# 6.3: Definition

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## Definition and Meaning

The sloppy or misleading use of ordinary language can seriously limit our ability to create and communicate valid reasoning. As philosopher John Locke pointed out three centuries ago, the achievement of human knowledge is often hampered by the use of words without fixed signification. Needless controversy is sometimes produced and perpetuated by an unacknowledged ambiguity in the application of key terms. We can distinguish disputes of three sorts:

• Genuine disputes involve disagreement about whether or not some specific proposition is true. Since the people engaged in a genuine dispute agree on the meaning of the words by means of which they convey their respective positions, each of them can propose and assess logical arguments that might eventually lead to a resolution of their differences.
• Merely verbal disputes, on the other hand, arise entirely from ambiguities in the language used to express the positions of the disputants. A verbal dispute disappears entirely once the people involved arrive at an agreement on the meaning of their terms, since doing so reveals their underlying agreement in belief.
• Verbal—but also fundamentally genuine—disputes can occur as well, of course. In cases of this sort, the resolution of every ambiguity often only reveals an underlying genuine dispute. Once that’s been discovered, it can be addressed fruitfully by appropriate methods of reasoning. In the backyard barbecue setting, for instance, sometimes it is important to deconstruct the verbal argument all the way back to its definitive grounds. Sometimes, this means looking a term up in a dictionary or clarifying the history of a concept or idea.

We can save a lot of time, sharpen our reasoning abilities, and communicate with each other more effectively if we watch for disagreements about the meaning of words and try to resolve them whenever we can. (1)

## Kinds of Definition

The most common way of preventing or eliminating differences in the use of languages is by agreeing on the definition of our terms. Since these explicit accounts of the meaning of a word or phrase can be offered in distinct contexts and employed in the service of different goals, it’s useful to distinguish definitions of several kinds:

• lexical definition simply reports the way in which a term is already used within a language community. The goal here is to inform someone else of the accepted meaning of the term, so the definition is more or less correct depending upon the accuracy with which it captures that usage. In these passages, my definitions of technical terms of logic are lexical because they are intended to inform you about the way in which these terms are actually employed within the discipline of logic.
• At the other extreme, a stipulative definition freely assigns meaning to a completely new term, creating a usage that had never previously existed. Since the goal in this case is to propose the adoption of shared use of a novel term, there are no existing standards against which to compare it, and the definition is always correct (though it might fail to win acceptance if it turns out to be inappropriate or useless). If I now decree that we will henceforth refer to Presidential speeches delivered in French as “glorsherfs,” for instance, I have made a (probably pointless) stipulative definition. The idea of “national security” is a concept of stipulation. If a federal agent felt that he needed to commandeer my vehicle, he might do so under an edict of “national security.” Whether he took my car to pursue a criminal or he used it to run to the corner store for a sandwich, the wide-reaching qualities of the term allow for a stipulative use of the vehicle.
• Combining these two techniques is often an effective way to reduce the vagueness of a word or phrase. These rhetorical definitions begin with the lexical definition of a term but then propose to sharpen it by stipulating more narrow limits on its use. Here, the lexical part must be correct and the stipulative portion should appropriately reduce the troublesome vagueness. If the United States Postal Service announces that “proper notification of a change of address” means that an official form containing the relevant information must be received by the local post office no later than four days prior to the effective date of the change, it has offered a (possibly useful) valid definition.
• Theoretical definitions are special cases of stipulative or rhetorical definition, distinguished by their attempt to establish the use of this term within the context of a broader intellectual framework. Since the adoption of any theoretical definition commits us to the acceptance of the theory of which it is an integral part, we are rightly cautious in agreeing to it. Newton’s definition of the terms “mass” and “inertia” carried with them a commitment to (at least part of) his theories about the conditions in which physical objects move.
• Finally, what some logicians call a persuasive definition is an attempt to attach emotive meaning to the use of a term. Since this can only serve to confuse the literal meaning of the term, persuasive definitions have no legitimate use. (1)

## Extension and Intension

A rather large and especially useful portion of our active vocabularies is taken up by general terms, words, or phrases that stand for whole groups of individual things sharing a common attribute. But there are two distinct ways of thinking about the meaning of any such term.

The extension of a general term is just the collection of individual things to which it is correctly applied. Thus, the extension of the word “chair” includes every chair that is (or ever has been or ever will be) in the world. Theintension of a general term, on the other hand, is the set of features which are shared by everything to which it applies. Thus, the intension of the word “chair” is (something like) “a piece of furniture designed to be sat upon by one person at a time.”

Clearly, these two kinds of meaning are closely connected. We usually suppose that the intension of a concept or term determines its extension—that we decide whether or not each newly-encountered piece of furniture belongs among the chairs by seeing whether or not it has the relevant features, for instance. Thus, as the intension of a general term increases, by specifying with greater detail those features that a thing must have in order for it to apply, the term’s extension tends to decrease, since fewer items now qualify for its application. (1)

## Denotative and Connotative Definitions

With the distinction between extension and intension in mind, it is possible to approach the definition of a general term (concerning any of the types of previously discussed definitions) in either of two ways:

denotative definition tries to identify the extension of the term in question. Thus, we could provide a denotative definition of the phrase “this rhetoric class” simply by listing all of our names. Since a complete enumeration of the things to which a general term applies would be cumbersome or inconvenient in many cases, though, we commonly pursue the same goal by listing smaller groups of individuals or by offering a few examples instead. In fact, some philosophers have held that the most primitive denotative definitions in any language involve no more than pointing at a single example to which the term properly applies.

But there seem to be some important terms for which denotative definition is entirely impossible. The phrase “my grandchildren” makes perfect sense, for example, but since it presently has no extension, there is no way to indicate its membership by enumeration or example. In order to define terms of this sort at all, and in order to more conveniently define general terms of every variety, we naturally rely upon the second mode of definition.

connotative definition expresses the contemporary attitudes that adhere to a term through long usage. Language is fixed, so a term like “gay” has a continuous meaning that expresses such ideas as “happily exuberant” or “brilliant in color” (from the Merriam-Webster Dictionary), but it also has come to describe aspects of the homosexual community in the last half-century. Terms like “intimate” and “familiar” have remarkably similar denotative definitions, but the word “intimacy” carries connotations with it that society often equates with sex or romance. In many instances, arguments hinge on both the denotative (literal) definitions of terms as well as their connotative (social) definitions, and this can become a tricky point of contention for establishing the grounds of a debate. It is important for a speaker or writer to clearly define how they view a particular term, and this should happen fairly early in the argument that is being advanced. (1)

## Definition by Genus and Differentia

Classical logicians developed an especially effective method of constructing connotative definitions for general terms, by stating their genus and differentia . The basic notion is simple: we begin by identifying a familiar, broad category or kind (the genus ) to which everything our term signifies (along with things of other sorts) belongs; then we specify the distinctive features (the differentiae ) that set them apart from all the other things of this kind. My definition of the word “chair” earlier in this learning module, for example, identifies “piece of furniture” as the genus to which all chairs belong and then specifies “designed to be sat upon by one person at a time” as the differentiathat distinguishes them from couches, desks, etc.

Logicians Irving M. Copi and Carl Cohen list five rules by means of which to evaluate the success of connotative definitions by genus and differentia . A successful definition should:

1. Focus on essential features. Although the things to which a term applies may share many distinctive properties, not all of them equally indicate its true nature. Thus, for example, a definition of “human beings” as “featherless bipeds” isn’t very illuminating, even if does pick out the right individuals. A good definition tries to point out the features that are essential to the designation of things as members of the relevant group.
2. Avoid circularity. Since a circular definition uses the term being defined as part of its own definition, it can’t provide any useful information; either the audience already understands the meaning of the term, or it cannot understand the explanation that includes that term. Thus, for example, there isn’t much point in defining a “cordless ‘phone” as “a telephone that has no cord.”
3. Capture the correct extension. A good definition will apply to exactly the same things as the term being defined, no more and no less. There are several ways to go wrong. Consider alternative definitions of “bird”:
• “warm-blooded animal” is too broad, since that would include horses, dogs, and aardvarks along with birds.
• “feathered, egg-laying animal” is too narrow, since it excludes those birds who happen to be male.
• “small flying animal” is both too broad and too narrow, since it includes bats (which aren’t birds) and excludes ostriches (which are).

Successful intentional definitions must be satisfied by all and only those things that are included in the extension of the term they define.

4. Avoid figurative or obscure language. Since the point of a definition is to explain the meaning of a term to someone who is unfamiliar with its proper application, the use of language that doesn’t help such a person learn how to apply the term is pointless. Thus, “happiness is a warm puppy” may be a lovely thought, but it is a lousy definition.This doesn’t refute the value of figurative language in the argumentative process, as outlined earlier in the module. Figurative (picturesque and abstract) language is still important for clarifying concepts, reporting and describing features, and creating reader interest. It only means that most successful definitions, in and of themselves, take the form of direct and straightforward explanations.
5. Be affirmative rather than negative. It is always possible in principle to explain the application of a term by identifying literally everything to which it does not apply. In a few instances, this may be the only way to go: a proper definition of the mathematical term “infinite” might well be negative, for example. But in ordinary circumstances, a good definition uses positive designations whenever it is possible to do so. Defining an “honest person” as “someone who rarely lies” is a poor definition. Instead, an “honest person” might be “someone who does the just and truthful thing whenever possible” is more convincing.In the interests of advancing a personal (subjective) definition for a concept, however, negation can also be a useful tool in explaining an ideology or the boundaries of a standpoint. Negation is the act of defining something by illustrating what it is not. In a political debate on expanding social programs, for instance, a candidate might enumerate those areas in which expansion might be appropriate while also indicating which programs should either be untouched or reduced. He or she might make a statement as follows: “While I agree that our current budget is inadequate in funding programs to reduce homelessness, I am not advocating that we expand our spending on blight reduction or transportation.” Sometimes, explicitly stating any aspects of a subject that are being excluded during a contentious debate can be a positive move toward Rogerian compromise. (18)