Pinocchio Paradox

There is a widely known story of Pinocchio. The story goes that a puppet master made a puppet that could speak, jump and dance. However, Pinocchio had a bad habit that he usually lied to others. In order to make him honest, the fairy cast a spell on Pinocchio. If Pinocchio told a lie, his nose would then grow, and if him told the truth, then his nose would shrank to the original length.

Nevertheless, we can consider the following condition:

What if Pinocchio says,” My nose will be growing.”?

Will his nose grow? Or just maintain the original length?

We can suppose that the sentence” My nose will be growing.” is true, which means Pinocchio’s nose will grow because he truthfully says it is. Nonetheless, due to the fairy’s magic, Pinocchio’s nose will not grow if he tells the truth. Now by our supposition, he doesn’t tell any lie, so his nose shouldn’t be going to grow. Hence, we come to a contradiction in the sentence underlined.

If we suppose the sentence is false, it will finally contradict, too. Therefore, there are no answer to this question. That is, it is a paradox.

Pinocchio paradox is a special case of the liar paradox, which arises when you write down” This sentence is false”. If what you write is true, then the sentence is false. Sarcastically, “the sentence is false” means what you write is false. And then you can’t acquire any answer this time, either.

Interestingly, Pinocchio paradox comes from an only 11 year-old child. Perhaps it infers children is endowed with strong imagination and that paradoxes are of infinite interest. Whenever we probe into the mysteries of paradoxes, we’ll get different appreciation.