3 ms·
My solution, which I haven't come across elsewhere and is thus quite likely to be wrong or incomplete: (Update: upon rereading the article this is essentially t
by orangecat 12y ago
My solution, which I haven't come across elsewhere and is thus quite likely to be wrong or incomplete: (Update: upon rereading the article this is essentially the Carnap solution)
If you have no knowledge of the distribution of ravens and non-ravens, then picking an object at random and observing that it is not a raven should slightly decrease your estimate of the number of ravens in the population. In turn that makes it more likely that all ravens are a single color. 100 ravens are less likely to all be the same color than 5 ravens. (In the limit, if no ravens exist than all ravens are black, and purple, and polka-dotted).
So under those conditions, it is true that observing a white cat should slightly increase your belief that all ravens are black, but it should also increase your belief that all ravens are purple, and even that all ravens are white. That's entirely because the non-raven reduces the expected number of ravens, thereby increasing the probability that all ravens are a single color.
On the other hand, if you already know how many ravens exist, then observing a non-raven tells you nothing about the color of ravens, and your prior for "all ravens are black" should be unchanged.