From the Introduction to Objectivist Epistemology: "A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted." (p.13)
Just what is a mental integration, and how is it done? To see what it is, imagine that you have sorted out your personal papers into a number of piles that are lying on the desk in front of you. There is a pile of bank statements—all different, but not so different from one another as from that pile of receipts. If you widen your focus a bit, you can see that while all those piles on the table are different, they are not so different from one another as they are from the TV. That's why they are all in the concept "pile". Notice that in making that thought, you did not push the piles together on the desk; you pushed them together in your mind. You made a mental integration by forming the concept "pile".
Now, by following the directions in Ayn Rand's definition, form the concept "concept".
The definition begins by telling you what it is: a mental integration. Are all mental integrations concepts? Is it the case that whenever you combine things in your mind, you are forming a concept? No, says the definition; only if you combine similar things—things with measurable characteristics in common. The things are units, which means they can themselves be concepts. The measurements are omitted, which means you have to know they exist, but you don't have to keep track of them.
Is that all you need to know about concept formation? Not by a long shot. The definition tells you how to distinguish one aspect of reality from all others. It lets you make a mental pile that can be treated as a unit. It does not have the slightest ambition to tell all about anything. The definition is a vital tool of concept formation, but it deals only with the bare essentials: where in reality you look to find this group, and how you tell this group apart from those around it.
In a bow to tradition, the first is called the genus, and the second is called the differentia. To form the concept "man," you look in the genus "animal," and pick out the ones that have the characteristic of rationality. You pick out the rational animals, combine them mentally, and treat the combination as a unit: man.
Which brings you to the word. To make a concept, you must have a group of similars, a definition by essentials, and a specific word. That word is your mental pile. It embodies the combination and lets you think of it as a unit. For thinking, you must know what the word means. For communication, everyone must know what the word means. Dictionaries, however, do not as a rule give definitions by essentials; they give synonyms and descriptions. One way to increase the clarity of your thought is to increase the clarity of your definitions by learning about essentials.
The essential characteristic of a group of similars is the commonality that makes them similar. Thus the essential characteristic of a group of balls is roundness, but that is not the essential characteristic of a group of balloons. Getting similarity wrong makes you get essentials wrong, which makes you get definitions wrong, which throws all thought into confusion.
Is the essential of friendship mutual esteem, or companionship? Your answer to that will determine your attitude toward people you call friends. Is the essential of government that it is an agent, or that it is a ruler? Tom Jefferson said agent, and helped found a nation on that definition. But we are still arguing about the definition of "agent." Is the essential of "agent" what Jefferson said, that it helps us protect ourselves and our property? Or is it what others say, that it takes care of us? If that is the case, how does the definition separate an agent from one who takes care of subjects—a ruler?
That shows the motive for using inessential characteristics to get definitions wrong on purpose. The motive is often called subjectivism. The subjectivist decides before looking at reality how things should be, and chooses "essentials" accordingly. If balloons should be round, then that is chosen for an essential, and other inflated shapes will have to be called something else.
The subjectivist is doomed to a life of frustration, because reality is always what it is, and never what it should be. Since essentials are chosen by the wrong method, everything is defined wrong, and elaborate explanations only increase the confusion. The subjectivist gives up by deciding that the essential of efficacy is not action but intention. He cannot do well, but at least he means well.
To make sure your definitions use only essentials, trace them back to similarity. What is the common characteristic that makes all of the genus similar? What is the more restrictive characteristic that differentiates the group you want from the rest of the genus, but keeps the similarity of that group? As long as you keep objective similarity, you can make definitions in many useful ways without getting them wrong.
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