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10:55 PM
This is a good answer except for the irrelevant stuff about the incompleteness theorem, which is just misleading. It really doesn't matter at all whether laws are decidable; they're only supposed to work in the most obvious cases anyway, since surely you've forgotten to write down something important.
"They're only supposed to work in the obvious cases anyways" is a pretty contentious argument. While I agree with you, and that's what I was getting towards with the idea of "partial rules," I find that the vast majority of Americans in particular have a fascination with the idea of rules which work perfectly in all cases. I mention Godel because his theorem basically shuts down any shred of hope that such a perfect rule can be found, and that frees us to start looking for those rules which work in the most obvious cases.
That there is any room for precedent indicates that in practice decidability has often not been reached on a first pass, and given that precedent continues to grow around the same issue, it seems doubtful that successive passes are guaranteed perfect decidability either. But you have made a very grand claim, without evidence, that it is actual formal mathematical undecidability that has anything to do with the problem instead of more prosaic issues of imprecision of definition, difficulty of measurement, inherently subjective concerns, etc..
For evidence I might sight the public response to the Ferguson shooting. There was a huge clamor to put rules in place to "prevent a shooting like Ferguson from ever occurring." In every debate I faced with this, eventually somebody made a statement which was transformable to a statement that "we should find an axiomatic system with a particular set of properties" which fell into the class of problems Godel was looking at. Every single one of the arguments brought forward was literally a search for something that was proven mathematically impossible decades ago.
For another point of evidence I came across the same pattern with abortion debates. Every debate I came across which sought a legal rule-based solution to the problem fell afowl with Godel's incompleteness theorem, showing not only that there was a flaw with their particular solution, but that the entire class of solutions they were looking at were flawed.
I make a big deal about the use of Godel's incompleteness theorem because, entering every single debate, the other side acknowledged that "there were some details to be worked out," but was confident the details could be nailed down with a little more debate. Godel was very helpful in showing that such an assumption was unfounded.
As more of an opinion, i have found that most of the places where Godel surprised people debating rules dealt with life-or-death issues. Issues which are smaller than that, it seems to be reasonable to come up with rules. Once death is part of the issue, there seems to be a strong tendency for rule based thinking to break down around incompleteness-related issues. Given that the OP was explicitly talking about life-or-death examples, I felt Godel was worth mentioning.
Maybe chat is a better place for this, but you have only explained that you believe you found instances, not provided any evidence that incompleteness was actually pertinent. Also, I think you may be mistaking rhetorical hyperbole ("never again") used to emphasize emotional commitment with a strong philosophical statement of possibility.
10:55 PM
Perhaps, but none of those I debated with gave any indication that that was the case. They seemed to truly believe that a rule was all that was needed. Regardless, I didn't make the claim that "100% of rules don't work because of Godel," I claimed that "If you're looking into such rules, you should probably familiartize yourself with Godel." Given that I found every debate on life-or-death topics I've had has ended with me winning via invoking Godel, it seemed like a reasonable addition to the answer (even if it is perhaps opinion based)
Moving to chat, the actual pattern that I have seen has been based on the theory that "correct rules always make the situation better," which I have found is not actually an accurate claim
In the case of all rules, there is an agreement that the rule should function in the following form: "either the rule works correctly, or the individual is in a position to disregard the rule and pay an acceptable penalty."
However, death is such a huge issue for most Americans that there really isn't a valid "acceptable penalty" clause that works. We expect that each person will fight ot the death
To take the police shooting example, we find it is valid to assume that a policeman is allowed to respond with force if his life is on the line. However, virtually all of the solutions portrayed for Ferguson involved restraining how a policeman could deal with a life-and-death situation
Accordingly each of them needed to make sure that when it restrained the policeman, the rule actually performed better than the policeman did for self-preservation
This goal turns out to be rediculously difficult to achieve without accidentally causing the rules of the law to admit Peano arithmetic via set-theory constructions
And thus each set of rules had some pathological pattern which rendered the rule unsuitable in one of the ways Godel laid out
This issue does not show up in issues below life-and-death situations as badly because its always assumed an individual will throw any rules to the wind if they turna normal situation into a life-and-death situation anwyays
A related pattern shows up with the famous argument that everyone commits 3 felonies every day. This isn't a problem until you tighten the screws and actually start procescuting these felonies. Then the laws start binding people into catch-22 situations and the people start arguing the laws are bad.
As a particular class of solutions which were popular and crushed by Godel, I found people suggesting wordings like "If case A, then the officer shall do action X"
Then you find a hole where the obligation to do X in case A allows an intelligent adversary to trap the officer where the officer cannot retain their life and simultaniously uphold the rule
And now we find a new hole where the obligation to do Y instead of X again allows an intelligent adversay to trap the officer
so the other person makes the argument "well, at some point we'll patch all of the holes using {insert heuristic here}, we just have to spend some time applying this heuristic to find a rules
At this point they are no longer claiming they have a rule which does the job, they're claiming a rule exists (and thus arguing that we should search for said rule)
Godel comes into play by making it easy to show that any heuristic like the particular one they are suggesting MUST fail
And then, by modus poens, we show that their particular heuristic can never possibly discover the rule they want.
Without the help of Godel, once you beat down that particular heuristic, they just manipulate it slightly, and make the same argument "this heuristic will eventually find the magic rule"
11:53 PM
Okay, but I still don't see that the problem has anything to do with formal decidability as opposed to practical decidability.
And I'm not sure that your rhetorical success in using the incompleteness theorem to enlighten people this way has much to do with its validity in making this argument.
In particular, if you're not using a diagonalization argument in your proof, you'll run into practical limits before you run afoul of the halting theorem (for instance). People are finite.
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Discussion between Cort Ammon and Rex…
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