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August 12, 2008

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A related sense of "arbitrary", which is common in math and CS, is "could be anything, and will probably be chosen specifically to annoy you".

wikipedia on nets:

net or Moore-Smith sequence is a generalization of a sequence, intended to unify the various notions of limit and generalize them to arbitrary topological spaces.

I came up with, a decision or belief is arbitrary if it is not caused by the factors that would be expected to cause that sort of decision or belief. This reduction has the nice quality that it also explains arbitrary variable choices in mathematics - for example if you are trying to show that your compression algorithm gets good results on arbitrary data (heh), then it is data that was not, as might be otherwise expected, chosen to play well with your compression algorithm.

"Friendly AI"? What's one of those then? Friendly - to whom?

Or, in other words, arbitrary statement is one you won't accept as (an influence on) your own belief, one for which you can't trace the causal history back to its referent, given what you currently know. If you see a documentary about anthropomorphic aliens on TV, it is a fact about documentary-making process, not about aliens; the message of this documentary can't be dereferenced.

It would really rock if you could show the context in which someone used the word "arbitrary" but in a way that just passed the recursive buck.

Here's where I would use it:

[After I ask someone a series of questions about whether certain actions would be immoral]

Me: Now you're just being arbitrary!
Eliezer Yudkowsky: Taboo "arbitrary"!
Me: Okay, he's deciding what's immoral based on whim.
Eliezer Yudkowsky: Taboo "whim"!
Me: Okay, his procedures for deciding what's immoral can't be articulated with finite words to a stranger such that he, and the stranger using his morality articulation, yield the same answers to all morality questions.

I'll send my salary requirements if you want. ;-)

Like Larry, I'm more used to hearing the word mean something like "It could be otherwise without making a difference to the point I'm trying to get across".

I stopped to answer your definitional questions while reading and defined "arbitrary" as "some variable in a system of justifications where the variable could be anything and be equally justified regardless of what it is" and "justification" as "the belief that the action that is justified will directly on indirectly further the cause of the utility function in the terms of which it is defined and does it more effectively than any other action; for beliefs, the belief that the belief that is justified will reflect the territory in the most accurate way possible (I hope I'm not passing the buck here)"

Like Larry, I'm more used to hearing the word mean something like "It could be otherwise without making a difference to the point I'm trying to get across".

I'd say that's close, but too specific. A better definition would be "there are no rational reasons to select this position rather than any of the alternatives" or "there are no rational restrictions on the possibility space from which the selection is chosen randomly".

An arbitrary decision is one not founded in objective, shared principles and rules of logic that permit derivations to be made from them.

How about 'content that we expect to come with attached justifications, and those justifications are not present in the mind of the person putting forth the content.'

"Let's treat my car as a point mass of seven grams."

You may suspect that 7 is an arbitrary number having nothing to do with my car. If I said 683kg then you might think it is near the actual mass of my car. In neither case do you have justification.
If I tell you I don't have a car, then you KNOW it's arbitrary, because it's a number I made up. Your label of arbitrariness depends on where you think I got the number.

As for "morals", I like Theodore Sturgeon's definition from "More Than Human":

Morals are society's rules for individual survival.
Ethics are the individual's rules for society's survival.

Then there is Heinlein's definition of "love":

Love is when the happiness of another is essential for your own.

http://en.wikipedia.org/wiki/List_of_cognitive_biases

thought someone might be interested.

(I'm catching up, so that's why this is posted so far after the original.)

When I attempted this exercise I tried to think of how I use the word "arbitrary" and came up with a definition along the lines of "Something is arbitrary if its choice from a set makes no difference to the veracity of a particular statement", i.e. arbitrary is a 2-part function, taking as input a choice and a statement, since without a statement to evaluate against calling something arbitrary to me just looks like membership.

But then I read on and realized that I was being too narrow in what I considered to be arbitrary. Perhaps from too much mathematical training, I didn't even think of the common use as described above. This is an subtle kind of error to watch out for: taking a technical term that happens to have the same spelling and pronunciation as a non-technical term and trying to apply the definition of the technical term back to the non-technical term. The effect is either that you confuse other people because you use a technical term that looks like a non-technical one or you confuse yourself by misunderstanding what people mean when they use the term in a non-technical sense. This sort of thing becomes a bigger problem, I reckon, as you become more and more specialized in a field with lots of technical language.

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