README.md

A Fact about Kestrels

Problem

Prove that if a Kestrel is egocentric, it must be hopelessly egocentric.

Solution

If a Kestrel K is egocentric, it returns itself when called with itself:

K(K) => K;

But K(K) is itself fixated on K, because the Kestrel fixates on its first argument:

K(K)(y) => K; // where `y` is any arbitrary bird

Since K(K) and K are the same bird, we can simplify that to:

K(y) => K;

And voilà—this Kestrel is hopelessly egocentric!

Notes

Smullyan boils the proof down to even simpler terms: per problem 9, any bird that the Kestrel is fond of is hopelessly egocentric. An egocentric Kestrel is fond of itself, and thus hopelessly egocentric.

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