Ravens Paradox

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 $E$ confirms $H$ and $H$ and $H'$ are logically equivalent, then $E$ confirms $H'$.

IC: Statements of the form "All $F$s are $G$s" are confirmed by positive instances. That is, "All $Fs$ are $G$s" is confirmed by an $a$ that has both property $F$ and property $G$.

Let $H$ be the hypothesis "All ravens are black", and $H'$ be the hypothesis "All non-black things are not ravens". Then, consider the following argument:

1. By IC, observing a red sweater confirms $H'$.
2. $H'$ and $H$ are logically equivalent.
3. By EC, observing a red sweater confirms $H$.

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.).

Lecture

Slides

Consult the following video for further discussion of the Paradox of the Ravens: