The Pinocchio Paradox "Now" is a place in time though. — ProbablyTrue
I understand the language implies duration or a particular moment, but the point of the paradox is not to fixate on the time interval between the lie and the growth, but merely to point out the causal connection between a self-referential statement and the outcome.
I am not sure exactly what you mean here. If you say "now" is the cause of the growth then it is obviously false because he has not said anything before this to cause it to happen. So his nose will grow for lying. — Sir2u
The word "now" was only meant to indicate that the statement is an indexical and that the cause of lying (i.e., Pinocchio's nose growing) is tied to the utterance (i.e., self-referential). The word is indexical insofar as the truth condition of the statement is dependent on the statement itself, but not the time of the utterance.
But there isn't a world in which Pinocchio exists. — Michael
There is a fictional world of Pinocchio whereby his nose grows if and only if he claims any falsehood. In replying that it is impossible by virtue of a contradiction is to import metaphysical baggage into the Pinocchio world. What justification is there for the import of that baggage? Are "true contradictions" impossible? If so, why? The Pinocchio paradox does not shed light on how to resolve the contradiction.
The dialetheists would contend that the contradiction will be simultaneous, not oscillating. Our cognitive faculties want to resolve the paradox by collapsing it into a definite state (i.e., by oscillating truth values), but there doesn't appear to be a reasonable justification for that collapse. Pinocchio's nose will grow and not grow simultaneously.
If helpful, it can be likened by analogy to Schrödinger's cat.