Why? Because you can't formalize away the fact that humans can't think of everything ahead of time. We make laws about your rights regarding messages you write on paper, then telegraphs and telephones and email come along. Either you try to interpret the law to cover them, or you revise your definitions of "messages" to include or exclude them.
In a "specify everything" system, everything that the courts currently interpret would have to be sent back to the legislature. The effect would depend on what you do with gray areas in court.
Option 1 would be "if a case is ambiguous, put it on hold until the legislature clarifies the law." That would clog up the courts and effectively merge the court and the legislature.
Option 2 would be "decide cases based strictly on existing law and let the legislature revise things for the next go round." That would create a lot of absurd outcomes, where a small loophole, with no ability to apply "common sense", means innocent people are convicted or guilty people are freed.
Like a group of elected officials who's only job is to close these loopholes without massive fanfare and a simple vote. A process that is incredibly fast and decisive in order to get double digits done per day.
Because, y'know, having officials crank through tons of difficult decisions per day is such a supremely effective[1] and corruption-free way to create a social process. It's worked so very well for the patent system, why not for law and jursiprudence?
[1] cf. "decision fatigue": https://www.nytimes.com/2011/08/21/magazine/do-you-suffer-fr...
Many things involve context (it is illegal to murder someone, but a killing in the context of self-defense is often not murder). Even where context is not explicitly recognized by the law, we want judgment and discretion to exist (speeding because you are drag racing is very different than speeding to a hospital with a bleeding passenger.)
So, you're saying that's more dystopian than the thought of secret laws for 'national security', on top of a body of laws that already spans over 200,000 pages, whereby even with non-poorly-written laws, you're still likely breaking one every single day?
Because that's what we have now. So if those are my options, then shit yes, I will take mathematical certainty of the legality of my actions any day.
I don't expect laws to be formally defined, I just expect them to be few, sensible, and transparent. Reasonable people shouldn't have a hard time inferring whether a specific activity is illegal.
Right now, our body of law is vast, complex, opaque and uncertain. Because of this, as I said above, most people likely break the law every single day. This gives rise to tyranny by selective enforcement (http://en.wikipedia.org/wiki/Selective_enforcement), burdened economies and reduced investments due to untested and protectionist regulatory regimes, and an overall reduction in freedom and civil liberties.
By contrast, yes, the knowability and certitude afforded by a hypothetical-but-impossible legal system based on mathematics would be preferable. This is really not a complicated idea.
“Corruptissima republica plurimae leges. [The more numerous the laws, the more corrupt the state.]” — Tacitus, the Annals ca. AD 69
So's our society. Roman law was quite a bit simpler, but justice in ancient Rome was extremely unpredictable.
By contrast, yes, the knowability and certitude afforded by a hypothetical-but-impossible legal system based on mathematics would be preferable. This is really not a complicated idea.
As HL Mencken said, 'For every complex problem there is an answer that is clear, simple, and wrong.' Godel's theorem tells us that in any sufficiently expressive formal system (such as mathematics), you can have consistency or completeness, but not both. A hypothetical mathematically-precise legal system would thus yield cases that either couldn't be judged because there was no prescription for such a situation (a div zero problem, if you will), or else would yield contradictory results on the same facts at different times.
People are emotional and subjective by their very nature. It is not possible to be objective - one can only tend towards objectivity by applying constant introspection and reassessing one's world view. Nonetheless, an Ape is not capable of being a Vulcan. It is, frankly, a travesty that people's fates are being decided by other people's stomachs.
I'd argue that you really can't say anything with such certainty. If true friendly AI is ever possible (and that is up in the air), such a system would be a better one. Obviously, this is all speculation.
In other words, by the time we have consistent laws (in the mathematical sense), "Precrime" could already exist.
I guess that one positive impact of your idea would be moving mathematicians into the almost celebrity status of lawyers. They'd be fun to watch when interviewed too.
Just to be clear, I'm not proposing to teach kids to be lawyers. Being a lawyer would be like having a PhD in mathematics. But we do teach kids basic calculus, algebra and stuff like that, so why not "basic legal stuff" (whatever it's called)?
New rule: (forall ?X (implies (and (isa ?X USCitizen) \
(locatedIn ?X UnitedStatesLegalJurisdiction)) (bearArms ?X)))
- Rule 2 added.
New rule: (thereExists ?X (isa ?X USCitizen) \
(locatedIn ?X UnitedStatesLegalJurisdiction))
- Rule 20 Added
New rule: (implies (and (locatedIn ?X ?Y) (isa ?Y USState)) \
(locatedIn ?X UnitedStatesLegalJurisdiction))
- Rule 21 Added
...
New rule: (isa California USState)
-Rule 1850-342 Added
...
New rule: >(forall ?Y (implies (locatedIn ?Y California) (not (bearArms ?Y)))
- Error: New Rule #4422 conflicts with Rule #2
Request Ruling:
(locatedIn JamieBriant224112344 California)
(bearArms JamieBriant22411234)
- Data is consistent.
1. You need a law degree to even practice - control.
2. The government can selectively prosecute - corruption.
3. Fear of losing, even when morally right.
4. Everyone is a criminal.