The Black Vault

If you exchange the word "lie", which is about intent, to one of true versus false, I'll accept there is a paradox, yes.

There is still the question of whether the statement "my nose will grow" can be true or false at the time of asking, though. Surely only future events can determine the truth of that statement, ie, whether his nose grows or not?

Something to consider, perhaps.

I think there is a simpler way of showing your paradox, though, which will probably result in less debate about its validity.

How about:

Bob is a man who can only tell lies.

Bob says:

"I can only tell lies". That is a paradox, because Bob's statement must be a lie, yet it has to be true.

Anyway, let's accept that such a paradox exists, now what?

Well an even simpler related version is

"this sentence is not true"
Is the above sentence true or not true?


What exactly is the source of the paradox?
Does the paradox mean that Pinocchio can not exist?
Or perhaps "my nose will grow" shouldn't be considered a statement
Could "Does the nose grow or does it not grow" be a loaded question?
Is there a flaw with the law of the excluded middle which implies in this case that either his nose does or does not grow? Or perhaps a flaw in that it doesn't apply to this situation for some reason?

I think it proves there is a problem with the definition of Pinnochio.

A good question that relates to a discussion we're having in another thread is, how different does a thing have to be from our description of it before we can state it doesn't exist?

For instance, does my friend Bob exist?

Well, who is Bob? I need to define what I mean by "Bob". I could give his full name, but what if he changed it yesterday? He still exists, but now my definition is wrong. What if he didn't change his name but he lied to me about his real name, and he is actually called Dave? Does my friend Bob exist now? Did he before I knew about the name change?

If I say he has grey hair, but he dyed it black, does he exist?

It's an interesting point because at some point you have to declare that my definition is so far off that "my friend Bob" does not exist at all.

If the Bible describes God as "Omnipotent" but there are things he cannot do, does that mean the Bible God does not exist? If he doesn't exist, then who are we comparing our definition to?

If our definition is waaaaay off, then does it make sense to say the Bible God is real, if in fact the thing we're comparing to is not even a God at all, but a goat?

I think this is where you might be going with this?

To answer in short, Pinnochio can exist, but not exactly as described. If he does exist, our definition is imperfect, but perhaps close enough to a real being that we can conclude he exists.

No definition is going to be perfect because language is imperfect. I think we make a subjective judgement on whether a definition is close enough to correct, and in this case if his nose acts differently to as expected when he says "my nose will grow", that is not enough to make the definition outright false.

I keep mentioning Newton's laws, and they are related here, as the laws work, but they are imperfect. I suspect all laws may be like this. When we get to the quantum level, they break down, but they work well enough at the macro level to be labelled "correct".

It seems pretty much everything in life becomes a grey area if you dig deep enough. Nihilism anyone?

Yes, I am keeping things like omnipotence in mind.

No definition is going to be perfect because language is imperfect.

aha
Now what does this mean in terms of "God" and "omnipotence"?

You know what's queer about you saying Pinocchio can't exist exactly as defined? If I defined it so that Pinocchio's nose will grow if, and only if, he utters a true statement (instead of a statement that isn't true), then there is no problem. [***]

The Pinocchio whose nose grows if and only if he utters a statement that isn't true can't exist exactly as described BUT
the Pinocchio whose nose grows if and only if he utters a statement that is true can exist exactly as described.

Weird, huh?

Years ago I nosed around this site: http://www2.imm.dtu.dk/~tb/
He delves into self-reference maths. I wish I could say which document this is in but I recall him concluding somewhere that the liar paradox only occurs when a formula is a reference to its own truth value in a negative way, ie, by saying itself is not true.









[***]
Let's say he utters the statement "my nose will grow." Remember that temporarily his nose grows when he utters a true statement. The question is does his nose grow when he utters that statement.

Case 1 [YES, his nose grows]
Pinocchio's nose grows. He uttered the statement "my nose will grow" and since his nose did grow, "my nose will grow" is true.
There is no contradiction.



Case 2 [NO, his nose doesn't grow]
Since Pinocchio's nose does not grow, Pinocchio has uttered a statement that isn't true. Then "my nose will grow" isn't true. So, his nose does not grow.
There is no contradiction.

Pinnochio's nose growth is a metaphor for self reference

You got that right.