Here's one to melt your frontal cortex. I won't even try to explain it, read the full article then feel more clever as a result.
The Raven paradox, also known as Hempel's paradox or Hempel's ravens is a paradox arising from the question of what constitutes evidence for a statement. Observing objects that are neither black nor ravens may formally increase the likelihood that all ravens are black—even though intuitively these observations are unrelated.
This problem was proposed by the logician Carl Gustav Hempel in the 1940s to illustrate a contradiction between inductive logic and intuition. A related issue is the problem of induction and the gap between inductive and deductive reasoning. [...read more]