“Negatives” aren’t special

The oft-repeated claim that you can’t prove a negative is, frankly, dumb. Really, really dumb. It implies that you can’t prove Jesus didn’t rise from the dead, but you can prove he stayed dead.

I’m not just being flippant. Negative statements always imply positive statements and vice-versa. If p is true, not-p must be false. If you prove p, you disprove not-p. I think this point has wide-ranging philosophical implications, which I’ve been thinking about lately because of two books I read recently.

The first is Nassim Nicholas Taleb’s The Black Swan. On the whole, I liked this book, and would recommend it to others. Taleb has a background in finance, and on that subject, he’s great.

The book’s key idea is that improbable events are often not quite as improbable as they seem. If your calculations tell you to be 99% certain, maybe you should allow for a 5% chance that the assumptions behind the calculation are significantly mistaken. So far, so good.

Taleb stumbles, though, when he tries to write about abstract philosophy. He declares himself a Popperian, after Karl Popper, who proposed that scientific theories can never be verified, only falsified.

This claim is not quite as stupid as the naive “you can’t prove a negative!” If you think science aims at universal generalizations, well, it’s true that no number of examples can logically prove a universal generalization, while a single counterexample can logically disprove one.

Only it’s not quite as simple as that. In the real world, how can you be certain that your counterexample is really a counterexample? Say you’re citing the proverbial black swan to disprove the claim that all swans are white. How do you know the black swan was there?

I mean, maybe you saw it. Or think you did. Do you imagine it’s a universally true generalization that every time you seem to see an animal of a given color, you’re really seeing one? But how can you prove that, if you’re a Popperian? That’s the problem.

In fact, sometimes, it’s not even clear Taleb is carefully limiting himself to Popperian claims about universal generalizations. He says things like, “Negative knowledge is more robust to error than positive knowledge” (actually from his later book Antifragile). That sounds a lot like the silly “you can’t prove a negative!” mistake.

The other book that’s had me thinking about the negative vs. positive distinction is Joshua Greene’s Moral Tribes. This may literally be one of the best books I’ve ever read, right up there with Dawkins’ and Pinker’s best work. It’ll probably inspire quite a few blog posts, time permitting, right now I want to focus on one point.

In Moral Tribes, Greene defends utilitarianism, a moral philosophy notorious for, among other things, making no distinctions between acts and omissions. That means that letting someone die when you could have saved them is just as bad as murder.

Most people think letting someone die when you could have saved them is bad, but if they think about it for awhile, they’ll also think the idea that it’s just as bad as murder is crazy. Greene responds to this objection by trying to debunk the act vs. omission distinction through work in moral psychology that seems to show people’s intuitive responses in this area make no coherent sense.

From personal experience, you don’t need a psychology lab to attack the act vs. omission distinction. A philosophy classroom might do. My first ethics course in college spent a lot of time on the act vs. omission distinction, and it seemed like the more we talked about it, the more confused we got.

Sure, it seemed straightforward at first. But then we started considering thought experiments that challenged whether the distinction was important, or even coherent. By the end, we were talking about things like trying to compare the sizes of infinitely large spaces of possible actions.

Greene proposes the distinction between acts and omissions seems natural because of how our brains are set up. It’s easier to evolve a mental module for thinking about something, than it is to evolve a module for thinking about everything that isn’t one particular thing. But that’s probably as far as the distinction goes.

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