Hempel’s Paradox Revisited
Understanding the Raven Paradox
In a Nutshell
In the mid-20th century, philosopher Carl Gustav Hempel introduced a paradox that came to be known as ‘Hempel’s Paradox’ or the ‘Raven Paradox’. It stems from a logical point that he raised. That the statement “All ravens are black” is the same thing as saying “Everything that is not black is not a raven”. So if I see something that’s not black, and not a raven, say a blue tennis shoe, that should lend at least a tiny bit of support to the proposition that all ravens are black! Sounds strange, though!
HEMPEL’S PARADOX AND THE COLOUR OF FLAMINGOS
Let’s try it with flamingos.
Suppose my hypothesis is that all flamingos are pink. This is logically equivalent to saying that everything that is not pink is not a flamingo.
Now I see my blue tennis shoe again. It isn’t pink and it isn’t a flamingo. So, according to the same reasoning, it provides evidence for the proposition that all flamingos are pink. Weird, but logically airtight. That’s Hempel’s Paradox.
TESTING THE HYPOTHESIS
Normally, if we wanted to test the claim that all flamingos are pink, we would find some flamingos and look at them. But Hempel’s reasoning suggests another way. We could look at random things that aren’t pink and check that they aren’t flamingos. A white tennis shoe? Not a flamingo. A blue car? Not a flamingo. A green garden shed? Not a flamingo.
With each observation we have added a little more evidence for the proposition that everything that isn’t pink isn’t a flamingo, and that therefore all flamingos are pink. On the other hand, it might be a better use of time to directly study flamingos. Still, there’s nothing wrong with Hempel’s logic.
THE ACCESSIBILITY PRINCIPLE
There is another way of looking at this which I think helps. Imagine two undiscovered species. Species A is a bird which, if it existed, would live in towns and cities and regularly appear in people’s gardens. Species B is a lizard living in some remote and almost inaccessible part of the world.
Neither has ever been observed.
Which are we more entitled to believe might nevertheless exist?
Surely Species B. If Species A existed, somebody ought to have seen it by now. But the failure to observe Species B tells us much less because it would be difficult to find even if it were there.
I call this the Accessibility Principle, or perhaps the Observational Likelihood Principle. The basic idea is simple. The significance of failing to observe something depends partly on how likely we would have been to observe it if it existed.
This is just the familiar point that absence of evidence is not necessarily evidence of absence. But sometimes it is. If something should have been easy to find and nobody has found it, that matters.
Now return to the flamingos.
We have:
Proposition 1: All flamingos are pink.
Proposition 2: Everything that is not pink is not a flamingo.
And Proposition 3: Failure to observe something tells us more when that thing would have been easy to observe if it existed.
So when I see my white tennis shoe, perhaps I really should become ever so slightly more confident that all flamingos are pink. And that confidence might increase a little more if any non-pink flamingos that existed would be very easy to spot.
There is just one problem.
Not all flamingos are pink.
So I would still be wrong. But at least I would be wrong for the right reasons.
THE OBSERVATION PARADOX
Hempel’s Paradox is interesting because there is no mistake in the logic. That, I think, is where the paradox earns its keep. It makes us distinguish between evidence in the purely logical sense and evidence that changes what it is reasonable to believe. In this sense, the white tennis shoe does indeed tell us something about all flamingos being pink. Just not very much. And then we see an orange flamingo. And suddenly we know!
