Surfaces and Essences

by Douglas Hofstadter

  There’s little of great moment in the foregoing, except that Emmanuel’s coffee wasn’t a coffee and Doug’s pastry wasn’t a pastry. And yet no one would accuse them of lying. Even if Doug had ordered a lemon tea instead of his crème, it would have seemed perfectly fine to say that the co-authors had gone out for a coffee. And so, what exactly is meant by “a coffee”?

  We can distinguish at least four types of context — four levels of abstraction, in this case — in which the term is understood differently and yet always with ease. First of all, there are situations where “having a coffee” means “chatting while eating or drinking something light”. In such a context, the word “coffee” is so open and abstract that it covers any type of drink, or a sandwich, or an ice cream, or for that matter nothing at all, as long as the establishment doesn’t object. We’ll call this “coffee4”.

  Next, there are situations in a restaurant where, after the meal, the server asks the customers, “Who’ll have a coffee?” A reply such as, “A tea for me, please” would seem perfectly in order here, and no one would think that it contradicted the question that was asked, whereas asking for a cognac, or worse yet, some more wine or another order of fries, would seem totally incongruous. In other words, there is still some abstraction involved, but it is not as great. We’ll call this “coffee3”.

  Then we come to a situation in a café where two regulars are greeted with the customary question, “And what might your coffees be this morning, ladies?” Here the server is expecting answers such as “A crème and a decaf, please”, or “Two macchiatos, please”, since those belong to the category explicitly mentioned. Here the word “coffee” is taken more narrowly, but despite the approach towards literality, there are still numerous ways for it to be realized (and so we’ll label this case “coffee2”).

  Lastly, there’s the type of situation where someone walks into a Paris café and says, “Un café, s’il vous plaît”, or “A coffee, please.” Here it’s clear that it couldn’t possibly mean a tea or an ice cream (etc.); the drink being requested is a straight espresso, without cream. This is the default interpretation for the word “coffee” in Paris cafés, and that’s what we’ll mean by “coffee1”. We’ve hit the rock-bottom level of abstraction in our spectrum of coffees, and so we’ll temporarily draw our exploration of “cafégories” to a close.

  What has this exercise shown us? That the members of a category change with context; that we effortlessly understand the nature of the context that we are in; that a single word in a given language can denote numerous different categories; and that these categories can have different levels of abstraction.

  Road Map of This Chapter

  Our first three chapters were an attempt to give an answer to the question “What is a category?” by examining various types of categories, including those covered by a single word (Chapter 1), those covered by a composite lexical entity (Chapter 2), and those that have no lexical label at all (Chapter 3). With this chapter, we open a new phase in our book, in which we analyze how categorization works. In particular, we will look carefully at “leaps” or “slippages” between categories (and in the interest of less repetition, we’ll use both terms).

  Our goal is to reveal the fundamental importance of slippages between categories in the act of thinking, and specifically slippages that carry one up or down a vast range of abstraction. First we’ll say what we mean by “abstraction” and then we’ll show that the fate of objects and situations in this world is to be shunted around, in a manner that is both facile and unconscious, from one category to another. Just as Molière’s Monsieur Jourdain spoke prose without realizing it, so we are all experts in making leaps from one category to another without realizing it. We are all constantly practicing the art of mentally shifting objects and situations from one category to another.

  To show that a good part of what we call “flexibility” and “creativity” is tied to the eminently human faculty of extending categories and making leaps between them, we’ll take a close look at a particular phenomenon that gives insight into the processes underlying the development of concepts — specifically, the linguistic phenomenon called marking, which is extremely widespread in language, although people seldom notice it at all; in fact, few even know it exists. The idea is that a single word of a language can designate both a narrower and a broader category, where the narrower one is wholly contained inside the broader one, as was illustrated above by the word “coffee”. Although marking can occasionally hinder communication and lead to confusion, it is mostly a useful tool, imbuing language with greater fluidity by allowing several categories to be labeled simultaneously by a single term and by taking advantage of our mind’s natural sensitivity to context.

  Next we will scrutinize a process at the core of human thought, and which we already introduced in Chapter 1: the development of concepts through category extension. As we saw in that chapter, when categories are born, they are tiny — often they have just one member — and then cores and halos begin to form. Categories grow by welcoming new members, which sometimes are central and other times lie way out at the fringes, at the city limits. The act of welcoming such unexpected members into the fold requires either “pushing the envelope” or else the creation of new categories. In any case, analogy is the motor that drives all such extensions. We will analyze the process at the root of this human ability to understand situations in terms of pre-existing concepts, and at the same time to modify those concepts under the influence of new situations.

  We will then turn to another fundamental question, closely linked to the previous one: What makes an expert? This question is important because the concept of expertise applies not only to a specialist’s knowledge of some narrow domain but also to an average person’s ability, developed over a lifetime, to deal with their daily environment. More specifically, we shall see that being an expert doesn’t mean just that one has acquired more categories than other people have, but also that one has organized them in such a way as to facilitate useful categorizations at different levels of abstraction, and in such a way as to allow one to glide smoothly, when under contextual pressure, from one category to another.

  This indeed is one of the wellsprings of creativity — namely, the ability to make certain crucial leaps that at first seem surprising but that come to make eminent sense after the fact. Even if conceptual slippage is the most ordinary mental phenomenon, there are contexts where it is subtle, rare, and anything but straightforward. Discovery via conceptual slippage gave rise to many of the greatest ideas in history, including scientific discoveries (which we will discuss in more detail in Chapter 8). As the above outline shows, the present chapter has many ambitions; we shall take them one at a time, starting with the notion of abstraction.

  What is Abstraction, and What is its Purpose?

  Abstraction comes in different varieties. Here we will focus on the variety that we will call “generalizing abstraction”. We will say that category A is more abstract than category B if B is a subcategory of A — that is, if anything that belongs to category B also belongs to category A. For example, coffee4 is more abstract than coffee3, because all coffee3’s (basically, after-dinner drinks including tea but not wine) are also coffee4’s (basically any light thing ordered at all), and moreover a diabolo menthe and a Coke belong to coffee4 but not to coffee3. For much the same reason, coffee3 is more abstract than coffee2, which in turn is more abstract than coffee1.

  The notion of abstraction (from now on, we’ll omit the modifier “generalizing”, since that’s the only type of abstraction that we’ll be concerned with) applies to classical categories of things occurring in nature (thus the category bird is more abstract than the category sparrow) as well as to categories of human-made objects (the category furniture is more abstract than the category chair), and also, of course, to categories of actions (moving is more abstract than walking) and to categories named by adjectives (red is more abstract than scarlet, and colored is more abstract than
red). It also applies to categories named by idiomatic phrases, proverbs, or fables (thus, little misdeeds lead to big misdeeds is a more abstract category than little thefts lead to big thefts, and better safe than sorry is a more abstract category than an ounce of prevention is worth a pound of cure), and last but not least, it applies to categories that are not lexicalized at all, like those that were examined in the previous chapter.

  In short, one category is more abstract than another when it includes the latter category as a special case. The existence in our minds of categories enjoying several different levels of abstraction makes it possible to take different perspectives on a single entity. Sometimes, for instance, a particular entity will be seen as a sparrow, and other times as a bird.

  If we lacked the ability to abstract, our lives would resemble that of Ireneo Funes, the main character in Jorge Luis Borges’ short story “Funes, the Memorious”, for whom a fall from a horse had the devastating consequence that “Funes not only remembered every leaf on every tree of every wood, but… he was almost incapable of general, platonic ideas. It was not only difficult for him to understand that the generic term dog embraced so many unlike specimens of differing sizes and differing forms; he was disturbed by the fact that a dog at three-fourteen (seen in profile) should have the same name as the dog at three-fifteen (seen from the front).” In contrast to Funes, the standard human mind has not only the ability but the proclivity to abstract, in order to deal with the world’s vast diversity. It pulls together into a single category items that it sees as similar, and it further organizes its categories according to their levels of generality. We see the dog at 3:15 as being the same as the dog at 3:14, we consider that dogs and cats are the same as each other in that they are all animals, and so on.

  The Good Side of Abstraction

  Any situation can be categorized in an essentially limitless number of different fashions. Thus one can use many different words to label a situation, and also many different idioms or proverbs. An old piano might be a musical instrument to a music teacher, a piece of furniture to movers, a dust trap to the person who does the weekly dusting, and a status symbol to those who proudly display it in the middle of their living room. A tomato might be a fruit in a botany course and a vegetable in a cooking course. And there are times when a given situation can spontaneously evoke completely opposite and thus contradictory concepts in the minds of different observers; the very same situation can bring to mind the category all that glitters is not gold for one person and the category where there’s smoke there’s fire for another.

  A given situation can be labeled at many different levels of abstraction because sometimes we wish to make distinctions and other times we wish to see commonalities. While dining, one naturally wishes to keep track of which glass is one’s own and which is one’s neighbor’s, but while washing them, one will blithely ignore that difference. A refrigerator and a piano have very different purposes, but for movers, they are both simply big heavy objects. When one is bringing up children, one wants all of them to be involved in activities; for one child this might mean acting, for another it might mean judo, and taking flute lessons, for a third. Indeed, what better way to distinguish two things than to assign them to different categories? For example, the distinction between an eagle and a swallow, or between a barn swallow and a cliff swallow, depends on the existence of distinct categories in the mind of the categorizer. But on the other hand, the barn swallow and the cliff swallow can both be seen as swallows, and the swallow and the eagle can both be seen as birds. This idea of highlighting a commonality uniting two things, just as valid and useful as the idea of drawing a distinction between them, depends on the existence of a common category to which they both belong.

  Our ability to categorize things in many different ways determines how adaptable we are. Indeed, we often shift our perceptions of mundane situations with great speed and fluency, although such reperceptions tend to seem so bland that they usually go unnoticed. And yet such cases reveal the remarkable suppleness of everyday human intelligence, as a small example will now show.

  A Mini-saga of Dizzyingly Fast Category Shifts

  You open the cupboard and pull out a glass. To do this, you had to recognize that the object was indeed a glass. This seems as simple as simple gets: any object has its intrinsic conceptual box, these boxes are called “categories”, and categorization is simply the placing of each object in its proper box, end of story. But perhaps it’s not quite the whole story, after all…

  You don’t know me. In fact, I don’t know myself either; I’m unconscious. But whatever. Here’s my story. I was produced on July 11, 2005 in a French factory. From my birth onwards, I have been categorized left and right. So in no particular order, here’s what I have been: artifact, industrial product, commodity produced in the European Union, consumer article, fragile object, glass, item of dishware, drinking glass, water glass, transparent object, recyclable object. When I was being shipped to the store, I became a piece of freight and also a piece of merchandise, and while I was sitting on the shelf, I was an item for sale. Since my designer seems not to have been super-inspired that day, I remained on the shelf for several months, and the clerks variously reclassified me as an unsold object, a casting error, an unsellable object, and then a dust-gatherer, at which point I was declared a discounted item. My drastically slashed price finally allowed me to find an owner, and thus I became a purchase. Mr. Martin, who certainly is no great shakes in the creativity department, is nonetheless forever shunting me back and forth between categories, and he does so without realizing it in the least. When he’s thirsty, he never confuses me with the plates, bowls, cups, or mugs (let alone the silverware!); indeed, for him I’m not even a piece of dishware or a glass — all I am is a glass for cold drinks. I can thus relish being the host for water, soft drinks, and milk, but I’m never given the chance to welcome wine into my person — that role is granted only to a certain special elite that occupies the shelf just above mine. One time, though, a confused guest actually promoted me to the swanky status of wineglass, and as such I did a rather commendable job, if I don’t say so myself, even though I’m not as sophisticated as my cupboard-neighbors. Usually, after having done my duty, I wind up in the dishwasher, and during that brief stay, no one cares that I’m a glass; I’m just dishware and that’s that. My peripatetic life has occasionally given me the chance to be categorized in some rather extreme fashions. Thus the lady of the house has more than once employed me as a spider carrier and quite often as a knickknack holder. One time when the family went on vacation, I did duty as a toothbrush holder for an entire month, and the next year I was recruited to serve as a sugar bowl. I’ve also done stints as a home for tadpoles (this after the Martin children had been playing in the woods), and as a vase (a couple of times when the kids had picked some wildflowers for their mother). I was once even a piece of construction material, when the kids decided to make a tower using me and some of my peers. Alas, they forgot that I was a fragile object and things came to an abrupt and unhappy end when the tower fell down. Luckily, though, since I’m a recyclable object, a new life is awaiting me just around the corner, rich in undreamt-of new categorizations.

  Categorization pervades every facet of our existence and is never fixed, even in the most mundane of circumstances. Our mini-saga has just demonstrated this, as did our various portraits in Chapter 1 of the 60-kilogram mosquito-attracting mirror-symmetric insomniac object known as “Ann”, and as do innumerable other examples. Being moved from one categorical “box” to another, often by being slid up or down the rungs of an abstraction ladder, is the inevitable fate of all objects, actions, and situations.

  Some readers might nonetheless feel tempted to think that, despite the incessant bouncing back and forth of our story’s unconscious narrator from one category to another, it still has just one true and permanent identy — namely, it is a glass. But to think that way is to fall into the trap of Plato’s “objectivist” vision, acc
ording to which objects have one and only one true identity. That is a naïve vision.

  It’s nonetheless true that psychological studies have identified certain types of “default” categorizations, usually called basic-level categories. For example, people tend to find it more natural to call an object a “chair” than an “armchair” or a “piece of furniture”, and likewise they prefer “glass” over “water glass” or “piece of dishware”, and this experimentally confirmed intuition might reinforce one’s intuition that each object really does have a “true identity” in terms of its genuine category. But at any moment, an entity is what its categorization says it is, and that’s all. Some objects are of course more glass-like while others are more chair-like, and they become glasses in those contexts when “glass” is the word that they tend to evoke in human minds, but in other contexts they become members of other categories. Thus, as we just saw, a glass-like object can become dishware, artifact, commodity, spider carrier, knickknack holder, and so forth.

  (Incidentally, when we write “The glass was categorized as a knickknack holder”, we are in fact using sloppy language and we should, in principle, say something more like this: “The entity that in many contexts is categorized as a glass has, in this case, been categorized as a knickknack holder.” That, however, would be heavy and pedantic, so we refrain from such precision.)