Raven paradox

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.

Hempel describes the paradox in terms of the hypothesis:

In strict logical terms, via contraposition, this statement is equivalent to:

It should be clear that in all circumstances where (2) is true, (1) is also true; and likewise, in all circumstances where (2) is false (i.e. if a world is imagined in which something that was not black, yet was a raven, existed), (1) is also false. This establishes logical equivalence.

Given a general statement such as all ravens are black, a form of the same statement that refers to a specific observable instance of the general class would typically be considered to constitute evidence for that general statement. For example,

is evidence supporting the hypothesis that all ravens are black.

The paradox arises when this same process is applied to statement (2). On sighting a green apple, one can observe:

By the same reasoning, this statement is evidence that (2) everything that is not black is not a raven. But since (as above) this statement is logically equivalent to (1) all ravens are black, it follows that the sight of a green apple is evidence supporting the notion that all ravens are black. This conclusion seems paradoxical, because it implies that information has been gained about ravens by looking at an apple.

Nicod's criterion says that only observations of ravens should affect one's view as to whether all ravens are black. Observing more instances of black ravens should support the view, observing white or coloured ravens should contradict it, and observations of non-ravens should not have any influence.

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