17 Rules to Make a Definition that Avoids the 37 Ways of Words Being Wrong
Eliezer’s writing style of A->B, then A, then B, though generally clear, results in a large amount of redundancy.
In this post, I have attempted to reduce the number of rules needed to remember by half. The numbers are the rules from the original post.
So, without further ado, a good definition for a word:
can be shown to be wrong37 and is not the final13 authority18 19
has strong justifications33 for the word’s existence32 and its particular definition,20 which leave no room for an argument17 22
agrees with conventional usage4
explains what context the word depends on36
limits its scope to avoid overlap with other meanings25
does not assume that definitions are the best way of giving words semantics12
directs a complex mental paintbrush35 to paint detailed pictures of the thing you’re trying to think about23
is a brain inference aid13 that refers to and instructs one on how to find a specific/unique24 similarity cluster21 that is apparent from empirical experience28 29 30, the cluster’s size being inversely proportional to the word’s length31
is not a binary category9 11 and cannot be used for deductive inference27
requires observing only14 a few3 real-world1 properties that can be easily5 verified2 and are less abstract6 than the word being defined (in particular, the definition cannot be circular16)
is not just a list of random properties10 21
contains no negated properties10 33
specifies exhaustively all of the correct connotations of the word25 26
makes the properties of a random object satisfying the definition be nearly independent34
has examples6 which satisfy the definition, including the original example(s) that motivated the definition being given15 and typical/conventional examples7
tells you which examples are more typical or less typical9
captures enough characteristics of the examples to identify non-members8
And there you go. 17 rules, follow them all and you can’t use words wrongly.
Dear mathnerd314, please define “prime number”.
A prime number n is a number whose only factors are multiplicative units and n*a multiplicative unit (and these two sets are distinct). Typical examples include 2, 3, 5, 7 and 11. Less-typical examples include −2 and 1+i; they are often excluded from consideration in mathematics.
“whose only factors”—that’s where you are hiding the negation
(“only” = “there is no other”)
Well, there’s a tricky thing in mathematics called “the law of excluded middle”. Using the law, you can e.g. prove that a implies b is logically equivalent to (not a) or b. It also lets you do existence proofs by proving it isn’t possible for there to be no examples. So in classical logic every statement is confused with its double negation.
I generally try to use intuitionistic logic though, where a->b is not logically equivalent to anything else and double negations have to be written out. You do have
Not necessarily: see mathnerd314′s comment below (or above). In fact, in “there is no other”, there is a double negation (the second being in “other”, which hides “not equal to”), which can be eliminated.
Well done (although it is still a useful binary category; numbers are either prime or composite, semiprimes be damned).
Indeed, but one of Eliezer’s points was that mathematical objects, e.g. the set of prime numbers, don’t need labels. I can write
I will upvote any similarly succint and correct-enough summary of an Eliezer sequence post.
I’m aware I didn’t properly define any of that.
Eliezer never claimed that his 37 ways a definition can be bad constitute an exhaustive list of ways for definitions to be bad, still less that bad definitions are the only way to use words wrongly. In fact he said the reverse:
In response to the second of the observations (from NoahTheDuke) I see you’ve combined your list with two further principles: know your definitions (which are to meet your criteria) and then use words according to their definitions.
But (as your point 6 says) definitions aren’t always the best way to give semantics to words, and most of the ways of abusing words have to do with things other than how we define them.
I’m bemused by this article. Is it perhaps intended as some sort of parody—the wide-eyed cultist slightly rewording the cult leader’s pronouncements and declaring that obeying these rules is the One True Guarantee Of Success? (For the avoidance of doubt, I don’t regard LW as a cult or Eliezer as a cult leader, but I know some people do and if this is intended as parody then I guess that’s what lies behind it.) If it’s not parody, then all I can say is that it seems remarkably overoptimistic.
You missed the context, which is when someone claims “This can’t be wrong.” Rule #1 clearly states the definition can be wrong. On the other hand, there are different levels of wrongness. Sure, these rules are most likely wrong and incomplete, but they are more correct than having no rules at all. And the reason definitions aren’t the best way to give semantics is because we already have a better semantics, namely the “similarity cluster”. (Map is not the territory, etc.) But forcing someone to give a definition that follows these 17 rules gives you the similarity cluster, and avoids pretty much all of Eliezer’s 37 ways of using words wrongly (See the superscripts!). There might be other ways of using words wrongly, but they’re going to be either obvious or so subtle that nobody can catch them anyway.
As for why I wrote this article, it’s simple: I need definitions of the things on my GTD list (in particular, I need a direct specification of what constitutes a “physical, visible action” for the next-actions list), and I recalled an EY post about definitions which was his 37 ways. But that was all about how to do it wrongly, and one of my tasks is “don’t think negatively”, so I rewrote it. It was and is sitting in my WhatIs:definition zim wiki page. I posted it here to get some commentary and maybe someone checking that I interpreted his points correctly, which I’ve been getting. (Thanks guys! :-))
First thing I did was print it on a A4 page and tape it in plain view.
It’s not always feasible to follow all these rules. In particular, conventional usage often has negated properties, quirky definitions from historical accident, and so forth.
Generally, I don’t have much hope for any attempt to set down practical sufficient conditions for proper language usage.
Indeed, it’s very depressing. I doubt I’ll ever be able to understand other people, but I do have some hope for internal consistency in my usage (so mathnerd314_February2014 writes things that seem comprehensible to mathnerd314_July2020). I’ve collected my early 1990′s writings and they all sort of “click” into place, in that I understand them well enough to rewrite them word-for-word. Perhaps by writing down definitions for my words I’ll be able to see how the concepts have evolved over time (or that they haven’t changed).
If you are really a math nerd, then you might notice that things (human language) are not as hopeless as it looks.
Imagine that words (the identifiable mental identities behind the utterable sylable sequences) are entities that the human brain uses to trigger some (but mostly not all) of the aspects of the concept (the mental identities of human thought) that is intended to be communicated by an utterance (or written sentence).
Words are only parts of the aggregate communication. They are less building blocks (implying compositionality) and more shards. Each shard adding meaning. Words must almost always be used together.
This is because each word is chosen by the brain to add as much meaning to the already output speech as possible by selecting that word which implies the most features (neuronal activation patterns) of the concept to be transported currently or next (that is the reason we can choose shorter more ambiguous words when the context implies them).
The fact that we try to give precise meanings to words doesn’t mean that precise definitions are necessary (nor efficient) for communication. Having precise definitions has another benefit: It allows for the relationship between words and complex concepts to be easier acquired. And by this route more complex concepts can be aquired and communicated more efficiently.
The conclusion is that you don’t need definitions for your words to communicate more clearly with your future self. It is sufficient to have a sufficiently large corpus of text of yourself. That would allow you to infer more about your earlier self than a few condensed definitions.
It sounds like we’re in violent agreement here. I’ve already verified experimentally that writings by mathnerd314_1998 are clear to mathnerd314_2009. My brain doesn’t change that much over time.
Instead, I have two other questions:
can mathnerd314_2014 understand Gunnar_Zarncke_2014 on the same level he understands mathnerd314_1998?
If both mathnerd314_2014 and mathnerd314_2020 independently write down definitions, will they be textually different?
My hypothesis is that #1 is “no”, because internal organization of concepts varies dramatically from person to person, and that #2 is “yes”, because people do change over time.
I agree.
But first of all you can likely better understand me than yourself when you were less than ten years old. Surely less than 5 but possibly even less than when you were less then 15. We often underestimate how much we change over time (there must be studies confirming this).
And then it is rather likely that you produce differnt textual definitions on the same day a) when you are in different mind states (sleepy<->alert, intoxicated<->clean, happy<->sad), b) in different social circumstances, c) likely even in differnent locations. This is because the context these circumstances provide leaks into your speach and your definitions.
I’m having a hard time interpreting the superscripts.
Indexes to the original article.
3 is a big deal. Specifically, one really problematic thing that people do when trying to convince other people is to define a word just slightly different then everyone else is defining it, and then construct arguments around that word defined in that way that then are hard for humans to take apart. This is common in politics; a libertarian definition of “violence” is different from the common one, for example, in such a way as to subtly change the assumptions of the argument in a way that is invisible to most (the libertarian definition assumes that taxation is inherently “violence”, but that using force to defend your property is not “violence”.) You might agree or disagree with those assumptions, this post isn’t meant to start a political debate, but I think it’s always harmful to clear logic thinking when people hide their assumptions that way.
To be clear, there’s nothing wrong with defining a word in a certain way if everyone in the conversation already understands and agrees with that definition, but when people don’t, it can be a sneaky way of hiding your argument’s real weak points (perhaps even from yourself).
Well, taxation has the threat of violence, in that if you don’t pay your taxes you will eventually be caught and sentenced to jail for tax evasion… hmm, maybe I should do a “The definition of X” series. They should really be wiki pages though, not posts...
Yeah, I understand the logic behind it, but still most people would not include “taxation” within their definition of “violence”. Many people would consider taxation by a democratically elected government to be legitimate; people may not like it, but they don’t consider it an act of violence. And it’s worth noting that that libertarian definition does not consider it “violence” to, say, have someone arrested for violating a contract, or for theft, ect.
Basically, the word is being used in a non-standard way that hides a number of assumptions that not everyone would necessarily agree with. I tend to think it’s better to clearly lay out what your assumptions are and how you came to them when making an argument.
I don’t understand. I thought the purpose was to develop rules for writing definitions of words, not for using words. What have I missed? Or maybe, how would this list look were it to be written as maxims for writing?
If you require every word you use to have a definition, and ensure the definitions follow these rules, and then consistently use the words according to their definitions, then it follows that you are using the words correctly and not wrongly.
So I guess that could be the maxims for writing:
know the definition of every word you use
ensure the definitions follow these 17 rules
use words according to their definition