T Nation

Pinocchio Paradox


#1


I'd be interested to know what you guys make of this.


#2

I had to think about that one for a minute. It's funny you should post this because just the other day I wikipediaed paradox, and the pinnochio paradox was listed. I think paradoxes are great humor devices personally.


#3

That it isn't the case that there is such a thing as a function that for any possible subject or input must always generate an untrue statement.


#4

it depends on his intent. the growth of the nose is a response to intent to deceive rather than the falsehood of a statement.

not NECESSARILY a paradox.


#5

^^^^^^^^^^^^^^^I'm using that craz sentence randomly mid conversation sometime soon.^^^^ Thanks!


#6

A little-known fact is that my home is carpeted with the pulled-out hair of frustrated English professors.


#7

Yeah Pinocchio also likes to say that he's a compulsive liar too.


#8

I tried to cross reference your answer with wikipedia. The sad result is that I fully understood neither.


#9

His nose grows. It never says his nose cannot grow while telling the truth, only that it will grow when lying. The two are independent of each other. Neeeeeeeext.


#10

With "now" being the moment he was speaking the word, it would appear that he is telling the truth, but in fact was lying, because his nose started growing after he said now.


#11

Another solution.


#12

For the simplest example:

"This statement is untrue."

The existence of this statement demonstrates that an assumption that statements must be either true or false -- or at least directly true or false in the plain sense -- is unwarranted.

And where is the proof that statements absolutely must be one or the other?

There are statements that don't give a useful truth about anything, yet are not provably false, but exactly how that would be put into rigorous logic, I would have no idea.

With regard to the specific problem: It would be an assumption that it is possible to always create a false statement about anything of any kind. There is no proof that that is so, and there are examples that arguably show that it is not so (although often contortions can be created to try to claim "truth in one way and untruth in another" or such things.)


#13

I think also that if he really believes that it will grow, even if it doesn't, it doesn't mean he is lying.

Just because someone believes in something they say, and it is not a fact, it does not constitute a lie. This may just be a dumbed down version of what Bill Roberts said.


#14

This was my reaction as well.


#15

It would seem to me that that would be playing lawyer with the wording in an attempt to change the statement into something clearly different than what was intended by the author of the paradox.

The intended meaning was, "My nose will grow as a result of my making this statement," under an understood stiuation where his nose never grows as a consequence of telling the truth, but always grows as a consequence of making an untrue statement.

(Typically we understand Pinocchio's situation as nose growth being a result of lying, but for the purposes of the paradox, the necessary situation is one of telling an untrue statement.)

Yes, one can convert the statement and situation to one different than intended. But that escapes thinking about the real point.


#16

When making a statement about a future event, I feel you are never really lying, unless you are intending to deceive when you have information about future event, or control, and try to make your previous statement untrue.

So if I'm like; "The senators are going to win the stanley cup this year" because I think they're going to win that's one thing. If someone asks me who they should put money down on, and knowing that they're trailing 3-1 in the series and I say the senators, then that's an intentional falsehood.

Just my own moral code's justification of the Pinocchio paradox.


#17

Got it!


#18

So.......

  1. he is not really lying to begin with

  2. his nose will not grow because he is not lying

  3. it isn't a paradox


#19


#20

Well, more briefly:

Many are ASSUMING that there is something impossible about a statement being neither simply true nor false, and then coming to conclusions based on that assumption. Without being aware that a "problem" exists only if making that assumption, which they cannot prove is correct.

It is like freaking out about someone -- for example -- making better gains by using lighter weight than he had previously, on an assumption that this is impossible, and as a result coming up with contorted explanations such as accusations of steroid use, etc.

Instead, evaluate the assumptions.

On statements being neither simply true nor false, here's a totally different sort of example:

"If the moon were made of green cheese, and there were giant space rats, they would be able to eat the entire moon in a space of 1000 years."

Is that statement true, or false?

Yes, most statements can be divided into true or false, but there are situations where this is more likely not to be so. Particularly, statements about non-factual conditions -- e.g. a puppet whose nose "always grows" when making an untrue statement -- or self-referential statements are particularly able to be neither simply true nor false.