16 Chapter 2 Wittgenstein Family Resemblances The first major crack in the classical theory is generally acknowledged to have been noticed by Wittgenstein(1953,1:66-71).The classical category has clear boundaries,which are defined by common properties.Witt- genstein pointed out that a category like game does not fit the classical mold,since there are no common properties shared by all games.Some games involve mere amusement,like ring-around-the-rosy.Here there is no competition-no winning or losing-though in other games there is. Some games involve luck,like board games where a throw of the dice de- termines each move.Others,like chess,involve skill.Still others,like gin rummy,involve both. Though there is no single collection of properties that all games share, the category of games is united by what Wittgenstein calls family resem- blances.Members of a family resemble one another in various ways:they may share the same build or the same facial features,the same hair color, eye color,or temperament,and the like.But there need be no single col- lection of properties shared by everyone in a family.Games,in this re- spect,are like families.Chess and go both involve competition,skill,and the use of long-term strategies.Chess and poker both involve competi- tion.Poker and old maid are both card games.In short,games,like fam- ily members,are similar to one another in a wide variety of ways.That, and not a single,well-defined collection of common properties,is what makes game a category. Extendable Boundaries Wittgenstein also observed that there was no fixed boundary to the cate- gory game.The category could be extended and new kinds of games introduced,provided that they resembled previous games in appropriate ways.The introduction of video games in the 1970s was a recent case in history where the boundaries of the game category were extended on a large scale.One can always impose an artificial boundary for some pur- pose;what is important for his point is that extensions are possible,as well as artificial limitations.Wittgenstein cites the example of the cate- gory number.Historically,numbers were first taken to be integers and were then extended successively to rational numbers,real numbers,com- plex numbers,transfinite numbers,and all sorts of other kinds of numbers invented by mathematicians.One can for some purpose limit the cate- gory number to integers only,or rational numbers only,or real numbers only.But the category number is not bounded in any natural way,and it can be limited or extended depending on one's purposes
16 Chapter 2 Wittgenstein Family Resemblances The first major crack in the classical theory is generally acknowledged to have been noticed by Wittgenstein (1953,1:66-71). The classical category has clear boundaries, which are defined by common properties. Wittgenstein pointed out that a category like game does not fit the classical mold, since there are no common properties shared by all games. Some games involve mere amusement, like ring-around-the-rosy. Here there is no competition--no winning or losing-though in other games there is. Some games involve luck, like board games where a throw of the dice determines each move. Others, like chess, involve skill. Still others, like gin rummy, involve both. Though there is no single collection of properties that all games share, the category of games is united by what Wittgenstein calls family resemblances. Members of a family resemble one another in various ways: they may share the same build or the same facial features, the same hair color, eye color, or temperament, and the like. But there need be no single collection of properties shared by everyone in a family. Games, in this respect, are like families. Chess and go both involve competition, skill, and the use of long-term strategies. Chess and poker both involve competition. Poker and old maid are both card games. In short, games, like family members, are similar to one another in a wide variety of ways. That, and not a single, well-defined collection of common properties, is what makes game a category. Extendable Boundaries Wittgenstein also observed that there was no fixed boundary to the category game. The category could be extended and new kinds of games introduced, provided that they resembled previous games in appropriate ways. The introduction of video games in the 1970s was a recent case in history where the boundaries of the game category were extended on a large scale. One can always impose an artificial boundary for some purpose; what is important for his point is that extensions are possible, as well as artificial limitations. Wittgenstein cites the example of the category number. Historically, numbers were first taken to be integers and were then extended successively to rational numbers, real numbers, complex numbers, transfinite numbers, and all sorts ofother kinds of numbers invented by mathematicians. One can for some purpose limit the category number to integers only, or rational numbers only, or real numbers only. But the category number is not bounded in any natural way, and it can be limited or extended depending on one's purposes
Austin 17 In mathematics,intuitive human concepts like number must receive precise definitions.Wittgenstein's point is that different mathematicians give different precise definitions,depending on their goals.One can define number to include or exclude transfinite numbers,infinitesimals, inaccessible ordinals,and the like.The same is true of the concept of a polyhedron.Lakatos(1976)describes a long history of disputes within mathematics about the properties of polyhedra,beginning with Euler's conjecture that the number of vertices minus the number of edges plus the number of faces equals two.Mathematicians over the years have come up with counterexamples to Euler's conjecture,only to have other mathematicians claim that they had used the"wrong"definition of poly- hedron.Mathematicians have defined and redefined polyhedron repeat- edly to fit their goals.The point again is that there is no single well-defined intuitive category polyhedron that includes tetrahedra and cubes and some fixed range of other constructs.The category polyhedron can be given precise boundaries in many ways,but the intuitive concept is not limited in any of those ways;rather,it is open to both limitations and ex- tensions. Central and Noncentral Members According to the classical theory,categories are uniform in the following respect:they are defined by a collection of properties that the category members share.Thus,no members should be more central than other members.Yet Wittgenstein's example of number suggests that integers are central,that they have a status as numbers that,say,complex num- bers or transfinite numbers do not have.Every precise definition of num- ber must include the integers;not every definition must include transfinite numbers.If anything is a number.the integers are numbers;that is not true of transfinite numbers.Similarly,any definition of polyhedra had better include tetrahedra and cubes.The more exotic polyhedra can be included or excluded,depending on your purposes.Wittgenstein suggests that the same is true of games."Someone says to me:'Show the children a game.'I teach them garning with dice,and the other says'I didn't mean that sort of game'"(1:70).Dice is just not a very good example of a game. The fact that there can be good and bad examples of a category does not follow from the classical theory.Somehow the goodness-of-example structure needs to be accounted for. Austin Wittgenstein assumed that there is a single category named by the word game,and he proposed thatthat category and other categories are struc-
Austin 17 In mathematics, intuitive human concepts like number must receive precise definitions. Wittgenstein's point is that different mathematicians give different precise definitions, depending on their goals. One can define number to include or exclude transfinite numbers, infinitesimals, inaccessible ordinals, and the like. The same is true of the concept of a polyhedron. Lakatos (1976) describes a 10lig history of disputes within mathematics about the properties of polyhedra, beginning with Euler's conjecture that the number of vertices minus the number of edges plus the number of faces equals two. Mathematicians over the years have come up with counterexamples to Euler's conjecture, only to have other mathematicians claim that they had used the "wrong" definition of polyhedron. Mathematicians have defined and redefined polyhedron repeatedly to fit their goals. The point again is that there is no single well-defined intuitive category polyhedron that includes tetrahedra and cubes and some fixed range of other constructs. The category polyhedron can be given precise boundaries in many ways, but the intuitive concept is not limited in any of those ways; rather, it is open to both limitations and extensions. Central and Noncentral Members According to the classical theory, categories are uniform in the following respect: they are defined by a collection of properties that the category members share. Thus, no members should be more central than other members. Yet Wittgenstein's example of number suggests that integers are central, that they :lave a status as numbers that, say, complex numbers or transfinite numbers do not have. Every precise definition of nzunber must include the integers; not every definition must include transfinite numbers. If anything is a number. the integers are numbers; that is not true of transfinite numbers. Similarly, any definition of polyhedra had better include tetrahedra and cubes. The more exotic polyhedra can be included or excluded, depending on your purposes. Wittgenstein suggests that the same is true of games. "Someone says to me: 'Show the children a game.' I teach them gaming with dice, and the other says'I didn't mean that sort of game'" (1 :70). Dice is just not a very good example of a game. The fact that there can be good and bad examples of a category does not follow from the classical" theory. Somehow the goodness-of-example structure needs to be accounted for. Austin Wittgenstein assumed that there is a single category named by the word game, and he proposed that that category and other categories are struc-
18 Chapter 2 tured by family resemblances and good and bad examples.Philosopher J.L.Austin extended this sort of analysis to the study of words them- selves.In his celebrated paper,"The Meaning of a Word,"written in 1940 and published in 1961,Austin asked,"Why do we call different [kinds of]things by the same name?"The traditional answer is that the kinds of things named are similar,where“similar'”means“partially identical..” This answer relies on the classical theory of categories.If there are com- mon properties,those properties form a classical category,and the name applies to this category.Austin argued that this account is not accurate. He cited several classes of cases.As we will see in the remainder of this book,Austin's analysis prefigured much of contemporary cognitive se- mantics-especially the application of prototype theory to the study of word meaning. If we translate Austin's remarks into contemporary terms,we can see the relationship between Austin's observation and Wittgenstein's:the senses of a word can be seen as forming a category,with each sense being a member of that category.Since the senses often do not have properties in common,there is no classical category of senses that the word could be naming.However,the senses can be viewed as forming a category of the kind Wittgenstein described.There are central senses and noncentral senses.The senses may not be similar(in the sense of sharing properties), but instead are related to one another in other specifiable ways.It is such relationships among the senses that enable those senses to be viewed as constituting a single category:the relationships provide an explanation of why a single word is used to express those particular senses.This idea is far from new.Part of the job of traditional historical semanticists,as well as lexicographers,has been to speculate on such relationships.Recent re- search has taken up this question again in a systematic way.The most de- tailed contemporary study along these lines has been done by Brugman (1981),and it will be discussed below in case study 2. Let us now turn to Austin's examples: The adjective healthy':when I talk of a healthy body,and again of a healthy complexion,of healthy exercise:the word is not just being used equivocally...there is what we may call a primary nuclear sense of healthy':the sense in which 'healthy'is used of a healthy body:I call this nuclear because it is 'contained as a part'in the other two senses which may be set out as 'productive of healthy bodies'and 'resulting from a healthy body'....Now are we content to say that the exercise,the complexion,and the body are all called 'healthy'because they are similar?Such a remark can- not fail to be misleading.Why make it?(P.71) Austin's primary nuclear sense corresponds to what contemporary lin- guists call central or prototypical senses.The contained-as-a-part relation-
18 Chapter 2 tured by family resemblances and good and bad examples. Philosopher J. L. Austin extended this sort of analysis to the study of words themselves. In his celebrated paper, "The Meaning of a Word," written in 1940 and published in 1961, Austin asked, "Why do we call different (kinds of] things by the same name?" The traditional answer is that the kinds of things named are similar, where "similar" means "partially identical." This answer relies on the classical theory of categories. If there are common properties, those properties form a classical category, and the name applies to this category. Austin argued that this account is not accurate. He cited several classes of cases. As we will see in the remainder of this book, Austin's analysis prefigured much of contemporary cognitive semantics--especially the application of prototype theory to the study of word meaning. If we translate Austin's remarks into contemporary terms, we can see the relationship between Austin's observation and Wittgenstein's: the senses of a word can be seen as forming a category, with each sense being a member of that category. Since the senses often do not have properties in common, there is no classical category of senses that the word could be naming. However, the senses can be viewed as forming a category of the kind Wittgenstein described. There are central senses and noncentral senses. The senses may not be similar (in the sense of sharing properties), but instead are related to one another in other specifiable ways. It is such relationships among the senses that enable those senses to be viewed as constituting a single category: the relationships provide an explanation of why a single word is used to express those particular senses. This idea is far from new. Part of the job of traditional historical semanticists, as well as lexicographers, has been to speculate on such relationships. Recent research has taken up this question again in a systematic way. The most detailed contemporary study along these lines has been done by Brugman (1981), and it will be discussed below in case study 2. Let us now turn to Austin's examples: The adjective 'healthy': when I talk of a healthy body, and again of a healthy complexion, of healthy exercise: the word is not just being used equivocally ... there is what we may call a primary nuclear sense of 'healthy': the sense in which 'healthy' is used of a healthy body: I call this nuclear because it is 'contained as a part' in the other two senses which may be set out as 'productive of healthy bodies' and 'resulting from a healthy body'.... Now are we content to say that the exercise, the complexion, and the body are all called 'healthy' because they are similar? Such a remark cannot fail to be misleading. Why make it? (P. 71) Austin's primary nuclear sense corresponds to what contemporary linguists call central or prototypical senses. The contained-as-a-part relation-
Austin 19 ship is an instance of what we will refer to below as metonymy-where the part stands for the whole.Thus,given the relationships "productive of"and "resulting from,"Austin's examples can be viewed in the follow- ing way: Exercise of type B is productive of bodies of type A. Complexion of type C results from bodies of type A. The word healthy names A. With respect to naming,A stands for B.(Metonymy) With respect to naming,A stands for C.(Metonymy) Thus,the word "healthy"has senses A,B,and C.A,B,and Cform a cate- gory whose members are related in the above way.A is the central mem- ber of this category of senses (Austin's primary nuclear sense).B and C are extended senses,where metonymy is the principle of extension. I am interpreting Austin as making an implicit psychological claim about categorization.In the very act of pointing out and analyzing the dif- ferences among the senses,Austin is presupposing that these senses form a natural collection for speakers-so natural that the senses have to be differentiated by an analyst.No such analysis would be needed for true homonyms,say,bank(where you put your money)and bank (of a river), which are not part of a natural collection(or category)of senses.In point- ing out the existence of a small number of mechanisms by which senses are related to one another,Austin is implicitly suggesting that those mechanisms are psychologically real(rather than being just the arbitrary machinations of a clever analyst).He is,after all,trying to explain why people naturally use the same words for different senses.His implicit claim is that these mechanisms are principles which provide a "good rea- son"for grouping the senses together by the use of the same word.What I have referred to as "metonymy"is just one such mechanism. From metonymy.Austin turns to what Johnson and I(Lakoff and Johnson 1980)refer to as metaphor,but which Austin,following Aris- totle,terms "analogy." When A:B:X:Y then A and X are often called by the same name,e.g.,the foot of a mountain and the foot of a list.Here there is a good reason for calling the things both "feet"but are we to say they are "similar"?Not in any ordinary sense.We may say that the relations in which they stand to B and Y are similar relations.Well and good:but A and X are not the relations in which they stand.(Pp.71-72) Austin isn't explicit here,but what seems to be going on is that both mountains and lists are being structured in terms of a metaphorical pro- jection of the human body onto them.Expanding somewhat on Austin's analysis and translating it into contemporary terminology,we have:
Austin 19 ship is an instance of what we will refer to below as metonymy-where the part stands for the whole. Thus, given the relationships "productive of" and "resulting from," Austin's examples can be viewed in the following way: Exercise of type B is productive of bodies of type A. Complexion of type C results from bodies of type A. The word healthy names A. With respect to naming, A stands for B. (Metonymy) With respect to naming, A stands for C. (Metonymy) Thus, the word "healthy" has senses A, B, and C. A, B, and C form a category whose members are related in the above way. A is the central member of this category of senses (Austin's primary nuclear sense). Band C are extended senses, where metonymy is the principle of extension. I am interpreting Austin as making an implicit psychological claim about categorization. In the very act of pointing out and analyzing the differences among the senses, Austin is presupposing that these senses form a natural collection for speakers-so natural that the senses have to be differentiated by an analyst. No such analysis would be needed for true homonyms, say, bank (where you put your money) and bank (of a river), which are not part of a natural collection (or category) of senses. In pointing out the existence of a small number of mechanisms by which senses are related to one another, Austin is implicitly suggesting that those mechanisms are psychologically real (rather than being just the arbitrary machinations of a clever analyst). He is, after all, trying to explain why people naturally use the same words for different senses. His implicit claim is that these mechanisms are principles which provide a "good reason" for grouping the senses together by the use of the same word. What I have referred to as "metonymy" is just one such mechanism. From metonymy, Austin turns to what Johnson and I (Lakoff and Johnson 1980) refer to as metaphor, but which Austin, following Aristotle, terms "analogy." When A :B::X: Y then A and X are often called by the same name, e.g., the foot of a mountain and the foot of a list. Here there is a good reason for calling the things both "feet" but are we to say they are "similar"? Not in any ordinary sense. We may say that the relations in which they stand to B and Yare similar relations. Well and good: but A and X are not the relations in which they stand. (Pp. 71-72) Austin isn't explicit here, but what seems to be going on is that both mountains and lists are being structured in terms of a metaphorical projection of the human body onto them. Expanding somewhat on Austin's analysis and translating it into contemporary terminology, we have:
20 Chapter 2 A is the bottom-most part of the body. X is the bottom-most part of the mountain. X'is the bottom-most part of a list. Body is projected onto mountain,with A projected onto X. (Metaphor) Body is projected onto list,with A projected onto X'. (Metaphor) The word“foot”names A. A,X,and X'form a category,with A as central member.X and X'are noncentral members related to A by metaphor. Austin also notes examples of what we will refer to below as chaining within a category. Another case is where I call B by the same name as A,because it resembles A,C by the same name because it resembles B,D...and so on.But ulti- mately A and,say D do not resemble each other in any recognizable sense at all.This is a very common case:and the dangers are obvious when we search for something 'identical'in all of them!(P.72) Here A is the primary nuclear sense,and B,C.and D are extended senses forming a chain.A,B,C,and D are all members of the same category of senses,with A as the central member. Take a word like 'fascist':this originally connotes a great many characteristics at once:say,x,y,and z.Now we will use 'fascist'subsequently of things which possess only one of these striking characteristics.So that things called 'fascist'in these senses,which we may call 'incomplete'senses,need not be similar at all to each other.(P.72) This example is very much like one Fillmore(1982a)has recently given in support of the use of prototype theory in lexical semantics.Fillmore takes the verb climb,as in John climbed the ladder. Here,"climbing"includes both motion upward and the use of the hands to grasp onto the thing climbed.However,climbing can involve just mo- tion upwards and no use of the hands,as in -The airplane climbed to 20,000 feet. Or the motion upward may be eliminated if there is grasping of the ap- propriate sort,as in -He climbed out onto the ledge. Such contemporary semantic analyses using prototype theory are very much in the spirit of Austin
20 Chapter 2 A is the bottom-most part of the body. X is the bottom-most part of the mountain. X' is the bottom-most part of a list. Body is projected onto mountain, with A projected onto X. (Metaphor) Body is projected onto list, with A projected onto X'. (Metaphor) The word "foot" names A. A, X, and X' form a category, with A as central member. X and X' are noncentral members related to A by metaphor. Austin also notes examples of what we will refer to below as chaining within a category. Another case is where I call B by the same name as A, because it resembles A, C by the same name because it resembles B, D ... and so on. But ultimately A and, say D do not resemble each other in any recognizable sense at all. This is a very common case: and the dangers are obvious when we search for something 'identical' in all of them! (P. 72) Here A is the primary nuclearsense, and B, C, and D are extended senses forming a chain. A, B, C, and D are all members of the same category of senses, with A as the central member. Take a word like 'fascist': this originally connotes a great many characteristics at once: say, x, y, and z. Now we will use 'fascist' subsequently of things which possess only Oile of these striking characteristics. So that things called 'fascist' in these senses, which we may call 'incomplete' senses, need not be similar at all to each other. (P. 72) This example is very much like one Fillmore (1982a) has recently given in support of the use of prototype theory in lexical semantics. Fillmore takes the verb climb, as in - John climbed the ladder. Here, "climbing" includes both motion upward and the use of the hands to grasp onto the thing climbed. However, climbing can involve just motion upwards and no use of the hands, as in - The airplane climbed to 20,000 feet. Or the motion upward may be eliminated if there is grasping of the appropriate sort, as in - He climbed out onto the ledge. Such contemporary semantic analyses using prototype theory are very much in the spirit of Austin