Zadeh 21 Fillmore's frame semantics is also prefigured by Austin. Take the sense in which I talk of a cricket bat and a cricket ball and a cricket umpire.The reason that all are called by the same name is perhaps that each has its part-its own special part-to play in the activity called cricketing:it is no good to say that cricket means simply 'used in cricket':for we cannot explain what we mean by 'cricket'except by explaining the special parts played in cricketing by the bat,ball,etc.(P.73) Austin here is discussing a holistic structure-a gestalt-governing our understanding of activities like cricket.Such activities are structured by what we call a cognitive model,an overall structure which is more than merely a composite of its parts.A modifier like cricket in cricket bat, cricket ball,cricket umpire,and so on does not pick out any common property or similarity shared by bats,balls,and umpires.It refers to the structured activity as a whole.And the nouns that cricket can modify form a category,but not a category based on shared properties.Rather it is a category based on the structure of the activity of cricket and on those things that are part of the activity.The entities characterized by the cogni- tive model of cricket are those that are in the category.What defines the category is our structured understanding of the activity. Cognitive psychologists have recently begun to study categories based on such holistically structured activities.Barsalou (1983,1984)has stud- ied such categories as things to take on a camping trip,foods not to eat on a diet,clothes to wear in the snow,and the like.Such categories,among their other properties,do not show family resemblances among their members. Like Wittgenstein,Austin was dedicated to showing the inadequacies of traditional philosophical views of language and mind-views that are still widely held.His contribution to prototype theory was to notice for words the kinds of things that Wittgenstein noticed for conceptual catego- ries.Language is,after all,an aspect of cognition.Following Austin's lead,we will try to show how prototype theory generalizes to the linguis- tic as well as the nonlinguistic aspects of mind. Zadeh Some categories do not have gradations of membership,while others do The category U.S.Senator is well defined.One either is or is not a sena- tor.On the other hand,categories like rich people or tall men are graded, simply because there are gradations of richness and tallness.Lotfi Zadeh (1965)devised a form of set theory to model graded categories.He called it fuzzy set theory.In a classical set,everything is either in the set (has membership value 1)or is outside the set (has membership value 0).In a
Zadeh 21 Fillmore's frame semantics is also prefigured by Austin. Take the sense in which I talk of a cricket bat and a cricket ball and a cricket umpire. The reason that all are called by the same name is perhaps that each has its part -its own special part-to play in the activity called cricketing: it is no good to say that cricket means simply 'used in cricket': for we cannot explain what we mean by 'cricket' except by explaining the special parts played in cricketing by the bat, ball, etc. (P. 73) Austin here is discussing a holistic structure-a gestalt-governing our understanding of activities like cricket. Such activities are structured by what we call a cognitive model, an overall structure which is more than merely a composite of its parts. A modifier like cricket in cricket bat, cricket ball, cricket umpire, and so on does not pick out any common property or similarity shared by bats, balls, and umpires. It refers to the structured activity as a whole. And the nouns that cricket can modify form a category, but not a category based on shared properties. Rather it is a category based on the structure of the activity of cricket and on those things that are part of the activity. The entities characterized by the cognitive model of cricket are those that are in the category. What defines the category is our structured understanding of the activity. Cognitive psychologists have recently begun to study categories based on such holistically structured activities. Barsalou (1983, 1984) has studied such categories as things to take on a camping trip, foods not to eat on a diet, clothes to wear in the snow, and the like. Such categories, among their other properties, do not show family resemblances among their members. Like Wittgenstein, Austin was dedicated to showing the inadequacies of traditional philosophical views of language and mind-views that are still widely held. His contribution to prototype theory was to notice for words the kinds of things that Wittgenstein noticed for conceptual categories. Language is, after all, an aspect of cognition. Following Austin's lead, we will try to show how prototype theory generalizes to the linguistic as well as the nonlinguistic aspects of mind. Zadeh Some categories do not have gradations of membership, while others do. The category U.S. Senator is well defined. One either is or is not a senator. On the other hand, categories like rich people or tall men are graded, simply because there are gradations of richness and tallness. Lotfi Zadeh (1965) devised a form of set theory to model graded categories. He called it fuzzy set theory. In a classical set, everything is either in the set (has membership value 1) or is outside the set (has membership value 0). In a
22 Chapter 2 fuzzy set,as Zadeh defined it,additional values are allowed between 0 and 1.This corresponds to Zadeh's intuition that some men are neither clearly tall nor clearly short,but rather in the middle-tall to some de- gree. In the original version of fuzzy set theory,operations on fuzzy sets are simple generalizations of operations on ordinary sets: Suppose element x has membership value v in fuzzy set A and member- ship value w in fuzzy set B. Intersection:The value of x in A n B is the minimum of v and w. Union:The value of x in A U B is the maximum of v and w. Complement:The value of x in the complement of A is 1 -v. It is a natural and ingenious extension of the classical theory of sets. Since Zadeh's original paper,other definitions for union and intersec- tion have been suggested.For an example,see Goguen 1969.The best discussion of attempts to apply fuzzy logic to natural language is in Me- Cawley 1981. Lounsbury Cognitive anthropology has had an important effect on the development of prototype theory,beginning with Floyd Lounsbury's(1964)studies of American Indian kinship systems.Take the example of Fox,in which the word nehcihsahA is used not only to refer to one's maternal uncle-that is,one's mother's mother's son-but also to one's mother's mother's son's son,one's mother's mother's father's son's son,one's mother's brother's son,one's mother's brother's son's son,and a host of other rela- tives.The same sort of treatment also occurs for other kinship categories. There are categories of“fathers,"“mothers,”sons,”and“daughters'”with just as diverse a membership. The Fox can,of course,distinguish uncles from great-uncles from nephews.But they are all part of the same kinship category,and thus are named the same.Lounsbury discovered that such categories were struc- tured in terms of a "focal member"and a small set of general rules extending each category to nonfocal members.The same rules apply across all the categories.The rules applying in Fox are what Lounsbury called the“Omaha type'”: Skewing rule:Anyone's father's sister,as a linking relative,is equiva- lent to that person's sister. Merging rule:Any person's sibling of the same sex,as a linking rela- tive,is equivalent to that person himself
22 Chapter 2 fuzzy set, as Zadeh defined it, additional values are allowed between a and 1. This corresponds to Zadeh's intuition that some men are neither clearly tall nor clearly short, but rather in the middle-tall to some degree. In the original version of fuzzy set theory, operations on fuzzy sets are simple generalizations of operations on ordinary sets: Suppose element x has membership value v in fuzzy set A and membership value w in fuzzy set B. Intersection: The value of x in A n B is the minimum of v and w. Union: The value of x in A U B is the maximum of v and w. Complement: The value of x in the complement of A is 1 - v. It is a natural and ingenious extension of the classical theory of sets. Since Zadeh's original paper, other definitions for union and intersection have been suggested. For an example, see Goguen 1969. The best discussion of attempts to apply fuzzy logic to natural language is in McCawley 1981. Lounsbury Cognitive anthropology has had an important effect on the development of prototype theory, beginning with Floyd Lounsbury's (1964) studies of American Indian kinship systems. Take the example of Fox, in which the word nehcihsiihA is used not only to refer to one's maternal uncle-that is, one's mother's mother's son-but also to one's mother's mother's son's son, one's mother's mother's father's son's son, one's mother's brother's son, one's mother's brother's son's son, and a host of other relatives. The same sort of treatment also occurs for other kinship categories. There are categories of "fathers," "mothers," sons," and "daughters" with just as diverse a membership. The Fox can, of course, distinguish uncles from great-uncles from nephews. But they are all part of the same kinship category, and thus are named the same. Lounsbury discovered that such categories were structured in terms of a "focal member" and a small set of general rules extending each category to nonfocal members. The same rules apply across all the categories. The rules applying in Fox are what Lounsbury called the "Omaha type": Skewing rule: Anyone's father's sister, as a linking relative, is equivalent to that person's sister. Merging rule: Any person's sibling of the same sex, as a linking relative, is equivalent to that person himself
Lounsbury 23 Half-sibling rule:Any child of one of one's parents is one's sibling. The condition"as a linking relative"is to prevent the rule from applying directly;instead,there must be an intermediate relative between ego(the reference point)and the person being described.For example,the skew- ing rule does not say that a person's paternal aunt is equivalent to his sis- ter.But it does say,for example,that his father's paternal aunt is equiva- lent to his father's sister.In this case,the intermediate relative is the father. These rules have corollaries.For example, Skewing corollary:The brother's child of any female linking relative is equivalent to the sibling of that female linking relative.(For example,a mother's brother's daughter is equivalent to a mother's sister.) Lounsbury illustrates how such rules would work for the Fox maternal uncle category.We will use the following abbreviations:M:mother,F: father,B:brother,S:sister,d:daughter,s:son.Let us consider the fol- lowing examples of the nehcihsahA(mother's brother)category,and the equivalence rules that make them part of this category.Lounsbury's point in these examples is to take a very distant relative and show precisely how the same general rules place that relative in the MB (mother's brother)category.Incidentally,all the intermediate relatives in the following cases are also in the MB category-e.g.,MMSs,that is, mother's mother''ssister''sson,etc.Let“→”stand for"is equivalent to.” 1.Mother's mother's father's sister's son:MMFSs MMFSs MMSs [by the skewing rule MMSs MMs [by the merging rule MMs MB [by the half-sibling rule] 2.Mother's mother's sister's son's son:MMSss MMSss MMss by the merging rulel MMss → MBs by the half-sibling rule MBs MB by the skewing corollary 3. Mother's brother's son's son's son:MBsss MBsss → MBss [by the skewing corollary] MBss → MBs [by the skewing corollary MBs → MB by the skewing corollary Similarly,the other "uncles"in Fox are equivalent to MB. Not all conceptual systems for categorizing kinsmen have the same skewing rules.Lounsbury also cites the Crow version of the skewing rule: Skewing rule:Any woman's brother,as a linking relative,is equivalent to that woman's son,as a linking relative
Lounsbury 23 Half-sibling rule: Any child of one of one's parents is one's sibling. The condition "as a linking relative" is to prevent the rule from applying directly; instead, there must be an intermediate relative between ego (the reference point) and the person being described. For example, the skewing rule does not say that a person's paternal aunt is equivalent to his sister. But it does say, for example, that his father's paternal aunt is equivalent to his father's sister. In this case, the intermediate relative is the father. These rules have corollaries. For example, Skewing corollary: The brother's child of any female linking relative is equivalent to the sibling of that female linking relative. (For example, a mother's brather's daughter is equivalent to a mother's sister.) Lounsbury illustrates how such rules would work for the Fox maternal uncle category. We will use the following abbreviations: M: mother, F: father, B: brother, S: sister, d: daughter, s: son. Let us consider the following examples of the nehcihsiihA (mother's brother) category, and the equivalence rules that make them part of this category. Lounsbury's point in these examples is to take a very distant relative and show precisely how the same general rules place that relative in the MB (mother's brother) category. Incidentally, all the intermediate relatives in the following cases are also in the MB category--e.g., MMSs, that is, mother's mother's sister's son, etc. Let "~" stand for "is equivalent to." 1. Mother's mother's father's sister's son: MMFSs MMFSs MMSs [by the skewing rule] MMSs MMs [by the merging rule] MMs MB [by the half-sibling rule] 2. Mother's mother's sister's son's son: MMSss MMSss MMss [by the merging rule] MMss MBs [by the half-sibling rule] MBs MB [by the skewing corollary] 3. Mother's brother's son's son's son: MBsss MBsss MBss [by the skewing corollary] MBss MBs [by the skewing corollary] MBs MB [by the skewing corollary] Similarly, the other "uncles" in Fox are equivalent to MB. Not all conceptual systems for categorizing kinsmen have the same skewing rules. Lounsbury also cites the Crow version of the skewing rule: Skewing rule: Any woman's brother, as a linking relative, is equivalent to that woman's son, as a linking relative
24 Chapter 2 Skewing corollary:The sister of any male linking relative is equivalent to the mother of that male linking relative These rules are responsible for some remarkable categorizations.One's paternal aunt's son is classified as one's "father."But one's paternal aunt's daughter is classified as one's "grandmother"!Here are the deriva- tions: Father's sister's son:FSs FSs FMs [by skewing corrollary] FMs FB [by half-sibling rule] FB F by merging rule Father's sister's daughter:FSd FSd → FMd [by skewing corollary] FMd FS [by half-sibling rule] FS FM [by skewing corollary] Moreover,Lounsbury observed that these categories were not mere mat- ters of naming.Such things as inheritance and social responsibilities fol- low category lines. Categories of this sort-with a central member plus general rules-are by no means the norm in language,as we shall see.Yet they do occur.We will refer to such a category as a generative category and to its central member as a generator.A generative category is characterized by at least one generator plus something else:it is the "something else"that takes the generator as input and yields the entire category as output.It may be either a general principle like similarity or general rules that apply else- where in the system or specific rules that apply only in that category.In Lounsbury's cases,the "something else"is a set of rules that apply throughout the kinship system.The generator plus the rules generate the category. In such a category,the generator has a special status.It is the best ex- ample of the category,the model on which the category as a whole is built.It is a special case of a prototype. Berlin and Kay The next major contribution of cognitive anthropology to prototype the- ory was the color research of Brent Berlin and Paul Kay.In their classic, Basic Color Terms (Berlin and Kay 1969),they took on the traditional view that different languages could carve up the color spectrum in arbi- trary ways.The first regularity they found was in what they called basic color terms.For a color term to be basic
24 Chapter 2 Skewing corollary: The sister of any male linking relative is equivalent to the mother of that male linking relative. These rules are responsible for some remarkable categorizations. One's paternal aunt's son is classified as one's "father." But one's paternal aunt's daughter is classified as one's "grandmother"! Here are the derivations: Father's sister's son: FSs FSs --? FMs [by skewing corrollary] FMs --? FB [by half-sibling rule] FB --? F [by merging rule] Father's sister's daughter: FSd FSd --? FMd [by skewing corollary] FMd --? FS [by half-sibling rule] FS --? FM [by skewing corollary] Moreover, Lounsbury observed that these categories were not mere matters of naming. Such things as inheritance and social responsibilities follow category lines. Categories of this sort-with a central member plus general rules-are by no means the norm in language, as we shall see. Yet they do occur. We will refer to such a category as a generative category and to its central member as a generator. A generative category is characterized by at least one generator plus something else: it is the "something else" that takes the generator as input and yields the entire category as output It may be either a general principle like similarity or general rules that apply elsewhere in the system or specific rules that apply only in that category. In Lounsbury's cases, the "something else" is a set of rules that apply throughout the kinship system. The generator plus the rules generate the category. In such a category, the generator has a special status. It is the best example of the category, the model on which the category as a whole is built. It is a special case of a prototype. Berlin and Kay The next major contribution of cognitive anthropology to prototype theory was the color research of Brent Berlin and Paul Kay. In their classic, Basic Color Terms (Berlin and Kay 1969), they took on the traditional view that different languages could carve up the color spectrum in arbitrary ways. The first regularity they found was in what they called basic color terms. For a color term to be basic
Berlin and Kay 25 -It must consist of only one morpheme,like green,rather than more than one,as in dark green or grass-colored. -The color referred to by the term must not be contained within an- other color.Scarlet is,for example,contained within red. -It must not be restricted to a small number of objects.Blond,for ex- ample,is restricted to hair,wood,and perhaps a few other things. -It must be common and generally known,like yellow as opposed to saffron. Once one distinguishes basic from nonbasic color terms,generalizations appear. Basic color terms name basic color categories,whose central members are the same universally.For example,there is always a psychologi- cally real category RED,with focal red as the best,or "purest,"exam- ple. The color categories that basic color terms can attach to are the equivalents of the English color categories named by the terms black, white,red,yellow,green,blue,brown,purple,pink,orange and gray. -Although people can conceptually differentiate all these color catego- ries,it is not the case that all languages make all of those differentia- tions.Many languages have fewer basic categories.Those categories include unions of the basic categories;for example,BLUE+GREEN.RED +ORANGE YELLoW,etc.When there are fewer than eleven basiccolor terms in a language,one basic term,or more,names such a union. -Languages form a hierarchy based on the number of basic color terms they have and the color categories those terms refer to. Some languages,like English,use all eleven,while others use as few as two.When a language has only two basic color terms,they are black and white-which might more appropriately be called cool(covering black, blue,green,and gray)and warm(covering white,yellow,orange,and red).When a language has three basic color terms,they are black,white, and red.When a language has four basic color terms,the fourth is one of the following:yellow,blue,or green.The possibilities for four-color-term languages are thus:black,white,red,yellow;black,white,red,blue;and black,white,red,green.And so on,down the following hierarchy: black,white red yellow,blue,green brown purple,pink,orange,gray
Berlin and Kay 25 - It must consist of only one morpheme, like green, rather than more than one, as in dark green or grass-colored. - The color referred to by the term must not be contained within another color. Scarlet is, for example, contained within red. - It must not be restricted to a small number of objects. Blond, for example, is restricted to hair, wood, and perhaps a few other things. - It must be common and generally known, like yellow as opposed to saffron. Once one distinguishes basic from nonbasic color terms, generalizations appear. - Basic color terms name basic color categories, whose central members are the same universally. For example, there is always a psychologically real category RED, with focal red as the best, or "purest," example. - The color categories that basic color terms can attach to are the equivalents of the English color categories named by the terms black, white, red, yellow, green, blue, brown, purple, pink, orange and gray. - Although people can conceptually differentiate all these color categories, it is not the case that all languages make all of those differentiations. Many languages have fewer basic categories. Those categories include unions of the basic categories; for example, BLUE + GREEN, RED + ORANGE + YELLOW, etc. When there are fewer than eleven basic color terms in a language, one basic term, or more, names such a union. - Languages form a hierarchy based on the number of basic color terms they have and the color categories those terms refer to. Some languages, like English, use all eleven, while others use as few as two. When a language has only two basic color terms, they are black and white-which might more appropriately be called cool (covering black, blue, green, and gray) and warm (covering white, yellow, orange, and red). When a language has three basic color terms, they are black, white, and red. When a language has four basic color terms, the fourth is one of the following: yellow, blue, or green. The possibilities for four-color-term languages are thus: black, white, red, yellow; black, white, red, blue; and black, white, red, green. And so on, down the following hierarchy: black, white red yellow, blue, green brown purple, pink, orange, gray