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.