It seems, that simplistically, that Gödel's incompleteness theorems can be applied to ethics in a very straightforward way by:
- Replacing "True" and "False" with "Right" and "Wrong"
- Assuming real world situations display a minimum amount of complexity - analogous to the "capable of proving statements of basic arithmetic" clause.
- Completeness means that an ethical systems can definitively answer whether any proposition about the world is "Right" or "Wrong"
- Consistency means that an ethical system never leads to propositions that are both "Right" and "Wrong".
We could then use Gödel's proof to conclude that no ethical system can be both complete and consistent: Any consistent ethical system would have to prescribe courses of action that are right, but whose righteousness we cannot prove.
This wouldn't be just a mere exercise in linguistics: It would mean that any consistent set of ethics would have to rely on an outside source (Religious scripture, Social convention, evolutionary and game theoretical considerations,....) for at least some of it's rules?
This is very simplistic, where are the holes in this reasoning? Can a more formal, serious version of this argument be made to show that any ethical system is inherently limited?