Thursday, 3 May 2012

The 'Pinocchio paradox'

As usual, Philosoraptor makes an intriguing point. It's a type of self-reference paradox; a variant of the 'liar' paradox.

The possible paradox can be phrased as follows: 

Pinocchio says 'My nose will now grow.' There are two possibilities:
  1. Pinocchio's nose grows; therefore he is telling the truth. However, if so, his nose does not grow, since it only grows when he tells a lie.
  2. Pinoccho's nose does not grow; therefore he is lying. However, if so, his nose will grow, since his nose grows when he tells a lie.
Thus, we have a seemingly possible utterance which must lead to one of two self-contradictory outcomes.

Pinocchio is defined as 'a being whose nose grows if and only if he utters a lie'. We might object that a statement such as 'my nose will now grow' can never be a lie, since it is impossible to tell a lie about a future event. Thus, Philosoraptor's question can be easily answered - nothing happens when Pinocchio says this. Additionally, if Pinocchio himself is confused by the supposed paradox, then he is unlikely to be able to lie either way, since lying is just reporting a known falsehood about a situation as the truth!

We can enforce the paradox by re-defining Pinocchio as 'a being whose nose grows whenever he utters a falsehood.' Since uttering a falsehood need not be lying, the 'problem' remains. Now we must consider if statements about future events have a truth value when uttered in the present; many philosophers argue that they do not, since determinism about future events may not hold. I personally have no idea on this one.

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