Epistemic status: content summarized and synthesized (0-1 steps of reasoning) from the Sequences by Eliezer Yudkowsky, specifically A Human’s Guide to Words.
Guiding Puzzle: Is X a Y?
Questions of the form “is X a Y” are all over the place, and a huge amount of cognitive power goes into trying to answer them. Some of them are fun or trivial, like “is water wet” or “is cereal a soup”. Others are very serious, like “are transgender women real women” or “is abortion murder”. I do not plan to provide a definitive answer to these questions in this article. However, one of the most important things I’ve learned from reading the Sequences was a new way of thinking about this type of question that I think has been extremely important in leading me to some of my current views. In this post I will attempt to communicate this way of thinking, because I think it will be useful to you too.
Symbols Are Arbitrary
You’ve probably heard this idea in some form or another before. If the whole world started using the symbol “ujmikolp” to represent the color of grass and emeralds instead of the symbol “green”, we could all go along our daily business just the same. Our communication would be totally unimpeded, except for maybe the minor problem of occasionally sounding like we’re struggling to swallow a whole jellyfish. Point is, neither the written symbol “green” nor the verbal symbol “guh-rEEn” really have anything to do with the actual meaning of the word, and it really doesn’t matter what symbol we all use. So what does determine the meaning?
Dictionary Definitions are Circular
Maybe the meaning of the word “green” can be found in the dictionary? Let’s give the ol’ Oxford dictionary a try. They define “green” as “of the color between blue and yellow in the spectrum”. This is a definition of one word in terms of other words, which is called an intensional definition, or the intension of the word “green”. This definition links the meaning of the word “green” to the other words in the definition. Perhaps if we knew what “blue” and “yellow” meant, we would know what “green” meant. Problem is, the Oxford dictionary defines “blue” as “a color intermediate between green and violet”. It’s not hard to see how this pattern will continue around the color wheel until we’ve defined each color in relation to all the others – but we have no way to anchor these relationships in reality. Intensional definitions rely on the fact that we know the meanings of many words, so by defining a simple relationship from those known quantities to the new variable we are wondering about, they can quickly explain the meaning of that new variable in terms of the others. But without this background assumption of some known meanings to work with, intensional definitions come completely unmoored from reality, only defining relationships between symbols. These definitions are often helpful, but cannot be the only source of the meaning of words. They have to bottom out somewhere.
Words Are Cluster Labels
So if you had to explain to someone the meaning of the word “green” without using a dictionary definition, how would you go about doing it? I know I would probably just start pointing at a bunch of green stuff until they caught on to the pattern. I wouldn’t want to point to just one shade, either, since that might lead them to think “green” mean only that specific shade. Maybe I would want to show them something like this:
This just-point-at-examples method is called an extensional definition, or the extension of the word “green”. Could this region of color-space be the meaning of “green”? It seems quite plausible, since there’s no infinite regress like with dictionary definitions (but we do have to hope that you’re explaining to someone capable of inductive reasoning). One potential refinement of this simple boundary is that it seems like the colors in the center of this region of color-space are more “green” than the colors at the edge. If I were pulling up random examples of stuff I thought was “green”, the center would probably be the densest, with the density trailing off towards the edges. So perhaps rather than a simple boundary, the meaning of “green” is best represented as a cluster in color-space, with some highly typical center and edges that just barely qualify.
We can use this cluster notion for other words as well. Perhaps instead of drawing our cluster on the RGB plane, we consider a two-dimensional space with temperature and luminosity as our coordinates. This is the coordinate scheme used to represent the classes of stars, and gives us a great demonstration of these concept clusters:
In this case, there is some natural cluster structure already to the distribution of stars in this thing-space, and so there is a natural way to draw our concept-clusters. The symbol “white dwarfs” is the label for the natural cluster around Temp=10,000 and Lum=10^-2, for example.
So this is where the meanings of words come from! Words serve as labels for clusters in thing-space, preferably clusters that match some existing cluster-like structure in the world. Dictionaries provide intensional definitions that establish relationships between clusters (now the “green is between blue and yellow” definition can be seen as identifying a cluster location in color-space) as a shortcut to identify new clusters based on more common clusters with widely known extensional definitions.
Illusory Disagreement (And Illusory Agreement)
Now we are equipped to take a closer look at our guiding puzzle. When we ask “is X a Y”, this is equivalent to asking “is the cluster labeled X contained in the cluster labeled Y”. This is technically just a question about labels, now that we look at this way. But since we’ve established that labels are arbitrary and don’t matter, the question we’re really trying to ask here is an empirical one, about the locations of clusters in reality. Problem is, we can’t ask that question about clusters directly, not without enumerating all of the points in the cluster. We use labels to point to them, and ask questions about labels as a proxy for questions about reality. Let’s take a look at some example of how this disconnect can cause problems. In the following diagram, each quadrant represents a different potential worldview:
A disagreement about whether X is a Y in the top row seems quite silly – there’s nothing different about the world! The upper-left and upper-right positions would make exactly the same predictions about the qualities of any point in this thing-space that they’re asked about. This is an illusory disagreement, where they agree on the facts of the world but think they disagree because of the terms they use to describe it.
However, disagreeing about whether X is a Y in the bottom row does actually say something about the world. The lower-left and lower-right positions would actually make different predictions about the world, since they don’t share the same worldview. The proxy questions about labels have successfully detected a disagreement about the clusters they refer to. This is a real disagreement, since they actually disagree about the facts. Importantly, real disagreements can be answered empirically, since the expected point structures are actually different on each worldview.
Of course, an agreement between the worldviews in the left column or the right column would also be quite silly. The upper-right and lower-right quadrants both think that X is a Y, but they actually have completely different worldviews! Similarly, the upper-left and lower-left quadrants both think that X is not a Y, but they also have different worldviews. Both of these are illusory agreements, where they differ on the facts of the world but think they agree because of their choice of symbols.
So what constitutes a real agreement? In this diagram, each worldview is only in real agreement with itself. To have a real agreement with another person, we need to have the same beliefs about the clusters present in reality, and use the same labels to describe them. Only then will our proxy questions about labels be able to successfully tell us that we agree about reality.
Basic Techniques for Having Real Discussions
If we are interested in communicating with each other about the facts of the world, we have to be careful to avoid false agreements and false disagreements. Illusory agreements are particularly hard to detect, since there is no visible disagreement that would suggest anything might be amiss. Here are some ideas about how to make sure your agreements and disagreements are real, and made-up dialogues to demonstrate.
Make sure your working definitions are clear before you start. This is the essential bread and butter of clear communication. It is simple, easy, and good for preventing illusory agreements and disagreements from cropping up in the first place. Remember that dictionary-style intensional definitions only work if they point to a word your partner has a clear extension for the words you are pointing them to for reference, so choose the phrasing of your definitions accordingly.
A: Is water wet?
B: Well, what do you mean by “wet”?
A: You know, wet. Like moist, but more.
B: -_-
A: Ok, fine. By “wet” I mean “surrounded by water molecules”.
B: Well then the majority of the water molecules in any given body of water are “wet”, but the ones on the edges are not. Why was this a question?
A: Huh. I’m not sure. I had a hunch this conversation was going to turn into a whole thing. Glad we cleared that up.
Rationalist Taboo: if you are already in a discussion and suspect the labels may be causing problems, temporarily abandon them. This technique is essentially a way to clear up definitions mid-discussion. Replace the symbols with their intensional definitions or with the membership criteria for the cluster you’re thinking of, or whatever you think is most likely to communicate the substance of what you’ve been talking about to your partner. A good way to know when this technique might be useful is if your partner’s reasoning sounds so nonsensical that they might not be talking about the same thing you are.
A: If a tree falls in the forest and nobody is there to hear it, it does not make a sound.
B: No, why would it matter if anyone is there or not? It still makes a sound.
A: Of course it matters, what are you talking about?
B: Wait, that sounds like nonsense to me – we might not even be talking about the same thing here. I think we forgot to clarify our definitions. Let’s Taboo “sound” real quick to make sure we’re actually disagreeing.
A: Sure. If a tree falls in the forest and nobody is there to hear it, it does not satisfy the test [this event generates a qualitative auditory experience].
B: If a tree falls in the forest and nobody is there to hear it, it still produces vibrations in the air.
B: Oh.
A: Oh.
Ask yourself why it matters which view is correct. This is good for clearing up illusory disagreements that are being discussed as proxies for some other real disagreement. This can happen when the connotations typically attached to certain symbols sneak their way in through intuitive definitions, so the thing explicitly being discussed is not the real crux of the issue. This can also reveal what the implicit crux actually is.
A: Abortion is not murder, because life begins at birth.
B: Abortion is murder, because life begins at conception.
A: I have a feeling this might be an illusory disagreement. Why does it matter if life begins at birth or if it begins at conception?
B: I see what you mean. I suppose the reason it matters if the fetus is alive is whether it’s conscious or not, since I believe killing conscious humans is murder.
A: Ok, I agree that killing conscious humans is murder, but I disagree that the fetus is conscious at the time of abortion. It sounds like maybe this is where our disagreement really lies.
Conclusion
This view of clusters and cluster membership can help us explain why “is water wet” and “is cereal a soup” seem so impossible to conclusively answer. There is no real disagreement here – it seems overwhelmingly likely that if asked to predict the properties of things interacting with water or collections of things interacting with milk, both camps would make the same predictions. They are disagreeing on terminology, not about the facts of the world.
This view can also provide some useful insight into how to deal with real, important disagreements. For example, on the “is abortion murder” question, a disagreement over whether life starts at conception or at birth seems likely to be illusory (depending on the specific views involved, of course). If both camps acknowledge the same biological reality, they would both make the same predictions. However, a disagreement over when the fetus is or is not conscious seems, at least in principle, answerable. One camp might expect the “second-trimester” and “third-trimester” clusters to not vary significantly on the “response to stimulus” axis of fetus-space, while the other camp might predict very different empirical outcomes. This is a real disagreement, and needs to be resolved with information about the facts of the world, not with arguments over the borders of the “consciousness” cluster.
From what I’ve personally witnessed, it seems like a tremendous amount of cognitive power is wasted on disagreements of terminology. I hope it is now clear that at the end of the day, the categories don’t matter – they’re just a communication tool. What matters is the distribution of points in thing-space, the actual facts. If you don’t disagree on the distribution in thing-space, you’re experiencing a communication problem, not a disagreement. And if you do disagree on the distribution in thing-space, the way to answer the question is by acquiring empirical information about the distribution, not by debating irrelevant cluster labels.