H1: All ravens are black.

H1': If it is not black, it is not a raven.

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.

Question: H1 and H1' appear to be logically equivalent to:

H1'' There do not exist any things which are both not black, and a raven.

And this seems to have different implications in a finite universe and an infinite universe.

For instance, in a finite universe of 10,000 things, if you've found 99 yellow bananas and 1 black raven, there are 9,900 things which could potentially disprove H1''. If you then observe an additional 100 yellow bananas, there are now only 9,800 things that could potentially disprove H1'', so it would make sense that H1'' becomes a small amount more likely, since if all of the remaining untested things were yellow bananas, and you tested them all, at the point at which you tested the last thing you would be much more confident about H1'', and presumably that confidence grows as you get closer to testing the last thing as opposed to coming all at once at only the last thing.

But:

In a infinite universe of infinite things, if you've found 99 yellow bananas and 1 black raven, there are infinite things which could potentially disprove H1''. If you then observe an additional 100 yellow bananas, there are still an infinite number of things that could potentially disprove H1'', so H1 would not necessarily become a small amount more likely because of the argument I just gave since there is no 'last thing' to test.

When I looked at http://en.wikipedia.org/wiki/Raven_paradox , I'm not sure if anything I just said is any different from the Carnap approach, except that the Carnap approach described in the article does not appear to mention infinities, so I'm not sure if I'm making an error or not.