If two statements are logically equivalent, if they assert exactly the same thing, then any evidence for one is evidence for the other.
This principle appears to be truism. Consider the two statements “Terry and Judith are my parents” and “I am Terry and Judith’s child”. These statements are logically equivalent, they say the same thing. There is no evidence that would support one of them without supporting the other.
No matter how superficially plausible this principle, however, the Hempel’s Ravens paradox seems to show that it is false. The Hempel’s Ravens paradox uses the principle to prove the absurd conclusion that an observation of a green parrot is evidence that ravens are black. The only way of avoiding this clearly unacceptable conclusion is to reject the principle above.
The paradox goes like this:
Consider the two statements:
(1) “All ravens are black.”
(2) “Everything that isn’t black, isn’t a raven.”
These two statements say exactly the same thing. The first statement says that everything of a particular kind has a certain property. The second statement says that everything that lacks that property isn’t of that kind.
The two statements are therefore logically equivalent; they are true and false in exactly the same circumstances. If there is anything that is a raven but isn’t black then both (1) and (2) are false; oherwise, they are both true. As the two statements are logically equivalent, any observation that supports one will also support the other.
Suppose, then, that I observe a green parrot. This observation confirms (2), “Everything that isn’t black isn’t a raven”. A green parrot isn’t black and isn’t a raven. The observation is evidence that (2) is true.
Given what has been said so far, my observation of a green parrot must also confirm (1). (1) and (2) are logically equivalent, so any evidence for one is evidence for the other. My observation of a green parrot, then, is evidence for the statement, “All ravens are black”. In fact, any observation of something that isn’t black and isn’t a raven is evidence that ravens are black.
This, though, is absurd; there is no way that we can discover what colour a raven is without looking at a raven.