1.6 Constructing Definitions
Definitions do not appear out of thin air. It’s up to us to construct our own. To come up with definitions that satisfy the rules we’ve learned, we need a procedure we can follow—a technique for constructing definitions.
Of the six rules of definition, the first three are the most important. If you can find a genus and differentia that, together, are neither too broad nor too narrow, and that state the essential attributes of the referents of the concept, you can be pretty sure that your definition will satisfy the remaining three rules. We can think of those other rules as backup tests. To define a concept, therefore, the first step is to find the genus. Then look for a differentia that states the essential attributes of the referents and distinguishes them from other species of the same genus. Finally, double-check your definition by looking for counterexamples and by making sure that your definition is not circular, negative, or unclear. Let’s look a little more closely at each step. Then we’ll apply our techniques to a particular case.
If we start by finding the genus, it will make the rest of the job easier. Suppose we want to define CUP. We would use what we know about classification to locate the concept in a genus–species hierarchy:
The diagram is titled, drinking vessel, with a large bracket on either side. It encloses its three types, namely: cup, mug, and glass.
Now we know that our definition will have the form, “A cup is a drinking vessel that ___.” And we’re in a good position to fill in the blank—to find the differentia. We know we have to distinguish cups from mugs and glasses, so we’ll look for properties such as shape or function that will best do the job.
In defining a term, we are concerned only with its literal meaning, not with any metaphorical use. A metaphor typically applies a concept from one genus to things in some other genus. An army, for example, is a military organization, but the term “army” is used metaphorically to describe nonmilitary groups that are similar in one way or another, such as an army of ants. If we tried to define ARMY in such a way as to include these metaphors, we couldn’t use MILITARY ORGANIZATION as the genus. Indeed, there is no genus we could use, because we could not possibly anticipate every metaphorical use of the term. But we don’t need to include the metaphorical uses. The purpose of a definition is to give the literal meaning of a concept.
When we choose a genus, we need to consider the appropriate level of abstraction. As noted, the genus of CUP would be DRINKING VESSEL. But a drinking vessel is a kind of utensil, which is a kind of tool, which is a kind of man-made object. Each of these terms is more abstract than the one before and covers a wider range of things. Any of them could serve as the genus. Why choose the narrowest one, DRINKING VESSEL? The answer lies in the rule that a definition should state essential attributes. If we choose UTENSIL as the genus for CUP, then our differentia would still have to include the information that a cup is a utensil used for drinking. That’s the function of a cup, and the function explains why a cup has a certain size and shape. The function is an essential attribute, so we might as well include it in the genus.
In contrast, we used ANIMAL as the genus in defining HUMAN, but this is not the narrowest genus. Humans are also vertebrates, mammals, and primates. Each of these terms is narrower, less abstract, than the one before. Again, any of them could serve as the genus. Why choose the wider genus, ANIMAL? Once again, we consider which features of humans are essential. The feature we share with other vertebrates, for example, is a spinal column. However important that feature of our anatomy may be, it is not as fundamental as the biological attributes we share with all animals: being alive, having needs for sustenance, reproducing, etc. Our similarities to other primates, mammals, or vertebrates are not as essential as our similarity to all animals. So unless we have a specialized purpose, as biologists do, there is no need to mention these other similarities. Remember that a definition is selective. Its purpose is to condense the information we have about a concept by stating only the fundamental facts.
The main thing to keep in mind when you look for a differentia is that it should distinguish the referents of the concept from the referents of other species in the same genus. It should name an attribute possessed by all the referents of the concept and not possessed by members of the other species; this will ensure that the definition is neither too broad nor too narrow (rule 2). You may be able to find many attributes shared by all the referents, but you should not include them all unless they are all necessary to distinguish the concept from other species in the genus. Once again, a definition should be selective, so look for the essential attribute (rule 3).
When we apply rule 2, we should keep in mind the possibility of borderline cases. Suppose we’re defining CITY. Cities are distinguished from other municipalities mainly on the basis of population. Our definition should thus include any place large enough to be considered a city and exclude any place too small. A place with 1,000 residents is obviously a village or town, while a metropolis of 2 million is clearly a city. But there is no sharp line between a large town and a small city. So how would we define CITY?
We have two choices. If we do not have any specialized need for precision, then we should define a city simply as a large metropolis. The term “large” clearly includes the metropolis of 2 million, it clearly excludes the village of 1,000, and it leaves the borderline area unclear. Thus it matches the content of the ordinary concept, including the indefinite areas around the borders. In general, we can expect a definition to help clarify boundaries, but we cannot expect it to set more definite boundaries than the concept itself has. However, if we do need a concept with a precise borderline, as we may if we are taking a census or doing economic research, then we will have to specify a precise criterion of population size and turn the concept into a technical one. A definition of this type is sometimes called a “precising definition.”
A precising definition is a special case of a more general type: the stipulative definition. A stipulative definition introduces a new word by specifying that it shall mean such and such. We may need to do this in the case of new technological products (e.g., blockchain software), new scientific discoveries (e.g., quarks), new professions (e.g., programming), and so forth. We may also need to give a new meaning to an old word; in physics, for example, “work” is defined as the product of the force applied to an object and its displacement in the direction of that force. Stipulative definitions are not subject to rule 2. Because the term being defined has no antecedent meaning, the definition cannot be too narrow or too broad. But this does not mean that such definitions are arbitrary. They are appropriate only when the referents of the new term are important enough, and distinctive enough, to require their own concept. And once we have created the new concept, its definition is still subject to rule 3: It should state the essential attributes of those referents.
When we apply rule 3 to a definition (whether stipulative or ordinary), there’s another qualification to keep in mind. As we have seen, an essential attribute is one that underlies and explains other attributes of the referents. One of the goals of science is to identify such attributes. But it is not always appropriate to incorporate scientific theories when we define a concept for ordinary use. We can define water as the substance with the chemical structure H2O, because that chemical structure, which explains many of the other properties of water, is so well established that it has become common knowledge. But it would not be appropriate to define man as the animal with the most complex brain—even though that complexity is likely to be what gives us our capacity for reason. The problem here is that the relationships between the brain and reason are not very well known yet; the available theories are speculative and incomplete, and it wouldn’t serve our purpose to incorporate them into a definition. So the rule of essentiality must be qualified: The differentia should name the most essential attributes that are fairly well understood.
SOLVE Constructing Definitions
To construct a definition for a concept C:
Find the genus of the concept—the broader concept that includes C and other, related concepts from which one needs to distinguish C.
Choose a differentia that distinguishes C from other concepts in the same genus. If there is more than one distinguishing attribute, choose the most essential one.
Check to make sure that the resulting definition is not circular, unnecessarily negative, or unclear.
Look for counterexamples to your definition.
For the same reason, it is not a good idea to include controversial information in a definition. Our concepts, and the definitions we give them, provide the framework for thought and discussion. Ideally, the framework should be a neutral one, so that people on opposite sides of an issue can rely on a common understanding of the relevant concepts in presenting their arguments and thus understand each other. I may be convinced, for example, that psychological depression results from repressed anxiety, but this theory about the unconscious cause of depression is controversial. If I’m going to discuss the matter with a psychologist who rejects that theory, we should define depression in terms of properties we can agree on, such as the conscious feelings involved.
Once we have established the genus and differentia, the final step is to test our definition. We should make sure that it is not circular, that it is not negative (unless the concept itself is a negative one), and that it does not use vague, obscure, or metaphorical language. And we should make an effort to find counterexamples. That is, we should look for things that are included in the concept but would be excluded by the definition: They would prove that the definition is too narrow. And we should look for things that are not included in the concept, but would be included by the definition; in that case, our definition is too broad. If we have looked for counterexamples and haven’t found any, then we can be more confident that our definition is correct.
Let’s see how the general procedure works in practice by trying to define the concept GAME. This is a fairly abstract concept, covering indoor games played with cards, boards, or dice; outdoor games played with balls; races of all kinds; and even simple things like throwing a ball against a wall and catching it before it hits the ground. Let’s see whether we can come up with a definition that covers all of these diverse activities.
As usual, we should start by looking for the genus. A game is a kind of human activity, so we need to contrast it with other human activities. The first thing that should occur to us is that games can be contrasted with jobs. There’s a basic difference between working and playing; games belong in the second category. Of course, people sometimes describe their jobs as games, as in “I’m in the real-estate game.” But this is clearly a metaphor: It’s intended to startle the listener precisely because a job is not literally a game. So games belong in the genus we’ve described as “play.” To make it clear that we are talking about the leisure activities of adults as well as children, let’s use the term recreation. What else does this genus include? In addition to games, RECREATION includes activities such as hobbies and pastimes, vacation traveling, and dancing. Our classification now looks like this:
The diagram for Recreation with a large bracket on either side, encloses four types, namely: Games, Hobbies, Vacation, and Dancing. These types have a pair of smaller brackets each and appear beside each other at the bottom of the diagram. The diagram for Work, with a large bracket on either side, is blank.
This is not an exhaustive list of recreational activities. (Can you think of any others?) And of course recreation and work are not the only activities that human beings engage in. Among other things, we have left out family and social life. But this classification is enough for our purposes.
Before we turn to the differentia, let’s pause to consider the nature of the genus we have isolated. Recreation is an activity and so is work. The difference clearly has something to do with goals and rewards. It will help us to understand games if we explore this difference a little further. What goal does one pursue in work? Take a doctor as an example. In one respect, a doctor’s goal is restoring people to health: That is the function of medicine. In another respect, a doctor’s goal may be to make money, or to help people, or to use his mind in solving problems. Notice that the first goal is common to all doctors: Restoring health is a goal intrinsic to medicine; it is the function of medicine. However, the personal goals that doctors have are not intrinsic to medicine as a profession. They vary from one doctor to another; they’re a matter of the individual’s motivation. We could draw this same distinction between function and motivation in any line of work.
Now let’s consider recreation. Here, too, personal motivation differs from one individual to another. Some people play to relax, while others play to prove themselves; professional athletes and gamblers play for money. The common element in any given type of recreation, therefore, will have to be a goal intrinsic to the activity itself—a goal analogous to the function of a given line of work. This is where the essential difference lies between work and recreation. In any type of work, the function is producing a good or service that has value in its own right, apart from the activity of producing it. In recreation, the intrinsic goal is not productive in that sense. The activity is an end in itself, something we do merely for the sake of doing it. This would be true even for a professional athlete, who is being paid to play the game, to create an exciting spectacle that other people want to see. In that sense the athlete is working, not playing. But the game itself (football, golf, or whatever) is still a form of recreation because the goals internal to the game (getting a touchdown, sinking the putt) are not valuable in and of themselves. They have value only as elements in an activity that people value for its own sake.
Keeping all this in mind, let’s try to find a differentia that will distinguish games from other types of recreation. Some games are played with cards, others with balls, others with boards; some are physical, some are mental; some involve mostly skill, others mostly luck. So none of these properties can serve as our differentia, which has to be a property common to all the referents. What about competition between players? Most games do have a competitive element, but this definition would still be too narrow, because some games do not involve competition. Solitaire and sudoku are counterexamples. Couldn’t we say, though, that in these cases we are competing against ourselves? We often do describe solitary games this way. The problem is that this description is metaphorical. If we took it literally, it would mean that you are your own opponent. If you are competing against yourself, and you win, who loses?
But let’s not give up yet. When you play solitaire, you may not literally be competing, but it’s still true that you can win or lose. That’s because the rules of the game set a certain goal, such as turning up all the cards; if you achieve the goal, you win. Here we have something that looks like a universal property, and an essential one. What would a game be without rules? In every game, there is a set of rules that says what the goal is (the object of the game) and also says what means you can use to achieve the goal. This is what creates the challenge of a game and leads us to use the metaphor of competing with ourselves. Even in competitive games, the existence of rules is a more essential attribute than competition, because the rules create the competition: They specify the number of players and the terms on which they will compete.
Our definition, then, might be stated as follows:
A game is a form of recreation constituted by a set of rules that specify an object to be attained and the permissible means of attaining it.
Notice the word “constituted” here. It was carefully chosen to convey the idea that the very structure of the game depends on the rules. Notice also that the differentia fits in well with our analysis of the genus. We saw that recreation should not be distinguished from work in terms of personal goals. Either activity can be done for fun or profit. They should be distinguished rather in terms of the goals intrinsic to the activities. And our differentia tells us where a game’s internal goal comes from.
Let’s test the definition by looking for counterexamples. Is it too broad? Would it include anything that is not a game? It’s certainly true that other recreational activities are governed by rules. In skiing, there are traffic rules—you shouldn’t bump into other people. In stamp collecting, stealing the stamps you want would violate the law. But each of these rules is superimposed on an activity that could be done without them. They do not give the activity its goal; they merely impose external constraints on the means one can use. So these activities are not constituted by rules in the way our definition requires.
Is the definition too narrow? Would it exclude any games? What about throwing a ball against a wall and catching it? Well, in a sense, there is a rule here that specifies a goal and the permissible means: “Throw the ball against the wall and catch it before it bounces.” That isn’t much of a rule. But then this isn’t much of a game. It is not clear whether this activity satisfies our definition, but it’s equally unclear whether the activity should be considered a game. What we have here is a borderline case, and, as we have seen, we cannot demand that a definition have sharper boundaries than the concept it defines (unless we need to turn the concept into a technical one). All we can ask is that the definition include everything that is clearly a member of the concept, exclude everything that is clearly not a member, and leave the same set of borderline cases uncertain.
So far as we can see, therefore, our definition is a good one. You’ll have to decide for yourself whether you agree—perhaps there is something we have overlooked. But regardless of whether we agree on the outcome, the process of reasoning behind it illustrates the technique to follow in defining a concept.
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