The Pinocchio 'Paradox'

This curious bagatelle is wending its way through the World Wide Web.  The cartoon is supposed to be paradoxical in some way.  The reader who brought it to my attention writes, "A friend and myself actually debated this at length over lunch, and I argued that at best it is a performative inconsistency.  I'm sure you have a more nuanced opinion on this silly meme!"   

Well, let's see.  The salient feature of Pinocchio is that his nose grows whenever he tells a lie.  From this one guesses that the paradox has something to do with lying.  Now a lie is not the same as a false statement; it is a false statement made with the intention to deceive  by someone who knows the truth.  (Or so I will assume for the space of this post.)  If this is what a lie is, then one cannot lie about matters that are not objectively the case and known to be such.  Suppose I predict that tomorrow morning, at 6 AM, my blood pressure will be 125/75, but my prediction turns out false: my blood pressure the next morning is 135/85.  No one who heard my prediction could claim that I lied when I made it even if I had the intention of deceiving my hearers.  For although I made (what turned out to be) a false statement with the intention to deceive, I had no way of knowing exactly what my blood pressure would be the next day. 

Similarly with 'My nose will grow now.'  This  sentence does not express an intention on Pinocchio's part to bring about a nose lengthening by the power of his will since presumably he never has such an intention.  The sentence is a future tense sentence which predicts what is about to happen.  'Now' does not refer to the time of utterance, but to a time right after it.  (If you argue that the presence of 'now' renders the sentence present tense, then the sentence is incoherent, and the 'paradox' cannot get off the ground.) 

It follows that Pinocchio cannot be lying.  Assuming the Law of Excluded Middle and Bivalence, what he says is either true or false.  Either way, no paradox arises that I can see.

But suppose Pinnochio utters the present tense sentence, 'My nose grows now' or 'My nose is growing now.'  Does this issue in paradox?

If  Pinocchio says 'My nose  grows now,' he is either lying or not.   If he is lying, then he is making a false statement, which implies that his nose does not grow now.  If he is not lying, then his statement is either true or false, which implies that either his nose does grow now or his nose does not grow now.  Therefore, either his nose does not grow now or his nose does grow now.  But that is wholly unproblematic. 

Therefore I fail to find any paradox here if a paradox is either a logical consistency or a performative inconsistency. 

What am I missing?  There is a 2010 Analysis article under this rubric.  But I don't have access to it at the moment, and I'm not sure the topic is exactly the same.

Comments

[John Jones]

It can't be a case of "he is lying or not lying". We lie to others and not to ourselves. By conflating both private and public language we find paradox.

[Bill Vallicella]

I agree that, strictly speaking, "we lie to others and not to ourselves." But how do you know that Pinocchio is speaking to himself? One cannot infer that from the cartoon.

[David]

I agree with your analysis. I was imagining a situation where Pinnochio tells a lie, and then wants to describe his presently growing nose. Presumably he could not do this because uttering a true statement would halt or cease the growing of his nose. I think I may be remembering the actual story incorrectly on that point.

Would that situation present a performative inconsistency?

[David]

Minor correction: "halt or cease" should read "halt or reverse"

[John Jones]

We can't infer from the cartoon whether what Pinocchio says is what Pinocchio thinks. That's not because what Pinocchio says is either true or false.

The statement "my nose will grow now", loses its meaning when it is used in lying (as does any statement) - and not just if it is false. It loses its meaning in the sense that it becomes an empty sign or utterance that veils a hidden object. We do not know what that hidden object is, because that is the language game of lying. But the point is, is that the phrase that is used to veil the hidden object of lying has no meaning in that context, and not that it is either true or false.

AS a general rule here, elements or statements cannot be transferred across language games as the latter are incommensurable. If we do try and transfer them, then we only succeed in transferring the empty mark or sign.

[doctor(logic)]

Suppose I predict that tomorrow morning, at 6 AM, my blood pressure will be 125/75, but my prediction turns out false: my blood pressure the next morning is 135/85. No one who heard my prediction could claim that I lied when I made it even if I had the intention of deceiving my hearers.

But what if you knew that every morning, your BP was 135/85? You would certainly be lying in that case.

I think you would also be lying if you told me you knew something highly unpredictable. Say, the top 5 stories in the New York Times in sequence. You could know that you don't know something, and deliberately deceive me into thinking you do.

Pinocchio knows that when he tells a lie, the agency of the curse will judge that he has lied, and cause his nose to grow. The real question is whether he can predict what the curse will do in this peculiar situation.

I think the inventor of the paradox wants to make us think that if Pinocchio is telling a lie, then the curse must make his statement truthful (in retrospect, at least). And if his statement is true, then the curse would have to make him a liar. This would give Pinocchio a perverse satisfaction. (Well, it would give me a perverse satisfaction, if I were him.)

Alas, in order for Pinocchio to lie about what will happen, he has to know how the curse behaves in such situations, and then try to deceive us about it. How the curse behaves in special cases is ambiguous to us (the mechanism is not fully described in the story), but for there to be a lie or non-lie, Pinocchio must know what that behavior is. Perhaps he alone knows this from prior experimentation.

For his statement to be a lie, he has to know that his nose will not actually grow in response to his statement. This contradicts the function of the curse.

For his statement to be a non-lie, he has to know that his nose will grow in response to the statement. If his statement is a non-lie, then he knows his nose will grow. That's a contradiction of the curse, too.

Either it's a paradox, or the curse has an indeterminate response to such statements, preventing Pinocchio from knowing what will happen, and disabling his ability to lie about it. Evil curse!

Or, maybe, Pinocchio, having done extensive testing, doesn't know what the curse will do, so he's lying when he tells us that he does know. In that case, the curse will activate, and his nose will grow. The irony being that he could just as well have told us his nose would not grow now, and his nose would grow.

[Allan]

Lying involves intent. It requires 6 elements-- that (1) the speaker makes a statement (2) that he believes to be false or highly unlikely, 3) with the intent that (4) a person the speaker believes to be a likely or definite hearer (5)will conclude that the speaker believes (6) that his statement is true or likely to be true.

In the case of the picture, we have to decide who the speaker is. If the character in the picture, we cannot assess his intent. Because he is Pinocchio, we are led to believe by the person who drew the cartoon (a metaspeaker?) that he does not believe his nose is growing, and that he intends to deceive us. But perhaps the metaspeaker is lying.

My conclusion is that in fictional depictions, one cannot attribute motives to the character without good signs from the metaspeaker. This is especially true when, as in Pinocchi's case, the consequenses (nose growth) of a natural act (lying) can't possibly occur in nature.

Here is an analogous "paradox". Assume that neurologists can read your thoughts with a powerful PET scan. If a person is thinking or saying something, the scanner could read the words. An author depicts a character named Rapunzel who says or thinks "My name is Pinocchio, and I am telling the truth," and posits that her brain readings are consistent with her thinking she is telling the truth, even though she knows she isn't. This isn't a paradox. It is a physically impossible situation.

So it is with Pinocchio. Were it not for the fairy tale, which inserts the physical impossibility of the growing nose, there would be no apparent paradox.

[John Jones]

But this makes my point. You said:
2Lying involves intent. It requires 6 elements-- that (1) the speaker makes a statement (2) that he believes to be false or highly unlikely, 3) with the intent that (4) a person the speaker believes to be a likely or definite hearer (5)will conclude that the speaker believes (6) that his statement is true or likely to be true. "

The statement that a liar utters is neither true nor false. It's an offer to consider truth and falsity. That is, it is a tautology.
It is because we consider a tautology as expressive of a truth OR a falsity that we are led into a system of errors.

[Zao Thanatoo]

It appears to me to be a rather ham-handed attempt at colorfully illustrating the Liar Paradox. If Pinocchio lies, his nose grows. He must lie in order for his nose to grow, so if his statement is true then his nose will not grow, which means the statement is false. But if the statement is false then his nose will grow, so the statement must be true. Something to that effect, anyway.

Or maybe I've missed something.