Knaph
Stories

The Story of the Counterexample

A black swan with a bright red beak swimming on calm brown water.
A black swan. For centuries Europeans used the phrase for something that could not exist.

Image: Photo: Charles J. Sharp. A black swan (Cygnus atratus) on Bruny Island, Tasmania (2023) · CC BY-SA 4.0

A Knaph story

The Story of the Counterexample

How one case learned to break an "all"

c. 375 BCE – 1988

A mad friend, a plucked chicken, three black swans and one stubborn number. How people learned that a single case can break a claim, however many cases agree with it.

A Knaph story

The Story of the Counterexample

How one case learned to break an "all"

c. 375 BCE – 1988

A mad friend, a plucked chicken, three black swans and one stubborn number. How people learned that a single case can break a claim, however many cases agree with it.

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