Higher Levels of Abstraction
Let's continue on the theme of concepts. We've discussed the process of concept formation already, and this is most easily seen when the referents are perceptual existents. That means it's easiest when you can directly see what you're talking about. So length, color, and cars are all easy examples. These are all concepts formed at the perceptual level. You see them out in the world, and can point to them.
But you can also form abstractions from abstractions. We talked about 'blue', for instance. But what about the concept 'color'? This is a more abstract concept. You don't see 'color' in the world. You see specific colors. You see blue or green or red. Remember that to form the concept we go through a process of differentiation. For a specific color like blue, we can contrast it with other colors. But what do you contrast 'color' with? Certainly not the individual colors, since they would all be encompassed by this larger concept. You probably have to contrast it with things that aren't colors. Attributes would be the easiest thing. You compare it to length, or volume, or flexibility, or whatever else. And as you might guess, attribute is an even higher level of abstraction.
The first thing to note is that once you've formed concepts, there's two ways you can expand your knowledge. You can either integrate concepts into higher level concepts, like the example of color from above. Or you can subdivide concepts even further. Let's look at each in a little more detail.
Integrating concepts into higher level concepts is similar to the process of integrating perceptual data into concepts. You need a variety of things to compare and contrast, and you need to see that some are more similar to each other than others. The color example is easy. You can see how 'green' and 'blue' and 'red' are similar. So you can abstract from these particular concepts, and form the higher level concept 'color'. But this process needs some things that are different from the individual colors, but that's close enough to form the concept color. That's complicated, so let's see how it might work.
Imagine you're contrasting 'blue', 'green', and 'red' with some very different concepts, like 'dogs', 'humans', and 'televisions'. You might notice that all of the specific colors are attributes of entities, whereas the latter examples are all entities. If this is your data, you might form the concept 'attribute' instead of 'color'. The issue here is the Conceptual Common Denominator. The process of differentiation has to use some standard in order to see that these instances are less different from each other than they are from the other things. In this example, the CCD might be described as something like "Kind of existence". When you contrast, you'll see that there's a difference between them, and the concept you form will be based on the difference. In this case, it will be the difference between and attribute and an entity (or an attribute, and everything else).
So to grasp the concept 'color', we need to differentiate the specific colors with something more similar. It would probably have to be some visual attribute. We don't need to go into it. The point is merely that concept formation requires this act of differentiation, and the CCD used for the differentiation is going to be a defining attribute of the concept.
One thing that was implied in this discussion is that you can treat concepts as if they were "mental entities". When you form a higher level concept, you do it by referring to the lower level concepts themselves, not to their referents. You are actively focusing on the concept and its defining attributes. You're abstracting from the already abstracted information. You're taking the concept's CCD, and focusing on particular elements of it, abstracting the rest. In other words, you're not trying to abstract from the referents of the concept, but from the relationship of those referents within the concept. So when you take 'blue' and use it to form 'color', you're focusing on the characteristics of the referents of 'blue' that are used to from the concept 'blue'. You're taking the fact that these colors fit within a spectrum of color, called blue, and then integrating it with all of the other colors to form the concept 'color'.
There are other easy examples of this integration of concepts into higher level concepts. Rand uses the concepts 'chair' and 'table' and 'couch', and from these you abstract to the concept 'furniture'. You can also do this with concepts like 'love', 'hate', and 'jealousy', and form the concept 'emotion'. Or 'taco' and 'hamburger and 'steak' to form 'food'. And each of these higher level concepts can be integrated even further. 'Emotion' and 'Concept' and 'Memory' may be integrated into 'Mental Entities'. 'Furniture' and 'Toys' and 'Clothes' might become 'Merchandise'.
Let's go back now to the other way of expanding knowledge using concepts. You can subdivide the concepts. For instance, you might have a concept called 'table'. But then you can get more specific, noticing differences between things that were lumped together before. 'Table' might become 'Coffee Table', 'Dining Room Table', and 'Ping Pong Table'. This is pretty straightforward. To form these concepts, you need more detailed understanding of the referents of a concept, and then notice that there are differences among them. Of course, there also has to be similarities. To form even these more narrow concepts, you have to obey the rules of differentiation. You need to see that some are less different than others.
And again, the subdivision can happen at any level of concept. You can do it for things as simple as colors, where you'd have things like 'off-white', and 'ocean blue' or whatever. But you can also have it at much higher levels of abstraction. The concept 'government', for instance, can be subdivided into 'democracy', 'theocracy', 'monarchy', etc.