6.2.1. Individual terms

The chief examples of individual terms are proper names, for the central function of a proper name is to refer to the bearer of the name. But a proper name is not the only sort of expression that refers to an individual; the phrase the first U. S. president serves as well as the name George Washington. In general, descriptive phrases coupled with the definite article the at least purport to refer of individuals. These phrases are the definite descriptions discussed briefly in 1.3.4, and we have been counting them as individual terms. Still other examples of individual terms can be found in nouns and noun phrases modified by possessives—for example, Mt. Vernon’s most famous owner. Indeed, expressions of this sort can generally be paraphrased by definite descriptions (such as the most famous owner of Mt. Vernon). Still examples of expressions that refer to individuals are demonstrative pronouns this and that and other pronouns whose references are determined by the context of use—such as I, you, and certain uses of third person pronouns. On the other hand, anaphoric pronouns, pronouns that have other noun phrases as their antecedents, do not refer independently even though they play much the same grammatical role as expressions we do count as individual terms.

There is no traditional grammatical category or part of speech that includes individual terms but no other expressions. In particular, the class of nouns and noun phrases is too broad because it includes simple common nouns, such as president, as well as quantifier phrases—such no president, every president, or a president. And neither common nouns nor quantifier phrases make the kind of reference that is required for an individual term.

The following table collects the examples we have just seen on both sides of the line between individual terms and other noun phrases:

In a moment, we will look further at the reasons for drawing the line in this way; but one way of seeing the difference between individual terms and other nouns and noun phrases is to note that, while a proper name or a definite description provides a direct answer to the question Which person, place, thing, or idea are you referring to?, a common noun or quantifier phrase either provides no answer at all or, as in the case of a president, constitutes only an incomplete or evasive one.

Perhaps the most that can be done in general by way of defining the idea of an individual term is to give the following rough semantic description: an individual term is

At any rate, this formula can be elaborated to explain the reasons for rejecting the noun phrases at the right of the table above.

The formula above is intended as a somewhat more precise statement of the idea that an individual term names a person, place, thing or idea. It uses object in place of the list person, place, thing, or idea partly for compactness and partly because that list is incomplete. Indeed it would be hard to ever list all the kinds of things that might be referred to by individual terms. If the term object and other terms like entity, individual, and thing are used in a broad abstract sense, they can apply to anything that an individual term might refer to. In particular, in this sort of usage, these terms apply to people. The main force of the formula above then lies in the ideas of referring to a single thing and referring in a definite way.

The requirement that reference be to a single thing rules out most of noun phrases on the right of the table above. First of all, if a common noun can be said to refer at all, it refers not to a single thing but to a class, such as the class of all presidents. Now this class can be thought of as a single thing and can be referred to by the definite description just used—i.e., the class of all presidents—but the common noun president refers to this class in a different way. Common nouns are sometimes labeled general terms and distinguished from singular terms, an alternative label for individual terms. The function of a general term is to indicate a general kind (e.g., dogs) from which individual things may be picked out rather than to pick out a single thing of that kind (e.g., Spot), as an individual term does. Thus the individual term the first U. S. president picks out an individual within the class indicated by the common noun president; and the class of all presidents picks out an individual within the class indicated by the common noun class. That is, a general term indicates a range of objects from which a particular object might be chosen while an individual term picks out a particular object. Although there is much that might be said about the role of general terms in deductive reasoning, we will never identify them as separate components in our analyses of logical form, and the word term without qualification will be used as an abbreviated alternative to individual term.

The remaining noun phrases at the right of the table are like individual terms in making use of a common noun’s indication of a class of objects. However, they do not do this to pick out a single member of the class but instead to contribute to claims made about the class as a whole. The claims to which they contribute can all be described roughly as saying something about the number of members of a class that have or lack a certain property, and that is the reason for describing them as quantifier phrases. It’s probably clear that the phrases every president and no president, even though they are grammatically singular, do not serve the function of picking out a single object. But that may be less clear in the case of a president.

Sentences containing quantifier phrases like a president and some president share with those containing definite descriptions, such as the president, the feature that they can be true because of a fact about a single object. For example, The first U. S. president wore false teeth and A president wore false teeth can be said to both be true because of a fact about Washington. The difference between the two sorts of expression can be seen by considering what might make such sentences false. If Washington had not worn false teeth, The first U. S. president wore false teeth would be false but A president wore false teeth might still be true. That’s because the second could be true because of facts about many different presidents (in many different countries), so its truth is not tied to facts about any one of them. It would be made false only by a fact about all presidents. So the expression a president does not function to single out a particular president facts about whom will determine the truth of a sentence which has this expression as its subject. It merely marks the claim that there is at least one example of a president of whom the predicate is true. If the expression a president is thought of as referring at all, its reference is an indefinite one. This is one reason for adding the qualification definite to the formula for individual terms given above, but this qualification also serves as a reminder that the presence of a definite article marks an individual term while an indefinite article indicates a quantifier phrase.

The hedge or purports to refer used in the formula acknowledges the fact that not all individual terms actually succeed in picking out an individual as their reference. In spite of notorious exceptions like the name Santa Claus, proper names can usually be relied on to refer to something. But definite descriptions succeed in referring only when there is something that fits the description they offer and that does so without real competition. Mathematicians sometimes speak of these two requirements for a definite description to make a definite reference as existence and uniqueness. Both must be met before a mathematician can speak of, say, the solution of a certain equation; there must be a solution (the solution must exist) and there must be no more than one (the solution must be unique). When a description does not have these two properties, a definite description employing it does not succeed in referring to an individual; if there is no solution or more than one, the phrase the solution does not refer.

At least this is so for the strictest and most explicit use of language. In most cases where a description is fulfilled by several entities, something in the context will distinguish one among them, and this one will be taken as the reference of the definite description. In such cases, the definite description functions as if the description it contains was more specific than its explicit statement suggests and the requirement of uniqueness really was satisfied. That is, we will understand, for example, the college as perhaps the college (we all know and love) and the task as perhaps the task (at hand). The philosopher David Lewis (1941-2001) suggested that definite descriptions drew on a general contextual feature of salience. One way of using this idea is to think of the X as the (most salient) X.

Of course, existence, too, may fail; there may be no entity at all that fulfills the description. As was noted in 1.3.4, we assume that every individual term has a reference value. When the term succeeds in referring, this reference value is the individual the term refers to. When a term does not refer to anything, we say that the term is undefined and its reference value is an empty or nil value. It is natural to assume that there is just one nil value that is shared by all undefined terms. That is because reference values are extensions in the sense of 2.1.7 and are intended to capture only the object of reference, not all aspects of meaning. When an individual term has a defined reference, its reference value is the same no matter how the reference was made. This is why, in the example used in 2.1.7, the definite descriptions the author of Poor Richard’s Almanack and the inventor of the lightning rod both have the same reference value. And, while undefined terms may refer in different ways, all are alike in what they refer to because none of them refers to anything.