Pinocchio paradox

[1] The liar paradox is defined in philosophy and logic as the statement "This sentence is false."

Any attempts to assign a classical binary truth value to this statement lead to a contradiction, or paradox.

Pinocchio, an animated puppet, is punished for each lie that he tells by undergoing further growth of his nose.

Eldridge-Smith liked the formulation of the paradox suggested by his daughter and wrote an article on the subject.

The article was published in the journal Analysis, and the Pinocchio paradox became popularized on the Internet.

[2]Eldridge-Smith believes Alfred Tarski's theory, in which he states that liar paradoxes should be diagnosed as arising only in languages that are "semantically closed".

By this he means a language in which it is possible for one sentence to predicate the truth (or falsehood) of a sentence in the same language should not be applied to the Pinocchio paradox: The Pinocchio paradox raises a purely logical issue for any metalanguage–hierarchy solution, strict or liberal.

A metalanguage hierarchy approach cannot explain this based on Tarski's analysis, and therefore cannot solve the Pinocchio paradox, which is a version of the Liar.

For although I made (what turned out to be) a false statement with the intention to deceive, I had no way of knowing exactly what my blood pressure would be the next day.

However, Pinocchio, operating within the framework of having observed that his nose grows when and only when he lies, would be making an inductively reasoned statement which he believes to be true based on his past experiences.

In this context, the statement "my nose grows now" is a prediction or an 'educated' guess, which in its nature cannot be construed as a truth.