jpg
What happens if Pinocchio says "My nose will grow now"?
Answer: most likely the nose won't grow, but there's a smaller chance that it will. Let me explain why I think so.
Pinocchio's nose grows only when he himself knows whether he's lying or not. His nose can't be some great god that knows the answer to every question; it's just a part of his body. Also, Pinocchio's nose doesn't grow when he talks nonsense or talks about something he doesn't understand (though I'm less sure about this one; it's more like undefined behavior).
And when Pinocchio claims that his nose will grow, that can be treated either as nonsense or as a statement about the future that he can't be sure enough about.
From there, it all depends on his subconscious, which controls his nose. Most likely it will tell the nose not to grow. That gives the first part of the answer.
But of course, like any other bodily process, the growth of the nose can be influenced somehow. Surely Pinocchio could learn to masterfully trick his subconscious through autosuggestion, say, to amaze his friends. That gives the second part of the answer, the one about the small probability.
Why is there no paradox here, you might ask?
Because the paradox only arises when people treat Pinocchio's nose as a divine seer that possesses all knowledge. But it isn't one. It makes sense to consider Pinocchio an ordinary guy, and his nose an ordinary body part. All I did was extrapolate what we know about the real world onto a fictional "nose that grows from lies".
If you're interested in this problem specifically with the nose seen as a divine creation that knows the answer to every question, then mathematics, set theory and so on are there for you. Otherwise,