Pinocchio Paradox

[needimprovement]

While this is essentially not a puzzle, I think it presents an interesting subject for sciency people. It's called the Pinocchio Paradox, and is based on the idea that when Pinocchio tells a lie, his nose grows longer (see the attachment). Using the following definition of "paradox" from the American Heritage Dictionary: " An assertion that is essentially self-contradictory, though based on a valid deduction from acceptable premises" is this actually a paradox?

 

Now, discuss.

 

Edited September 14, 2010 by needimprovement

[tomgwyther]

Does his nose grow if he makes a statement about the past which is false, or does it grow if he makes a false assumption or prediction about a future event. or both?

it's quite a good example of a paradox.

Edited September 14, 2010 by tomgwyther

[Mr Skeptic]

Some statements are neither true nor false. The above is an example of one.

[the tree]

I think the mixing of tenses, is enough to call it nonsensical - so it cannot have a truth value anyway.

[needimprovement]

Does his nose grow if he makes a statement about the past which is false, or does it grow if he makes a false assumption or prediction about a future event. or both?

it's quite a good example of a paradox.

It's not as simple as it seems at first glance. My initial take was that Pinocchio is making a prediction, which shouldn't be necessarily be classified as a lie unless we know that the prediction was knowingly dishonest. Even at that, we're still left with what constitutes a "lie." Is a lie any knowingly dishonest utterance?

[Mr Skeptic]

It is just a variation of the sentence, "This statement is false".

 

A variation which removes the self-referential aspect, sort of, by replacing it with reference to a different sentence which then refers back to the first:

"The following statement is true"

"The preceding statement is false"

 

Having Pinocchio there just complicates matters.

[Equilibrium]

Some statements are neither true nor false. The above is an example of one.

If it isn't true or false, then what is it?

[imatfaal]

mu

 

see "godel escher bach"

[Sisyphus]

If it isn't true or false, then what is it?

 

I suppose the implication is that it has to be one or the other, but it does not. For example, not every grammatically correct statement has meaning, even if it seems like it does.

 

You could also make the argument that it is simply false, because every statement implies its own truth. "It is true that we are on SFN," "it is a true statement that we are on SFN," or "this statement is true and we are on SFN" contains no more information than "we are on SFN." So the statement is equivalent to "this statement is true and this statement is false." This takes the form of "P and ~P," which is simply self-contradictory and false.

[lemur]

That's a really funny paradox. I actually pictured his nose starting to grow because it knew he wasn't telling a lie and then suddenly stopping after it started and the lie became true. Maybe this is the statement that makes Pinnochio's nose grow the absolute minimum length possible for any nose-growing statement.

[xbc97]

At first glance it seems to be a false prediction. False predictions aren't lies, are they?

[HelloSkitty]

When he says "My nose will grow NOW", he lied when his nose did not grow. So immediately after, his nose grows, there's no contradiction because it didn't grow when he said now.

 

This sentence is false.

 

It is false when said. Then its opposite becomes true immediately after, and the whole statement is true afterwards.

 

This sentence is always false.

 

We originally see it as false. That would mean the statement's opposite is true, that it's not always false. It can't be true after, because that would mean it's always false, a contradiction. So after the statement is proclaimed (and during), it is false. The only way to make sure the statement it false, is to make it true at some time. So it USED to be true before it was said, but after the statement is said, it becomes false.

 

My way of circumventing the paradox, bringing in the idea of time. Truth values, instead of being a boolean, would instead be an array of booleans along the time axis. So I guess that could be a solution to the problem...

[36grit]

sounds to me llike either way he's probably going to wind up being a near sighted wittler.

[GreyDergal]

Hes telling the truth because his nose is constantly growing because hes made of atoms (just like everyone else) and so the electrons moves around and one of them goes farther than it more than likley was before.

[Pwyll Pendefig Dyfed]

This is a little known example of Schroedingers Pinnochio. His nose both grows and doesn't grow at the same time.

[SID66]

If it isn't true or false, then what is it?

 

This is where the word "Truce" comes in.

Edited May 10, 2011 by SID66

[Schrödinger's hat]

Having Pinocchio there just complicates matters.

 

Pinocchio does complicate matters, but I don't think it does so in a trivial way.

If we observe his nose after he says that one of two things will be true:

It is the same or smaller size;

It is larger.

Thus, after this observation his statement has a definite truth value which will be different to what has happened.

 

The only resolution to this I can think of is that the outlined situation is absurd and we have disproved the existence of pinocchio.

 

Also, this type of pinocchio would be the perfect oracle.

You'd just have to break down any situation or set of situations or pieces of information down into a binary tree, and science would be solved within weeks.

"Pinocchio, say 'P=NP'. Now say 'string theory is completely wrong'."