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The Parity Paradox

Consider a finite list of n statements:

S1: At least one of statements S1-Sn is false.
S2: At least two of statements S1-Sn is false.

Sn-1: At least n-1 of statements S1-Sn is false.
Sn: At least n of statements S1-Sn is false.

Is this a paradox? It depends: The statements form a self-consistent system if n is even, but not if it’s odd.

From Roy T. Cook’s new book Paradoxes — which is dedicated in part to “anyone whom I don’t discuss in this book.”