‘Ignore all rules’ paradox

Ethel asked:

If I ignore the rule ‘ignore all the rules,’ am I obeying a rule?

Answer by Geoffrey Klempner

This seems an unanswerable question – and that is in fact a clue to the answer.

The rule says, ‘Ignore all the rules.’ If you are to ignore ALL rules then you must ignore this rule. But if you ignore this rule, you are doing what the rule says – you are obeying, or attempting to obey it. Which you are not permitted to do!

The problem is a variant of the Barber paradox. If I told you that in the town where I live there is a barber who shaves all and only those men who do not shave themselves, you would know that I am lying. If he shaves himself, then it is false that he shaves a man ‘who does not shave himself’. If he does not shave himself, then it is false that he shaves ‘all’ the men who do not shave themselves. The paradox is apparent not real, because the solution is readily available.

The solution is that the statement I made about the barber is necessarily false. It cannot be true, any more than the statement ‘there exists a square circle’ can be true.

Just as there are statements whose logical structure entails that they cannot be true, so there are commands whose logical structure entails that they cannot be obeyed. One such command would be, ‘Find me a square circle.’ Another is the command, ‘Ignore all the rules.’

Thank you for this question, Ethel!

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