Categories (quotes)

"No, the mind has to get something out of forming categories, and that something is inference. Obviously we can't know everything about every object. But we can observe some of its properties, assign it to a category, and from the category predict properties that we have not observed. If Mopsy has long ears, he is a rabbit; if he is a rabbit, he should eat carrots, go hippety-hop, and breed like, well, a rabbit. The smaller the category, the better the prediction. Knowing that Peter is a cottontail, we can predict that he grows, breathes, moves, was suckled, inhabits open country or woodland clearings, spreads tularemia, and can contract myxomatosis. If we knew only that he was a mammal, the list would include only growing, breathing, moving, and being suckled. If we knew only that he was an animal, it would shrink to growing, breathing, and moving.

On the other hand, it's much harder to tag Peter as a cottontail than as a mammal or an animal. To tag him as a mammal we need only notice that he is furry and moving, but to tag him as a cottontail we have to notice that he has long ears, a short tail, long hind legs, and white on the underside of his tail. To identify very specific categories we have to examine so many properties that there would be few left to predict. Most of our everyday categories are somewhere in the middle: "rabbit," not mammal or cottontail; "car," not vehicle or Ford Tempo; "chair," not furniture or Barcalounger. They represent a compromise between how hard it is to identify the category and how much good the category does you. The psychologist Eleanor Rosch called them basic-level categories. They are the first words children learn for objects and generally the first mental label we assign when seeing them.

What makes a category like "mammal" or "rabbit" better than a category like "shirts made by companies beginning with H" or "animals drawn with a very fine camel's hair brush"? Many anthropologists and philosophers believe that categories are arbitrary conventions that we learn along with the other cultural accidents standardized in our language. Deconstructionism, poststructuralism, and postmodernism in the humanities take this view to an extreme. But categories would be useful only if they meshed with the way the world works. Fortunately for us, the world's objects are not evenly sprinkled throughout the rows and columns of the inventory list defined by the properties we notice. The world's inventory is lumpy. Creatures with cotton tails tend have long ears and live in woodland clearings; creatures with fins tend to have scales and live in the water. Other than in the children's books with split pages for assembling do-it-yourself chimeras, there are no finned cottontails or floppy-eared fish. Mental boxes work because things come in clusters that fit the boxes."

"How the Mind Works" by Steven Pinker ch.5 pg.307

"The human mind must be given credit for one more cognitive feat that is difficult to wring out of connectoplasm, and therefore difficult to explain by associationism. Neural networks easily implement a fuzzy logic in which everything is a kind-of something to some degree. To be sure, many common-sense concepts really are fuzzy at their edges and have no clear definitions. The philosopher Ludwig Wittgenstein offered the example of "a game," whose exemplars (jigsaw puzzles, roller derby, curling, Dungeons and Dragons, cockfighting, and so on) have nothing in common, and earlier I gave you two others, "bachelor" and "vegetable." The members of a fuzzy category lack a single defining feature; they overlap in many! features, much like the members of a family or the strands of a rope, none of which runs the entire length. In the comic strip Bloom County, Opus the Penguin, temporarily amnesic, objects when he is told he is a bird. Birds are svelte and aerodynamic, he points out; he is not. Birds can fly; he cannot. Birds can sing; his performance of "Yesterday" left his listeners gagging. Opus suspects he is really Bullwinkle the Moose. So even concepts like "bird" seem to be organized not around necessary and sufficient conditions but around prototypical members. If you look up bird in the dictionary, it will be illustrated not with a penguin but with Joe Bird, typically a sparrow.

Experiments in cognitive psychology have shown that people are bigots about birds, other animals, vegetables, and tools. People share a stereotype, project it to all the members of a category, recognize the stereotype more quickly than the nonconformists, and even claim to have seen the stereotype when all they really saw were examples similar to it. These responses can be predicted by tallying up the properties that a member shares with other members of the category: the more birdy properties, the better the bird. An auto-associator presented with examples from a category pretty much does the same thing, because it computes correlations among properties. That's a reason to believe that parts of human memory are wired something like an auto-associator.

But there must be more to the mind than that. People are not always fuzzy. We laugh at Opus because a part of us knows that he really is a bird. We may agree on the prototype of a grandmother—the kindly, grayhaired septuagenarian dispensing blueberry muffins or chicken soup (depending on whose stereotype we're talking about)—but at the same time we have no trouble understanding that Tina Turner and Elizabeth Taylor are grandmothers (indeed, a Jewish grandmother, in Taylor's case). When it comes to bachelors, many people—such as immigration authorities, justices of the peace, and health care bureaucrats—are notoriously ufuzzy about who belongs in the category; as we all know, a lot can hinge on a piece of paper. Examples of unfuzzy thinking are everywhere. A judge may free an obviously guilty suspect on a technicality. Bartenders deny beer to a responsible adult the day before his twenty-first birthday. We joke that you can't be a little bit pregnant or a little bit married, and after a Canadian survey reported that married women have sex 1.57 times a week, the cartoonist Terry Mosher drew a woman sitting up in bed beside her dozing husband and muttering, "Well, that was .57."

In fact, fuzzy and crisp versions of the same category can live side by side in a single head. The psychologists Sharon Armstrong, Henry Gleitman, and Lila Gleitman mischievously gave the standard tests for fuzzy categories to university students but asked them about knife-edged categories like "odd number" and "female." The subjects happily agreed to daft statements such as that 13 is a better example of an odd number than 23 is, and that a mother is a better example of a female than a comedienne is. Moments later the subjects also claimed that a number either is odd or is even, and that a person either is female or is male, with no gray areas. 

People think in two modes. They can form fuzzy stereotypes by uninsightfully soaking up correlations among properties, taking advantage of the fact that things in the world tend to fall into clusters (things that bark also bite and lift their legs at hydrants). But people can also create systems of rules—intuitive theories—that define categories in terms of the rules that apply to them, and that treat all the members of the category equally. All cultures have systems of formal kinship rules, often so precise that one can prove theorems in them. Our own kinship system gives us a crisp version of "grandmother": the mother of a parent, muffins be damned. Law, arithmetic, folk science, and social conventions (with their rites of passage sharply delineating adults from children and husbands from bachelors) are other rule systems in which people all over the planet reckon. The grammar of a language is yet another. 

Rule systems allow us to rise above mere similarity and reach conclusions based on explanations. Hinton, Rumelhart, and McClelland wrote: "People are good at generalizing newly acquired knowledge. If, for example, you learn that chimpanzees like onions you will probably raise your estimate of the probability that gorillas like onions. In a network that uses distributed representations, this kind of generalization is automatic." Their boast is a twentieth-century echo of Hume's remark that from a body similar to bread in color and consistency we expect a similar degree of nourishment. But the assumption breaks down in any domain in which a person actually knows something. The onion-loving gorilla was intended only as an example, of course, but it is interesting to see how even this simple example underestimates us. Knowing a bit of zoology and not much about gorillas, I would definitely not raise my estimate of the probability that gorillas like onions. Animals can be cross-classified. They may be grouped by genealogy and resemblance into a taxon, such as the great apes, but they also may be grouped into "guilds" that specialize in certain ways of getting food, such as omnivores, herbivores, and carnivores. Knowing this principle leads me to reason as follows. Chimpanzees are omnivores, and it is not surprising that they eat onions; after all, we are omnivores, and we eat them. But gorillas are herbivores, who spend their days munching wild celery, thistles, and other plants. Herbivores are often finicky about which species they feed on, because their digestive systems are optimized to detoxify the poisons in some kinds of plants and not others (the extreme example being koalas, who specialize in eating eucalyptus leaves). So it would not surprise me if gorillas avoided the pungent onion, regardless of what chimpanzees do. Depending on which system of explanation I call to mind, chimpanzees and' gorillas are either highly similar category-mates or as different as people and cows.

In associationism and its implementation in connectoplasm, the way an object is represented (namely, as a set of properties) automatically commits the system to generalizing in a certain way (unless it is trained out of the generalization with specially provided contrary examples). The alternative I am pushing is that humans can mentally symbolize kinds of objects, and those symbols can be referred to in a number of rule systems we carry around in our heads. (In artificial intelligence, this technique is called explanation-based generalization, and connectionist designs are an example of the technique called similarity-based generalization.) Our rule systems couch knowledge in compositional, quantified, recursive propositions, and collections of these propositions interlock to form modules or intuitive theories about particular domains of experience, such as kinship, intuitive science, intuitive psychology, number, language, and law. Chapter 5 explores some of those domains.

What good are crisp categories and systems of rules? In the social world they can adjudicate between haggling parties each pointing at the fuzzy boundary of a category, one saying something is inside and the other saying it is outside. Rites of passage, the age of majority, diplomas, licenses, and other pieces of legal paper draw sharp lines that all parties can mentally represent, lines that let everyone know where everyone else stands. Similarly, all-or-none rules are a defense against salami tactics, in which a person tries to take advantage of a fuzzy category by claiming one borderline case after another to his advantage.

Rules and abstract categories also help in dealing with the natural world. By sidestepping similarity, they allow us to get beneath the surface and ferret out hidden laws that make things tick. And because they are, in a sense, digital, they give representations stability and precision. If you make a chain of analog copies from an analog tape, the quality declines with each generation of copying. But if you make a chain of digital copies, the last can be as good as the first. Similarly, crisp symbolic representations allow for chains of reasoning in which the symbols are copied verbatim in successive thoughts, forming what logicians call a sorites:
    
    All ravens are crows.
    All crows are birds.
    All birds are animals.
    All animals need oxygen.
    
A sorites allows a thinker to draw conclusions with confidence despite meager experience. For example, a thinker can conclude that ravens need oxygen even if no one has ever actually deprived a raven of oxygen to see what happens. The thinker can reach that conclusion even if he or she has never witnessed an experiment depriving any animal of oxygen but only heard the statement from a credible expert. But if each step in the deduction were fuzzy or probabilistic or cluttered with the particulars of the category members one step before, the slop would accumulate. The last statement would be as noisy as an nth-generation bootleg tape or as unrecognizable as the last whisper in a game of broken telephone. People in all cultures carry out long chains of reasoning built from links whose truth they could not have observed directly. Philosophers have often pointed out that science is made possible by that ability."

"How the Mind Works" by Steven Pinker ch.2 pg.126