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Yablo's paradox

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Yablo's paradox is a liar-like paradox without any apparent self-reference published by Stephen Yablo in 1993.

The paradox

The paradox arises from considering the following infinite set of sentences:

  • (S1): for all k > 1, Sk is false
  • (S2): for all k > 2, Sk is false
  • (S3): for all k > 3, Sk is false
  • ...
  • ...

The set is paradoxical, because it is unsatisfiable (contradictory), but this unsatisfiability defies immediate intuition.

Moreover, none of the sentences refers to itself, but only to the subsequent sentences; this leads Yablo to claim that his paradox does not rely on self-reference.

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