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Also, if the world of things is infinite, then this doesn't hold up, right? if the number of things is infinite then observations of nonblack nonravens is not evidence of the proposition, right?

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It still does hold up, but becomes more complicated. In general, there is no uniform distribution over any infinite set. We might: a) think about a pipe spitting out objects that have two possible features - being a raven and being black, or b) use a nonuniform distribution over an infinite set of objects and integrate (sum) to get a similar Bayesian result.

What do you mean there is no uniform distribution over any infinite set? There is the uniform distribution over [0,1] which is both infinite and not even countable.

I'm confused.

I meant a distribution with "discrete" probability, i.e. a distribution where the probabilities of singletons are all equal and nonzero, so that a simple Bayesian argument could possibly be extended. My bad for not being precise enough.

Perhaps I should have stuck to natural numbers in my previous comment, otherwise yes, you can have uniform distributions with respect to some additional structure of the probability space (like [0,1] with the Lebesgue measure you suggest).

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