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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

• xxxyy 12y ago
  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.
  • x0x0 12y ago
    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.
    • xxxyy 12y ago
      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).