> Maybe it’s naive, but I’ve often thought law itself should be spelled out in code
Any formal system can either be consistent or complete - not both. Therefore, you will always need an oversight to check for most individual legal cases.
Your therefore doesn't follow. You haven't established that the law would even need to form a "complete" logic, which means it must be able to encode both addition and multiplication. There is little reason to think this is the case.
Furthermore, oversight wouldn't necessarily yield any further insight even if it were. Humans aren't extra-logical, we have similar limitations.
> You haven't established that the law would even need to form a "complete" logic, which means it must be able to encode both addition and multiplication. There is little reason to think this is the case.
The very basics of a legal system are consistency (fairness) and completeness (coverage). Are you making an argument against these two basics?
Please don't quote the incompleteness theorem without knowing it's precise statement. Far too many people do this to make absurd claims.
In particular, the tradeoff between soundness and completeness only holds for those mathematical systems which can internally encode peano arithmetic (naturals, addition, multiplication, first order logic)
Therefore, to invoke the incompleteness theorem, you need to prove that a legal system is powerful enough to encode arithmetic, which to me at least is not obvious.
There are many systems that are both consistent and complete, but are just not as expressive.
>The very basics of a legal system are consistency (fairness) and completeness (coverage).
You are using words that have a very precise formal meaning into a completely different (informal) sense. Probably this is the source of your confusion.
Any formal system can either be consistent or complete - not both. Therefore, you will always need an oversight to check for most individual legal cases.