Logic? I doubt they'd use the inhabitant of the empty set, and if there is no such inhabitant then the biggest thing left is logic. Oath could be: "I swear on

Logic? I doubt they'd use the inhabitant of the empty set, and if there is no such inhabitant then the biggest thing left is logic. Oath could be: "I swear on my reasoning that I will take $OATHSUBJECT as an axiom in all my decision making and that I am willing to be stripped of all trust and influence if I ever go against sound logic based on $OATHSUBJECT."