That’s not what it means. It means there will be things not covered by law, which is probably fine. There is no need for law to be all covering. I posit that the set of things that is desireable for law coverage is finite.
I think it raises a really interesting question. Since our legal system is based on rationalism and the scientific process, and we know that an axiomatic, logical system cannot completely describe all truths within its domain, then how can we hope to provide a fair judicial process, or to make sure that our collection of laws actually disambiguates rules in concordance with their supposed ethical justifications?
But ethics is an ill defined social construct. It might also apply to a finite set of circumstances.
Going back to concrete laws, there vast swaths of human effort not covered by law. For example, there is no law either guaranteeing my right to or forbidding me from thinking certain thoughts. You can say that’s a gap in the legal system, but I think that’s outside our legal system. Similarly, you can (fairly trivially) construct other situations that are not covered (I don’t think there is a law about flipping pages when reading books). Goedel’s theorem says that you can never create an axiomatic system where every proposition can be rewritten as true or false, and therefore you can’t create laws that cover literally every situation in life, but vast majority of things do not need to be covered.
For example, a system that has as its only law “you must give XXX money to the taxman on April 15 in such a way that a jury of 12 of your peers selected at random believes this has occurred” will not suffer from any coverage issues (at most you need to define some terms). This is because it is a finite rule that covers a finite set of situations.
Our laws are not so rigorous a system that we need to be worried about how to handle determining whether or not a computer program halts for the purpose of enforcing a law against writing programs that don't halt. Enforcement frequently differs based on whether laws are even remembered, and the last time the US federal government attempted just to count the number of laws they failed and gave up. Remember, the incompleteness theorem says that a consistent system can't prove its own consistency. Amidst the mess and imprecision of any legal system there's no chance that consistency is preserved anyway.
Not quite, if a ‘truth’ is defined as some ‘justice’ then there could be an unprovable ‘justice’ that should be carried out, we just can’t reason our way there.
(again disagreements like this are usually because of a disagreement of terms)
Sure, my claim is exactly that there are infinitely more propositions that are not about justice. My claim is that justice concerns a finite set of propositions that can be enumerated (as in, murdering someone involves propositions related to justice, making decision about whether to take a deep breath right now does not involve propositions related to justice).
