Does a green apple prove all ravens are black?

A strange puzzle about what counts as evidence.

Start with something nobody argues about. All ravens are black.

How would you test that? You'd go look at ravens. Every black raven you find is a little more support. Simple.

In the 1940s, a philosopher named Carl Hempel pointed out a problem.

"All ravens are black" means exactly the same thing, logically, as "anything that isn't black isn't a raven." If one is true, the other has to be. They're two ways of saying one thing.

So evidence for one should count as evidence for the other.

Which means a green apple supports the claim that all ravens are black. It isn't black, and it isn't a raven. So does a white shoe. So does a blue car. In theory, you could study birds without leaving your kitchen.

That's the raven paradox, and it has bothered people for about 80 years.

The obvious reaction is that it's silly. But the logic holds up, and philosophers have spent a long time trying to explain why it still feels wrong.

Hempel himself didn't flinch. He accepted the conclusion. A red herring or a white shoe really does confirm that all ravens are black, he argued. The sense that something has gone wrong comes from a misguided intuition, not from a flaw in the logic.

The most popular answer comes from probability. Yes, the green apple counts. It just counts for almost nothing.

Think about the numbers. There are far fewer ravens in the world than there are things that aren't black. When you check a raven, it really could have turned out white, so finding a black one tells you something. When you check an apple, there was never any real chance it would turn out to be a raven. So it tells you almost nothing.

Good evidence agrees with your idea, and it would have been unlikely if your idea were wrong.

That second part is where people get into trouble.

Psychologists have a test that shows it. In 1966, Peter Wason showed people four cards. Each had a letter on one side and a number on the other. The rule to check: if a card has a vowel on one side, it has an even number on the other. Which cards do you need to turn over to find out if the rule holds?

Most people pick the vowel and the even number. The even number can't break the rule, though. Whatever's on the back, the rule survives. The card that matters is the odd number, because a vowel behind it would prove the rule wrong. In Wason's study, fewer than one in ten people got it right.

People check the cards that can agree with them. They skip the one that could prove them wrong.

Most people collect evidence like a pile. Every agreeing example goes on top, the pile gets bigger, and they feel more sure. But a lot of what goes on the pile is green apples. It agrees with what they already believe. It also would have shown up either way.

A friend who says your plan is great. A study that says what you hoped it would. A success story that fits your theory, told by someone whose theory it is. None of these are worthless. They're just lighter than they feel.

The heavy evidence is the kind that could have gone against you. The test you could have failed. The raven that might have been white.

So the next time you feel very sure of something, it's worth weighing what's in the pile.

How much of it is ravens? And how much of it is apples?

"Extraordinary claims require extraordinary evidence." Carl Sagan, Cosmos (1980). The idea is older: the sociologist Marcello Truzzi and, much earlier, the mathematician Pierre-Simon Laplace said versions of it first.