Pinocchio Paradox

History

Pinocchio is the main character of the 1883 novel The Adventures of Pinocchio, written by Italian author Carlo Collodi. His nose grows each time he lies, with no limits to its length. The Pinocchio paradox was suggested by 11-year-old Veronique Eldridge-Smith in 2001. Veronique's father, Peter Eldridge-Smith, is a specialist in logic and the philosophy of logic. Peter introduced the liar paradox to his children, asking them to create their own versions, and Veronique proposed "Pinocchio says, 'My nose will be growing'." This formulation of the paradox gained popularity and was published in the journal Analysis.

The Paradox

The proposed paradox, "My nose grows now" or "will be growing," is open to interpretation. The analysis of this statement and how it relates to the liar paradox depends on whether Pinocchio spoke only this sentence, whether he lied before saying it, or whether he planned to lie afterwards. The present tense version of the statement, "My nose grows" or "is growing now," seems better suited for generating the liar paradox.

When Pinocchio says "My nose grows now," we can analyze two cases:

1. If the statement is true, Pinocchio's nose shouldn't grow as he's telling the truth, leading to a contradiction in which his sentence is both true and false.
2. If the statement is false, Pinocchio's nose should grow, indicating that he's lying. However, this makes his sentence true, causing another contradiction.

This paradox challenges conventional solutions to the liar paradox, such as excluding semantic predicates from object-languages, as "is growing" isn't a semantic predicate. Furthermore, it poses problems for Alfred Tarski's theory that liar paradoxes arise only in semantically closed languages.