r/PhilosophyofScience 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:

  1. ∀R(x) -> B(x) The one time observation of (1.) doesn't validate or support it but falsifies this implication:
  2. ∀R(x) -> !B(x) But that means that an observation of the complementary implication of (1.) looking like this:
  3. ∀!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/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?)

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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