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This statement is false

paradoxself-referencelogic

Consider the sentence: "This statement is false."

  1. Is it true or false? Show that each answer leads to a contradiction.
  2. A card has two sides. Side 1 says: "The sentence on the other side of this card is true." Side 2 says: "The sentence on the other side of this card is false." Neither sentence refers to itself. Is there a consistent assignment of true and false to the two sides?
  3. Pinocchio's nose grows exactly when he lies. He says: "My nose is about to grow." What happens?

What is the common structure, and how do logicians deal with it?

Show a hint

Try to assign truth values and follow the consequences round in a loop. The loop is the whole phenomenon.

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The theory behind this question.

One Question, Two Guards, One DoorCheryl's Birthday and Iterated KnowledgeLogic and QuantifiersProof Techniques: Direct, Contrapositive, ContradictionSelf-Referential Quiz Puzzles

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