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Tyrrell_McAllister comments on Notion of Preference in Ambient Control - Less Wrong
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Some axioms are definitions.
Previous theorem: All unmarried men are not married New definition: "Bachelor" means "unmarried man" New theorem: All bachelors are unmarried men.
I'm pretty sure that's what he means. Hopefully clarified, if not made perfectly in accord with standard definitions.
I think that he means something analogous to the way that we can add some axioms involving the symbol "+" to the Peano axioms, and then show in second-order logic that the new axioms define addition uniquely.