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Pinocchio paradox
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- Pinocchio paradox causes Pinocchio's nose to grow if and only if it does not grow. The Pinocchio paradox arises when Pinocchio says "My nose grows now" and is a version of the liar paradox. The liar paradox is defined in philosophy and logic as the statement "This sentence is false."
en.wikipedia.org/wiki/Pinocchio_paradox
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The premise that Pinocchio's nose grows if and only if he claims any falsehood is given as: ∀x: G ↔ C(x) ∧ ¬x If Pinocchio's claim is that his nose will grow then this is given as:
- Does Pinocchio's nose grow only when he knows he is lying?
If Pinocchio’s nose grows whenever he pronounces a false...
- Does Pinocchio's nose grow only when he knows he is lying?
Sep 19, 2018 · If Pinocchio’s nose grows whenever he pronounces a false statement, it would make a marvellous tool for science, and Pinocchio could test any hypothesis easily and instantly. source.
The paradox suggested by Veronique, "My nose grows now", or in future tense: "will be growing", leaves room for different interpretations. In the novel, Pinocchio's nose continues to grow as he lies: "As he spoke, his nose, long though it was, became at least two inches longer." [3]
The paradox is naturally to the effect of Pinocchio’s truth- or lie-telling. If the statement is false (i.e. his nose doesn’t grow), then he must be lying (i.e. his nose should grow) – which amounts to him telling the truth and making us wonder why his nose grew if Pinocchio was telling the truth.
Feb 15, 2009 · Pinocchio knows that when he tells a lie, the agency of the curse will judge that he has lied, and cause his nose to grow. The real question is whether he can predict what the curse will do in this peculiar situation.
Dec 23, 2019 · As Peter Eldridge-Smith explains: “So, Pinocchio’s nose is growing iff it is not growing. It is clearly a version of the Liar [paradox].” However, there is an important difference between the original Liar paradox and the Pinocchio paradox.
If Pinocchio says 'My nose grows now,' he is either lying or not. If he is lying, then he is making a false statement, which implies that his nose does not grow now. If he is not lying, then his statement is either true or false, which implies that either his nose does grow now or his nose does not grow now.
