Jourdain’s paradox (1913)

Named after its discoverer, the mathematician Philip Edward Bertrand Jourdain (1879-1919).

The paradox is equivalent to the sentence ‘The second part of this sentence is true and the first part of this sentence is false’, which contradicts itself whether the first half is true or not. However, the halves of the sentence refer indirectly to themselves, so any rule prohibiting statements that refer to themselves resolves the paradox.

The paradox

Suppose there is a card with statements printed on both sides:

Front: The sentence on the other side of this card is True.
Back: The sentence on the other side of this card is False.

Trying to assign a truth value to either of them leads to a paradox.

  1. If the first statement is true, then so is the second. But if the second statement is true, then the first statement is false. It follows that if the first statement is true, then the first statement is false.
  2. If the first statement is false, then the second is false, too. But if the second statement is false, then the first statement is true. It follows that if the first statement is false, then the first statement is true.

The same mechanism applies to the second statement. Neither of the sentences employs (direct) self-reference, instead this is a case of circular reference. Yablo’s paradox is a variation of the liar paradox that is intended to not even rely on circular reference.

One thought on “Jourdain’s paradox (1913)

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