Prototype Theory
Encyclopedia
Prototype theory is a mode of graded categorization
in cognitive science
, where some members of a category are more central than others. For example, when asked to give an example of the concept furniture, chair is more frequently
cited than, say, stool.
Prototype theory also plays a central role in linguistics
, as part of the mapping from phonological structure
to semantics
.
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
(Foundations of 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.
Cognitive Representation of Semantic Categories (J Experimental Psychology v. 104:192-233),
Eleanor Rosch asked 200 American college students to
rate, on a scale of 1 to 7, whether they regarded the following items as
a good example of the category furniture. The resulting ranks are as
follows:
While one may differ from this list in terms of cultural specifics, the point is that such a graded categorization is likely to be present in all cultures. Further evidence that some members of a category are more privileged than others came from experiments involving:
Subsequent to Rosch's work, prototype effects have been investigated
widely in areas such as colour cognition (Brent Berlin
and Paul Kay
, 1969), and also for more abstract notions. Subjects may be asked,
e.g. "to what degree is this narrative
an instance of telling a lie?" [Coleman/Kay:1981]. Similarly
work has been done on actions (verbs like look,
kill, speak, walk [Pulman:83]), adjectives like "tall" [Dirven/Taylor:88], etc.
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).
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 sensory-motor affordance
s — 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
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.
More 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.
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 Gärdenfors
(Conceptual Spaces, MIT Press 2000) has elaborated a possible partial explanation of 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.
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).
Categorization
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 purpose. Ideally, a category illuminates a relationship between the subjects and objects of knowledge...
in cognitive science
Cognitive science
Cognitive science is the interdisciplinary scientific study of mind and its processes. It examines what cognition is, what it does and how it works. It includes research on how information is processed , represented, and transformed in behaviour, nervous system or machine...
, where some members of a category are more central than others. For example, when asked to give an example of the concept furniture, chair is more frequently
cited than, say, stool.
Prototype theory also plays a central role in linguistics
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
, as part of the mapping from phonological structure
Phonology
Phonology is, broadly speaking, the subdiscipline of linguistics concerned with the sounds of language. That is, it is the systematic use of sound to encode meaning in any spoken human language, or the field of linguistics studying this use...
to semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
.
As formulated in the 1970s by Eleanor Rosch
Eleanor Rosch
Eleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
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
Extension (semantics)
In any of several studies that treat the use of signs - for example, in linguistics, logic, mathematics, semantics, and semiotics - the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of...
or intensional
Intensional
Intensional* in philosophy of language: not extensional. See also intensional definition versus extensional definition.* in philosophy of mind: an intensional state is a state which has a propositional content....
semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
. Thus instead of a definition
Definition
A definition is a passage that explains the meaning of a term , or a type of thing. The term to be defined is the definiendum. A term may have many different senses or meanings...
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
Cognitive science
Cognitive science is the interdisciplinary scientific study of mind and its processes. It examines what cognition is, what it does and how it works. It includes research on how information is processed , represented, and transformed in behaviour, nervous system or machine...
and cognitive semantics
Cognitive semantics
Cognitive semantics is part of the cognitive linguistics movement. The main tenets of cognitive semantics are, first, that grammar is conceptualisation; second, that conceptual structure is embodied and motivated by usage; and third, that the ability to use language draws upon general cognitive...
, e.g. in the work of George Lakoff
George Lakoff
George P. Lakoff is an American cognitive linguist and professor of linguistics at the University of California, Berkeley, where he has taught since 1972...
(Women, Fire and Dangerous Things, 1987) or
Ronald Langacker
Ronald Langacker
Ronald Wayne Langacker is an American linguist and professor emeritus at the University of California, San Diego. He is best known as one of the founders of the cognitive linguistics movement and the creator of Cognitive Grammar....
(Foundations of Cognitive Grammar, vol. 1/2 1987/1991).
The term prototype has been defined in Eleanor Rosch
Eleanor Rosch
Eleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
'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.
Cognitive representation of semantic categories
In her 1975 paper,Cognitive Representation of Semantic Categories (J Experimental Psychology v. 104:192-233),
Eleanor Rosch asked 200 American college students to
rate, on a scale of 1 to 7, whether they regarded the following items as
a good example of the category furniture. The resulting ranks are as
follows:
- 1 chair
- 1 sofa
- 3 couch
- 3 table
- 5 easy chair
- 6 dresser
- 6 rocking chair
- 8 coffee table
- 9 rocker
- 10 love seat
- 11 chest of drawers
- 12 desk
- 13 bed
- ...
- 22 bookcase
- 27 cabinet
- 29 bench
- 31 lamp
- 32 stool
- 35 piano
- 41 mirror
- 42 tv
- 44 shelf
- 45 rug
- 46 pillow
- 47 wastebasket
- 49 sewing machine
- 50 stove
- 54 refrigerator
- 60 telephone
While one may differ from this list in terms of cultural specifics, the point is that such a graded categorization is likely to be present in all cultures. Further evidence that some members of a category are more privileged than others came from experiments involving:
- 1. Response Times: in which queries involving a prototypical members (e.g. is a robin a bird) elicited faster response times than for non-prototypical members.
- 2. Priming: When primed with the higher-level (superordinate) category, subjects were faster in identifying if two words are the same. Thus, after flashing furniture, the equivalence of chair-chair is detected more rapidly than stove-stove.
- 3. Exemplars: When asked to name a few exemplars, the more prototypical items came up more frequently.
Subsequent to Rosch's work, prototype effects have been investigated
widely in areas such as colour cognition (Brent Berlin
Brent Berlin
Overton Brent Berlin is an American anthropologist, most noted for his work with linguist Paul Kay on color, Basic Color Terms: Their Universality and Evolution .He originally received his Ph.D...
and Paul Kay
Paul Kay
Paul Kay is an emeritus professor of linguistics at the University of California, Berkeley, United States. He joined the University in 1966 as a member of the Department of Anthropology, transferring to the Department of Linguistics in 1982 and now working at the International Computer Science...
, 1969), and also for more abstract notions. Subjects may be asked,
e.g. "to what degree is this narrative
an instance of telling a lie?" [Coleman/Kay:1981]. Similarly
work has been done on actions (verbs like look,
kill, speak, walk [Pulman:83]), adjectives like "tall" [Dirven/Taylor:88], etc.
Another aspect in which Prototype Theory departs from traditional Aristotelian categorization is that there do not appear to be natural kind
Natural kind
In philosophy, a natural kind is a "natural" grouping, not an artificial one. Or, it is something that a set of things has in common which distinguishes it from other things as a real set rather than as a group of things arbitrarily lumped together by a person or group of people.If any natural...
categories (bird, dog) vs. artefacts (toys, vehicles).
Basic level categories
The other notion related to prototypes is that of a Basic Level incognitive 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 sensory-motor affordance
Affordance
An affordance is a quality of an object, or an environment, which allows an individual to perform an action. For example, a knob affords twisting, and perhaps pushing, while a cord affords pulling...
s — 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
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
categories. Thus, they
- maximize the number of attributes shared by members of the category, and
- minimize the number of attributes 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.
More 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.
Distance between concepts
The notion of prototypes is related to Wittgenstein's (later) 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 discussion 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
Family resemblance
Family resemblance is a philosophical idea made popular by Ludwig Wittgenstein, with the best known exposition being given in the posthumously published book Philosophical Investigations It has been suggested that Wittgenstein picked the idea and the term from Nietzsche, who had been using it,...
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 Gärdenfors
Peter Gärdenfors
Bjorn Peter Gärdenfors is a professor of cognitive science at the University of Lund, Sweden. He is a member of the Royal Swedish Academy of Letters, History and Antiquities and recipient of the Gad Rausing Prize . He received his doctorate from Lund University in 1974; his thesis title was...
(Conceptual Spaces, MIT Press 2000) has elaborated a possible partial explanation of 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
Tsonga
Tsonga may refer to:* Tsonga language, a Bantu language spoken in southern Africa* Tsonga people, a large group of people living mainly in southern Mozambique* Jo-Wilfried Tsonga , French tennis player...
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.
Combining categories
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).
Literature
- Berlin, B.Brent BerlinOverton Brent Berlin is an American anthropologist, most noted for his work with linguist Paul Kay on color, Basic Color Terms: Their Universality and Evolution .He originally received his Ph.D...
& Kay, P.Paul KayPaul Kay is an emeritus professor of linguistics at the University of California, Berkeley, United States. He joined the University in 1966 as a member of the Department of Anthropology, transferring to the Department of Linguistics in 1982 and now working at the International Computer Science...
(1969): Basic Color Terms: Their Universality and EvolutionBasic Color Terms: Their Universality and EvolutionBasic Color Terms: Their Universality and Evolution is a book by Brent Berlin and Paul Kay. Berlin and Kay's work proposed that the kinds of basic color terms a culture has, such as black, brown or red, are predictable by the number of color terms the culture has.Berlin and Kay posit seven levels...
, Berkeley. - Dirven, R. & Taylor, J. R. (1988): "The conceptualisation of vertical Space in English: The Case of Tall", in: Rudzka-Ostyn, B.(ed): Topics in Cognitive Linguistics. Amsterdam.
- Lakoff, G. (1987): Women, fire and dangerous things: What categories reveal about the mind, London.
- LoftusElizabeth LoftusElizabeth F. Loftus is an American psychologist and expert on human memory. She has conducted extensive research on the misinformation effect and the nature of false memories. Loftus has been recognized throughout the world for her work, receiving numerous awards and honorary degrees...
, E.F., "Spreading Activation Within Semantic Categories: Comments on Rosch’s “Cognitive Representations of Semantic Categories”", Journal of Experimental Psychology: General, Vol.104, No.3, (September 1975), p.234-240. - RoschEleanor RoschEleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
,, E., "Classification of Real-World Objects: Origins and Representations in Cognition", pp. 212–222 in Johnson-Laird, P.N. & Wason, P.C., Thinking: Readings in Cognitive Science, Cambridge University Press, (Cambridge), 1977. - RoschEleanor RoschEleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
, E. (1975): “Cognitive Reference Points”, Cognitive Psychology 7, 532-547. - RoschEleanor RoschEleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
, E., "Cognitive Representations of Semantic Categories", Journal of Experimental Psychology: General, Vol.104, No.3, (September 1975), pp. 192–233. - RoschEleanor RoschEleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
, E.H. (1973): "Natural categories", Cognitive Psychology 4, 328-350. - RoschEleanor RoschEleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
, E., "Principles of Categorization", pp. 27–48 in Rosch, E. & Lloyd, B.B. (eds), Cognition and Categorization, Lawrence Erlbaum Associates, Publishers, (Hillsdale), 1978. - RoschEleanor RoschEleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
, E., "Prototype Classification and Logical Classification: The Two Systems", pp. 73–86 in Scholnick, E.K. (ed), New Trends in Conceptual Representation: Challenges to Piaget’s Theory?, Lawrence Erlbaum Associates, Hillsdale, 1983. - RoschEleanor RoschEleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
, E., "Reclaiming Concepts", Journal of Consciousness Studies, Vol.6, Nos.11-12, (November/December 1999), pp. 61–77. - RoschEleanor RoschEleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
, E., "Reply to Loftus", Journal of Experimental Psychology: General, Vol.104, No.3, (September 1975), pp. 241–243. - RoschEleanor RoschEleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
, E. & Mervis, C.B., "Family Resemblances: Studies in the Internal Structure of Categories", Cognitive Psychology, Vol.7, No.4, (October 1975), pp. 573–605. - RoschEleanor RoschEleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
, E., Mervis, C.B., Gray, W., Johnson, D., & Boyes-Braem, P., Basic Objects in Natural Categories, Working Paper No.43, Language Behaviour Research Laboratory, University of California (Berkeley), 1975. - RoschEleanor RoschEleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...
, E., Mervis, C.B., Gray, W., Johnson, D., & Boyes-Braem, P., "Basic Objects in Natural Categories", Cognitive Psychology, Vol.8, No.3, (July 1976), pp. 382–439. - Taylor, J. R.(2003): Linguistic Categorization, Oxford University Press.
- Wittgenstein, L.Ludwig WittgensteinLudwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...
, Philosophical InvestigationsPhilosophical InvestigationsPhilosophical Investigations is, along with the Tractatus Logico-Philosophicus, one of the most influential works by the 20th-century philosopher Ludwig Wittgenstein...
(Philosophische Untersuchungen), Blackwell Publishers, 2001 (ISBN 0-631-23127-7).