The Term as a Part of a Proposition

The term must be defined from two points of view: from the point of view of its being a sign of a concept and from the point of view of its being the ultimate structural element into which a proposition is resolved. We shall define the oral term. (“Term” sometimes signifies the oral term, sometimes the mental term, and sometimes the written term, depending on the context.)

From the point of view of its being a sign of a concept, the oral term is defined as an articulate sound that serves as a conventional or arbitrary sign of a concept. We shall explain this definition at length in a later chapter. We mention it now only to call attention to the fact that logic does not deal with terms insofar as they are mere sounds or mere print on a page but only insofar as they are signs of thought and things—signs, that is, of concepts (or mental terms), mental propositions, and mental argumentation as well as of the things that are set before the mind by thought. This is clear from what we mean when we use words. For instance, when we say “The dog is wagging his tail,” we do not mean that the word dog is wagging its tail, but that an animal whose nature is signified by “dog” is wagging its tail. Hence, it is clearly not the mere word “dog” but what the word "dog” stands for that is the true subject of this proposition.

From the point of view of the term’s being the ultimate structural element into which a proposition and argumentation can be resolved, the term is defined as a word or group of words that can serve as the subject or predicate of a proposition. Thus, in the proposition “A dog is an animal,” the words "dog” and “animal’ are terms—“dog” is the subject and “animal” the predicate.

A term is simple if it consists of a single word, as in the examples given above.

A term is complex if it consists of a group of words that signify one thing or kind of thing when they are taken together as a unit. For instance, in the proposition “The black little cat-like animal with the white stripe down its back is a skunk,” the complete subject (“the black little cat-like animal with the white stripe down its back”) consists of a dozen words but still is only one term, because the dozen words constitute a single unit.

Sometimes we use “term” in a broader sense, as signifying any word or group of words that has meaning and that can be a part of a proposition either by itself or in combination with other words. In this sense, “black,” “little,” “cat-like,” “white,” and so on, are terms even when they are taken singly.

Most terms signify the quiddity, essence, or nature, of the thing or things they stand for; they express what a thing is or, more precisely, what kind of thing a thing is. “Quiddity” is derived from the Latin word quid, which means “what?”; hence, “quiddity” means “whatness.” In this context, “essence” and “nature” are nearly synonymous with “quiddity.” Terms that signify quiddities are called significant terms.

Significant terms signify concepts directly and immediately. Since concepts are mental representations of things, significant terms also signify things—but only indirectly and through the intermediacy of concepts.

Some terms merely point out things without signifying their quiddities or natures. Such terms are called nonsignificant terms [Note: In a certain sense, of course, all terms--including nonsignificant terms--signify something; mere nonsense syllables, which stand for nothing all, are not terms]. Demonstrative pronouns and adjectives (words, that is, like “this,” “that,” and “those”) are of this sort. When we say “This is what I’ll buy,” we are not expressing the nature of the thing we intend to buy, but are merely pointing it out. (“Demonstrative” is derived from demonstro, the Latin word for “I show, indicate, or point out.”)

Proper names are likewise nonsignificant terms, since they, too, merely indicate, or point out, an individual person or thing without expressing its nature. When we call a certain man Mr. Smith, for instance, we do not imply that he is a metal worker; and when we call a man Mr. Green, we do not imply that he is green. The proper names “Mr. Smith” and “Mr. Green” do not in any way signify what kind of man their bearer is.

On the one hand, we can consider the quiddity (essence, or nature) signified by a term, directing our attention to the intelligible elements involved in it—that is, to its definition and properties. If we do this, we are considering the COMPREHENSION of the term (and of the concept signified by the term), as when we think of a triangle as a plane figure bounded by three straight lines. On the other hand, we can consider the subjects whose quiddity (essence, or nature) is signified by the term as when we think of a triangle as being either equilateral, isosceles, or scalene. If we do this, we are considering its EXTENSION.

a. Comprehension

The comprehension of a term (or concept) is the sum total of the intelligible elements of the quiddity signified by the term (or concept ). These intelligible elements are referred to as notes. This sum total includes, in the first place, the basic elements that a thing has to have in order to be thought of as the kind of thing signified by the term; it includes, in the second place, whatever is deducible from these basic elements. It includes nothing, however, that a thing does not have to have in order to be the kind of thing signified by the term.

The comprehension of “man,” for instance, includes “rational, sentient, animate, corporeal substance” (the notes that are looked upon as basic to the quiddity of man), together with all the notes that are deducible from these, such as “capable of speech,” “social being,” “risible,” and “tool-using.” “Man” cannot be thought of, without contradiction, as lacking any of the elements belonging to the comprehension of “man.” If a man lacked any element of the comprehension of “man,” he would both be a man and not be a man—which is a contradiction and therefore impossible.

Notice how “capable of speech” adds nothing to the comprehension of “man” but merely expresses what is in it implicitly and deducible from it. All a being needs for speech is the ability to think (so he will have something to say) and the ability to make some kind of external movement that can serve as a sign of thought (so he will have something to say it with). As a rational animal, man has each of these abilities. Because he is rational, he has at least the basic ability to think and therefore to have something to say; because he is an animal (that is, a sentient, animate, corporeal substance), he has the ability to make some kind of movement, which is all he needs to express his thought. (These abilities may be undeveloped, as in infants and morons, or accidentally impeded, as in the insane.)

The comprehension of “man” does not include “tall, white, and European,” for a man can be thought of without contradiction as neither tall nor white nor European.

Note that the comprehension of a term is not limited to what we explicitly think of when we grasp the meaning of a term; nor does it include only those implications that we actually deduce from a quiddity. Comprehension is not subjective but objective. It includes all the intelligible elements objectively contained in a quiddity, whether we actually think of them or not. The comprehension of a term usually contains many notes of which we have no explicit knowledge at all. For instance, when an eight-year-old child grasps the quiddity of a right triangle, his concept has many implications of which he is completely ignorant. He does not know that the sum of the interior angles is 180°, that the square on the hypotenuse is equal to the sum of the squares on the sides, and so on. Nevertheless, these implications belong to the comprehension of his concept.

Our treatment of the predicables (especially of genus, specific difference, and property) and of definition will throw further light on the nature of comprehension.

b. Extension

The extension of a term includes the subjects signified by the term. Extension is either absolute or functional, depending on whether the term is considered in itself and outside of discourse or as a part of a proposition.

1. ABSOLUTE EXTENSION. The absolute extension of a term and concept is the sum total of the subjects—of the actual subjects as well as the possible subjects—whose quiddity (essence, or nature) is signified by the term and concept.

This sum total includes everything that has the comprehension of the term—both the kinds of things possessing it, such as genera and species, and the individuals possessing it. Thus, the term “man” includes in its extension all races of men of the past, present, and future; all individual men, both actual and possible; and even, in a way, the men of fiction and fairy tale. “Animal” includes both man and the irrational animals in its extension, for the entire comprehension of “animal” is realized in each of them. A man is an animal; a mouse is an animal; a mosquito is an animal; each of them has all the constitutive notes of “animal” (sentient, animate, corporeal substance) and all their implications.

The subjects whose quiddity (essence, or nature) is signified by a term are called its inferiors. In relation to them, the term itself is called a superior. “Man,” “brute,” “winged horse,” “dog,” “Rover,” and so on, are inferiors of the superior “animal.”

2. FUNCTIONAL EXTENSION. The functional extension of a term or concept includes only those subjects that it actually sets before the mind when it is used in discourse. In this sense, the extension of a term and concept is said to be universal, particular, or singular. It is universal if it sets before the mind each of the subjects whose nature it signifies; for instance, “every dog” and “each man.” It is particular if it sets before the mind an indeterminately designated portion of its total possible extension, as do “some men” and “a few animals.” It is singular if it sets before the mind one definitely designated individual or group, as do “this man,” “that team,” and “the tallest man in the room.”

This meaning of extension is very important in inference. We shall explain it fully after we have considered the inverse ratio of comprehension and extension and the division of terms into distributive, or divisive, and collective. We shall recur to it a second time when we take up the supposition of terms.

c. Inverse Ratio of Comprehension and Extension

In a series in which inferior terms are subordinated to superior terms (as in the series “man, animal, organism, body, substance”), the greater the comprehension of a term (and concept) the less its absolute extension, and vice versa. For instance, the comprehension of '“man” is greater than that of “animal.” Man is a rational animal; therefore “man” has all the comprehension of “animal” and, besides that, it also has “rational.” But the absolute extension of “animal” is greater than that of “man,” for it includes both men and the irrational animals. [Graphical diagram of the inverse ratio] If you start with “substance” at the top of the diagram and go down, you will see how, as the comprehension increases, the extension decreases. “Substance” has the least comprehension, but includes “angel,” “mineral,” “plant,” “brute,” and “man” in its extension; “body” includes “corporeal” in its comprehension, but omits “angel” from its extension; and so on. Thus, as the comprehension increases, the extension decreases, all the way to “man,” whose comprehension is the greatest of the series, including “rational, sentient, animate, corporeal substance,” but whose extension is the smallest, including only “man.”

If asked which of two terms has the greater comprehension, you must ask yourself two questions:

First you must ask yourself whether the terms are related as a superior and an inferior term. For instance, of the two terms “iron” and “silver,” you cannot say that either of them has greater comprehension than the other, because they are related as coordinate species rather than as superior and inferior terms—that is, you cannot say “Iron is silver” or “Silver is iron.” However, “metal” and “iron” are related as a superior and inferior term because “Iron is metal.”

Secondly you must ask yourself which of the two terms gives more information about the subject of which it is predicated—which term gives all the information that the other gives and something else besides. For instance, “iron” has greater comprehension than “metal” because the proposition “This is iron” tells me all that the proposition “This is metal” tells me and something else besides.

Does a term signify the quiddity (essence, or nature) of individuals taken singly or only of groups of individuals? The answer to this question is the basis for the division of terms into distributive, or divisive, and collective.

a. Distributive or Divisive

A term (and concept) is distributive, or divisive, if it signifies the quiddity (essence, or nature) of individuals taken singly; for instance, “soldier,” “player,” and “duck.”

b. Collective

A term (or concept) is collective if it signifies the quiddity (es¬ sence, or nature) of a group of individuals but not of those individuals taken singly. The individuals must have some note in common or must be related to one another in some way, so that the mind can grasp them together as a unit. “Army,” “team,” and “flock” are collective terms.

Terms like “family,” “herd,” “bevy,” “tribe,” “labor union,” and so on, are collective by their very nature, since they signify a group by their very definition and independently of the context in which they occur; moreover, the individual member of a family, herd, bevy, tribe, or labor union is not a family, herd, and so on, but only a part of one.

At this point we must call attention to the collective use of terms that are not collective by their very nature. For instance, in the proposition “All the ducks covered the entire pond,” the subject term “all the ducks” is used collectively. No single duck covered the entire pond but only all of them taken together as a group. Note, however, that the individual ducks of the group covering the entire pond are ducks, whereas the individual birds making up a flock are not a flock.

Note, too, that collective terms can be universal (“every herd”), particular (“some herd”), and singular (“this herd”).

A thorough understanding of the division of terms into singular, particular, and universal is an absolutely necessary prerequisite to the study of inference.

As we have seen, according to its first meaning, the extension of a term is the sum total of the subjects that the term can be applied to. This is called its absolute extension. According to a second meaning, the extension of a term includes only those subjects to which a term is actually applied in discourse. This is called its functional extension. In this latter sense, the extension of a term is said to be singular if the term is applied to one definitely designated individual or group; particular, if it is applied to an indeterminately designated portion of its absolute extension; and universal, if it is applied to each of the subjects to which it can be applied—that is, if it stands for each one of an unlimited class of subjects, or for its total absolute extension.

This division of terms is so important that we shall explain each of its members in detail.

a. Singular Terms

A term is singular if it stands for one individual or group and designates that individual or group definitely. (Notice that “individual does not mean “person” only but “person or thing.”)

Proper names, such as “Chicago,” “France,” and “John Jones,” are singular. Although many people have the name “John Jones,” still, when we use this name, we use it for one definite individual whom we intend to designate definitely.

Superlatives in the strict sense are singular by their very nature. Within any given set of circumstances and from any single point of view, there can be only one best, highest, lowest, tallest, and so on; and the designation of a thing as the best, highest, lowest, tallest, and so on, is a definite designation.

The demonstrative pronouns “this” and “that” are singular inasmuch as they definitely designate a single individual or group.

Common nouns are singular when they are restricted in their application by demonstrative adjectives or other modifiers to a single definitely designated individual or group; for instance, “this man,” “that dog,” “the tallest man in the room,” and “the girl in the front row nearest the window.”

Note that collective nouns (“herd,” “team,” “army,” “group”) are singular if they stand for a definite group that they designate definitely. Note, too, that nouns that are grammatically plural are singular from the point of view of logic if they definitely designate one group; for instance, “those five men” in the proposition “Those five men make up a basketball team,” and “the ducks” in the proposition “The ducks covered the entire pond.”

b. Particular Terms

A term is particular if it stands for an indeterminately designated portion of its absolute extension.

A term, therefore, is particular, first, if it stands for one individual or group without designating it definitely; and, secondly, if it stands for more than one, but not clearly for all, of the individuals or groups to which it can be applied. “Some man,” “some horses,” “three boys,” “several girls,” “a few apples,” and “most Americans” are particular.

In the proposition “A horse trampled on the lettuce,” the term “a horse” is particular; it stands for a definite horse, but does not designate that horse definitely. On the other hand, in the proposition “This horse trampled on the lettuce,” the term “this horse” is singular because it not only stands for a definite individual horse but also designates this horse definitely.

c. Universal Terms

A term is universal if it stands for each of the subjects to which it can be applied—that is, if it stands for each one of an unlimited class of subjects. For instance, the terms “every man,” “each man,” “men without exception,” and “whatever is heavier than water” are universal.

Note that a term that is grammatically singular is not necessarily singular from the point of view of logic but might be particular or universal. The definite article “the” is prefixed to both singular and universal terms. “The dog” is singular in “The dog is barking ex¬ citedly,” but universal (at least virtually) in “The dog is an animal.” The indefinite article “a” and “an” is prefixed to both particular and universal terms. “A dog” is particular in “A dog is yelping” but universal (at least virtually) in “A dog is an animal,” where “a dog” stands for a dog as such and therefore for every dog.

A term that is used universally (that is, for each individual being as well as for each kind of being to which it can be applied) is said to be distributed. A term that is not used for its entire extension is said to be undistributed. A singular term actually stands for the only individual or group it can be applied to and is therefore used for its entire extension. Consequently, in a certain limited sense, a singular term is also universal. For this reason universal and singular terms are distributed; particular terms are undistributed.