Concepts are the categorization of objects, events, or people that share common properties. By using concepts, we are able to organize complex notions into simpler, and therefore more easily usable forms. Concept formation is the process by which we learn to form classes of things, event, people, and so forth.
While research on learning in animals has been used by some psychologists as evidence that primates at least, if not other species, are capable of concept formation, and computers have been programmed to process information by using and developing classification rules, these accomplishments are all relatively impoverished compared to human concept formation. For human beings, concept formation is essential to our life in the complex world of interactions with not only objects but also people and abstract ideas.
Child developmentalists, such as Jean Piaget and Lev Vygotsky, have researched the way children form their own concepts through experience, assimilate existing concepts such as cultural values, norms, and beliefs from adults, and further create and develop their own concepts as they mature toward adulthood. Cognitive psychologists, like Eleanor Rosch, have suggested that rather than a strictly logico-mathematical form of classification people develop natural categories that are graded, involving "prototypes," or typical examples.
Prototype theory has helped us to understand how we form concepts about our world, which contains from the start naturally occurring things. However, as Vygotsky noted, we learn much from our social interactions, and thus human concept formation is neither based on purely physical, concrete characteristics of objects, nor strictly on abstract, logico-mathematical principles. It reflects the everyday experiences we have with the natural and social worlds, together with our subjective, personal, and cultural interpretations we give to them, creating and defining new concepts as we interact with our world, ever seeking to understand all that we encounter and innovating, creating new and better concepts and substantial objects that improve the quality of our lives.
Concepts and categorization
Concepts are generalized ideas that represent a class of objects or events. A concept is an abstract idea or a mental symbol, typically associated with a corresponding representation in language or symbol, that denotes all of the objects in a given category or class of entities, interactions, phenomena, or relationships between them. Concepts are abstract in that they omit the differences of the things in their extension, treating them as if they were identical. They are universal in that they apply equally to every thing in their extension. Concepts are also the basic elements of propositions, much the same way a word is the basic semantic element of a sentence. Unlike perceptions, which are particular images of individual objects, concepts cannot be visualized. Because they are not, themselves, individual perceptions, concepts are discursive and result from reason. They can only be thought about, or designated, by means of a name. Words are not concepts. Words are signs for concepts.
Concepts lighten the load on memory and enhance our ability to communicate. For example, at the airport when asked what you have in your suitcase, you never answer with a detailed list of items: two jackets, a pair of Austrian shoes, four Greek shirts, the Bible, Introduction to Psychology, documents on Western Civilization, and so forth. More likely your answer will be "clothes" and "books." Using these categories reflects the operation of concepts.
Categorization is the process in which ideas and objects are recognized, differentiated and understood. Categorization implies that objects are grouped into categories, usually for some specific and cognitive purpose. Ideally, a category illuminates a relationship between the subjects and objects of knowledge. Categorization is fundamental in decision making and in all kinds of interaction with the environment. There are, however, different ways of approaching categorization.
Concept formation in humans and animals
Generally speaking, concepts are (a) acquired dispositions to recognize perceived objects as being of this kind or of that kind, and at the same time (b) to understand what this kind or that kind of object is like, and consequently (c) to perceive a number of perceived particulars as being the same in kind and to discriminate between them and other sensible particulars that are different in kind. Therefore, we can also say that concepts are shaping and directing forces in behavior. In fact, concept formation for animals is the process that we traditionally call learning. Experiments in animal learning generally involve discrimination between stimuli with different characteristics, say a red object rather than ones of other colors, a lighted passageway over a darkened one, the larger of two objects, or even the different one from a group. Such studies have suggested to some psychologists that animals are capable of a primitive level of concept formation.
There should be a few additions for human behavior, however: Concepts are acquired dispositions to understand what certain kinds of objects are like both (a) when the objects, though perceptible, are not actually perceived, and (b) also when they are not perceptible at all, as is the case with all the conceptual constructs we employ in physics, mathematics, and metaphysics.
Images, concepts, and symbols are the basic units of thought. Images are picture-like mental representations. Seeing something in our "mind's eye" is similar to seeing real objects. Information from the eyes normally activates the brain's primary visual area, creating an image. Other brain areas help us recognize the image by relating it to store knowledge. When we form a mental image, the system works in reverse. Brain areas where memories are stored send signals back to the visual cortex, where once again, an image is created. For example, if we visualize a friend's face, the area of our brain that specializes in perceiving faces will become more active.
Geologists use the earth's sediment layers to infer past events. Physicists cannot observe gravity directly, even though they study its effects. In similar fashion, we use images to think, remember, solve problems, and make decisions. Images allow us to scan information stored in memory, and to help us plan a course of actions. The insight of Albert Einstein into the Theory of relativity occurred when he created a visual image of chasing after and matching the speed of a beam light (Kosslyn and Koenig, 1992). Later he turned this visual image into "words and symbols."
Though visual imagery is dominant in our everyday life, images do not have to be only visual. They can also be auditory and even olfactory (involving the sense of smell). According to the data of cognitive psychology, ninety-seven percent of people have visual images, ninety-two percent have auditory images, and fifty percent have imagery for movements, touch, and smell.
Concepts and performance
Concepts can influence and determine behavior. We would assume, for instance, that it might be appropriate to pet an animal after determining that it is a dog, whereas we would behave differently after classifying the animal as a wolf.
To describe figuratively the influence of concepts on our performance, consider the following example. Suppose, we are driving a car in New York City and want to arrive at a specific location in the center of the city. A street map of the city would be a great help to us in reaching our destination. Suppose, however, we were given the wrong map, say the map of Los Angeles. The map by itself is not wrong; but it is useful for driving in Los Angeles, not in New York. Thus, it is easy to understand the ineffectiveness of trying to reach our destination. In this example, the map is the prototype for a concept. Only in the case of having the right map, the right prototype, does our behavior become effective. So, the map, or the prototype, should be the right one in order to perform an adequate and effective behavior.
Concepts are the categorization of the world
We acquire concepts by learning and forming rules. For example, orange, apple, and pear are included into the concept "fruit." A conceptual rule is a guideline for deciding whether objects or events belong to a concept class. A triangle must be a closed shape with three sides made of straight lines. Concepts help us classify newly encountered objects on the basis of our past experience. We can surmise that someone tapping a hand held screen is probably using some kind of computer, even if we have never encountered that specific brand before. One way we classify something as an example of a concept is to use rules that tell us what an instance of the concept is and what is not. Objects that follow the rules and have certain properties are called positive instances of the concept. The absence of such properties is the mark of a negative instance of the concept. Such rules work well for defining a concept such as "triangles" delineated above: closed, two-dimensional figures, with three sides, and angles that sum to 180 degrees.
Language is the communication of information through symbols according to definite and systematic rules. Language consists of symbols and/or words, as well as of rules for combining them. Grammar is the system of rules that determine how our thoughts can be expressed. Semantics are the rules governing the meaning of words and sentences. Concept formation is the process of integrating a series of features that group together to form a class of ideas or objects, in that way classifying information into meaningful categories. Conceptual rules are formal rules for deciding whether an object or an event is an example of a particular concept.
Types of concepts
Three types of concepts are differentiated: Conjunctive, rational, and disjunctive. Conjunctive concepts are defined by the presence of at least two features, which means that a conjunctive concept is a class of objects that have two or more common features. Rational concept is defined by the relationship between the features of an object or between an object and its surroundings. This means that rational concepts are based on how an object relates to something else, or how its features relate to one another. Disjunctive concepts are either/or: they have at least one of several possible features. Disjunctive concepts are defined by the presence of at least one of several possible features.
Denotative and connotative meanings
Concepts have two meanings: denotative and connotative. When saying denotative meaning, we understand the objective meaning of a word or a concept, how the word or the concept described in dictionaries and encyclopedias. When saying connotative meaning, we understand the subjective meaning of a certain word or concept, its emotional meaning, the meaning deriving from personal perceptions.
Those philosophers, who emphasize the connotative meaning of words and concepts, declare that systems of categories are not objectively "out there" in the world but are rooted in people's experience. Therefore, many conceptual categories—especially value-based categories—are not connotatively identical for different cultures, or for each individual within the same culture.
Prototypes, stereotypes, and faulty concepts
Images, concepts, and symbols are not enough for the functioning of human thought. We can have many situations when the usage of rules and features is not enough for our thought. Thinking of the concepts, fruit or bird we usually do not use rules and features; we base our thinking on prototypes which are ideal models used as a prime example of particular concepts. Prototypes are typical and highly representative examples of a concept. Rules are an efficient way to learn concepts, but examples remain important. It is unlikely that memorizing rules would allow a new listener to accurately categorize music as punk, hip hop, fusion, salsa, heavy metal, grunge rock, rap music, and so forth.
Stereotyping is used for concepts about people and refers to our cognizing and understanding of the socially, racially, and ethnically diverse world. Social stereotypes are oversimplified images of people in various groups. This means that stereotyped thinking tends to simplify the images of the traits of individuals who belong to a particular group. In general, the top categories on which most stereotypes are based are gender, age, race/ethnicity, place of residence, and social class. As a rule, stereotypes are either positive or negative, and tend to divide people into "us" and "them" categories.
On the one hand, stereotypes make the social world more manageable. On the other hand, stereotypes tend to grow into faulty concepts which can lead to thinking errors as well as to behavior and/or personality maladjustment. Stereotypes may be viewed as "all-or-nothing thinking." In this case, we classify things right or wrong, good or bad, fair or unfair, black or white, honest or dishonest. Thinking this way prevents us from appreciating the subtleties of life and also makes the world appear very poor and colorless. Placing people in categories always causes them to appear more similar than they really are. As a result, we tend to see out-group members very much alike, even when they are as varied as our friends and family. People who are not prejudiced work hard to actively inhibit stereotyped thoughts and to emphasize fairness and equality. A good way to tear down stereotypes is to get to know members from various ethnic and cultural groups as individuals.
Algorithms, heuristics, and decision making
When solving a certain problem or making any decision, human beings are apt to use definite strategies of thinking, which psychologists call algorithms and heuristics. Algorithms are systematic procedures for solving problems by evaluating all possible solutions until the correct one is found. An example of an algorithm is the method of picking out the largest number from an unsorted list of numbers. The solution necessarily requires looking at every number in the list, but only once at each. From this follows a simple algorithm:
- Assume the first item is the largest.
- Look at each of the remaining items in the list, and if a particular item is larger than the largest item found so far, make a note of it.
- The last noted item is the largest in the list when the process is complete.
Algorithms do not provide answers when the problems are not clearly specified. There are no procedures that can be set up in advance to guarantee a solution for such problems. Some problems are so vast that algorithms are simply out of question. Chess players cannot rely on algorithms only.
Heuristics constitute another strategy or technique that aids problem solving by limiting the number of possible solutions to be tried. Imagine you are in Athens, Greece and decide to look up an old friend Artemis Pipinelli. You open the phone book and find fifty-three A. Pipinellis. Certainly, you would not dial all 53 numbers until you find the right one. You will probably think, "Is there any way I can narrow the search." You remember hearing that Artemis lives by the beach. You take out the map and call only the numbers with addresses near the waterfront (Ellis and Hunt, 1992). You are using the heuristic strategy of problem solving and decision making. Like algorithms, a heuristic strategy is also an example of trial-and-error thinking, in which all possibilities are tried.
Computers and problem solving
Computers have provided scientists with a way to develop and test models that can be used to understand human thinking more thoroughly. The calculation of possible moves when playing chess is one example. In these applications, a machine is essentially performing the process of problem solving used in concept formation. Many aspects of human concept formation have not yet been successfully modeled by computer, yet there is also no evidence that human concept formation is based on any method of handling information that could not be programmed into a machine.
In medicine, physicians are interested in structural and functional imaging of brain (which is done through computers) for diagnostic purposes in order to make the treatment more effective. At the same time, researchers obtain new knowledge about the functions of higher mental processes, including the process of concept formation. Contemporary neuroscientists use four computerized techniques—microelectrodes, macroelectrodes, structural imaging, and functional imaging—to understand and to diagnose the principles of brain work.
Theories of Concept Formation
Theories of concepts and concept formation are those which try to understand and explain the principles and ways concepts are formed and how the thinking process as a whole develops.
Concept formation is one of the basic terms in the theory of cognitive development of Jean Piaget. Children loved talking to Jean Piaget, and he learned much by listening to them carefully—especially to their explanations, which no one had paid attention to before. All his life, Piaget was absorbed with studying the way children think, form concepts in their mind, and gain knowledge about the world as they grow. His research revealed that children begin by classifying based on concrete, physical attributes, later forming abstract concepts, developing hierarchical structures, and being able to perform complex transformations.
The development of language also involves concept formation. While some aspects, such as name learning, may be based on the same principles as discrimination learning, grammatical structures and their transformations involve complex concept formation.
The sociocultural theory of Lev Vygotsky seeks to explain persons' knowledge and the process of concept formation in terms of the guidance, support, and structure provided by the elders and the society as a whole, according to its social values and societal principles. This approach is particularly significant in studying the development and learning of cultural beliefs and other subjective concepts that are based more on human interpretation than on purely objective features of the physical world.
The Classical View
The classical Aristotelian view claims that categories are discrete entities characterized by a set of properties which are shared by their members. These are assumed to establish the conditions which are both necessary and sufficient to capture meaning.
According to the classical view, categories should be clearly defined, mutually exclusive, and collectively exhaustive. This way, any entity of the given classification—universe belongs unequivocally to one and only one of the proposed categories.
Ayn Rand's formulation
The first step in concept formation, called differentiation, is to isolate two or more things as belonging together, as units of the same class. Where many theories of concept formation hold that such isolation begins by noticing degrees of similarity, Ayn Rand's Objectivism holds that it starts by noticing degrees of differences. In psychology, particularly studies of animal learning, this process is known as discrimination. At the perceptual level, everything is different; however, some things are more different than others. The difference between two tables, for instance, is less than the difference between a table and a chair. Because two tables are less different from one another when contrasted against a third object, we group them together as units, as members of a group of similar objects.
Ayn Rand defines similarity as: "the relationship between two or more existents which possess the same characteristic(s), but in different measure or degree." Similarity is a matter of measurement. Going back to the table versus chair example, the difference between tables is a quantitative one-we can easily stretch one table into another, so we call them similar. The difference between tables and chairs, on the other hand, is qualitative, so we distinguish between these as belonging to another group. They are different qualitatively both physically, since chairs have a back that no amount of normal stretching can produce from a table, and functionally, since the purposes of chairs and tables are different. However, by going a little further in the manipulation one can make a chair from a table, and one can certainly sit on a table and put a plate of food on a chair. Thus on a broader level the difference between chairs and tables is quantitative, and indeed both can be categorized as furniture.
The second step of concept formation, integration, is based on a process Ayn Rand called measurement omission. In this step, we combine or integrate the units into a new, single mental unit by eliding the quantitative differences between the two units. We retain the characteristics of the units, but we elide the particular measurements-on the principle that these measurements must exist in some quantity, but may exist in any quantity. For example, when forming the concept table we retain the distinguishing characteristics—a flat, level surface and supports—but omit the particular measurements of those features. Based on this two-step process, Ayn Rand defined concepts as: "a mental integration of two or more units possessing the same distinguishing characteristics, with their particular measurements omitted."
Cognitive science: Prototype theory
Since the research by Eleanor Rosch and George Lakoff in the 1970s, categorization can also be viewed as the process of grouping things based on prototypes. The term prototype was been defined in Eleanor Rosch's study "Natural Categories" (1973) and was first defined as a stimulus, which takes a salient position in the formation of a category as it is the first stimulus to be associated with that category. Later, she redefined it as the most central member of a category.
It has been suggested that categorization based on prototypes is the basis for human cognitive development. This proposal is particularly significant since necessary and sufficient conditions are almost never met in categories of naturally occurring things. A cognitive approach accepts that natural categories are graded (they tend to be fuzzy at their boundaries) and inconsistent in the status of their constituent members. Prototype Theory uses graded categorization, where all members of a category do not have equal status. For example, chair is more prototypical of the concept furniture, than, say, lamp.
As formulated by Eleanor Rosch, prototype theory was a radical departure from traditional necessary and sufficient conditions as in Aristotelian logic, which led to set-theoretic approaches of extensional or intensional semantics. Thus instead of a definition based model, e.g., a bird may be defined as elements with the features [+feathers], [+beak] and [+ability to fly], prototype theory would consider a category like bird as consisting of different elements which have unequal status, e.g. a robin is more prototypical of a bird than, say a penguin. This leads to a graded notion of categories, which is a central notion in many models of cognitive science and cognitive semantics, such as in the work of George Lakoff (Women, Fire and Dangerous things, 1987).
The other significant notion related to prototypes is that of a "Basic Level" in cognitive categorization. Thus, when asked What are you sitting on?, most subjects prefer to say chair rather than a subordinate such as kitchen chair or a superordinate such as furniture. Basic categories are relatively homogeneous in terms of sensori-motor affordances—a chair is associated with bending of one's knees, a fruit with picking it up and putting it in your mouth, and so forth. At the subordinate level (e.g. [dentist's chairs], [kitchen chairs] etc.) hardly any significant features can be added to that of the basic level; whereas at the superordinate level, these conceptual similarities are hard to pinpoint. A picture of a chair is easy to draw (or visualize), but drawing furniture would be difficult.
Rosch (1978) defined the basic level as that level that has the highest degree of cue validity. Thus, a category like [animal] may have a prototypical member, but no cognitive visual representation. On the other hand, basic categories in [animal], i.e. [dog], [bird], [fish], are full of informational content and can easily be categorized in terms of Gestalt and semantic features.
The notion of prototypes is related to the (later) discomfort of Wittgenstein with the traditional notion of category. This influential theory has resulted in a view of semantic components more as possible rather than necessary contributors to the meaning of texts. His discussion on the category game is particularly incisive (Wittgenstein, 1953 Philosophical Investigations 66):
Consider for example the proceedings that we call `games'. I mean board games, card games, ball games, Olympic games, and so on. What is common to them all? Don't say, "There must be something common, or they would not be called `games' " - but look and see whether there is anything common to all. For if you look at them you will not see something common to all, but similarities, relationships, and a whole series of them at that. To repeat: don't think, but look! Look for example at board games, with their multifarious relationships. Now pass to card games; here you find many correspondences with the first group, but many common features drop out, and others appear. When we pass next to ball games, much that is common is retained, but much is lost. Are they all `amusing'? Compare chess with noughts and crosses. Or is there always winning and losing, or competition between players? Think of patience. In ball games there is winning and losing; but when a child throws his ball at the wall and catches it again, this feature has disappeared. Look at the parts played by skill and luck; and at the difference between skill in chess and skill in tennis. Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! And we can go through the many, many other groups of games in the same way; can see how similarities crop up and disappear. And the result of this examination is: we see a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail.
Clearly, the notion of family resemblance is calling for a notion of conceptual distance, which is closely related to the idea of graded sets, but there are problems as well.
In the notion of game above, is there a single prototype or several? Linguistic data from color studies seem to indicate that categories may have more than one focal element; the Tsonga color term rihlaza refers to a green-blue continuum, but appears to have two prototypes, a focal blue, and a focal green. Thus, it is possible to have single categories with multiple, disconnected, prototypes, in which case they may constitute the intersection of several convex sets rather than a single one.
All around us, we find instances where objects like tall man or small elephant combine one or more categories. This was a problem for extensional semantics, where the semantics of a word such as red is to be defined as the set of objects having this property. Clearly, this does not apply so well to modifiers such as small; a small mouse is very different from a small elephant.
These combinations pose a lesser problem in terms of prototype theory. In situations involving adjectives (such as tall), one encounters the question of whether or not the prototype of [tall] is a six feet tall man, or a 400 foot skyscraper [Dirven and Taylor 1988]. The solution emerges by contextualizing the notion of prototype in terms of the object being modified. This extends even more radically in compounds such as red wine or red hair which are hardly red in the prototypical sense, but the red indicates merely a shift from the prototypical color of wine or hair respectively. This corresponds to Ferdinand de Saussure's notion of concepts as purely differential: non pas positivement par leur contenu, mais negativement par leurs rapports avec les autres termes du systeme ("not positively, in terms of their content, but negatively by contrast with other terms in the same system").
Peter Gardenfors (Conceptual Spaces 2004) has elaborated a possible implementation to prototype theory in terms of multi-dimensional feature spaces, where a category is defined in terms of a conceptual distance. More central members of a category are "between" the peripheral members. He postulates that most natural categories exhibit a convexity in conceptual space, in that if x and y are elements of a category, and if z is between x and y, then z is also likely to belong to the category.
Thus, to understand how we form concepts about our world, which contains from the start naturally occurring things, it seems that prototype theory has much to offer.
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