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; the Hempel’s Ravens paradox, however, seems to show that it’s false.

Using this principle, the Hempel’s Ravens paradox suggests that an observation of a green parrot is evidence that ravens are black. 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 color a raven is without looking at a raven.

Simple. One of your statements in that line of logic is false. Which one depends on the angle you look at it from.

If we assume everything up to the final statement is true, then obviously the final one is false; after all, if you take all your previous statements to be truths, then there is no need to observe a raven to discover it\'s color. You\'ve already proven that anything that isn\'t a raven and isn\'t black proves that ravens are black, so you obviously know that ravens are black by your proof; no need for observation.

Let us give these statements to a person who has never seen nor heard of a raven. They would either take your word as true, and believe that a raven is black, or they would have to observe a raven in an attempt to disprove the statements. Either way, the statement must be made by someone who has observed or believes that a raven is black. We rely on someone else\'s judgement until it is proven to us otherwise; hence, at some point someone must have observed a raven to make the statements.

I had a point in there somewhere, but I believe I\'ve tripped myself up and botched it.

I\'m confused on one point though. Maybe I just lack the comprehensive power to understand all of this, but where is a paradox involved in all of this? If both statements are always true, and neither contradicts the other, than what is the paradox created? Or was the paradox that we can\'t actually rely on this information because we must first observe the raven?

[Edited on 13-7-2005 by AimMan v2.5]