An important implication of my view is that no confirmation can arise from sampling a population which couldn't possibly falsify the hypothesis in any case. For example, coloured ravens might turn up in a population of coloured things, but not in a population of herrings. So if you sample coloured things and find a red herring, that (slightly) confirms that there are no coloured ravens. But finding a red herring when you're sampling from a bucket of herrings does not provide any confirmation whatsoever. For the same reason, finding black ravens in a sample of black things (as opposed to, say, a sample of ravens) would, surprisingly enough, do nothing at all to confirm that all ravens are black.
Doug wanted to deny this, and claim instead that even my bucket of herrings confirms the hypothesis C0: 'there are no coloured ravens'. He says that C0 "is disconfirmed by everything that is a coloured raven and confirmed by everything else." In other words, he agrees with Hempel's R1 account of confirmation. Now, I think that R1 is false, and that confirmation instead depends upon surviving attempted falsification, for reasons previously explained. But my lecturer offered a couple of interesting arguments which I want to consider here.
E.g., consider your bucket of red herrings. It's true that once you tell me it's a bucket of herrings then there is no point in me searching through it in order to obtain confirmation of the raven hypothesis. But that is because I already got all the relevant information when you told me it contained herrings.
But note that if R1 were true, then it would make a difference how many herrings were in the bucket. Each individual herring co-exemplifies the properties of 'being coloured' and 'being non-raven', and thus (according to R1) confirms that all coloured things are non-raven (restatement of C0). But we should recognize that it makes no difference whatsoever whether there are two or two million herrings in the bucket. If I sample the bucket of herrings and find two million red herrings inside, that does not provide any greater evidence for C0 than it would if I merely found two herrings in the bucket. Hence R1 is a mistaken account of confirmation.
Doug's next argument is more complicated. Here's my gloss on it: There are various rival hypotheses we might make about the number of coloured ravens in the world. On one hypothesis, call it H0 (=C0), there are no coloured ravens. On another, let's call it H1, everything is a coloured raven. The bucket of herrings allows us to disconfirm H1, and thus it slightly confirms the rival hypothesis H0.
I don't think this argument works, for two reasons. Firstly, there are infinitely many such rival hypotheses. (Let r be any real number between 0 and 1. Then Hr is the hypothesis that r is the proportion of worldly objects that are coloured ravens.) So when H1 is disconfirmed, the probability value we had previously assigned to it (which might be infinitesimal anyway) gets redistributed over infinitely many rival hypotheses. So the confirming increment to H0 in particular is 1/infinity = zero. [Update: This is mistaken - see comments. However, for some different and better counterarguments, see my new post.]
Second reason: we can develop a paradox of interpretation out of this. Although Doug divided the rival hypotheses up in proportional terms, we might instead list our rival hypotheses in terms of brute cardinality. Let Cn be the claim that there are n coloured ravens. But note that the observation of red herrings does not disconfirm any hypothesis Cn. (The world could contain n coloured ravens plus a bucket of red herrings.) So the observation fails to confirm C0, the claim that there are no coloured ravens.
An interesting paradox arises if we held that H0 was confirmed. For C0 is identical to H0, but C0 was not confirmed. This is contradictory. We assign different probabilities to one and the same state of affairs, depending on how we describe it. (Of course, we can easily avoid this paradox by simply denying that H0 was really confirmed after all, but let's put that aside for now.) This reminds me of Bertrand's paradox:
A factory produces cubes with side-length between 0 and 1 foot; what is the probability that a randomly chosen cube has side-length between 0 and 1/2 a foot? The tempting answer is 1/2, as we imagine a process of production that is uniformly distributed over side-length. But the question could have been given an equivalent restatement: A factory produces cubes with face-area between 0 and 1 square-feet; what is the probability that a randomly chosen cube has face-area between 0 and 1/4 square-feet? Now the tempting answer is 1/4, as we imagine a process of production that is uniformly distributed over face-area. This is already disastrous, as we cannot allow the same event to have two different probabilities...
The principle of indifference is pretty dodgy. That's all I have to say for now.