Part 12 of Ideas and Terms: Definition and Division
It has constantly been pointed out that clearness of ideas is essential to correct thinking. Vagueness and confusion are the greatest obstacles to clear thinking in the pursuit of truth. How many arguments could be quickly settled if only we made our ideas clear!
Our ideas will be clear when we have an accurate knowledge of their comprehension and extension. The comprehension, you will recall, tells us what the idea implies, what essential attributes or elements it contains in itself, and what information it has concerning the thing it represents.
Again, you will recall that the extension of an idea gives us the application of the idea to the individuals, shows us how and in how many objects the idea is realized, and delimits the extent of the field in which this idea can be found.
The comprehension and extension of ideas is very important to understand. Fortunately, there are two processes that will help us to gauge the comprehension and extension of ideas: definition and division.
A definition is a statement which explains what a thing is. It answers the question: “What is this thing?” We can give the answer when we know the comprehension of the idea which represents this thing.
There are different kinds of definitions and we need to be aware of these differences.
We distinguish between nominal definitions and real definitions. A nominal definition simply explains what a word means. A real definition explains what a thing is.
There are many times that a term is unclear or ambiguous to us. There are times it may be used in some “technical” sense, for instance in some branch of empirical science. There are times a particular speaker or writer wants to use a term in a definite meaning in order to avoid verbal disputes. In these cases, a nominal definition is a legitimate definition.
A real definition, on the other hand, is a statement explaining what a thing is in itself. A perfect real definition would be one which briefly but fully explains the essential nature of a thing. But there are so many different kinds of things in the world and things are often too complex in operation and structure, it is difficult to distinguish sometimes between their essentials and nonessentials.
A real definition is an essential definition when it explains the essence or nature of a thing. This means we have to define it by its proximate genus and specific differentia. This would be the perfect definition.
The proximate genus includes within its comprehension all the essential elements of the genera above it and therefore includes all the things that are similar in nature to the thing which is to be defined. The specific differentia brings the distinctive element which separates this thing from all others of a similar nature, by showing in what manner it is different from all the others. This may seem complicated to you but it really isn’t. Just to be sure we’re clear on this matter of proximate genus and specific differentia, we’ll look at an example of this in practice.
A real definition is a descriptive definition when it explains what a thing is in itself by enumerating the positive, but nonessential, elements of its nature.
We must recognize that certain terms and ideas and things are incapable of definition. They are known, but not defined.
Some qualities are so simple they cannot be analyzed, only experienced. For example, how would we explain to a blind person what the “red” of a rose looks like?
Some ideas are so general they cannot be defined by a strict definition. “Thing,” “one,” and “being” are examples.
Rules of Definition
Certain rules have been devised to ensure that a definition is correct. Let’s take a look at them.
1. The definition must be clearer than the thing defined. Metaphorical expressions, therefore, need to be avoided. In other words, don’t define a “lion” as the “king of beasts.” Metaphors are fine for poetry but not for logical thinking. Words which are more unusual than the idea to be explained should be avoided. Don’t define a “lie” as an “intentional terminological inexactitude.”
2. The definition must not contain the idea to be defined. Don’t make a “circular definition.” This is where a first idea is defined by a second, and then the second is defined by the first. If we define a “dollar” as “one hundred cents” and then define a “cent” as “one-hundredth of a dollar,” we would be guilty of a circular definition.
3. The definition must be convertible with the idea defined. The definition must not be wider or narrower in comprehension than the comprehension of the idea defined. If an “animal” is a sentient, living, bodily substance,” then a “sentient, living, bodily substance” must be an “animal.” On the other hand, we shouldn’t define “biology” as the “science which studies the world around us.” This is too wide a definition since other sciences also study the world around us. We shouldn’t define “biology” as the “science which studies animals,” because it is too narrow. Biology also studies plants.
4. Finally, the definition must be positive, not negative, whenever possible. A definition should explain what a thing is; not what it is not. “Health” is not the absence of sickness. I can’t know what sickness is without prior knowledge of what “health” means.
Besides definition, we have a second method of making ideas clear and arriving at a better understanding of their meaning. This method is called division.
Division means the resolving of a whole into its parts. Something is “whole” when it consists of parts which are bound together into some sort of unity. Since the “whole” consists of parts, it can be broken up (resolved) into these component parts. There are two kinds of division.
A real division is the resolution of a thing into the natural parts which it has independent of the mind. If these parts are physical, we have a physical division. If the parts are metaphysical, we have a metaphysical division.
Rules of Division
Logicians have certain rules which must be observed in division so that it fulfills its purpose of making ideas clear and accurate for science and for general knowledge. Here are the rules:
Rule 1. A division should be adequate. This means that all the parts taken together must equal the whole. There are a number of sections to this rule.
- No part may be omitted or the division is incomplete and faulty. Think, for instance, of the term “American politician.” If we divided this term into Democrats and Republicans, the division would be inadequate because some politicians, such as Socialists, Libertarians, Progressives, and so forth, would be omitted.
- No member of the division may equal or exceed the whole. A part can never equal and certainly cannot exceed the whole. It would be improper to divide the term “animals” into sentient and rational because sentient is the same as or equal to animal.
- No member may include the other. The parts must be distinct and exclusive among themselves. Such a division would enumerate more parts than the whole really contains. It would be incorrect to divide “Immigrants to America” into Englishmen, Germans, Europeans, Japanese, Asians, and Mexicans, because Englishmen and Germans are already included in the class of “Europeans” and Japanese are already included in the class of “Asians.”
Rule 2. The division should be clear. Here are the sections pertaining to this rule.
- A division should be orderly. We must not leap from a higher to a lower class and omit a middle class. The division should be a gradual process. It would be improper to divide “animals” into men, birds, reptiles, insects, fish, and mammals, because the next members of the class of “animals” are human beings and nonhuman animals.
- A division should be reasonably limited in members. To divide “insects” by producing a list of the thousands of names of insects would be ridiculous. Fortunately, empirical science enters the picture here with its taxonomic classifications whereby it organizes numerous insects, birds, and other animals into main classes, subclasses, and so on. This is an excellent example of science bringing order out of chaos.
Dr. Jonathan Dolhenty was the Founder and President of The Center for Applied Philosophy and the Radical Academy, and is Honorary Philosophy Editor at Self-Educated American. Self-Educated American has adopted these projects beginning with a republishing and preserving of all of Dr. Dolhenty’s work.
Self-Educated American recommends: Great Books of the Western World