The Liars Paradox: Pinocchio’s Nose

There are multiple versions of the Liar Paradox. Currently, I find the Pinocchio version most interesting. The paradox plays off the law of the excluded middle: A statement is either true or its negation is true. Now this particular version of the paradox goes as follows:

Pinocchio says: My nose will now grow. Now, Pinocchio knows that his nose only grows if he speaks a lie. Thus the problem is as follows:

  1. If he is telling you the truth then his nose will not grow, but then his lying.
  2. If his nose grows, then he didn’t lie. And the nose can’t grow.

One response I found on the Internet is that it isn’t a lie if you believe it. This is fascinating response. If Pinocchio has thought about the paradox, then he wouldn’t know if he was lying. However, we can specify that Pinocchio has not thought about the paradox. In fact, he believes that his nose will now not grow at the same time he says, “my nose will now grow”. Thus, he is lying and the problem continues.

There is a solution I tentatively hold to is that the law of excluded middle is partially false. It is partially false because it does not apply to future statements. If future statements have no truth value, then Pinocchio is neither saying something true or false. The future will never obtain in this instance because the action is dependent upon the value claim of the person speaking. One last note is that this solution does not work for all Liars Paradox. I think there are different solutions to different versions.

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