Raven paradox

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The Raven paradox is a paradox German logician Carl Gustav Hempel proposed in the 1940s. The paradox is about epistemology: It shows that inductive reasoning violates intuition. It reveals the problem of induction. According to the paradox, the properties of objects can be confirmed by observing other objects which do not have these properties. That way seeing a yellow car confirms the proposition "All ravens are black".

The paradox[change | edit source]

A black raven
Non-black non-ravens

In strict logical terms, saying:

(1) All ravens are black.

is equivalent to saying:

(2) Everything that is not black is not a raven.

Whenever (2) is true, (1) also is; 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,

(3) Nevermore, 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 (and therefore not black) thing is an apple (and not a raven).

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.