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12:01 AM
If this were not the case, when you said "what about situation A'?" then the person proposing the rule would say, "Well, A' is a subset of A, so yeah, officer should do X. What's the problem?"
Furthermore, I don't think that pushing on the "what if an intelligent adversary knows this rule and tries to exploit it" angle gets towards Godel's incompleteness theorem unless you craft it really, really carefully. You hit standard paradoxes much faster.
Except inasmuch as Godel's incompleteness theorem is basically a formalization of the liar paradox. But the Liar paradox is known much better, and the connection to provability is an unnecessary complication for the analysis here.
"If A then X, unless C knows you will follow "if A then X"" is pretty standard paradoxical fare.
(Given that C knows you will follow "If A then X, unless C knows you will follow "if A then X"")
In any case, although it's a fun tangent to go out on, logically, it has practically no bearing on actual decisions because nobody involve has time to go out on lengthy chains of logical reasoning.
(involved)
The officer just says, "Well, I thought he was taking advantage of the Ferguson Rule to hide a weapon", and the problem is not logic but that you can't know the contents of other minds.
 
12:31 AM
The issue is "Well, I just thoguht he was taking advantage of the Ferguson Rule to hide a weapon" is a valid statement, but if the Furgeson rule ways "any officer afowl of this rule is immediately ejected from his office in shame and embarassment," it is going to start leading to alternative solutions (such as a massive focus on riot gear and automatic rifles, which we have seen in response to other events)
The issue that I think I've seen is that, yes our intuition tells us "what the answer ought to be." However, the intuitions of individuals do not agree with eachother. There are those who argue both sides. Clearly we cannot achieve harmony through mere intuition
So we create rules which remove some of the intuition from the problem, so taht we can at least agree upon the wordings we think should be used
The most clear example is that 100% of people agree with the statement: "Officers should try to do the right thing in all situations." Intuitively it is gratifying. However, there are immense arguments about what is "right"
So we break it doesn into rules which are less intuitive
The path I have seen people take is one of "we should continually iteratively add rules until the behaviors we don't see stop happening"
That heuristic has been REALLY popular as I debate it
Unfortunately, the assumption is that the act of adding rules eventually convertes on the outcome they want
A perfect exaple is the original poster's question
Talk about whether we give criminals the benefit of the doubt, but we put down animals tells me he is framing a very specific target: determinig where we should draw the line between human and anmal so we can better understand which shoudl be put down and which should not.
I think you and I would rapidly agree upon an answer: you should not have a hard line, because that hard line is impossible to draw. The answer should be smoother, which allows for more room for use of intuition in the decision
However, I find so terribly many people think there "ought to be" a hard line
and Godel does a remarkably good job of showing that there exist a vast multitude of situations where it is provably impossible to draw enough hard lines to solve the problem. You MUST have a soft region somewhere
If the OP can accept that in many situations, hard lines are not the answer, he should be able to realize the better solution: stop trying to set up the punishment system to have a sudden jump from leniency to instant-death. Then you don't HAVE to draw such a hard line
I've simply gotten tierd of arguing the individual cases
I've had too many people argue 1=2. Then when I prove them wrong, they argue 2=3. Then 3=4. After N time, I get frustrated and tierd and prove that for-all X, X != X+1
Godel is the tool I use to make such proofs with respect to trying to define systems of rules, because it does such an unbelievably good job of telling people to stop looking for those kinds of answers, because someone already proved they cannot possibly ever exst.
Maybe then they can start looking for rules which involve intuition, like you recommend. I think that for a reasonable agreeable definition of what intuition is, you can demonstrate that intuition+rules can indeed find the best answer
but I find many people don't even start down that path until you first prove that rules on their own cannot
Just like many people don't start down that path until you also prove that intuition alone doesn't find the best answer. (However, science already does a VERY good job of proving this to people on a regular basis)
 
 
2 hours later…
2:33 AM
I think you and I agree on the problems (more or less), and at least somewhat on the solutions. I thought so before, and still think so.
 
It does lead to the interesting question of, given how much we apparently agree upon, why I find Godel's statements about formal proofs so helpful in this domain while you find them less helpful, though I suppose that doesn't have to be approached unless we want to.
 
But I still think you are looking at the wrong place for the source of the problem. Just because you can choose to construct liar's-paradox-type problems, it does not follow that the approach is unsound primarily because of anything to do with Godel's theorem.
Some situations aren't adversarial in this way and don't admit this sort of attack (e.g. because it doesn't matter what the intent of the parties are, such as with criminal liability for accidents).
But they suffer from exactly the same problem where you push hard on an edge-case and find that you need another rule and another and another and another to agree with intuition.
This suggests, to me anyway, that telling people about the incompleteness theorem isn't directly going to enlighten them as to why perfectly precise rules don't work in practice.
(Because it's useful specifically because of your strategy of showing weaknesses in exactness.)
 
I agree it is not direct. I have found it effective, but it is not direct.
Perhaps that might be where the different positions arise from
I have found that many of the debates I have entered have been with people who believed that exactness was strong
 
But I don't think it's even particularly justified. You haven't captured the essence of the problem, only demonstrated a specific instance where there is a problem.
 
Maybe its just that the people I associate with tend to like exactness =p
 
2:40 AM
(I freely grant that existence proofs are better than nothing, but they don't leave you with a great idea of how to get out of the quandary. In particular, avoiding liar's-paradox situations do not necessarily leave you with a situation where exactness is possible or desirable.)
 
I do agree with that: the approach I have taken is very effective at showing where NOT to look for a solution, but it does not begin to direct you towards where solutions might actually be
 
I guess if you talk with a lot of people who try to get out of inexactness by axiomatizing their rules, bringing up Godel is a good idea. Otherwise, standard contradictions and/or paradoxes are adequate.
 
Yeah, I'm used to people who start with "Thou shalt not kill," and assume that that phrase contains everything they needed. In reality, the MASSIVE context of Jewish life and Hebrew language contains what is needed to make that rule complete
 
I'm not sure it's complete even then.
There are certainly all sorts of opinions about self defence, war, negligence, failure to help, etc..
 
It actually is, but that's only because the REAL commandment in Hebrew is better translated as "Thou shalt not murder," and the Hebrew word translated as "murder" is actually very specific, and relates to any killing of a human not condoned by the tribe
 
2:43 AM
I know, but "condoned" is a pretty fuzzy concept.
 
I chose to write it as "thou shalt not kill" because most who enter a debate starting from that position don't even know they mistranslated the word when the KJV version standardized the wording
Basically, if the leaders of the community thought it was justified, it was justified. That is a very exacting definition, but the devil is in the details (it pushes towards your phrasing: it relies on the intuition of the elders of the tribe to deal with the troublesome corner cases)
 
We can always go down the same process of exactness: what is the tribe? By what mechanism do we tell whether something is "condoned"? What about edge cases like leadership struggles?
I know there are standard answers for many of these things, but all you need to do is keep pushing the border cases and you end up having to say something like, "Well, that might be an issue in principle, but in practice it's never come up in 3,000 years", or "Argh, I don't know, I need another rule."
 
Yes, that exactness path can be walked down. However, it becomes much easier to sidestep Godel because it includes the intuition of the elders. It would not be unreasonable to model the intuition of the elders as a non-recursively enumerable set of rules, which sidesteps the class of problems Godel looks like
 
Doesn't matter if we admit the kind of self-referential paradoxes that the incompleteness theorem uses.
You can't rely upon the intuition of the elders because you have to know who they are in order to follow the rule. And that relies upon an individual judgment.
And, as I was saying, Godel isn't the problem. It's a way to generate some problems, but not every problem is of that sort. (As a practical matter, I think it's very rare for it to be.)
("Practical matter" meaning things that come up in ordinary civilian debate.)
 
Hmm, now you've got me thinking about an interesting case where your statement may not hold. If your culture has a de jure religious leader (such as a Rabbi), and the handling of these issues within the culture are handled by the religious leader, exactness can be had. If the religious leader is not clearly defined, the culture's bounds are not clearly defined
 
2:51 AM
That's fine if it is utterly unambiguous who the religious leader is. This isn't always the case, though.
 
I think what Godel does is show very rapidly that there cannot be a final answer to the exactness. Other approaches (like the one I'm walking along) can demonstrate that one individual example can be torn apart by exactness
 
(Also, it fails the intuition test: what if you know unambiguously who the religious leader is, and they are making spectacularly bad decisions?)
 
The next step along such a debate, if I was really going down it, would be to begin dientifying dozens of ways to exactly identify the religious leader, and each one having to be shot down independently
 
Eh, I don't think Godel shows that, unless you don't know very much math. If you do, you just say, "Well, no problem! I just won't admit any self-referential statements in my rules. Take that, incompleteness theorem!"
Which is why I view it as more of a rhetorical trick (taking advantage of the relative lack of mathematical sophistication among most people) than really getting to the heart of the matter.
 
Yeah, when that happens I usually walk away with "It's hard to do, but go do it." I find people who make the claim that they're going to avoid self-referential statements tend to generate far more interesting debates =)
hmm... that might have actually arrived at the heart of the difference in our opinions
While I agree invoking Godel's theorems do not actually solve any problem directly, I find that the side effects of people trying to work around it lead to the kinds of debates I do enjoy.
 
2:55 AM
It's not very hard to avoid: just limit yourself to decision trees bounded by some absurd but finite limit (e.g. a tree with at most 10^100 leaf nodes).
Ah, well, If it generates the kind of debates you like, it's hard for me to argue with that :)
 
It just may have taken all of this discussion to arrive at that revelation =)
and from it, I take away a few wording hints that I may need to put in next time I throw Godel into an answer like I did to make it more palatable
 
If true, not a bad outcome. Many longer discussions end up revealing pretty much nothing except the preconceptions of those discussing.
It's an interesting trick, I must say. I hadn't really thought enough about attacking exactness claims that way.
 
It actually does come full circle to your approach, just from my point of view: the use of Godel in such rule-setting discussions is good at handling a set of simple cases, but it doesn't actually solve the more complicated corner cases (falling back on more intuitive debates to handle them)
Which makes it qualify as a good rule by your earlier definition, but in doing so forces me to accept the inherent limits implied by your definition of a good rule =)
 
Heh.
I think my experience is a bit different, but I can't say anything definitive because I haven't tried pressing the same way you have. Maybe most problems are softer in that regard than they appear. But, anyway, I like to get the entire problem delimited as well as possible since that does point a way to a solution.
And after a while, one (or I, at least), tires of just shooting holes in things. Eventually one wants something better, not just holes.
 
I agree with that one. Godel was just the biggest cannon I've found, so I went with shooting one big hole instead of a bunch of little ones =)
 
3:04 AM
Heh.
Anyway, it's been pleasant chatting with you! I need to focus my attention on other matters for a while.
 
Yes, thank you very much for this chat
It did not go where I expected, and where it went was more useful than I'd expected =)
 
Splendid!
 

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