Chapter VI

Extension and Intension

Claudio Gutierrez

Translated from Spanish by Inés Gutiérrez

38. Proper Names and Collective Terms

Proper names designate specific objects in the universe; when we want to refer to a singular object we use its proper name. But that is not the only form provided by language to refer to objects. When we mention San Lucas, we are referring to a concrete, well-determined prison in Costa Rica;(1) "San Lucas" is its proper name. But when we speak about Costa Rican prisons, to say for example that they do not meet the human-rights requirements proclaimed by the U.N.O.,(2) we are referring, jointly to San Lucas, to the Penitenciaría Central,(3) to the Buen Pastor,(4) etc. That is, the term “Costa Rican prison” serves to identify San Lucas, as does the term “San Lucas”; but the former applies to the insular prison and to all other prisons in Costa Rica, simultaneously. Such terms as “Costa Rican prison”, which can be applied indistinctly to various objects meeting some criterion, are called collective terms. They are not the name of a specific object, but rather the name of a class or collection of objects.

One of the great advantages of language is this ability to refer by means of only one term, –simultaneously and without distinction– to various objects which have something in common. If we wanted to say that Costa Rican prisons are inadequate, without using collective terms, we would have to say that San Lucas is inadequate, Penitenciaría Central is inadequate, Buen Pastor is inadequate, etc., which would be rather cumbersome. And at bottom, we could not even say this, because “inadequate” is also a collective term, since it can be applied simultaneously and indistinctly to many objects, namely, all objects that do not possess the required conditions. In short, then, if collective terms were not available we could hardly speak. Collective terms are all that important! It is worthwhile to briefly analyze their logical nature and –by so doing– shed some light on that of language.

39. Extension and Intension(5)

We are going to call the group of objects to which a collective term applies the extension of that term. All objects identified simultaneously and without distinction by that term form its extension. For example, the extension of “Costa Rican prison” is formed by the objects San Lucas, Penitenciaría Central, Buen Pastor, etc. We can also say that the term “Costa Rican prison” denotes each one of these objects (since "denotation" is a synonym of "extension"). Now then, each time we apply the term to one or more of the objects in its extension, for example with the statements “Penitenciaría Central is the largest Costa Rican prison” or “the living conditions in Costa Rican prisons are unfit for human beings”, the term tells us something informative about every one of the object it denotes. The term not only points out to the collection of objects; it also tells us how those objects are. If, standing in front of Penitenciaría Central, I point to it and say “this is a prison”, my listeners, tourists from Central America,(6) would learn something about the object pointed to, namely that it possesses the conditions required from an object to be a prison. They will know, for instance, that it is a building, that it is inhabited, that by far most of its population is confined there against their will, that it has a security regime, etc. All these characteristics form what is called the intension(7) of the term. The intension of a term is its content of meaning or information, what it tells us about the object to which it applies. Intension is also called connotation. Thus, we say that the term “Costa Rican prison” denotes San Lucas, Penitenciaría Central, Buen Pastor, etc, and that it connotes the characteristics of being a building, having a population confined against their will, … and, finally, its being located in Costa Rica.

Every collective term, then, possesses extension and intension, denotation and connotation. This means that every term refers to certain objects, and also tells us something about these objects. Most interesting is the fact that terms relate to one another from the point of view of both their extensions and intensions. Thus, the term “Costa Rican prison” relates to the term “prison”, and “prison” relates to the term “building”. Let us see what this relation consists of. From the extension’s point of view, it is obvious that the denotation of the term “building” is wider than that of the term “prison”, and this, in turn, wider than the term “Costa Rican prison”. Moreover: the extension of “building” contains the whole extension of “prison”, since all prisons are buildings, and the extension of “prison” contains the whole extension of “Costa Rican prison”, since all Costa Rican prisons are prisons. From the point of view of intension, on the other hand, it is obvious that the connotation of the term “prison” is not as rich as that of “Costa Rican prison”, but is richer than that of the term “building”. Besides, the intension of “Costa Rican prison” (its informative package, so to speak) contains entire intension of “prison”: it gives us all the information contained in “prison”, and more; in turn, the intension of “prison” contains the intension of “building”, since it expresses all its informative notes, and much more. In other words, everything that characterizes a building also characterizes a prison, and everything that characterizes a prison also characterizes a Costa Rican prison.

As we will immediately see, extension and intension have much to do with the topic of definition treated in the previous chapter.

40. Definition by Proximate Genus and Specific Differentia

Let us take the term “building” and try to define the term “prison” with its help. We will make use of the formerly examined circumstance that all prisons are buildings, i.e. that the extension of “prison” is immediately contained in the extension of “building”. If someone asks me what a prison is, I could answer that it is a building, a certain kind of building, and I would have made some point. In fact, all objects denoted by the word “prison” are also denoted by the word “building”. The problem with such an answer would of course be that a lot of other objects which are not prisons are also denoted by the word “building”. To remedy the definition, let us add something to exclude all those other non-prison buildings. We will perform that exclusion by appealing to the intension of “prison” which, as we already know, is richer than the intension of “building”. Thus, the difference between both intensions will allow us to exclude the undesired members of the "building" club, so as to reduce its numbers to the more exclusive "prison" club. For instance, we could say that the difference (or differentia, to be technical) is “for confinement of people who have broken the law or are awaiting trial." The complete definition would be generated by mentioning the proximate genus, i.e. the closest wider-extension term, together with the differentia of the definiendum, i.e. its distinguishing characteristic as species within the genus (its immediately less exclusive "club"). The complete definition intended would now be: “Prison is a building for the confinement of people who have broken the law or are awaiting trial."

Normally one calls genus the wider of two immediately related terms, and species the richer of them. Therefore, this kind of definition has been branded definition by proximate genus and specific differentia.

41. Rules of Definition

The definition by proximate genus and specific differentia must obey certain conditions, traditionally considered necessary for definitions to be correct. Below is a presentation of such conditions in the form of rules.

With the word “essence” we wish to convey that which cannot be lacking for the thing to continue being what it is. For example, it is said that the essence of humanity is rationality. Nevertheless, apart from the fact that our normal behavior is not always rational, there are a multitude of other features in human beings that cannot be absent for us to continue being what we are. For example, the ability to love, or to assume responsibilities, or even the ability to laugh or cry. So, what is considered essential very much depends upon social habits and values and is, to that extent, arbitrary. By tradition, though the definition of (generic) man as a rational animal is traditionally accepted as his essential definition. However, you are free to begin changing that tradition, and what is branded as the essence of mankind, and –as a starter– I suggest these differentiae: “historic”, “political”, “laughing”, "sadistic".

In the case of “prison”, although there are many characteristics of the objects included in the respective connotation, which are present in all members of the extension, the essence of the concept seems to be that its inhabitants cannot leave the precinct and that it is so because of a legitimate order given by a public authority. You are invited to try to remake the definition given above, which I looked up in the Webster's Dictionary, still complying with the rule.

We break this other rule when we give the definition in such a way that something not denoted by the defined term results included by the definition of it or, to the contrary, something denoted by the term is excluded by the definition. In the case of the definition of “prison”, we could break the rule by saying something like this: “Prison is a building whose inhabitants are submitted to disciplinary measures”, for we would be illegitimately including schools, barracks, and hospitals. We would likewise break it if we were to say: “prison is a building whose inhabitants have been condemned by courts of justice”, because there can also be in jail prisoners awaiting trial.

In addition, the concept to be defined must not be used within the definition, nor any equivalent expression of it. We break the rule, committing the error of circular reasoning, if we define "prison", for instance, like this: “Prison is the place where imprisoned people dwell”. But we also incur in error if we give two concatenated definitions that close a circle: “Prison is a place inhabited by convicts” and “convicts are imprisoned people”. The rule says nothing against the definition by synonyms; there may be cases where a person knows one of the synonyms but not the other, and the definition may fulfill a useful function. A case could be “prison" and "jail”. Still, it would not be a definition by proximate genus and specific differentia.

An obscure definition does not fulfill the end pursued by the definition, which is to enlighten us as to the meaning of the term. Nor would an ambiguous definition. An example of the former would be many definitions found in certain books on philosophy. An example: “Sound is the change in the specific condition of segregation of material parts, and in the negation of that condition” (Wilhelm Hegel in Natural Philosophy). An example of the latter would be the definition of democracy as government by the people, or of philosophy as love for knowledge. These definitions are faulty because the words used –especially “people” and “knowledge”– are ambiguous, in the sense that they may have several meanings.

The reason to reject negative definitions is that, in general, it is very difficult to sufficiently characterize a concept by saying what it is not; we can never be sure that our negative enumeration is complete. Thus, to say that a prison is a building that is not a school, nor a barracks, nor a hospital, nor a hotel, would leave us feeling insecure about having listed all the buildings that are not prisons. Besides, and this is more important, a definition of this kind would not indicate an essential attribute of the concept, and so the first rule would be violated. However, there are words that can only be defined negatively, part of their essence being some kind of negation. For example, “single” should be defined as “an unmarried person”; even the definition of “prison” contains an essential negative idea, i.e. the idea of privation of liberty.

42. Discursive Use of Definition

The fundamental purpose of definitions, as we saw in the previous chapter, is to establish or clarify the meaning of the terms we use. In that sense they are not part of language, but rather rules outside language governing it. This condition of definitions is especially evident when they are given in a language other than the one we are trying to learn, for example, in the case of a dictionary that relates two languages, such as English and Spanish. There, the words –in Spanish– receive a definition in another language –English–, the language in which the rules are given to the person learning the new tongue, i.e. Spanish. However, from another point of view, definitions can be considered as part of the same language to which they refer; they are not only formulae determining the meaning of terms, but propositions in themselves. In this manner, “man is a rational animal” can be considered not only as an explanation of the term "man", but also as an assertion by itself, a categorical proposition. This is important because propositions can form greater logical structures, called arguments. If definitions are also propositions, then definitions can be part of arguments. Indeed, they play extremely well as premises to demonstrate the truth of other propositions. We do not need to convince our interlocutor of their truth.

A definition, when adequate, is not only true. It is necessarily true, it cannot be false. It cannot be false unless a change occurred in the language itself that would affect the meaning of the terms we are using. This characteristic is not shared by other propositions. Most propositions which we assert and are not definitions are empirical propositions, namely propositions whose truth lies on experience, on the support of sense data. Consequently, from a logical viewpoint, they can well admit contradiction or exception. If I say, for example, that a public institution functions badly, and I want to use this as a premise to prove that no other institution should be founded; I’m liable to an attack on the premise from my contender at any moment during the discussion, even if he accepted it in the beginning. New data can demonstrate that the premise was a hasty judgment. Likewise, if I use as premise that every public institution is inefficient, I expose myself to the presentation of a contrary case, a public and efficient institution, which would destroy my premise. On the other hand, if I say that by definition every public institution is inefficient, based on the general idea that “the master’s eye fattens the horse” and the master in this case (society) is not there to guard it, or that “public assets are the assets of the deceased” that nobody is interested in defending, our premise acquires a different character. Of course, the problem here is formulating a good definition, so it complies with all the rules of definition, and it must be accepted by our contender, so that it prevails as foundation for our argument.

In short, a definition, once accepted as a premise within a discussion, allows you to arrive at true conclusions very easily. Its truth cannot be refuted by experience and its general character makes possible a great number of applications. Hence the practical importance of learning how to build correct ones.

Note 1: This prison disappeared in the period between the first edition of this work and the Internet edition. Nowadays, San Lucas is only an empty rocky island interrupting the monotony of a ferry trip in the west coast of Costa Rica. (2000-edition note)

Note 2: That disgraceful situation has improved considerably –though not sufficiently– since 1968, due to penitentiary reform. (2000-edition note)

Note 3: That old fortress has since been transformed into the cozy Museo del Niño (Children's Museum). (2000-edition note)

Note 4: Still today, a women’s prison. (2000-edition note)

Note 5: Correct spelling, sorry! (2000-edition note)

Note 6: In the year 1968, those were almost the only tourists who came to Costa Rica. My goodness, how the world has changed since! (2000-edition note)

Note 7: Notice the word’s spelling, which makes it a technical term different from the ordinary-languange “intention”. (2000-edition note)

Copyright © 1968-2006 Claudio Gutierrez