The Black Vault

What happens to Pinocchio's nose when he utters the following sentence:
"my nose will grow"

This is related to omnipotence, fyi.

at1with0 wrote:What happens to Pinocchio's nose when he utters the following sentence:
"my nose will grow"

That would depend on the context of the statement. If he is lying, his nose will grow. If he is telling the truth, it won't.


I do know that Pinocchio got married. And now he has the only wife in the world that wants her husband to lie to her.

I forgot an important rule: Pinocchio's nose will grow if, and only if, Pinocchio lies.

And to make things more clear, Pinocchio means to say "my nose will grow as soon as I finish uttering this sentence."

What happens to his nose after he utters that sentence?

A lie has less to do with the truth of the statement and more to do with the intent.

If he thinks his nose will grow, then it won't, as his statement will be, to his knowledge, truthful. If he doesn't think it will, it will, as his statement although correct, is still a lie as far as he is concerned.

If he is unsure, it will still grow, as that still counts as a lie.

humphreys wrote:If he thinks his nose will grow, then it won't, as his statement will be, to his knowledge, truthful.

If his nose does not grow, then "my nose will grow" is a lie. Since "my nose will grow" is a lie, his nose will grow.

If he doesn't think it will, it will, as his statement although correct, is still a lie as far as he is concerned.

If his nose grows that means he lied when he said "my nose will grow". Since "my nose will grow" was a lie, his nose does not grow.

If he is unsure, it will still grow, as that still counts as a lie.

Again, if his nose grows, that means he lied. IOW, "my nose will grow" was a lie. Consequently, his nose does not grow.

Yep, still a bona fide paradox.

at1with0 wrote:

humphreys wrote:If he thinks his nose will grow, then it won't, as his statement will be, to his knowledge, truthful.

If his nose does not grow, then "my nose will grow" is a lie. Since "my nose will grow" is a lie, his nose will grow.

It is not a lie if he thinks it's true.

It's not a paradox. Lying is about intent, not actual truth.

If I say, "when I take this cyanide capsule I will die", if by some miracle I survive, my original statement would not be a lie. To my knowledge I was telling the truth.

Similarly, if I ask my son "what's 100 x 120", and being 3 years old, he guesses incorrectly, does that make him a liar? No...

If a lie is a "false statement, made with the intent to deceive, then his nose will not grow regardless, actually.

When he says "My nose will grow", either:

a) he thinks it will
b) he does not think it will

In the case of a), he is telling the truth to the best of his knowledge, so his nose will not grow (this does not make his initial statement a lie, as he made if with the intent of telling the truth.

In the case of b), his nose still will not grow, as even though he had the intent of lying, it was actually true.

Where is the paradox?

humphreys wrote:If I say, "when I take this cyanide capsule I will die", if by some miracle I survive, my original statement would not be a lie. To my knowledge I was telling the truth.

Similarly, if I ask my son "what's 100 x 120", and being 3 years old, he guesses incorrectly, does that make him a liar? No...

To your knowledge??

You can't know something that is false. You of all people should know that.

But that's kind of a moot point. Is your son a liar? Well, I'm just trying to point to a genuine paradox so perhaps I should have said that Pinocchio's nose will grow if, and only if, Pinocchio utters a statement that is not true.

Pinocchio says "my nose will grow."

Assumption: Pinocchio's nose ONLY grows when Pinocchio utters a statement that is not true.

Question: has Pinocchio uttered a statement that is not true?

Equivalent question: will Pinocchio's nose grow?


Case 1: [YES]
Since Pinocchio's nose grew that means he uttered a statement that is not true (from assumption). That means "my nose will grow" is a a statement that is not true.
Since "my nose will grow" is a statement that is not true, Pinocchio's nose does not grow. But in case 1, Pinocchio's nose does grow.
Contradiction.

Case 2: [NO]
Since Pinocchio's nose does not grow, Pinocchio is telling the truth when he utters the statement "my nose will grow." Thus, Pinocchio's nose does grow.
Contradiction.