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Friday, April 17, 2020

Pinocchio’s Paradox

   A paradox is a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true. 
     The Pinocchio Paradox arises if Pinocchio said, "My nose grows now." It’s a version of the liar paradox in philosophy and logic as the statement, "This sentence is false." 
     Any attempt to assign truth to this statement leads to a contradiction. If the sentence is true, then it is false, but if it’s false, then it’s true. 
     The Pinocchio Paradox was proposed in February 2001, by 11-year-old Veronique Eldridge-Smith, the daughter of Peter Eldridge-Smith, who specializes in logic and the philosophy of logic. 

   The paradox says if his nose doesn't grow he would be lying, so it would grow and if it grows he would be telling the truth, so his nose would grow when he told the truth, which is only supposed to happen when he lies. 
     That's not what would happen though. Scenario #1: For that particular scenario playing out you can prove his nose didn't grow when he told the truth because he said his nose would grow "now." 
     His nose not growing had to happen before lie occurred, so the lie and his nose growing would be considered after his nose didn't grow, which establishes a now and a later. 
     His nose didn't grow when he said it would, which was "now", and it grew later. His nose growing wouldn't mean he was telling the truth because he was referring to now and not later. 
     Scenario #2: The other scenario could be that his nose did grow when he said it would, but his nose is only supposed to grow when he lies, and his nose would grow even though he told the truth, and the paradox appears to exist again. 
     You can prove that's not true because he created a self fulfilling prophecy when he said his nose was going to grow bigger because saying that was saying he was going to lie. 
     In order to lie; he had to tell the truth, and say that he was lying, when he was really telling the truth, which would be a lie. He did say he was lying because he said his nose was going to grow, and even though he said he was lying, he was actually telling the truth; which means he was lying about lying, or lying about not telling the truth. 
     His nose did grow, and he did tell the truth, but he said he was lying when he was telling the truth, which was the lie that made his nose grow. Since his nose didn't grow after he told the truth, but after he lied about not telling the truth; the paradox doesn't exist. 
     That second answer actually works for both scenarios, where as the first answer only works for the first scenario, so the second answer appears to be  the correct one.

Wikipedia has about the best article on this paradox, so check it out HERE.

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