Raven paradox

The Raven paradox is a paradox proposed by the German logician Carl Gustav Hempel in the 1940s to illustrate a problem where inductive logic violates intuition.

A statement of the problem

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:

Related Topics:
Law of gravity - Probability

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• 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 that all ravens are black. We go out and examine a million ravens, and observe that they are all black.

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After each observation, our belief in the theory "all ravens are black" will rise slightly. The principle of induction looks reasonable here.

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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.

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So by the principle of induction, observing a red apple should increase our belief that all ravens are black! This problem has been summarized (derived from a poem by Gelett Burgess) as:

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:I never saw a purple cow

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:But if I were to see one

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:Would the probability ravens are black

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:Have a better chance to be one?

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