring in the sample. Each offers equally weak evidence for S, merely in virtue of not being a coloured raven.
I hope that's all relatively clear. I've tried to explain it informally, but one could probably formalize my arguments with Bayesian statistics. Anyway, the point is that "Hempel's paradox of confirmation" isn't really paradoxical at all. It simply serves to highlight some common misunderstandings about the nature of inductive evidence.