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Raven paradox (en.wikipedia.org)

submitted 1 month ago* (last edited 1 month ago) by Plum@lemmy.world to c/wikipedia@lemmy.world

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The raven paradox, also known as Hempel's paradox, Hempel's ravens or, rarely, the paradox of indoor ornithology, is a paradox arising from the question of what constitutes evidence for the truth of a statement.

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[–] renegadespork@lemmy.jelliefrontier.net 5 points 1 month ago (1 children)

Given a general statement such as all ravens are black, a form of the same statement that refers to a specific observable instance of the general class would typically be considered to constitute evidence for that general statement. For example,
(3) My pet raven is black.
is evidence supporting the hypothesis that all ravens are black.
The paradox arises when this same process is applied to statement (2). On sighting a green apple, one can observe:
(4) This green apple is not black, and it is not a raven.
By the same reasoning, this statement is evidence that (2) if something is not black then it is not a raven. But since (as above) this statement is logically equivalent to (1) all ravens are black, it follows that the sight of a green apple is evidence supporting the notion that all ravens are black. This conclusion seems paradoxical because it implies that information has been gained about ravens by looking at an apple.

I'm probably misunderstanding, but this doesn't feel like a paradox to me. Logic that applies to a positive doesn't necessarily apply to an inverse statement. They are not stating the same thing.

[–] BlackRoseAmongThorns@slrpnk.net 3 points 1 month ago

You're correct, it says so in the article further down, It's not a paradox in the "formal" sense, it's only a paradox in the sense of what intuitively would be considered evidence, but in actuality isn't, I'll try to give an easier example to demonstrate use of actual basic logic.

Claim: "all natural* numbers are even".

Natural: whole number which is zero or greater. (Zero not always included, blame mathematicians)

Notice that pointing at a natural number which doesn't contradict the claim, isn't evidence, and that exists infinitely many natural numbers who don't contradict the claim (2, 4, ...), yet 1 does, and is considered evidence to the contrary.
Notice that pointing at a non-natural number, which doesn't satisfy the claim, also isn't evidence, also in this case there are infinitely many such numbers (-1, -3, ½,...).

Also as a demonstration, let's invert the claim formally, we swap "all" with "exists", and invert predicates: "exists a natural number which isn't even", this inverse is useful because it can point to how to disprove the original claim, because there exists such a number (1), i can say that i proved the inverse of the original claim, this is equivalent to disproving it.

Tldr: the paradox is a short exercise in how formal logic differs from naive intuition, there isn't really a paradox.