Gödel’s theorems don’t imply inconsistency for all large systems (unless “large” is taken to mean something strange), just for systems which are both not super-weak in what they can say, and complete (or if they have their own consistency as a theorem).

I don’t think Gödel’s theorems particularly support the claim you’re making.

In fact, here is an argument that a consistent rule-set (either can be extended to something consistent and complete, or ) can be extended to be made arbitrarily large and consistent:

take a ruleset which is consistent, but for which there is something for which it has no prescription one way or the other (neither explicitly nor implied collectively by other rules) (I.e. “not complete”). Then, add a rule specifying that thing and nothing else which isn’t implied by that thing. This will be consistent, as if it were not, then the negation of the rule added would have already been an implication.

This will either yield a larger ruleset of the same kind (consistent and incomplete), or it will yield one which is consistent and complete. Gödel’s theorems show that if the ruleset is an axiom system which is sufficiently expressive (e.g. contains Peano arithmetic) then the latter cannot be the result. So in this case, there are arbitrarily large extensions of the rule-set.

If it isn’t an axiom system, or is one for a rather weak system, then the “the result is a consistent and complete system” option, well, why would you want it to be larger?

Edit: perhaps what you are calling “inconsistencies” are what I would just call “exceptions”/“exceptional cases”?

To my mind, “embracing an inconsistency” doesn’t seem to make much sense in the case of law? Something has to be what actually happens. We (whether fortunately or unfortunately) cannot bring an actual contradiction into reality.

Well, I suppose if one takes a sub-truth(not sure if this is the right terminology? I mean the opposite of super-truth) approach to vague statements, one might say that a somewhat-bald man causes the statement “that man is bald, and also that man is not bald” to be true (and also false), and as such “bring a contradiction into reality”, but that’s not what I mean by the phrase.

I mean there is no full precise-ification of any statement, which we can cause to be simultaneously true and false irl.

Those acting as agents of the law must behave in some particular way.

When legal requirements contradict, people will not satisfy both of them. Perhaps one will be considered to take priority. Perhaps a compromise position between the requirements will be sought. Perhaps it will be left to the judgement of those following it in a case-by-case basis.

But in none of these cases is a contradiction implemented. Can they really be said to be embracing the contradiction?

Upon writing this edit I realize that I’m probably misinterpreting that part of your comment. I suppose the thing you are saying to embrace is not the individual contradictions themselves, so much as the system’s rules-as-written having contradictions, and therefore the necessity of dealing with such contradictions when implementing the rules, as the scenarios to which the contradictory statements apply, occur.

I think parent might have been referring to the inconsistency that Gödel noticed in the US Constitution when applying for citizenship.

This is less of a problem in legal systems as the legal system self admits to resting on unproven axioms.