“Girl Twenty, define a horse.”

In my last post (“Verbish Nouns and Nounish Verbs”) I began to talk about what a noun is and what a verb is, and I started with a couple of definitions: a verb is “a word expressing an action or a state of being”, while nouns are “used to name persons, places, things, animals, qualities, or actions”. A little thought, however, showed that these definitions are less than satisfactory. One problem is that they overlap, since both verbs and nouns express or name actions. Another problem is that they don’t cover all the possible cases. The noun “hope” (“Don’t lose hope”) doesn’t seem to name a person, place, thing, animal, or action, nor does the noun “cost” (“They increased the cost of this book”); and the verb “cost” (“This book costs five dollars”) doesn’t seem to express an action or a state of being. Perhaps we could add to the definitions. Maybe “hope” as a noun could be called an “attitude” or something like that, so a noun could be a person, place, thing, animal, action, or an attitude. The word attitude itself is a problem. What kind of a noun is that? It’s not a person, place, thing, animal, action, or attitude. Do we need to expand the definition again? We still haven’t figured out what to do with cost as a noun or cost as a verb. This road doesn’t seem to be leading anywhere. Maybe we need to take a different approach. Maybe we’re thinking about definitions and categories the wrong way.

I said in my last post that I’m not a great fan of definitions. Of course definitions have their uses. At the right time in the right situation it’s great to go to the dictionary to find a definition; I frequently consult a dictionary. But we also have to acknowledge the limits of definitions and dictionaries.

Here’s an example of a definition from Charles Dickens’ novel Hard Times. The novel begins with a scene in a school room. There’s a new girl in the class, Sissy Jupe (identified as girl number twenty), and she is being questioned by Mr. Thomas Gradgrind, a banker in the town who takes an interest in the school and the students. He finds out that Sissy’s father works with horses (in a circus), so he asks her for a definition of a horse. She is unable to come up with a definition, so Gradgrind turns to one of the boys, Bitzer, who comes up with this:

“Quadruped. Graminivorous. Forty teeth, namely twenty-four grinders, four eye-teeth, and twelve incisive. Sheds coat in spring; in marshy countries, sheds hoofs, too. Hoofs hard, but requiring to be shod with iron. Age known by marks in mouth.” And so on. Gradgrind says to Sissy, “Now, girl number twenty, you know what a horse is.”

Dickens’ point, of course, is that Sissy knows far more about horses from her personal experience than Bitzer knows from his books.

There are times, however, when a verbal definition is useful or even necessary. If I read an unfamiliar word, say “coatimundi”, I probably can’t get the experience I would need to know what a coatimundi is, so I turn to the dictionary and find that it’s a mammal in the raccoon family, but with a longer body and tail than a raccoon and with a long flexible snout. Even this definition, however, depends on some experience. Most people who read it will have some experience of a raccoon, so they will think, “Oh, a coatimundi is kind of like a raccoon, but different this way and that”. (I bet a standard English dictionary doesn’t define a raccoon by saying that it’s like a coatimundi, but smaller and with a shorter tail.)

Definitions come in several different forms. The definition of a noun that I quoted (“a person, place, thing, animal, quality, or action”) is a definition by enumeration—here’s one kind of noun, here’s another, and here’s another. Enumeration is probably the way we learn most words most of the time. A child hears people use the word “chair” to designate a whole variety of things to sit on and gradually forms an idea of the kinds of things that are called chairs. Now and again the child may be corrected: “No, that’s not really a chair, it’s a bench” or “no, that’s not a chair, it’s a stool”.

Definition by enumeration has some defects: you never know when a new case will come up which isn’t covered by the enumeration, and enumeration doesn’t in itself tell you why the various things enumerated all belong in the same group. Plato was very critical of definition by enumeration; in a number of his dialogues Socrates has to teach his interlocutor not to use enumeration, but to look for some essential quality in a word. The prejudice against definition by enumeration has been a persistent feature of philosophy ever since Plato. I recognize the defects in enumeration, but I don’t think we should scorn the way we actually learn almost all the words we know.

The definition of coatimundi works in a different way. It works in two stages: first, it puts the thing to be defined in a group, and then it distinguishes that thing from the other things in the group. This method is sometimes called definition by genus and species. The genus is the larger group and the species is the smaller group within the larger group. The definition of coatimundi first puts it in a large group, mammals, then within a smaller large group, the raccoon family; then it differentiates it within this group: it’s larger than a raccoon, has a longer tail, and a longer flexible snout.

Definitions are generally definitions of a group of things, rather than some individual object. We don’t usually define individuals; we give them names, if we need to. We give names to people, to pets (but not usually to wild animals), to important or notable places. But we usually wouldn’t talk about defining Mount Everest or Lake Ontario. There’s no definition of me. In general, we define a category or a class: “raccoon” is the word for a class of animals, “coatimundi” is the word for another class, “dog” is the word for another class, “poodle” for a class within the class “dog”, and so on and so on. (I’m using the terms “group”, “category”, and “class” more or less as synonyms.)

A definition might be looking for whatever it is that makes all the things in a group belong to that group. That’s how Plato (or Socrates in the Platonic dialogues) thought about definitions. If you can find that essence, then you can know if something belongs to the group. Let’s take the class of even integers. Integers are the counting numbers: 1, 2, 3, 4, and so on. In this case the larger category, the genus, would be integers, and the smaller category, the species, would be the even integers. And the essence of an even integer is that it can be divided by 2 with no remainder.  Given any integer, you can tell by that definition if it’s even or not; you can tell that the integer 4 is even, but the integer 5 is not.

What about the group of triangles? A triangle is a geometric figure made of three straight lines connected so that they form three angles. Given any geometric figure, you can tell by that definition if it’s a triangle or not. A square is not a triangle. The essence of a triangle is that it has three sides and three angles, and all triangles share this essence. Socrates thought that you should look for the essence which is shared by all the members of a group, all the instances of a category, all the members of a class. So there should be an essence which is shared by all the instances of justice, or moderation, or courage, or whatever.

A category which has this kind of essence has some interesting characteristics. In general, every member of this kind of class is just as good an example of the category as every other member of the class. The number 58 is just as good an example of an even integer as the number 114, and just as good as the number 8, and just as good as the number 174,224. And there is a sharp boundary dividing the class of even integers from the other integers. The number 4 is in the class, the number 3 is not, and there are no integers which are questionable. We can call this kind of class or category a classical category.

For some parts of life, this approach works really well. It works well for a lot of mathematics and for a lot of things that are kind of mathematical. Sometimes mathematics is seen as the model that all serious rational thought should imitate, and the search for classical categories and essences was the goal of serious thinking. Anything that didn’t seem to fit this model of thinking made some people uneasy.

Here’s an example of someone faced with a category which doesn’t fit this model. The great novelist E. M. Forster wrote a wonderful book about novels, Aspects of the Novel, published back in 1927; I recommend it as one of the very best books about novels ever written. At the beginning of his discussion he says, “Perhaps we ought to define what a novel is…. This will not take a second.” And his definition is that a novel is a fiction in prose of not less than 50,000 words. This is a classic definition. Any prose fiction over 50,000 words is just as much a prose fiction over 50,000 words as any other; and there’s a sharp boundary between things inside the class and things outside. If a prose fiction is 49,999 words it doesn’t belong to the class.

Forster seems to recognize that this definition may seem unsatisfactory, and in a somewhat defensive tone he asks the reader to come up with a better definition, “which will include The Pilgrim’s Progress, Marius the Epicurean, The Adventures of a Younger Son, The Magic Flute, The Journal of the Plague, Zuleika Dobson, Rasselas, Ulysses, and Green Mansions, or else will give reasons for their exclusion?” A lot of these I haven’t read—times change, and what Forster expected his readers to have read may not be familiar to today’s readers. (The Magic Flute, by the way, is not the opera by Mozart, but a fantasy novel by G. Lowes Dickinson published in 1920.) Forster seems to be searching for difficult cases, and many of his difficult cases are fantasies. I think we now accept fantasies as novels—fantasy novels—and our difficult cases might include non-fiction novels.

“Parts of our spongy tract,” Forster says, “seem more fictitious than other parts, it is true: near the middle, on a tump of grass, stand Miss Austen with the figure of Emma by her side, and Thackeray holding up Esmond. But no intelligent remark known to me will define the tract as a whole. All we can say of it is that it is bounded by two chains of mountains neither of which arises very abruptly—the opposing ranges of Poetry and of History—and bounded on the third side by a sea—a sea that we shall encounter when we come to Moby Dick.” Forster doesn’t know it, but he has just given an excellent characterization of a different way of thinking about categories and definitions, and that’s what I will talk about in my next post.

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