infundibulum

An interesting bit from Wikipedia, The Raven’s Paradox:

When numerous people over thousands of years observe something like the law of gravity, we tend to believe that it is true with very high probability.
This type of reasoning could be summarized by the principle of induction:

• If an instance X is observed that is consistent with theory T, then the probability that T is true increases.

Hempel gives an example of the principle of induction. The theory is that all ravens are black. We go out and examine a million ravens, and observe that they are all black. After each observation, our belief in the theory “all ravens are black” will rise slightly. The principle of induction looks reasonable here.

Now comes the problem. The statement “all ravens are black” is logically equivalent to the statement “all non-black-things are non-ravens”. If we observe a red apple, that is consistent with that statement. A red apple is a non-black-thing, and when we examine it, we observe that it is a non-raven. So by the principle of induction, observing a red apple should increase our belief that all ravens are black!

Chew on that while you’re waiting at the bus stop.