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The Raven Paradox

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The raven paradox, also known as Hempel’s paradox, Hempel’s ravens, or rarely the paradox of indoor ornithology, 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:[3][4]

(1) All ravens are black. In the form of an implication, this can be expressed as: If something is a raven, then it is black.

Via contraposition, this statement is equivalent to:

(2) If something is not black, then it is not a raven.
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.

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,

(3) My pet raven is black.
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:

(4) This green apple is not black, and it is not a raven.
By the same reasoning, this statement is evidence that (2) if something is not black then it 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.

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