The raven paradox forces us to question the value of information.
In his 1965 essay “Studies in the Logic of Confirmation,” the acclaimed philosopher of science Carl Hempel showcased a fundamental paradox in the scientific method using the simplistic observations of ravens. He started with the statement “all ravens are black.” Expressed in logic form, this statement would be “if an object is a raven, then that object is black.”
According to the laws of logic, a conditional is equivalent to its contrapositive. Said another way, “if A then B” is equivalent to “if not B then not A.” Therefore, “if an object is not black than it is not a raven.” In plain English, all non-black things are not ravens.
It’s general accepted that when we see a black raven it reinforces (confirms) our hypothesis that all ravens are black. Every time we see a raven and it’s black, the hypothesis is strengthened. It’s only if we saw a raven that wasn’t black that we would disprove the hypothesis. And since we can’t possibly see every raven in the world, we accept the hypothesis after some amount of evidence. This is inductive reasoning.
Now here’s where the paradox comes into play.
Since all non-black things are not ravens is equivalent to all ravens are black, then technically every time we see something that isn’t black and isn’t a raven this also adds evidence to the hypothesis. The walls in my room are mocha – more evidence all ravens are black. The plant on my desk is green. More confirmation.
While it’s virtually impossible to inspect every raven to ensure it’s black, it’s definitely impossible to inspect every non-black object to ensure isn’t not a raven.
If you accept the laws of logic, every observation of the hypothesis (all ravens are black) or observation of the contrapositive of the hypothesis (all non-black things are not ravens) provides incremental support. Even if it’s a very small amount of incremental support.
Does your brain hurt yet?
Well, the paradox gets worse (or better, depending on how much you like logic). If my green plant reinforces – even to some infinitesimal degree – that all ravens are black, then it has to also reinforce – to the same infinitesimal degree – the contradictory hypothesis that all ravens are white. After all, the contrapositive of all ravens are white is all non-white things are not ravens and a green plant definitely fits that description.
So what hypothesis, if any, does my green plant help prove or disprove?
The raven paradox is an intriguing way to force us to consider the actual value of incremental information.
No comments yet.