Re:Formal Models for Ethics
by logicchains on Sunday October 04, 2020 @10:51AM
(#24679457)
>Even simple enough math starting from formal axioms are incomplete (Godel) [1]. Real world ethics, starting by ethical assumptions will be 1000 times as full of holes and inconsistencies.
Just because a mathematical system like set theory is incomplete (can't prove its own consistency), that doesn't mean it's "full of holes and inconsistencies". And just because a system cannot prove itself consistent, doesn't mean it can't be proven consistent in some larger system (for instance how we can use ZFC to prove that Peano arithmetic is consistent).
Even simple enough math starting from formal axioms are incomplete (Godel) [1]. Real world ethics, starting by ethical assumptions will be 1000 times as full of holes and inconsistencies. And that's before we even consider language ambiguities in the much more complex "ethical assumptions".
[1] "The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency".