The Paradox of the Ravens was introduced by Carl Hempel in the 1940s, and has been widely discussed by philosophers, logicians and statisticians. Consider the following two principles:
EC: If confirms and and are logically equivalent, then confirms .
IC: Statements of the form "All s are s" are confirmed by positive instances. That is, "All are s" is confirmed by an that has both property and property .
Let be the hypothesis "All ravens are black", and be the hypothesis "All non-black things are not ravens". Then, consider the following argument:
- By IC, observing a red sweater confirms .
- and are logically equivalent.
- By EC, observing a red sweater confirms .
But this is an absurd conclusion: It seems to suggest that you can become more certain that all ravens are black by observing objects laying around your house (e.g., a red sweater, silver computer, etc.).
Consult the following video for further discussion of the Paradox of the Ravens: