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The paradox of the ravens

One black raven

In some discussions of the logic of induction, one runs into a paradox of the ravens, otherwise known as Hempel's paradox, in recognition of philosopher Carl Gustav Hempel. I'd like to run through it now, if only in an attempt to keep my mind nimble.

Hempel asks us to consider the hypothesis (1) all ravens are black. Now, we naturally think that if we can justify this proposition as a matter of induction, we can do so by looking at a lot of ravens, to see if all of them that we can find are black.

But we surely don't look at apples, to see if they are some color other than black (say, red or green). Because we implicitly but strongly believe (2) observations of non-ravens are not relevant to verifying a generalization about the look of ravens.

But ... Hempel's paradox challenges (2). After all, (1) would seem to be the logical equivalent of (3) All non-black items are non-ravens.

So: whenever I see a green apple, I see a non-black item that is a non-raven. Why do we revolt at the idea of treating this as an observation tending to support (1)?

There is a lot that one might say about this. I suspect that if I understood Bayesian probability theory better I would have a ready response.

One might, though, simply say, "nevermore."


  1. I am not competent to apply Bayesian probability or other technical rules of logic, but, although (1) and (3) do seem logically equivalent, it seems that we revolt against (3) because it would require so much more work than (1) to confirm by induction. We'd have to take note of every non-black item we encounter, every minute of every day that we are awake, and that would leave us no time to live our lives. With respect to (1), we could go about our business and take note only when a raven came upon the scene.

    But what about the fact that neither strategy would work, because induction does not constitute valid proof? We can never prove that no ravens are non-black. Finally, where did black ravens come in? I thought that the question was about white swans.


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