I once saw ah gantza pilpul on this, filled with chakiras and different peshatim. Apparently it's not as simple as it seems
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ETA: Found it, it was actually on
Wikipedia. Here's a part of it:
The paradox suggested by Veronique, "My nose grows now", or in future tense: "will be growing", leaves room for different interpretations. In the novel Pinocchio's nose continues to grow as he lies: "As he spoke, his nose, long though it was, became at least two inches longer."[3] So logicians question if the sentence "My nose will be growing" was the only sentence that Pinocchio spoke, did he tell a lie before he said "My nose will be growing", or was he going to tell a lie—and how long would it take for his nose to start growing?[2]
The present tense of the same sentence "My nose is growing now" or "My nose grows", appears to provide a better opportunity to generate the liar paradox.[2]
The sentence "My nose grows" could be either true or false.
Assume the sentence: "My nose grows now" is true:
Which means that Pinocchio's nose grows now because he truthfully says it is, but then
Pinocchio's nose does not grow now because according to the novel it grows only as Pinocchio lies, but then
Pinocchio's nose grows now because Pinocchio's nose does not grow now, and Pinocchio trustfully says it grows now, and it is false, that makes Pinocchio's sentence to be false, but then
Pinocchio's nose does not grow now because Pinocchio's nose grows now, and Pinocchio trustfully says it grows now, and it is true that makes Pinocchio's sentence to be true, but then
And so on without end.[2]
Assume the sentence: "My nose grows now" is false:
Which means that Pinocchio's nose does not grow now because he falsely says it is, but then
Pinocchio's nose grows now because according to the novel it grows only as Pinocchio lies, but then
Pinocchio's nose does not grow now because Pinocchio's nose grows now, and Pinocchio falsely says it grows now, and it is false that makes Pinocchio's sentence to be true, but then
Pinocchio's nose grows now because Pinocchio's nose does not grow now, and Pinocchio falsely says it grows now, and it is true, that makes Pinocchio's sentence to be false, but then
And so on without end.[2]
And just to make it easier, as Eldridge-Smith states, "Pinocchio’s nose is growing if and only if it is not growing", which makes Pinocchio's sentence to be "a version of the Liar."[2]
