How is the Raven Paradox a paradox?

[Pleonast]

@Pleonast

A white raven is a counter example to both.

“All ravens are black” means “if a thing is a raven, then it is black”. A white raven satisfies the hypothesis, but fails the result.

“All non-black things are non-ravens” means “if a thing is not black, then it is not a raven”. A white raven satisfies the hypothesis, but fails the result.

Substituting “raven” with “unicorn” should make it clear that the existence of unicorns doesn’t change the logic.

The statement “if a things is a unicorn, then it is pink” does not have any counterexamples if there are no unicorns. And the statement “if a thing is not pink, then it is not a unicorn” also does not have any counterexamples if there are no unicorns.

[TriPolar]

We tend to think that proving or disproving the statement “All ravens are black” would best be accomplished by looking for a non-black raven. If we found every raven and all of them are black the statement would be true, but finding a single raven that is not black proves it false and ends the search. We could also look for every non-black thing and if none of them was a raven the statement would be true, but finding a single non-black thing that is a raven proves it false and ends the search. It works either way. It might seem that it is far more practical to look for every raven than every non-black thing, but that is the real paradox here because neither approach is practical at all.

[Little_Nemo]

@griffin1977

Yes it can. It’s disproven with exactly the same single albino raven, it’s a non-Black object that is not a non-raven.

@Pleonast

A white raven is a counter example to both.

“All ravens are black” means “if a thing is a raven, then it is black”. A white raven satisfies the hypothesis, but fails the result.

“All non-black things are non-ravens” means “if a thing is not black, then it is not a raven”. A white raven satisfies the hypothesis, but fails the result.

Thinking about it, you guys are right and I’m wrong on the falsifiability issue I raised.

[Pleonast]

@Little_Nemo

Thinking about it, you guys are right and I’m wrong on the falsifiability issue I raised.

You are very logical!

[Little_Nemo]

It’s my own fault. The falsifiability issue occurred to me while I was writing my post on the existence issue. I decided to add it to the thread I was already writing rather than stop and think about it before writing a separate post.

[Pleonast]

I think a lot of the problem is English doesn’t express mathematical statements very well (and logic statements are a subset of those). Likely @Pardel-Lux fell into the same trap.

[Dr.Strangelove]

@Little_Nemo

I would feel that existing is a necessary prerequisite to having qualities like a color. So if a unicorn doesn’t exist, it can’t be pink or purple.

That may feel intuitive, but it’s not logically necessary. It’s called a vacuous truth in logic:

Vacuous truth

It may be hard to wrap your brain around, but there’s nothing wrong with vacuously true statements, and it would be hard to build a system of logic without them.

[Sam_Stone]

It seems to me that since the two populations are completely disconnected, you can’t learn anything about one by studying the other.

If I say, “All aliens are telepathic”, and “all non-aliens are non-telepathic”, are you saying that I can learn real information about alien telepathy by discovering that on-aliens are not telepathic? Even if we established that both aliens and telepathy are a real thing? I can certainly falsify that non-aliens are non-telepathic by finding a telepathic non-alien, But the only way I can discover anything about aliens is to search for a non-telepathic alien. I could examine non-aliens forever, and it won’t tell me anything about aliens.

If the paradox is that this is correct, but a straight reading of the two sentences shows that they should be equivalent, I would chalk up the problem to an English translation of the actual logical statements or a missing element of some sort, or some other confusion.

[Dr.Strangelove]

@Sam_Stone

It seems to me that since the two populations are completely disconnected

There’s a finite amount of stuff in the universe, so nothing is truly disconnected.

@Sam_Stone

If I say, “All aliens are telepathic”, and “all non-aliens are non-telepathic”

Those aren’t equivalent. The equivalent statement is “all non-telepathic beings are non-alien”.

[Pleonast]

@Dr.Strangelove

There’s a finite amount of stuff in the universe, so nothing is truly disconnected.

A finite amount in the visible universe, but the universe as a whole is bigger than that.

[Dr.Strangelove]

Sure. Presumably, we can take it as said that we’re talking about things in our future light cone. Otherwise, there would be no way to ever verify one of these statements.

[Sam_Stone]

Well, if we are talking logic and maybe set theory, then it matters if the sets overlap. It seems like we want to both abide by the rigid rules of the logical statements, while applying them to the universe in a way that invalidates the logic.

[Riemann]

@Left_Hand_of_Dorkness

I think I might see why it feels like a paradox. When you think of a white shoe, you tend to think of it as a shoe with one additional trait (white). Why should learning something about a shoe tell you anything about a raven? It feels silly.

Instead, think of it as an entity with two known traits: Shoeness, and Whiteness. Imagine you learned of the whiteness first: over there is a white thing, but you’ll have to get closer to tell what it is.

At that point, given what you believe to be true, you’ll see this white thing and think, “Better not be a raven, or my world is a lie!” When you learn that, sure enough, that white thing isn’t a raven, you’ll feel vindicated.

This is the crux of the matter. Some posters here are claiming that examining a shoe and discovering it is white tells us nothing about ravens. Of course - but only if you already knew that the object was a shoe. The point is that in order to ascertain whether all non-black objects are not ravens, what is relevant is only the universe of non-black objects whose identity is unknown and which could possibly be ravens. You must examine them one by one to find out if any of them are ravens. Discovering that one non-black object is a shoe must be new information, otherwise the case is irrelevant. If it is new information, it very slightly reduces the number of non-black objects that could be ravens.

If you already had some way of knowing with absolute certainty that all objects in a certain place (such as a shoe cupboard) cannot be ravens, then of course looking at them and discovering they are white tells you absolutely nothing about ravens. But you must be completely sure that none of the objects in there could possibly be a raven.