The card paradox is a variant of the

liar paradox In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the trut ...

constructed by

Philip Jourdain Philip Edward Bertrand Jourdain (16 October 1879 – 1 October 1919) was a British mathematician, logician and follower of Bertrand Russell. Background He was born in Ashbourne in Derbyshire* one of a large family belonging to Emily Clay and ...

. It is also known as the postcard paradox, Jourdain paradox or Jourdain's paradox.

The paradox

Suppose there is a card with statements printed on both sides: Trying to assign a truth value to either of them leads to a

paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictor ...

. # 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. # 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 Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in language, logic, mathematics, philosophy, and other fields. In natural or formal languages, self-reference ...

, instead this is a case of

circular reference A circular reference (or reference cycle) is a series of references where the last object references the first, resulting in a closed loop. Simple example A newcomer asks a local where the town library is. "Just in front of the post office," s ...

. Yablo's paradox is a variation of the liar paradox that is intended to not even rely on circular reference.

References

Self-referential paradoxes {{logic-stub