Hempel's Raven Paradox (Red Mini Example)
A logical demonstration showing that if you accept that observing a white swan confirms 'all swans are white', you must also accept that observing a red Mini Cooper confirms 'no black swans exist', thereby exposing the absurdity of naive confirmation.
THE IDEA
Saw Another Red Mini!
The following point further illustrates the absurdity of confirmation. If you believe that witnessing an additional white swan will bring confirmation that there are no black swans, then you should also accept the statement, on purely logical grounds, that the sighting of a red Mini Cooper should confirm that there are no black swans.
Why? Just consider that the statement “all swans are white” is equivalent to “all nonwhite objects are not swans.” What confirms the latter statement should confirm the former. Therefore, a mind with a confirmation bent would infer that the sighting of a nonwhite object that is not a swan should bring such confirmation. This argument, known as Hempel’s raven paradox, was rediscovered by my friend the (thinking) mathematician Bruno Dupire during one of our intense meditating walks in London—one of those intense walk-discussions, intense to the point of our not noticing the rain. He pointed to a red Mini and shouted, “Look, Nassim, look! No Black Swan!”
When to use it
Evaluating the strength of evidence in scientific hypothesis testing
Avoiding overconfidence in pattern recognition when analyzing data
Recognizing when a statement's logical equivalence leads to misleading confirmations in everyday reasoning
Designing experiments that account for the paradox to avoid false confirmations
FROM THEORY TO EVERYDAY LIFE
In practice
The Red Mini Cooper
Nassim Taleb and Bruno Dupire are walking in London. Dupire spots a red Mini Cooper and exclaims, 'Look, no Black Swan!' If one accepts that observing a white swan confirms 'all swans are white', then by logical equivalence (contrapositive) the observation of a non-white non-swan (like a red Mini) also confirms the same proposition, leading to an absurd result.
A MOMENT TO REFLECT
Put it to work.
Can you think of a real-world situation where you might unknowingly treat an irrelevant observation as confirming your belief?
How does Hempel's paradox challenge the way we typically gather evidence for a hypothesis?
What modifications to the logical structure could avoid the paradoxical conclusion?
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)