Concept: a collection of indistinguishable minimum sufficient causes

When thinking about definitions, I am always struck by how easily we can switch between different perspectives. We can define and think about something as complex as a human as a single coherent thing. Then we can change our perspective and think about ourselves as a collection of parts, as a skeleton plus muscles, organs, and a nervous system. And those parts have parts as well, and eventually we get down to the level of cells and then molecules. At every level, we can form a concept of what each part is. But we’re not forced to hold the idea of all the parts in memory all the time. If we did, eventually we’d end up seeing everything as just a collection of quarks. Instead, we have the ability to switch between thinking about a human as a single concept and as a collection of things representing many different layers of concepts.

What is a concept? How can it be so flexible? How can the building block of thoughts and beliefs be so difficult to define?

We have a working memory that can only hold a handful of things at a time. So if we want to think about anything more complex than a few fundamental particles interacting, we need to aggregate what we experience into useful groups. How do we make a group out of all the parts of a human? Sometimes things like our clothes or what we’re carrying are part of that concept and sometimes they’re not. What about a part like our hair, which falls out bit by bit or gets cut off? Again, it creates a fuzzy boundary between what’s part of the concept of the person and what isn’t. An even more difficult example is the air in our lungs. When does it become part of us? When it’s first inhaled into our nose? When it ends up in our lungs? Or not until it has been absorbed into our blood? It is seemingly impossible to draw a perfect line around someone and say that inside that line is everything that is definitely required to count as a person. How do we form a concept of a person when its parts are constantly changing?

If we start with fundamental particles and try to build our way up to the kinds of concepts we use every day, it’ll be a very long process. But I think there’s something about the way we think about fundamental particles that will be useful: we define them by the way they interact with something else. A single particle that doesn’t interact with anything else, that doesn’t have any effects, essentially doesn’t exist. And this stays true even at the level we’re used to thinking about—something that doesn’t interact, that doesn’t have any effects on anything else, isn’t a thing. We just can’t form the concept of something that never interacts with anything else. This is because our concept of something is defined by the effects that thing can have. Physical things take up space and bump up against other physical things. People have behaviors and feelings, and those behaviors and feelings can be described by the actions they cause or the effects they have on other people.

Having effects is a good first step in our definition, but we still have the problem of finding the limit of a concept. When we think of a person driving a car, sometimes we think of the whole package as a single thing—a single concept. If we say, “the car stopped at the red light,” we’re really talking about the car and person working together. Sometimes we even think of thousands of people and cars as a single thing, as “traffic.” Other times we think of the car and driver as two separate things. How do we draw the line between them? How do we find the boundary of the effects that create the concept of the car and the concept of its driver?

When I look at a glass holding water, it seems obvious that the concept of the glass is created because it has the effect of being able to contain liquid. But even looking at a specific example of a glass holding some water, I have to admit that the entire glass isn’t necessary to hold that water. If 1/100th of the atoms that make up this glass just popped out of existence at random, it would still look and work exactly the same, as far as I could tell. If we’re going to define the concept of that glass as the thing that’s holding that water, why should we include that random one percent of molecules if they aren’t really necessary?

We include them because they’re only unnecessary if removed randomly. Specific molecules that shared something in common couldn’t be removed without changing how we thought of the glass. If we drilled a hole through one percent of the glass, then it would leak, and our concept of it would change dramatically. When there’s some logic tying parts together (like all the molecules that used to be where the hole is now), there’s something to distinguish them. But with random molecules we can’t detect anything that differentiates one from another, and that means all the indistinguishable parts end up being included in concept of the glass. The concept is created by the effect it has—holding water—and the limits of that concept are described by the indistinguishable minimum sufficient parts of that effect. If we can’t tell if a part is really necessary or not, or if we can’t tell if one part is different than another part, then there’s no way to separate them out, and the whole thing becomes a single concept.

Describing concepts by effects means that we can have a concept of something even if we can’t pinpoint what the cause is. For example, we have the concepts of love and hate. Hate can be a specific feeling a single person has, or it can be a broad kind of feeling that exists within a group of people, or even just something that we know is possible. We don’t need to know exactly what specific physical thing causes us to feel hate to have the concept that it exists. We can see that hate has some effect on the world, and something must be the cause of that effect. Our concept of hate is the indistinguishable group of all the things that could be the cause. For example, we can say a war was caused by hate because we can identify a bunch of hateful actions that could’ve contributed to it. We can’t say which ones were the bare minimum necessary to cause the war, but there’s a group of indistinguishable minimum causes that form our concept of the hate that started the war.

When we define intelligence as the ability to make comparisons, what’s being compared is concepts. We’re holding in our minds the effects that one thing has as the sum of indistinguishable minimum sufficient causes and comparing that to another set of causes. They can only be compared because the two groups are distinguishable. If there is no way to tell them apart, there is no way to compare them. There has to be a difference, and intelligence is finding those differences.

Ultimately, every article I’ve written about a definition has been a way to describe a concept in detail. A definition is a way to list the important effects that describe our concept of one thing uniquely. The more carefully we constrain our definition the more information it conveys. For example, the idea of “chair” conveys more information than “seat” because it includes the information about the limitations of what counts as a chair. The idea of a seat for one that’s moveable and provides support uses up four spaces—seat, one, moveable, and support—in our working memory. If we define that concept as a chair, we can hold all that information in one spot in working memory. This is great as long as our definitions match. It’s an efficient way to talk about a bunch of complicated information easily. But if they don’t match, it can obviously lead to problems.

We could compare a definition to a technology standard like USB. It would be easier for every company to make a connector for their device that just did whatever they needed it to do, fit where it needed to go, and cost as little as possible. But if we want our devices to be able to interact easily, it makes sense to force ourselves to adopt a standard. The USB standard dictates the limits of how the communication will work, and everyone voluntarily agrees to work within those limits.

In scientific and technical fields these kinds of strict limitations can be very important. In other areas they’re less important or maybe even impossible. For example, if everyone uses the word “happiness” slightly differently, and perhaps no one is even entirely sure of what their own definition is when using the word in different situations, then it’s nearly impossible to agree on a definition. However, if some people recognize this problem and voluntarily limit the way they use the term, that choice can spread. If the limitation they impose on themselves turns out to be useful—if it allows more clarity without giving up too many options—then it can spread more easily. Eventually, a definition might be popular enough that we might even want to say that someone who uses the word in a different way is using it incorrectly.

This article ended up being about the concept of concepts and the definition of definitions. These aren’t necessarily easy ideas to describe. Maybe you’ll find an error in my approach. Maybe you’ll find a way to describe concepts and definitions more clearly or improve on this analysis in another way. It’s much better to have a definition that other people will agree on and find useful because they recognize it as a tool to help them think about complex ideas. I hope that I’ve succeeded in describing the underlying logic I see in these concepts and that you’ll find them interesting and useful.