Having now properly read Korb's paper, the basic problem he points out is that to do a Bayesian update regarding a hypothesis h in the presence of new evidence e, one must calculate the likelihood ratio P(e|h)/P(e|not-h). Not-h consists of the whole of the hypothesis space excluding h. What that hypothesis space is affects the likelihood ratio. The ratio can be made equal to anything at all, for some suitable choice of the hypothesis space, by constructions similar to those of the OP.
It makes the same negative conclusion when applied to bnonb ravens, or to European and non-European ravens.
Although this settles Hempel's paradox, it leaves unanswered a more fundamental question: how should you update in the face of new evidence? The Bayesian answer is on the face of it simple mathematics: P(e|h)/P(e|not-h). But where does the hypothesis space that defines not-h come from?
In "small world" examples of Bayesian reasoning, the hypothesis space is a parameterised family of distributions, and the prior is a probability distribution on the parameter space. New evidence will shift that distribution. If the truth is a member of that family, evidence is likely to converge on the correct parameters.
I have never seen a convincing account of how to do "large world" Bayesian reasoning, where the hypothesis space is "all theories whatsoever, even yet-unimagined ones, describing this aspect of the world". Solomonoff induction is the least unconvincing, by virtue only of being precisely defined and having various theorems provable about it, but one of those theorems is that it is uncomputable. Until I see someone make some sort of Solomonoff-based method work to the extent of becoming a standard part of the statistician's toolkit, I shall continue to be sceptical of whether it has any practical numerical use. How should you navigate in a large-world hypothesis space, when you notice that P(e|h) is so absurdly low that the truth, whatever it is, must be elsewhere?
Given the existence of polar bears, arctic foxes, and snow leopards, I wondered if there might be any white-feathered ravens in the colder parts of the world. A Google search indicates that while ravens are found there, they are just as black as their temperate relatives. I guess you don't need camouflage to sneak up on corpses. Now that looks like good evidence for all ravens being black: looking in places where it is plausible that there could be white ravens, and finding ravens, but only black ones. The not-h hypothesis space has room for large numbers of white ravens in a certain type of remote place. That part of the space came from observing polar bears and the like, and imagining a similar mechanism, whatever it might be, in ravens. Finding that even there, all observed ravens are black, removes probability mass from that part of the space.
The raven paradox, originated by Carl Gustav Hempel, is an apparent absurdity of inductive reasoning. Consider the hypothesis:
H1: All ravens are black.
Inductively, one might expect that seeing many black ravens and no non-black ones is evidence for this hypothesis. As you see more black ravens, you may even find it more and more likely.
Logically, a statement is equivalent to its contrapositive (where you negate both things and flip the order). Thus if "if it is a raven, it is black" is true, so is:
H1': If it is not black, it is not a raven.
Take a moment to double-check this.
Inductively, just like with H1, one would expect that seeing many non-black non-ravens is evidence for this hypothesis. As you see more and more examples, you may even find it more and more likely. Thus a yellow banana is evidence for the hypothesis "all ravens are black."
Since this is silly, there is an apparent problem with induction.
Resolution
Consider the following two possible states of the world:
Suppose that these are your two hypotheses, and you observe a yellow banana (drawing from some fixed distribution over things). Q: What does this tell you about one hypothesis versus another? A: It tells you bananas-all about the number of black ravens.
One might contrast this with a hypothesis where there is one less banana, and one more yellow raven, by some sort of spontaneous generation.
Observations of both black ravens and yellow bananas cause us to prefer 1 over 3, now!
The moral of the story is that the amount of evidence that an observation provides is not just about whether it whether it is consistent with the "active" hypothesis - it is about the difference in likelihood between when the hypothesis is true versus when it's false.
This is a pretty straightforward moral - it's a widely known pillar of statistical reasoning. But its absence in the raven paradox takes a bit of effort to see. This is because we're using an implicit model of the problem (driven by some combination of outside knowledge and framing effects) where nonblack ravens replace black ravens, but don't replace bananas. The logical statements H1 and H1' are not alone enough to tell how you should update upon seeing new evidence. Or to put it another way, the version of induction that drives the raven paradox is in fact wrong, but probability theory implies a bigger version.
(Technical note: In the hypotheses above, the exact number of yellow bananas does not have to be the same for observing a yellow banana to provide no evidence - what has to be the same is the measure of yellow bananas in the probability distribution we're drawing from. Talking about "99 ravens" is more understandable, but what differentiates our hypotheses are really the likelihoods of observing different events [there's our moral again]. This becomes particularly important when extending the argument to infinite numbers of ravens - infinities or no infinities, when you make an observation you're still drawing from some distribution.)