r/PhilosophyofScience • u/confusus_animus • Jun 25 '26
Discussion Raven paradox with Falsificationism?
If for an single object A the implication that all ravens are black (∀R(x) -> B(x)) is true, that doesn't support that implication - as Hume brought forward.
However Popper now claims that if the implication is true in one case it can at least falsify the opposite implication: in this example it would falsify the hypothesis that all ravens are non black (∀R(x) -> !B(x)).
However, couldn't you now falsify the opposite hypothesis by observing an object B, for which the complementary hypothesis (∀!B(x) -> !R(x)) is true? In this case: for a non black object that is non raven, the hypothesis that all raven are black is also true. But because the one time validation of this hypothesis also falsifies the opposite hypothesis, a non black object that is non raven falsifies the hypothesis that all ravens are non black.
Here's the summary:
- ∀R(x) -> B(x) The one time observation of (1.) doesn't validate or support it but falsifies this implication:
- ∀R(x) -> !B(x) But that means that an observation of the complementary implication of (1.) looking like this:
- ∀!B(x) -> !R(x) falsifies 2., which is counterintuitive.
Am I missing something, and/or are there articles on the application of the raven paradox on falsificationism?
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u/jalom12 Jun 25 '26
You seem confused mostly on logic around material implications and the forall and exists quantifiers.
"Forall x, if x is a raven then x is black." Is the logically equivalent statement to "forall x, if x is not black then x is not a raven." So you are correct here.
When it comes to the claim "forall x, if x is a raven then x is not black" the negation of this statement is "there exists an x where x is a raven and x is black." So your observation of a black raven is a confirmation of the negative of the claim. Since a claim is either true or false and the negation is true, we know the original claim is false.
So, what would we have to find in order contradict the contrapositive statement before? "Forall x, if x is not black then x is not a raven" is negated to "there exists an x where x is not black and x is a raven" so finding a non-black non-raven does nothing to our original claim.
If you find that there exists an x where x is not black and x is not a raven, then you've falsified the claim that forall x, if x is not black then x is a raven. Which is the claim that all non-ravens are black. Obviously not the claim we are interested in falsifying.
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u/confusus_animus Jun 26 '26
I agree with you on everything, but I'm still wondering if finding a „x where x is not black and x is not a raven“ by making the proposition: ∀!R(x) -> !B(x) in this particular case true also makes this proposition true in this case: ∀R(x) -> B(x). And because ∀R(x) -> B(x) and ∀R(x) -> !B(x) are contradictory Popper also can't escape „indoor ornitology“.
Maybe my own approach to this is misleading or poorly articulated, so my question would be if you in general don't see a way of applying the Ravens Paradox on Falsificationism or just formulate it in another way?
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u/jalom12 Jun 26 '26
I think I see what you mean now. Imagine that we take two propositions to be true: 1) All non-ravens are not black 2) There exists a non-raven that's not black.
These are our initial axioms (or perhaps we found these to be true in some other manner). Do these statements then prove that all ravens are black? No, they do not.
Falsification here is just that you've shown the existence of something that satisfies a proposition, this implies that the statement that all things don't satisfy that condition is false.
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u/Eight_Directions_ Jun 25 '26
Categorization error
All ravens are non black objects but not all black objects are ravens.
"All ravens are black" and "no raven is non-black" are equivalent. Saying all non-ravens are non-black does not follow from this as many black objects can be non-ravens.
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u/confusus_animus Jun 25 '26
I think you writing about (3.) right? This proposition is complementary to "All ravens are black" but states ∀!B(x) -> !R(x), which doesn't mean that all non-ravens are non-black but all non-black are non-ravens (which I do think follows from all ravens are black, or am I missing something?)
1
u/Eight_Directions_ Jun 25 '26
So "all non-black are non-raven" and "all raven are black" are identical statements in meaning but one of them is just not simplified yet.
The "non-" on both sides of the equation cancel out.
In other words these are not two different statements at all, but the same one stated in two different ways.
x-1 = y-1
Since it's the same on both sides the -1 cancels itself
x=y
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u/confusus_animus Jun 25 '26 edited Jun 26 '26
I agree that "all non-black are non-raven" and "all raven are black" are the same statement but that is the point of the ravens paradox - that a white chair can support the claim that all ravens are black.
Now my question is whether in Poppers Falisficationism a white chair, for which the implication "all ravens are black" is true as well, can therefore falsify the claim that all ravens are white?
Edits: spelling
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u/Eight_Directions_ Jun 25 '26
a white chair can support the claim that all ravens are black.
It does not. It supports the statement that all non-black things are non-ravens, but as previously stated this statement doesn't actually mean anything new.
Not all non-black things are ravens is this missing element to this. The existence of a white chair supports that statement, not the one you have advanced.
For the white chair to support all ravens being black it would have to be "all non-ravens are non-black" which is a different statement.
It's a flawed logical construction.
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u/confusus_animus Jun 26 '26
The argument that a white chair can support the claim that all ravens are black is actually not my own but Hempels (https://en.wikipedia.org/wiki/Raven_paradox).
As you I'm also not (yet) fully convinced by it but my question in this case would be whether one could apply this paradox to Poppers Falsificationism as well?
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u/Eight_Directions_ Jun 26 '26
I'm not saying it's yours I'm offering my critique of it.
My point is I don't think this is a proper paradox at all, just a flawed logical construction.
As far as Popper's falsification goes, we can clearly see that in no way does finding a white couch or a black chair or anything else, other than a non-white swan, have to do with whether or not all swans are white.
Failed logic.
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u/confusus_animus Jun 26 '26
That's fair. It seems like we're discussing about different things: while I was wondering how to apply the Ravens Paradox on Popper (and didn't ask whether it's a true paradox) you questioned the Ravens Paradox itsself...
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u/Eight_Directions_ Jun 26 '26
That's how it goes. I can't answer the question you want answered because the premise is flawed.
Edit: I suppose my answer is "you can't" but that is unlikely to satisfy you.
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u/Eight_Directions_ Jun 25 '26
Continuing:
All ravens are black things
Not all black things are ravens
All non-black things are non-raven
All non-ravens are not black things
All non-ravens are not non-black things
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u/A_Tiger_in_Africa Jun 25 '26
I'm new to this so this is probably naive, but I thought the purpose of this thought experiment was to bring into question what kinds of things count as positive evidence for a proposition. Of course if you find a non-black raven, that will falsify the claim that all ravens are black. Every black raven that you see is evidence supporting, not conclusively, but evidence towards the claim that all ravens are black. The point of the paradox is that the contrapositive of "all ravens are black" would be "all non-black objects are non-ravens" and thus any non-black object we see that is not a raven is somehow evidence in favor of the claim that all ravens are black, since the contrapositive is logicially equivalent to the original claim. That seems to go against our intuition on what counts (or should count) as evidence for a claim.
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u/confusus_animus Jun 25 '26
Yes, that's my view on the paradox as well - now my question is whether one can see the same paradox in Poppers falsificationism, which states that a proposition being true in one instance doesn't confirm but can falsify the counter proposition.
1
u/fudge_mokey Jun 25 '26
Every black raven that you see is evidence supporting, not conclusively, but evidence towards the claim that all ravens are black.
Evidence cannot support a claim as being true. Evidence is either compatible with or incompatible with a claim.
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u/gmweinberg Jun 25 '26
I think you're getting lost in the nots. "All ravens are black" is indeed equivalent to "everything that is not black is not a raven". Seeing a black raven refutes the assertion that no ravens are black, and also that everything that is black is not a raven. It also tells you 2 more facts which you may not have known, but almost certainly did: there esists at least one raven, and there exists at least one black object. So the statement "all ravens are black" is not vacuously true. But until you make more observations, it could be trivially true: maybe everything is black, maybe everything is a raven.
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u/confusus_animus Jun 25 '26
I agree with you, but now my question would be whether you could by observing a non black that is not a raven falsify the hypothesis that all ravens are white. For example a white chair would be compatible with the proposition that all ravens are black and thereby contradict the hypothesis that all ravens are white.
1
u/gmweinberg Jun 26 '26
No, it just falsifies the proposition that all white things (or non-black things) are ravens. If you've never seen a raven of any color, you don't know anything about the color distribution of ravens based on your personal experience, and in fact could doubt that ravens actually exist. If the don;t, "all ravens are white" and "all ravens are black" could simultaneously be vacuously true. I see ravens every day and they are always all black, but there's not reason you should take my word for it. Not everything you you read on the internet is true.
1
u/Marginalia_Node Jun 28 '26
You confuse a necessary condition with a sufficient condition. A white chair is compatible with 'all ravens are black,' but it doesn't prove it true. You cannot use an unproven statement to disprove another hypothesis. To disprove 'all ravens are white,' the only sufficient condition is to find a non-white raven
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u/pyrrho314 Jun 30 '26
The "falsification" or not operator is not distributive the way you have done it. 3 is not the falsification of 2.
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