He hangs the guy. It's pretty simple, this is by no means a paradox.
Scenario: The guy is lying and doesn't want to be hanged. Then he should be hanged by the hangman's own rules.
Scenario: The guy is telling the truth and wants to be hanged. Then the hangman has no qualms about hanging him anyway. It then becomes a moral problem instead.
New paradoxical problem: Can anybody explain the Twin Paradox...
Scenario: The guy is lying and doesn't want to be hanged. Then he should be hanged by the hangman's own rules.
Scenario: The guy is telling the truth and wants to be hanged. Then the hangman has no qualms about hanging him anyway. It then becomes a moral problem instead.
New paradoxical problem: Can anybody explain the Twin Paradox...