“Chapter 6. Definitions” in “Critical Thinking, Logic, and Argument”
Chapter6Definitions
6.1 Definition and Language Use
The meaning of a term in effect classifies what the term refers to. Definitions tell you what a term means. There is an intimate connection between definition and classification. The meaning that a term has is not a natural property of the term that could be discovered by investigation; a term has whatever meaning it has been given by the people using the term. Of course, some terms—for example, “water” or “gold”—refer to natural kinds of things, and the properties of those natural kinds are discovered by investigation and observation. Of course, not all parts of the natural world are as easy to define as molecules (water) and elements (gold), not to mention the social and imaginary world that language also describes.
Generally speaking, language users agree on what terms to use to pick out specific parts of the world, but this is not entirely arbitrary. The terms we use are, in some part, a consequence of the kind of thing in question. The meanings of words are a function of social practice stipulated by users, so it is important for successful communication that all the parties in an argument are using terms in the same way to mean the same thing.
For example, imagine two people are having a discussion about the moral permissibility of abortion. One person says it is impermissible and the other person says it is permissible. What if they are not using the word “abortion” to mean the same thing? What if one of them has defined abortion as terminating a pregnancy after three months (and is arguing that it is morally wrong)? What if the other one defines abortion as terminating a pregnancy before three months (and argues that it is morally permissible)? Do these two people really disagree? Is it possible that they both agree that abortions should not be allowed after three months?
Consider the disagreement in figure 6.1. This is what is often called talking past each other. Now what would this look like if there was an agreed-upon definition as illustrated in 6.2? We don’t know if there is a disagreement. We would have to ask A what their position is with the stipulated definition.
Figure 6.1 An example of a disagreement using two different definitions. Artwork by Jessica Tang.
Figure 6.2 What happens to the disagreement (6.1) with a stipulated definition. Artwork by Jessica Tang.
6.2 Classification and Language Use
There is a kind of order to the natural world that is independent of the meanings that human beings use. Dogs, for example, exist quite independently of the fact that we have a word, “dog,” that we use to refer to them. The same is true of cats. Cats and dogs are both animals, but they are different kinds of animals, and if we used one word to refer to both species, they would still be different and we would need other words to distinguish them in thought (e.g., barking cats versus purring cats, or tail-wagging dogs versus not tail-wagging dogs).
It is important to keep in mind that the meaning of a term does not stand alone; terms stand in relation to other terms that also have meanings. One of the principal uses of definition is to clarify the relationships between terms. When the English dictionary (created by human users!) defines “dog” as a “domesticated canine animal,” it provides us with the meaning of the word “dog” by referring us to several other terms (“domesticated,” “canine,” and “animal”). If we know the meanings of those terms, we should know the meaning of “dog.” If we looked those terms up and then looked up the terms those terms were defined by, and we continued to look up terms in a dictionary, we would ultimately find a closed circle of terms, meaning all the terms we looked up would be defined by using other terms we had looked up already.
Since definitions classify or group things together that are the same or similar in some respects, the language as a whole functions as a giant classification system. You might even call a language a super set of classification systems, which allows us to group the things in the world in a variety of ways depending on our interests and needs. Furthermore, the ways we can distinguish the things in the world from each other reflect real differences in things and facts about the world that are there for us to discover. As a result, there is an enormous amount of factual knowledge about the world that is embedded in word meanings, and we can gain access to that knowledge simply by paying attention to definitions. So knowing what words mean gives us a great deal of knowledge of what the world is like. This is one reason it is important to know what words mean and to have a large usable vocabulary.
6.3 Definitions and Reference
Definitions have more than one function; we have mentioned so far how they tell us a term’s meaning. Another use of definition is to tell us what is and what is not included in the reference of a term. This is important because arguments use words, and the meanings of the words are necessary for the success of the argument. Recall the example of talking past each other. Thus, we must get good at stipulating definitions.
Well-constructed definitions can do this because the terms we use classify things in systematic ways. In the definition of “dog” as “domesticated canine animal,” for example, the term “domesticated” rules out the other members of the class of canine animals (wolves, coyotes, etc.) because they are not domesticated, the word “canine” rules out other classes of animals (rodents, felines, etc.), and the word “animal” rules out other classes of beings (plants, minerals, etc.). Not all classification systems are equally orderly. But the careful use of terms that have systematic definitional connections with other terms makes using the terms in arguments much easier. This is because there are many truths that simply follow from the meanings of the words.
A good definition of a term will have a number of important features. Dogs are mammals—every single one of them is a mammal—so if we know that something is a dog, then we know it will be a mammal as well. We can put this as being a mammal is a necessary or essential condition for being a dog. Another way of explaining this is with the visual here that demonstrates there are other mammals (in the larger circle), and dogs are wholly within the set of mammals. There are no non-mammal dogs.
Figure 6.3 The relationship between two properties. Artwork by Jessica Tang.
On the other hand, lots of non-dogs are mammals as well (cats and horses and sheep and humans . . .). Keep in mind with the visual, these circles are not representative of the proportion but rather the relationship of properties.
So “being a mammal” is not an adequate definition of being a dog, since it is too wide—while it does include all the dogs, it also includes many animals in the definition that are not dogs. Poodles are dogs—every single one of them is a dog—so if something is a poodle, we know it will be a dog as well. We can put this as being a poodle is a sufficient condition for being a dog. In other words, you don’t have to be a poodle to be a dog, but being a poodle is sufficient for being a dog.
We don’t need to point out that lots of non-poodles are dogs (dachshunds, boxers, shepherds, terriers, and so on), so “being a poodle” isn’t an adequate definition of a dog either, since it is too narrow—it would fail to include all the animals that are dogs. Thus we can provide a definition of an ideally adequate definition (of a dog):
Another way of describing these relations is by way of the terms “genus” and “species” (which are here used in a more general way than they are in biology today). We understand “genus” as a broad concept that includes narrower concepts that pick out subgroups from all the referents in the genus. We understand “species” as a narrower concept included under some genus. A species picks out one type of that larger class. Genus and species are relative terms. For example, dog is a species of mammal, but dog is a genus for poodle.
Figure 6.4 Illustration of necessary and sufficient conditions. Artwork by Jessica Tang.
6.4 Rules for a Good Definition
With these terms in mind, we can give six rules for a good definition.
Rule 1. A Good Definition of a Term X Shouldn’t Be Too Broad (Include Too Much)
We can also put this as the requirement that the definition state the sufficient conditions that a thing must meet in order to be X. This means that it should include only things that ordinary usage calls X.
Example 1 is too broad because just being an animal is not enough to pick a horse out from the world. The definition needs to pick out horses specifically. This would have to include the characteristics that differentiate it from other animals.
Example 2 is also too broad because while a mirror does reflect, and reflecting is one of its expressed purposes for human use, there are other things in the world that reflect that this definition would pick out (e.g., glass, smooth clear ponds). It would be more specific to define a mirror according to its common properties: smooth glass surface with reflective coating of a specific type for viewing. We were going to say “for viewing clear images,” but some mirrors are fuzzy. Do they stop being mirrors?
And in example 3, simply identifying soda as a beverage doesn’t do enough either. It is sufficient for being a beverage that something is a soda, but it is not jointly necessary and sufficient for a soda to define it as a beverage. To give a necessary and sufficient definition, we would say it’s a flavoured carbonated beverage. In coming up with that definition, we’re asking ourselves if there are non-flavoured sodas, or non-carbonated sodas (maybe if they go flat . . .), or non-beverage sodas. We can make an argument that defining soda as a flavoured carbonated beverage is adequate for our purposes.
Rule 2. The Definition Shouldn’t Be Too Narrow (Exclude Too Much)
A good definition of a term X should state the necessary conditions for meeting the definition. This means that it should include in the definition all the things that ordinary usage calls X.
Example 1 is too narrow because it excludes people who are naturalized citizens. Again, we can always ask ourselves, Is being born in Canada necessary for being a citizen? It isn’t, since you can immigrate and acquire citizenship. It is certainly a sufficient condition—if you are born in Canada (and not born to foreign diplomats), you are a citizen. This is because Canada has something called “birthright citizenship,” and only some countries have this.
Example 2 is too narrow, since some games are cooperative (e.g., Pandemic), and some games don’t have explicit rules (e.g., pretend). In this case, “game” is going to be notoriously difficult to define, since there are games that do not keep score, games that are played against yourself, and games with no point whatsoever. So “games” will require a nuanced definition.
Example 3 is also too narrow. It uses one aspect of critical thinking—avoiding fallacies—and identifies it as standing in for all the qualities of critical thinking. It represents a feature that is necessary as if it is sufficient. Ask yourself, Is there anything else that this requires? What if we avoid fallacies but don’t have open minds about new information? Is being open-minded a quality of critical thinking? This is a much more difficult definition than those for “horse” or “violin.”
Rule 3. A Good Definition of a Term X Should Avoid Vagueness and Obscurity
The point of definition is clarity; it shouldn’t be harder for your audience to understand the definition of X than to understand the word X itself. This is also an important skill in writing summaries. In explaining someone’s view in a summary it should be easier to understand than the original work being summarized. Obscurity and vagueness often go together. Vagueness is a general lack of clarity, and one reason a definition might be unclear is because it is obscure, meaning using words that are out of use, overly clunky, or hide meaning (when the purpose of a definition is to illuminate).
Example 1 is simultaneously obscure and vague. It uses a bunch of overly complex words that don’t normally go together instead of simple words. Compare using the word “people” versus using “multitude of human inhabitants.” Using “multitude of human inhabitants” creates so many openings for interpretation, it doesn’t actually help the reader understand the original term (political party). Because of this unnecessary complexity, the definition is vague, meaning open to various understandings and therefore hard for your audience to understand.
Example 2 is also obscure and vague. What does it mean for a feeling to be meaningful? Responsive to what? From this definition, you are no further along in trying to understand what it means to be an empath.
Example 3 obscures by using a complex word, “transcendental,” without defining it.
Rule 4. A Good Definition of a Term X Must Not Be Circular (Define Itself)
A term cannot explain what its own meaning is. If we tell you that “podiatry” means the subject that a podiatrist practices but you don’t know what podiatry is, then the definition is useless, since it provides you with no information about how to use the term. Even if you already know what the term means, the definition doesn’t add anything. Circularity is also a problem with arguments, which we will discuss with fallacies.
Example 1 fails to explain the necessary and sufficient conditions for “detoxification.” Indeed, it uses the word “toxin,” which is part of the word “detoxification,” and thus this definition basically says “detox detoxifies.” Do you understand detoxification yet? Maybe it would be helpful to say that the liver filters chemicals or impurities out of the bloodstream. This definition is perhaps too narrow, since you might be able to detox things other than a body. But if we think of it as bodily detoxification, we’d need a stipulated definition of the process and what is being filtered from where.
Example 2 fails to explain “good business” because it basically repeats itself. It just defines good as successful, which is really close to the same thing. Here, good is being explained by “successful.” Are we any further in understanding “good business”?
Example 3 defines “free market” as a “market without restrictions.” This gives us a bit of information about restrictions, but we have to ask ourselves whether explaining free as “without restrictions” adds much of anything to our understanding. Are you any further along in understanding what a free market is?
Rule 5. A Good Definition of a Term X Should Not Be Negative (Unless Absolutely Necessary)
Negative definitions define a thing by what it is not rather than by what it is. For this reason, negative definitions are quite uninformative and they are also usually either too broad or too narrow. If we tell you that a cat is a domesticated animal that is not a dog or a horse, we have not ruled out enough (e.g., donkeys), but more importantly, we haven’t said anything positive about what makes something a cat.
All three examples are uninformative. They tell us what something is not, but they still include all the things it might be. So a sandal is not a shoe, but it might be a walrus, a laptop, a lamp, and so on. Either you have to say all of the things it isn’t, or you need to give an informative definition of what it is. In other words, you have to say what something is, which means you need to say something positive. Contrast “a desk is not a table” with “a desk is a flat surface used for working.”
This might seem like a tangent, but we think it illuminates what is wrong with negative definitions. When Starbucks was first breaking into the coffee market, there was a language change from “skim milk” to “non-fat milk.” This move to “non-fat milk” is interesting. “Skim milk” conveyed that the milk had fat skimmed out, but non-fat milk makes it seem like the milk is “all things except fat plus milk.” It is a weird point, but the idea here would be that telling us it doesn’t have fat doesn’t necessarily tell us what’s in it.
Rule 6. A Good Definition Should Not Be Slanted or Biased
Slanted definitions do not really state the necessary or sufficient conditions of being X, but they instead express the (positive or negative) attitudes or biases of the speaker toward the thing being defined. For example, if we tell you that politicians are professional liars who live off the public purse, we have not given you either necessary or sufficient conditions but instead have given a negative value judgment about politicians.
Two examples of defining “protestor” should demonstrate how both negative and positive evaluations can find their way into definitions. It would be more accurate to say that protestors are those who engage in acts of public demonstration to bring forth social and/or governmental change. This is perhaps a bit narrow, but it is at least neutral in attitude.
Example 3 uses the term “destructive,” which is biased, and then it adds a religious judgment about offending God. It would be best to say what euthanasia is without sentiment. If people want to argue about whether it is destructive or religiously offensive, then they can give reasons outside of the definition for that. Generally, “euthanasia” is ideally a consensual killing or letting die by active or passive means to someone who is experiencing intractable pain or a debilitating progressive and terminal illness. Hopefully taken together, this rules out the kinds of killings we would want to rule out.
It is possible for a definition to be both too broad and too narrow at the same time. For example, the definition “a swimming pool is an enclosed, artificially constructed area of water intended for public use” is both too broad and too narrow at once. It is too broad because it includes wading pools and fountains and other things that are not swimming pools. It is also too narrow because not all swimming pools are intended for public use; some swimming pools are privately owned.
Here is another example: a dog is a short-haired pet with four legs and paws rather than hoofs. This definition is too narrow in two different ways because it mentions two inessential characteristics. It excludes dogs with long hair, but it also excludes dogs that are not pets. Neither being a pet nor having long hair has anything essential to do with being a dog.
Key Takeaways
- • When arguing, users need to agree on using terms in the same way in order to successfully communicate.
- • Definitions can tell us a term’s meaning, but they can also help us determine what is not included in the reference of a term. Definitions stand in relation to each other.
- • Definitions are composed primarily of essential features that a thing must have if the term is to apply to them. Knowledge is embedded in definitions.
- • An adequate definition is one in which all parts of the definition are, when taken together, jointly necessary and sufficient.
- • Six rules for a good definition: the definition is not too broad, it is not too narrow, it avoids vagueness or obscurity, it is not circular, it is not negative, and it is not slanted or biased.
Exercises for Rules for Definitions
Evaluating Definitions
Here is a list of one-liner definitions; imagine that they are in a small pocket dictionary. Trying to be charitable, evaluate these definitions. Are they adequate, or are they too broad, too narrow, vague or obscure, circular, negative, or slanted?
- 1. The Conservative Party is a political organization of patriotic, civic-minded citizens dedicated to preserving the cherished freedoms of all Canadians.
- 2. A kite is a toy consisting of a light frame, with paper or other thin material stretched upon it, to be flown in a strong wind by means of a string attached and with a tail to balance it.
- 3. “Democracy” is not a feudal system.
- 4. “Postmodern” means a chaotic and confusing mishmash of images and references that leaves readers and viewers longing for the days of a good, well-told story.
- 5. An oar is a stout pole shaped into a wide and flat blade at one end that is held free hand and used to propel a boat through the water.
- 6. A poem is a rhymed composition in verse.
- 7. “Rectangle” means a two-dimensional figure with four sides.
- 8. A programmer is one who applies model C45D to seven-second ratios.
- 9. Life is what you make of it.
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