Key Concepts: Conceptual Common Denominator, Referents, Units, Measurement Omission, Borderline Cases, Differentiation, Integration, Abstraction
It's time to go over exactly how a concept is formed. Understanding this process can help you in several ways. First, by understanding how they are formed, you get a better idea of what a concept is. By understanding the method, you can learn to perform it more efficiently, and more accurately. You'll learn the kinds of mistakes that can happen if someone doesn't construct a concept correctly. You'll be able to understand the limits and advantages of conceptual thought.
For external reading material, I recommend Rand's own Introduction to Objectivist Epistemology. Also, David Kelley has a a very short booklet called "A Theory of Abstraction" that develops some of the theory in more detail. You can probably get that at TOC.
Let's define a few terms for later use. The first is the term "Unit". In the context of Concept Formation, this term is supposed to designate a member of a larger class or category. For instance, if you have the concept "Car", your own car could be considered a unit of that category. The point is that you are identifying the particular thing as part of a larger class. You're designating it as a member of a class.
There's also the term "referent", which means the thing you are referring to. In the example of the "Car" concept, every car is a referent. When you talk about cars, you're not referring to some abstract vision of only the essential qualities, you're referring to actual cars. Any of them. Your car, my car, whatever. Referents are always important because ultimately that's what you're referring to when you use a concept. You say "car", but you really mean any of these specific cars. It's a recognition of the fact that you are referring to actual things.
Now let's look at the process. The first thing to note is that a concept is an abstraction of a number of things. So the concept "table" is not referring to a specific table. It's referring to all tables. But to form the concept, you need more than one table. So the first part of the process is to identify things that are similar to each other in the same way. They have to have something in common in order to integrate them in the form of a concept.
Let's take an example. Say you're going to create the concept "blue". You can take more than one blue thing that exists in the world, and so integrate the different shades of blue into a single concept. Say you take the sky, the color of a car, the ocean, blue ink from a pen, and whatever else you want. The thing each of these has in common is it's color. They all have color, and they're all similar. So it's possible to focus on this aspect of them, and form a concept that integrates the different pieces.
There's a few issues here, first. We say that they're similar, but what does that mean? How is one shade of blue similar to other shades of blue? To retain objectivity, we have to have some method of knowing whether they're similar or not. Notice that this is obviously possible. When I talk about blue objects, you know what I'm talking about. What's the method here? How do we know if something is similar?
Well, related to being similar is being different. Similar actually means not very different. So to form the concept blue, we don't just need blue objects. We need other colored objects as well. We have to differentiate the blue ones from something else. By seeing that the blue ones are not very different with respect to each other as they are with respect to other colors like red, white, orange, green, and purple, we are able to place them in their own category. So the ability to integrate referents based on their similarity is actually part of the differentiation process. You'll notice that to see this kind of difference, you need two or more things that end up being "similar", and at least one other thing that's "different". To see that the difference between one shade of blue and another is not very big, it has to be compared to something that has a very big difference, relatively.
In fact, without differentiation, you can't even be aware of something. Imagine you could only see the color blue, and to further confuse the matter, it's uniform in shade. Everything shows up as blue. You wouldn't even notice the blue because it's always the same. There's no other color or other visual signals to let you differentiate it, which means you can't draw your attention to it. If everything were the same color, you wouldn't have a concept for color. It's the differences that make it possible to identify something because you're differentiating it from the background. Identification requires differentiation.
Now we talked about noticing the differences between the different colors, as well as the slighter differences between shades of the same color. How is this mental function performed? The first thing to notice is that we're making a comparison based on a standard of evaluation. When we say two things are similar and different from other things, we're saying that we've compared them all according to a single standard. From the Standards Of Evaluation thread, we know that we have to have a single standard that each thing can compare against. This standard needs to be a commensurable characteristic, meaning all of the things compared need to have this characteristic to some degree or another. This commensurable standard is called the Conceptual Common Denominator by Rand. She defines it as: "The characteristic(s) reducible to a unit of measurement, by means of which man differentiates two or more existents from other existents possessing it."
The next thing to note is that this measurement is quantitative. There's a measurement that you're making when you do the comparisons. That's why you know that some of the elements are less different than the others. The function that your brain performs is very simple in the end. It only has to measure quantitative data in relationship to other data. That means you don't really need to know how similar two shades of blue are. You only need to know that by contrasting their relative difference with other colors, the contrast is large.
One point of interest here is that some attributes are obviously easier to "measure" than others. Color is pretty easy. So is length, density, volume, roughness, and a bunch of others. But what about something like shape? How would you "measure" shape quantitatively? Well, is an oval more similar to a circle or a square. Is a cone closer to a pyramid or a box? You can kind of see that there are quantitative factors involve. You can measure area. You can measure the distribution of the area. You can measure the angles of the edges. There's a number of ways of comparing these individual factors. And you can even weigh the importance. Rand points to the answers in mathematics. Geometry, Trigonometry, and Calculus all deal with different shapes. You can represent shapes using a function. You can then measure how different the other shapes are from that function. Other characteristics may be even harder to understand how the measurement works, but that's partly a matter of introspection. If you concentrate on how some attributes can be less different than others, it makes it easier to see that there is a measurement going on.
As one final example of the difficulty of measurement, look at the characteristic "purpose". Analyze a table, a desk, and an umbrella. It shouldn't be too difficult to see that the purpose of the table and the desk are very similar, especially when compared to that of the umbrella.
Now back to the integration into a concept. We know that the different referents of a concept have similar attributes, but the measurements are different. This is where the idea of "measurement omission" comes into play. When we integrate the referents, we know that there has to be some kind of measurement of the CCD. But when you actually form the concept, the specific measurement doesn't matter. Take the color blue. Two things may be blue, and we integrate them together. But the concept doesn't care how blue something is. The specific details are ignored. Just as long as it's blue.
It also ignores the details unrelated to the CCD. If you're trying to form a concept of blue, you don't care if the ocean is cold, or the car is fast, or anything else. Those details are ignored as well. This is the process of abstraction. Abstraction, as defined by Rand, is "a selective mental focus that takes out or separates a certain aspect of reality from all others". In the case of blue, you're focusing on the color, and that's it. The other details you will mentally push aside. The integration has nothing to do with them. You're focusing on only one aspect, and when you form the concept blue, that's all that remains. The blue color. Of course, the referents still exists, and you can refer to them, but it's only this aspect of them that you retain in conceptual form.
To address one final issue, we talked about measuring differences and similarities. One question that might pop up is how different do things need to be? Well, remember that the difference is relative to other things. Something that looks blue in the context of a bunch of red things may not look so blue when contrasted with green things. This creates something called borderline cases. Here's an article explaining it in more detail:
And that's about it. Let's recap just to make sure we have it. We're identifying existents in reality, and identifying them through a process of differentiation. We can see that some things are similar or different in a particular context. This is done by a method of measurement along a standard called the Conceptual Common Denominator. We then abstract from the individual instances the characteristics of the CCD, and we omit the measurements. What's left is like a thread that runs through every referent of the concept. This is the concept. Whether it's the color blue, or length, or a car, or a person, or "running" or "intention" or any other concept, the process is essentially the same. We've can use the abstracted information directly, instead of referring to the specific characteristics of the referents. That means we can say 'blue' instead of "the color of the sky", or 'car' instead of "my small automated vehicle with 4 wheels".
Keep in mind that this is an attempt to distill an entire book. There's more in it than what's here. I'll get to some of it later. And some I may just miss. Like most of Rand's works, there's usually a lot more buried beneath the surface.
But before closing this thread, let me just say a few things about why this is important.
First, you're always using concepts. When you argue over the definition of a word, you're arguing over what is the nature of the concept. So understanding what a concept is can be crucial to effective communication, teaching, and understanding. Also, knowing how a concept is formed allows you to go straight to the source. Reality. You can observe the referents yourself. You can do the abstraction yourself. Instead of being stuck arguing at an abstract level, you can always tie your concepts to what you perceive in reality.
Another important point is the objectiveness involved in concept formation. Because you're performing measurements along objective standards, it means that not only is communication and understanding possible, but that it can be reproduced. And tying abstract thinking to reality is a huge deal when it comes to the reliability of your mind. If you were unable to show the connection between abstract ideas and reality, it would open the door to an argument saying that abstract thinking is invalid. Now you have some means of answering this (or at least a hint of the way to go).
Another point is that you don't ask too much from a concept. In the borderline article above, and from the discussion of relative differences, you can see that your knowledge is always based on a context. You can't hope or expect to have rigid concepts that somehow manage to escape context. More on this later.
That's it. There's a bit more on the topic, but I'll break it off into later discussions.