What if Pinocchio says I'm lying

What if Pinocchio says: My nose will grow [closed]

Bad question . In other words, you have constructed a paradoxical world. Check the self-reference. I will consider your question to be equivalent to the liar's paradox:

This sentence is not true.

Something tricky is going on here: Recursion :

This sentence is not true.

Let me make a substitution: "This sentence" → "This sentence is not true.":

"That sentence is not true." is not true.

But wait, what is referred to in "This Sentence"? The substitution did not bring any clarity! The problem here is that there is an infinite regression that goes through Self reference caused. That kind of paradox shows up elsewhere, like Russell's paradox trying to catch the crowd R. to be constructed with the membership criterion: "All sets that do not abstain as members".

  1. If R itself contains itself, it is not a member of R.
  2. If R. does not contain itself, it is a member of R.

It may take a while to completely wrap your head around, but it is a profound result of what is now called naive set theory. To circumvent this problem, axiomatic set theories were developed which could not produce such paradoxes. However, you lose something: you are axiomatic and therefore not ambiguous like natural language. Yet this ambiguity seems to have something profound. I won't go into that now, but it would ask a good separate question.

There is a theory of the computational aspect of self-reference, which manifests itself in the fact that Turing machines can print out their own description. This comes from the idea of Self-knowledge . And yet Thomas Breuer's The Impossibility of Accurate State Self-Measurements questions this whole perfect self-discovery company. This matter of self-reference of the Turing machine is very important; This can be seen in the holding problem, which is a major obstacle to the demonstrability of complete Turing systems. This means that we cannot guarantee any properties that we want to guarantee (so your phone won't crash).

Douglas Hofstadter introduced the idea of ​​the strange loops in his Gödel, Escher Bach. The book is a layperson's introduction to a proper theory of computational problems. I'm not pretending to understand this "strange loop" idea, but it definitely has to do with self-reference. It may be that consciousness itself has to do with self-reference; in fact, it is hard not to. So this liar paradox has a lot to offer!