Concept formation

Concepts are the categorization of objects, events, or people that share common properties. By using concepts, we are being able to organize complex notions into simpler, and therefore, more easily usable, cognitive categories.

Categories and Categorization

Concepts are generalized ideas that represent a class of objects or events. Concepts lighten the load on memory and enhance our ability to communicate. In the airports, when the Officer asks you 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 or blouses, 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.

A concept is an abstract idea or a mental symbol, typically associated with a corresponding representation in and language or symbology, 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.

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.

In addition, 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.

Concepts are categories that share common characteristics. 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.

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, i.e., what is 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, i.e., the meaning deriving from personal perceptions. Those philosophers who try 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 as well as for each individual even in the same socioculture.

Concepts are the categorization of the world

In our mind, orange, apple, and pear are included into the concept "fruit." We acquire concepts by learning and forming rules. A conceptual rule is a guideline for deciding whether objects or events belong to a concept class. E.g., a triangle must be a closed shape with three sides made of strait lines. Concepts help us classify newly encountered objects on the basis of our past experience. We can surmise that someone tapping a handheld 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 is an instance of the concept 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 expresssed. 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 and the process of concept formation

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 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. It 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.

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, e.g., 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's unlikely that memorizing rules would allow a new listener to accurately categorize, e.g., punk, hip hop, fusion, salsa, heavy metal, grunge rock,and rap music.

Stereotyping refers to our cognizing and understanding of the socially, racially and ethnically diverse world. Social stereotypes are oversiplified 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, SES/belongingness to a social class. As a rule, stereotypes are either positive or negative. Stereotypes 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 subtlties of most life problems 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 individuals from various ethnic and cultural groups.

Algorithms and heuristics in the process of problem solving and decision making

When solving a certain problem or making any decition, humans are apt to use definite strategies of thinking, which psychologists call algoritrhms and heurisrics. Algorythms are systematic procedure for solving a problem by evaluating all possible solutions until the correct one is found. An example of an algorithm is the mathematical formula used to determine the area enclosed by a rectangle: Length multiplied by width give the answer. 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 algothims are simply out of question. E.g., chess players cannot rely on algorithms only. Heuristic is 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 A.Pipinelli. You open the phone book and find 53 A.Pippinelis. 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 Pipinelli lives by the beach. Then 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, heuristic is also an example of trial-and-error thinking, in which all possibilities are tried, more or less randomly. Computers have provided scientists with a model that can be used to understand human thinking more thoroughly.

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 figuratively describe the influence of concepts on our performance, let's go through the following example. Suppose, we are driving a car in New York and want to arrive at a specific location in central New York. A street map of the city would be a great help to us in reaching our destination. But suppose, we were given the wrong map, 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's easy to understand the ineffectiveness of trying to reach our destination. In this example, the map is the prototype for a concept. Only in case of having the right map, i.e., the right prototype our behavior grows adequate. So, the map, i.e., the prototype should be the right one in order to perform an adequate and effective behavior.

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 visualise 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. We use images to think, remember, solve problems, and make decisions. Images allow us to scan information stored in memory, help us plan a course of actions. The insight of Albert Einstein into the Theory of relativity occured 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, i.e., 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, fifty percent have imagery for movements, touch, and smell.

Theories of Concept Formation

Theories of concepts and concept formation are those which try to understand and explain the principles and ways how concepts are formed and the thinking process as a whole develops.

Concept formation is one of the basic terms in the theory of Periods 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. 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.

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, Objectivism holds that it starts by noticing degrees of differences. At the perceptual level, everything is different; however, some things are more different from 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. Of course, at a broader level, even the difference between tables and chairs is quantitative-with enough stretching and pulling one could turn a chair into a table as well. However, the point is that the table-to-table stretching is much less than the table-to-chair stretching, so we consider one quantitative and the other qualitative.

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 idea of necessary and sufficient conditions is almost never met in categories of naturally occurring things. It has also been suggested that categorisation based on prototypes is the basis for human development, and that this learning relies on learning about the world via embodiment. 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.

Categories form part of a hierarchical structure when applied to such subjects as taxonomy in biological classification: higher level: life-form level, middle level: generic or genus level, and lower level: the species level. These can be distinguished by certain traits that put an item in its distinctive category. But even these can be arbitrary and are subject to revision.

Categories at the middle level are perceptually and conceptually the more salient. The generic level of a category tends to elicit the most responses and richest images and seems to be the psychologically basic level. Typical taxonomies in zoology for example exhibit categorisation at the embodied level, with similarities leading to formulation of "higher" categories, and differences leading to differentiation within categories.

Prototype Theory is a model of graded categorization in Cognitive Science, 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 in the 1970s by Eleanor Rosch and others, 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, e.g. in the work of George Lakoff (Women, fire and dangerous things, 1987) or Ronald Langacker (Cognitive Grammar, vol. 1/2 1987/1991).

The term prototype has 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.

Another aspect in which Prototype Theory departs from traditional Aristotelian categorization is that there do not appear to be natural kind categories (bird, dog) vs. artefacts (toys, vehicles).

The other 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, etc. 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) defines 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 categorised in terms of Gestalt and semantic features.

Clearly semantic models based on attribute-value pairs fail to identify privileged levels in the hierarchy. Functionally, it is thought that basic level categories are a decomposition of the world into maximally informative categories. Thus, they

- maximize the num of attributes shared by members of the category, and

- minimize the num of attribs shared with other categories

However, the notion of Basic Level is problematic, e.g. whereas dog as a basic category is a species, bird or fish are at a higher level, etc. Similarly, the notion of frequency is very closely tied to the basic level, but is hard to pinpoint.

Other problems arise when the notion of a prototype is applied to lexical categories other than the noun. Verbs, for example, seem to defy a clear prototype: [to run] is hard to split up in more or less central members.

The notion of prototypes is related to the (later) Wittgenstein's discomfort 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 discursion on the category game is particularly incisive (Philosophical Investigations 66, 1953):

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.

Recently, Peter Gardenfors (Conceptual Spaces, MIT Press 2000) 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.

However, In the notion of game above, is there a single prototype or several? Recent linguistic data from colour studies seem to indicate that categories may have more than one focal element - e.g. the Tsonga colour 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 (e.g. tall), one encounters the question of whether or not the prototype of [tall] is a 6 feet tall man, or a 400 feet 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 colour of wine or hair respectively. This corresponds to 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" [p.162; not positively, in terms of their content, but negatively by contrast with other terms in the same system (tr. Harris 83)].

Other problems remain - e.g. in determining which of the constituent categories will contribute which feature? In the example of a "pet bird" [Hampton 97], pet provides the habitat of the compound (cage rather than the wild), whereas bird provides the skin type (feathers rather than fur).

References

ISBN links support NWE through referral fees

• Ellis, H.C., and Hunt, R.R.(1992). Fundamentals of cognitive Psychology. Madison: WI: Brown and Benchmark.
• Goldstone, R.L. and Kersten, A. (2003). Concepts and categorization. In Handbook of Psychology: Experimental Psychology. Vol. 4, pp. 599-621. New York: Wiley.
• Margolis, E., and Laurence, S. (Eds).(1999). Concepts: Core readings. Cambridge, MA: MIT Press.
• Farah, M.J., Weisberg, L.L., Monheit, M.A.and Peronnet, F. (1989). Brain activity underlying mental imagery. Journal of Cognitive Neuroscience, 1(4), 302-316.
• Kosslyn, S.M., Koenig, O.(1992). Wet mind: The new cognitive neuroscience. New York: Free Press.
• Kosslyn, S.M., Thompson, W.L., and Alpert, N.N.(1995). Topological representation of mental images in primary visual cortex. Nature, 378 (6556), 496.
• O'Craven, K.M., and Kanwisher, N.(2000). Mental imagery of faces and places activates corresponding stimulus-specific brain regions. Journal of Cognitive Neuroscience, 12(6), 1013-1023.

Literature

• John R. Taylor, 2003, Linguistic Categorization, Oxford University Press.
• Berlin, B., P. Kay (1969): Basic Color Terms: their Universality and Evolution, Berkeley.
• Dirven, R./Taylor, J.R. (1988). "The conceptualisation of vertical Space in English: The Case of Tall," Brygida Rudzka-Ostyn (ed). Topics in Cognitive Linguistics. Amsterdam.
• Lakoff, G. (1987): Women, fire and dangerous things: What categories reveal about the mind, London.
• Rosch, E. Heider (1973). "Natural categories," Cognitive Psychology 4, 328 - 350.
• Rosch, E. (1975): “Cognitive reference points,” Cognitive Psychology 7, 532-547.
• Wittgenstein, L. (1997): „Philosophische Untersuchungen“, in: Tractatus Logico-Philosophicus, 1, Frankfurt, 225-580.

External links

• Cognition is Categorization
• Paper on the Discursive creation of categorisation
• Categories and Induction
• The Ayn Rand Institute
• Internet Encyclopedia of Philosophy: Gottlob Frege
• Stanford Encyclopedia of Philosophy: Abstract Objects
• Discussion at The Well concerning Abstraction hierarchy
• The Purpose of Abstraction (a must read)
• The Objectivist Center

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