The Juggler 1943 Marc Chagall (1887-1985)  Russian

What Is a Definition?

     Words are signs (symbols) and the problem of universals concerns what it is that signs point to (symbolize). When I use the word "chair," what do I mean? What am I pointing to? Throughout history, philosophers have developed three distinct views of what universals are. These views are called ante rem (Platonic -- "before the thing"), in re (Aristotelian -- "in the thing"), and post rem (Lockean -- "after the thing").

Ante rem Universals -- Plato's Forms -- Before the thing

     Plato (427?-347 B.C.) believed in a spiritual world, a world of ideal forms which are the models (designs) of everything that exists. Our souls, according to Plato, existed in this spiritual world before we were born. Our souls knew and understood the entire spiritual world of forms. Thus, a person's soul clearly knew both the word (symbol) and the form (thing symbolized) for "chair." At birth, however, our souls were enmeshed in the physical, imperfect, material world. In the physical world, the clarity of the world of forms is no longer easily perceptible. Consider the soul as the cat's eye in a cat's eye marble -- in the spiritual world, the cat's eye can see everything clearly, but in the physical world, the marble has been dropped into mud. Our souls remember the spiritual world of forms, but, through the mud, we have trouble recognizing the physical correlatives of the spiritual forms (the chair), not only because of the "mud" in which we are embodied and which blurs our vision, but also  because those correlatives themselves (such as the chair) are now imperfectly embodied in the physical world.
     Our language, however, is based on the spiritual world of forms. Thus, when I say "chair," I think (and hope) that I am accurately referring to an embodied correlative of the spiritual form "chair," and I am also supposing that, in hearing me say chair, my listeners likewise make the correct connection to the spiritual form for "chair." Thus, ideally, we understand each other. A major implication of the ante rem theory of universals is that words (symbols) have one and only one correct definition (spiritual form). Although they may not recognize its philosophical assumptions, this view of universals is the one held by people who want (or think they have) THE definition of a word.
     Although few modern philosophers believe in the ante rem theory, the theory is alive and well in the general population, including some linguists. After a conference presentation, for example, I was informed by a linguist that a clause cannot be defined as a subject/verb/complement pattern because "a clause is a subject / predicate pattern." Consciously, or probably more often unconsciously, some people who offer definitions of grammatical terms do so with the underlying assumption of ante rem universals. The popularity of the ante rem theory, whether conscious or unconscious, is probably strengthened by religious beliefs. As we will see, the other two theories leave the spiritual world (God) out of the equation. As a result, people with strong religious convictions tend to prefer an ante rem theory of universals. My point here is not to discuss religious convictions, but simply to suggest why ante rem assumptions are so strong.
     But even if we believe in an ante rem theory of universals, a major problem remains -- how do we know, through this physical world in which we are enmeshed, that we have made a correct correlation between a word and what it symbolizes? How do we know that a clause really IS a subject / predicate pattern and not a subject / verb / complement pattern? I have frequently seen (or heard) people give grammatical definitions and statements which appear to be based on ante rem assumptions -- "city" in "city hall" is a noun, not an adjective; "because" is not a subordinating conjunction, etc., and, in each case, I have to wonder on what authority these statements are being made. 
     Particularly troublesome are the negative components of these definitions, i.e., "x is y, NOT z." As I will try to explain below, there is another reason for some of these negations, but whatever the reason, we need to examine both the assumptions underlying the definition and the effects of adopting it. It is completely possible that in God's mind, a clause is a subject / predicate pattern, but if someone can show that, in this physical world in which we are embodied, students would find the subject / verb / complement definition more helpful in learning to deal with sentence structure, then I humbly ask that imperfect definitions be given serious consideration. Too often, they are not.

In re Universals -- Aristotle's Metaphysics -- In the thing

     Once many years ago, for about five seconds, I thought I understood Aristotle's concept of universals. Rejecting Plato's forms, Aristotle (384-322 B.C.) apparently believed that the essence of "chair" exists not in the spiritual world, but in chairs themselves. How language works, under this theory, I do not understand, nor have I seen any clear (to me) explanations of it. I have included it here because it is a possibility -- perhaps, starting from here,  someone can explain it and solve a basic problem in semantics.

Post rem Universals -- John Locke's Tabula Rasa -- After the Thing

     Our ancestors had a lot of problems to deal with, but the problem of the meaning of meaning was not one of them. As anyone even slightly acquainted with the history of ideas knows, the speculative, philosophical nature of the ancient Greeks was very unusual. Even today, for most of the world's people, words simply have meaning. How they have that meaning is not (and was not) a relevant question. After Plato and Aristotle, almost two thousand years passed before the question was addressed with a significantly different answer. The most famous proponent of the new view was John Locke (1632-1704). 
     Whereas Plato had believed that the essential spiritual world of forms existed "before the things," and Aristotle believed that forms exist "in things," Locke argued that our concepts (the only knowledge that we have of essences) exist "after the things." We come into the world, according to Locke, as a "blank slate" ("tabula rasa"). The only way, according to Locke, that we know what a chair is is by repeated association between the word and some sort of physical stimulus. My concept of "chair" is thus created in my brain by all the memories I have in which the word "chair" was used and I was able to make an association between the word and some perception. As a result, my concept of "chair" is determined by the environment in which I live. My concept, for example, includes recliners, but recliners were not part of the concept for people who lived five hundred years ago.
     "Chair," moreover, is a relatively easy concept to learn. Chairs are relatively large, commonly used, physical objects. In the post rem theory, all definitions are very tenuous. Definitions of abstractions are even more so. For Plato (and perhaps Aristotle), happiness, virtue, (and clauses) have an objective, definite existence. A person's definition might be more, or less, accurate, but there is a "true" definition. For Locke, "truth" gives way to utility. A definition can no longer be right or wrong, only more or less effective. It is effective to the extent that other people appear to understand whatever I mean when I use a word.

Implications for Teaching

     The philosophical implications of these three views of universals are staggering. They go to the core of what it means to be human. I have no desire to change anyone's philosophical beliefs, but we need to look at the pedagogical implications of these three theories. I want to suggest that the (often unconscious) assumption of the ante rem view causes some of the poor grammar pedagogy and ineffective learning.
     I want to be as specific as possible about my meaning. Even if one believes in ante rem universals, i.e., that the concept of "clause" objectively exists in God's mind, there are still the problems of 1) knowing exactly what that concept is, and 2) convincing others that they should believe what one knows. To my knowledge no religious text, including the Bible, defines grammatical constructions. Indeed, most of our grammatical definitions come to us from the ancient Greeks and Romans (not particularly religious) or from linguists (See below.) How then, are we to know whether, in God's mind, a clause is a subject / predicate pattern, or a subject / verb / complement pattern? For the purposes of teaching, therefore, it would seem that even if one believes in ante rem universals, effective teaching requires a post rem stance.
     This may seem like a big to-do about nothing, but let's look at typical instruction in grammar. Students are told that a "noun" is the name of a person, place, or thing, and that a "verb" shows action or a state of being. They are also taught that subjects (nouns) should agree with their verbs in "number." And then students are given twenty (or fifty) simple exercises in which they are to identify the nouns, the verbs, or the correct agreement. Implicit in this instruction is the ante rem concept of universals -- if the term is defined and students are given a few examples, the students should make the connection with the objectively existing concepts "noun," "verb," and "number," and thus the students will understand. Rare is the teacher who claims that this approach works, but in spite of their knowing that it doesn't, most teachers continue to teach this way (probably because that is the way it has always been done). 
     Pedagogically, the ante rem perspective focuses on the definition (the symbol) at the expense of the thing defined. Students learn, and are tested on, their knowledge of the definitions, but, in most cases, these same students are totally at a loss when asked to identify the subjects and verbs in a moderately complex sentence. And this same type of instruction is usually used to teach teachers! Future teachers are exposed to a wealth of grammatical concepts and definitions, but most of these future teachers, having finished their course work, cannot identify the subjects and verbs in their students' writing.  ^{# 1} The effect of this ante rem assumption is that the instruction is both frustrating and ultimately meaningless.
     As opposed to ante rem, the post rem stance says "point to examples!" It is the things being pointed to, not the definitions, that are important. According to Michael Sugrue, Wittgenstein calls this definition-by-pointing "ostensive definition," and believes that it is more effective than a traditional "Aristotelian" [in re?] definition. ^{# 2} If we want to know what "mauve" is, we don't ask for a definition, we ask for examples. I don't want to suggest that all grammatical terms should be defined ostensively -- in fact I will argue just the opposite. But perhaps ostensive definitions are the best way to convey the most troublesome of grammatical terms, "noun" and "verb." There is, for example, widespread agreement that the definition of a noun as "the name of a person, place, or thing," and the definition of a verb as "an action word or a state of being" are inadequate. In another essay in this series, I will suggest that these "Aristotelian" definitions, inadequate as they may be, are still useful tools for students, but that they should, in some cases, ultimately be subordinated to ostensive definitions. First, however, we have to address another problem with specifically grammatical definitions.

     In Understanding Grammar, my favorite grammar book, Paul Roberts discusses the "Three Bases of Definitions":

     Some confusion and argument can be avoided if we understand the bases of our definitions. There are at least three possible bases, which will be called in this book the formal, the syntactic, and the notional. By formal definition we shall mean definition based on form -- sounds in the spoken language, spelling in the written. By syntactic definition we shall mean definition based on syntax -- the relation of words to other words in the sentence. By notional definition we shall mean definition based on our understanding of the relationship of words to the actual, real world phenomena represented by the words.
     For illustration, let us make three brief and incomplete definitions of noun:

Formal:    A noun is a word that forms a plural in -s.
Syntactic: A noun is a word that may serve as subject of a verb.
Notional:  A noun is the name of a person, place, or thing.

Obviously none of these adequately defines noun, but each of them might be expanded and qualified so as to approach adequacy. Grammarians use sometimes one kind of definition and sometimes another, and sometimes a combination, as circumstances or as their temperament leads them. (10-11)

       The first thing we need to do is to understand that grammarians cannot agree among themselves -- not only about definitions of terms, but also about the purposes for studying (hence teaching) grammar in K-12. At the Tenth ATEG conference, I distributed a questionnaire and was surprised to learn that only 52% of the respondents believed that "students, as they study a grammatical concept, should have as an objective the ability to identify most of the examples of that concept in whatever they read or write." Perhaps these people interpreted the question differently from what I meant, but I always thought that the purpose of studying grammar is to be able to discuss the grammatical aspects of language -- spoken or written. In other words, why study about subjects and verbs, unless one learns how to apply that study to what one says and writes? But, in order to apply it, doesn't one have to be able to recognize subjects and verbs?
     Now I realize that there are people for whom the study of grammar is an interesting end in itself. And ATEG is composed of teachers and teachers of teachers, all of whom are interested in grammar. But I am worried by the 48% who are not sure that students should be able to identify constructions. If identification is not one of their primary objectives, then what is? The further discussion and debate over definitions? But if that is the case, are they helping to solve the problem, or are they adding to it?
     The primary purpose of pedagogical grammatical definitions should be to enable students to identify grammatical constructions and concepts in whatever they read or write, thereby enabling students to discuss grammatical and stylistic questions intelligently. The KISS Approach attempts to meet this primary criterion through what Roberts calls syntactic definitions. ("A noun is a word that may serve as subject of a verb.") But as Roberts' example suggests, one cannot understand syntactic definitions without, so to speak, first cracking the shell. The definition of a noun is meaningless unless one understands what a verb is. To crack the shell, I urge teachers to use Wittgenstein's idea of ostensive definitions, i.e., definition through numerous examples. As Roberts wrote:

Young learners do not master the definition of noun and proceed from that to an identification of nouns. They learn what nouns are by having a great many nouns pointed out to them, and they learn verbs in the same way. Their recognition is based on formal and positional characteristics of nouns and verbs, though they may pay lip service to the notional definition. Perhaps the notional definition is best characterized as a useful fiction. (Understanding, 18)

2. I am currently reading, not necessarily comprehending, Wittgenstein. But the concept of the ostensive definition is, as I try to explain, relevant to teaching grammar.