February 24, 1999

This lecture is on categorization. Where is categorization in the brain? The amoebae categorizes. It can tell food from non-food chemically. That is a simple form of categorization. There are 100 million fiber coming out of your retina and only 1 million going to the brain. There's a reduction of 100 to 1. Categorization is what's happening. Categorization occurs whenever lots of inputs are boiled down to a single output. This happens outside the retina and everywhere else in the brain, wherever a number of neurons give output to another neuron. Wherever there is a reduction of information, categorization occurs. Categorization is not just in language. All neural beings categorize. In some philosophical traditions, the belief is that we are supposed to rise above our categorizations and see the world as it really it, but this is impossible for neural beings.

Besides the simple categories, there are also more complex conceptual categories. A lot of what this course is about is how you link up the low level information at the neural level with higher level conceptual categories, like room, chair, school, blackboard. Walking down the street, we make categories of the pavement vs. the street, things that move vs. things that stand still, things to step on vs. things not to step on, people you know vs. people you don't know, dangerous vs. non-dangerous things. How can a neural system form conceptual categories? In order to answer this question, you need to know something about conceptual categories.

If a neural system is doing categorization, we would not expect categories to be all or none because neural systems have weighted connections, degrees of firing. That doesn't mean that you will never have an all or none categorization because neural systems also have thresholds above which they do fire and below which they don't. Also, mutual inhibition in a system can yield all or nothing categories, such as the Necker cube from 2-2. So it is natural to have all or nothing categories and it is also natural to have graded categories because neural response has degrees. What is it about neural systems that give rise to the properties of human categories? The purpose of this lecture is to explain the little we know about that question and a lot of what we know about higher level conceptual categories and to get you thinking about how neural systems can characterize the properties of higher level conceptual categories.

In classical formal logic categories are sets of necessary and sufficient conditions, like a mathematical definition. The assumption is that all categories are like this. When we do mathematics, we can make these kinds of categories up and understand them, but we wouldn't expect our naturally learned categories to be made up of necessary and sufficient conditions. ****The neural system is not well-suited to process necessary and sufficient conditions because neurons react to the output of other neurons. Output is examined as an amount on a scale rather than an a discrete 0 or 1.**** We have evolved to handle some all or none categories, such as dangers, flight, food, etc. But we have also evolved to see things in degrees.

The structures of most categories are graded. Eleanor Rosch has done studies in which she gave subjects cues such as "A robin is a bird," A chicken is a bird," "An pelican is a bird." She asked the subjects to respond true or false to each statement. The responses of true were faster for the cue involving a robin and for those with chicken or pelican. While each of these kinds of birds is definitely a bird, the robin is a better example of a bird than a chicken or pelican. So the category is graded. This is an example of an all or none category with boundaries and still have gradations within it.

This experiment also applies to numbers. For instance, a good example of an odd number is 3, 5, 7, etc. But 4987 is not such a great example. This effect comes from our greater familiarity and ease of manipulation with the lower numbers. As a general point, the kind of reasoning or processing that you usually do with particular members of a category that has an effect on the structure of the category.

There are also examples of cognitive reference points in the numbers. 100, 1000, etc. are cognitive reference points. In a true/false test on the cues, "99 is close to 100" and "100 is close to 99," the response to the first cue is always faster. A cognitive reference point is a standard, which has a special cognitive status. It is a prototype.

There are lots of types of prototypes. Each type involves different kinds of reasoning. The cognitive reference point is used to make estimates and for location in semantic space. Graded prototypes are used for linear scale reasoning. For instance, how tall is someone? If A is taller than B and B is taller than C, then A is taller than C. There is a frame-based prototype which is used for frame-based reference in which prototypes are defined by conceptual structure. Social stereotypes are used for snap judgments made usually about people, in a social context and they are challengeable. Examples include "Blondes are dumb," "Computer Science students are geeks."

There are typical case prototypes used for automatic inference about common cases. For instance, if someone says that there's a bird outside, we expect to see a small songbird, not a great auk or an ostrich. An experiment was done by Lance Ripps in which he told one group of subjects that all the robins on an island got a certain disease and asked them if they would expect the ducks to get it. Then he told another group of subjects that all the ducks on this island had a certain disease and asked if they would expect the robins to get it. The subjects were more likely to expect the ducks to catch a disease from the robins than vice versa. The inference goes from the typical case to the category as a whole, so the typical case stands for the category as a whole.

Ideal case prototypes are used for standards of judgment or comparison. They are different from typical prototypes as in the typical husband vs. the ideal husband or the typical used care vs. the ideal used car.

Paragon exemplars are ideal individual case. Michael Jordan is a paragon exemplar for basketball. In language, paragon exemplars are used for describing a person/thing as excellent, for instance, "That is the Cadillac of vacuum cleaners." The anti-paragon exemplar is the worst individual case of a category. Dennis Rodman is an anti-paragon exemplar of basketball. Exemplars are the actual members of a category which we perceive to be the best or the worst members of that category. Commercials use paragons and anti-paragons a lot. You can do reasoning with these prototypes as positive and negative role models.

Salient examples are used to make probability judgments. For instance, after a famous DC-10 crash, people judged all DC-10's to be unsafe and wouldn't travel on them, even though DC-10's had the best overall safety record at the time. Also, after the mad cow disease scare, fewer people would eat beef. The probability judgments based on salient examples are not rational.

Necessary and sufficient conditions have to do with essence, a special kind of prototype. When you have something defined by (usually conscious) necessary and sufficient conditions, there are essences which are used in causal reasoning about natural behavior. For example, a tree is made of wood, so it can be burned or cut. It has a particular shape with root, branches, a trunk, so it can be climbed; birds can nest in it. It has a particular pattern of grown. We can draw inferences about an item from what we take to be essential characteristics of it. We often categorize things in terms of a folk theory of essences. The folk theory of essences says that everything has an essence which makes it what it is and if you know the essence, you can predict the natural behavior. A thing cannot lose its essence. For instance, if a lemon gets squashed by a truck or dyed a different color, it is still a lemon. You can explain why it behaves as it does. The folk theory is what we all have about what objects are like. A lot of science consists of looking for essences of things, for instance the essences of molecules or species. The folk theory of essences fails a lot in the real world, but it structures our understanding of categories. We assume there are essences even if we don't know them and that there are experts who can test for the essences. Essences are imposed by us; they don't exist in the real world, so in some cases it doesn't make any sense to categorize something according to an essence.

Radial categories are very complex, particularly interesting categories, which we do not know how to characterize in a neural system. Radial categories are everywhere. They example of a radial category from the reading is 'mother'. What counts as a mother? The typical cases of mother are defined by the birth frame, the nurturance frame, the genetic frame, the marriage frame and the anthropological frame. In the central case, all of these frames apply, but in many cases only some of the frames apply, as in 'step mother'. In some cases only one model is satisfied. For instance, the woman who donates genetic material to a child, but doesn't give birth to it or raise is it is a kind of mother which satisfies only the genetic model. These models are important to understanding what a mother is. For instance a working mother is defined relative to the nurturance frame. A woman who gave up her child for adoption but is still working is not a working mother. The term 'working mother' presupposes that the mother is raising the child, which is an assumption of the nurturance frame. If all of the models are satisfied for a particular case, then it is a central case of the category. If only some of the models hold for a case, then that is a less central member of the category, but only one model needs to be satisfied for something to be a member of the category at all.

Another kind of radial category is one in which there is one central case (as opposed to a set of models) and other cases are extensions of that central one, for example 'harm'. The central kind of harm is physical, but there is also emotional, financial and social harm which are metaphorical extension of the central case.

A radial category is not the same as polysemy in that 'mother' and 'mother' have two different meanings. Instead there are several senses of 'mother' which are all part of the same complicated concept.

Radial categories do have gradations; some members are better and worse examples of the category. A genetic mother, for instance, is not a great example of a mother. The central case or cases in radial categories is the basis for extension to less central members of the category, so that we use that central case cognitively. In radial categories, better examples have more features of the central case and worse examples have fewer features. The central case of a category defines the concept of the category on which the extensions are based.

The purpose of learning about categories is to ask the question: Given our neural system how can we get structures that complicated with that many forms of reasoning. This question has to be addressed with each of the forms of reasoning and each of the types of cognition involved. However, the structures which we use to describe what we see happening with categories are not necessarily the same as the underlying structure giving rise to what we see. So we need a theory which can account for the totality of evidence from experimentation and other ways of investigation. When you start reading the literature in neural categorization, many people only address the graded categories, but the other cases are the hard ones.

How basic level categories arose. Roger Brown noticed that a dime was called a dime and that children quickly learned short words such as "kitty" which they interacted with and saw pictures of. Later on Brent Berlin was doing work on the categorization of plants in Chappas. He took a botanist down to Chappas and he looked at how plants were named and categorized and identified. He first looked at how many plants people could name and how accurate they were according to the botanist. He found that people used one name for a plant when it was identified from a distance and another name when it was identified from close up. The people were able to identify 800-900 species of plant. At the genus level of biological categorization, the botanist determined that the people of Chappas were 90-95% accurate in identifying the plants. At the species and sub-species level, though, they were only about 35-50% accurate. Above the level of genus, there is also much less accuracy. As it turns out, it is the genus level of distinction which is more important for ritual and culture, and the words to describe the genus level are much shorter.

In the first biological classification, set up by Linnaeus, the genus was intended to be the level which people should be able to easily distinguish and remember. Why was it set up this way? Why should anything cognitive correspond to divisions in the world? Or do they?

In Chappas, the botanists found that usually there was only one species of a plant in each ecological niche, but they all looked pretty much alike. The genus has to do with differences we can see, while the species distinction involves breeding, which is not easy to see. So its easiest for us to see the differences between things at the genus level. For instance, it is easy for us to tell sheep from goats, red woods from live oaks.

Berlin looked for defining characteristics of the genus and he found that they have gestalt perception; we can pick them out from a distance. He also found that children learn the distinction between genuses earlier than the distinction between species. Also, the words for genuses are shorter.

Eleanor Rosch asked if this happens with ordinary objects around us. She found that it did. If you look at a hierarchy of categories, such as furniture> chair> rocking chair, the middle of the hierarchy is a basic level category. In general basic level categories have mental images associated with them. Chairs do, but generalized furniture doesn't. Also, we have ease of gestalt perception. We have motor programs for interacting with these things. For instance, we have special motor programs for interacting with a chair, but there's not motor program for interacting in general with furniture. Children learn basic level distinctions first; the words are shorter and easier to remember. Also, most of our knowledge is organized at the basic level. We know a great deal about chairs and tables, but little about furniture in general.

Basic levels are optimal for interacting with the world with our bodies, perceptual systems, motor systems, etc. That means that the basic levels are not defined by the external world, but by our interactions in it. Part of that has to do with the structure of our bodies and our brains. We have evolved to make certain perceptual distinctions, mental images and motor programs, which have to do with how our bodies and brains are set up. This is closely related to the structure of basic level. The question for this course is how does the structure of our brains give rise to basic level categories? How are they represented differently neurally? We don't have the answer to this yet.