Pinocchio Paradox Can we make an equation out of it?

[JoseAriza]

The Pinocchio paradox arises when Pinocchio says: "My nose grows will now grow."

"The Pinocchio paradox is, in a way, a counter–example to solutions to the Liar that would exclude semantic predicates from an object–language, because ‘is growing’ is not a semantic predicate." - Wikipedia

"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. Therefore, either his nose does not grow now or his nose does grow now. But that is wholly unproblematic." - Wikipedia

Is there a way to describe this paradox mathematically?

 

[Galteeth]

The Pinocchio paradox arises when Pinocchio says: "My nose grows will now grow."

"The Pinocchio paradox is, in a way, a counter–example to solutions to the Liar that would exclude semantic predicates from an object–language, because ‘is growing’ is not a semantic predicate." - Wikipedia

"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. Therefore, either his nose does not grow now or his nose does grow now. But that is wholly unproblematic." - Wikipedia

Is there a way to describe this paradox mathematically?

see

http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems

http://en.wikipedia.org/wiki/Tarski's_undefinability_theorem