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<Paper uid="W03-1408">
  <Title>The Semantics of Metaphor in the Game Theoretic Semantics with at Least Two Cordination Equilibria</Title>
  <Section position="3" start_page="2" end_page="3" type="metho">
    <SectionTitle>
2 From Pragmatic Aproach to Semantic
Aproach
</SectionTitle>
    <Paragraph position="0"> In this section, I criticize Aristotle and Davidson as representatives of the pragmatic aproach to the study of metaphor and show that the semantic approach is necesary for the study of metaphorical expresions. Afterwards, I analyze Richard and Black's semantic aproaches and point out that pragmatic elements are stil left in their aproaches.</Paragraph>
    <Paragraph position="1"> A more abstract semantic aproach is neded.</Paragraph>
    <Section position="1" start_page="2" end_page="2" type="sub_section">
      <SectionTitle>
2.1 Aristotle and Traditional Rhetoric
</SectionTitle>
      <Paragraph position="0"> Aristotle's 'Poetics' and 'Rhetoric' have ben the foundation of rhetorical studies for more than 230 years. Aristotle regards metaphor as transference and this thought has lasted as the core idea in the tradition of rhetoric.</Paragraph>
      <Paragraph position="1"> Metaphor is the aplication of an alien name by transference either from genus to species, or from species to genus, or from species to species, or by analogy, that is, proportion. (1457b) Acording to Aristotle, expresion 'the twilight of gods' is a transference betwen 'twilight' and 'last' which have similarity (end of something). By similarity, words are conected and can have the other's meaning. In other words, similarity lets words have other meanings (metaphorical meanings) that the words originaly do not have. Black cals it the substitution view of metaphor (1962).</Paragraph>
      <Paragraph position="2"> Substitution theory insists that the reason for metaphorical expresion is in its psychological effects to hearers. Here, metaphor is studied in terms of how it is used and what the efect is of language use. This let us categorize substitution theory as a part in pragmatics. Pragmatics is the study about how and why language is used, using user and use as the terms. So does substitution theory.</Paragraph>
    </Section>
    <Section position="2" start_page="2" end_page="2" type="sub_section">
      <SectionTitle>
2.2 Davidson's Pragmatics
</SectionTitle>
      <Paragraph position="0"> Davidson is regarded as one of the leading philosophers in the pragmatic aproaches. He denies metaphorical meaning in metaphorical expresion, which has never ben doubted without much argument. Metaphorical expresions have literal meaning only. We realize an expresion is metaphorical though a purely pragmatic proces. An uterance is made and the conditions bring us to realize that the meaning of the uterance is not literal (Davidson, 1978).</Paragraph>
      <Paragraph position="1"> What Davidson explains is only this realization of non-literal meaning. Metaphorical meaning itself is denied and he makes it clear that there is no such thing as metaphorical meaning, a special kind of mental, cognitive property. This is remarkable progres from Aristotelian substitution theory in terms of avoiding problems of paraphrasing which I wil criticize in the next sub-section in detail. Davidson says; 'If this is right, what we atempt in &amp;quot;paraphrasing&amp;quot; a metaphor canot be to give its meaning, for that lies on the surface; rather we attempt to evoke what the metaphor brings to our atention.' (Davidson, 1978) What paraphrasing atempts is not similarity betwen literal meaning and metaphorical meaning.</Paragraph>
      <Paragraph position="2"> Since Davidson denies metaphorical meaning itself, he does not ned to compare two meanings.</Paragraph>
      <Paragraph position="3"> There are at least two points to criticize Davidson. Firstly, to pursue what is the meaning of metaphor itself is a very important question and Davidson's reply is just an escape from the problem, though it is quite a remarkable escape. One says 'he is a pumpkin' and if another does not understand the uterance and asks what it means, paraphrasing ('it means he is very stupid') is a possible answer and the paraphrasing does have sense. Paraphrasing may not be able to have exactly the same mental content that the original metaphorical expresion has, but it does have a part of it. Otherwise the hearer canot be persuaded.</Paragraph>
      <Paragraph position="4"> Secondly, insisting there is no such thing as metaphorical meaning is a revolution and very inspiring, but it might be to unatural since we can talk and wonder about it. In this field of study, reality has a special sense because what we argue about is mainly abstract objects that do not ned to exist. However, we should stick to our reality, our sense of naturalnes, not to recreate our language understanding to fit our theories. What maters to us with metaphorical expresions are not only the uterer's intention, but also the meaning of the expresions. null</Paragraph>
    </Section>
    <Section position="3" start_page="2" end_page="3" type="sub_section">
      <SectionTitle>
2.3 Problems in Substitution Theory
</SectionTitle>
      <Paragraph position="0"> The first two of the folowing points are major criticisms of substitution theory. Firstly, the metaphorical meanings of a metaphorical expresion do not substitute al of the literal meaning. The second point reflects my idea of understanding meanings.</Paragraph>
      <Paragraph position="1"> Substitution theory says that similarity makes a metaphor, similarity in the meanings of two compared ideas (literal meaning and metaphorical meaning) makes a metaphorical expresion. But this is complete oposite.</Paragraph>
      <Paragraph position="2"> The first objection, that metaphorical meanings in a metaphorical expresion do not substitute al the literal meanings of the expresion, is, in other words: paraphrasing of a metaphorical expresion canot present al the meanings that the original  metaphorical expresion has.</Paragraph>
      <Paragraph position="3"> (ex.3) She is a lily of valey.</Paragraph>
      <Paragraph position="4"> (ex.4) She is a dewy red rose.</Paragraph>
      <Paragraph position="5"> These expresions can be paraphrased; (ex.5) She is beautiful.</Paragraph>
      <Paragraph position="6">  It is aparent that (ex.5) hold a part of the meanings that (ex.3) and (ex.4) have, but not al of them, because the same person may not use (ex.3) and (ex.4) to the same woman with the same sense of values. Repetition of paraphrasing may increase the richnes of the explanation and lead to beter understanding, but it wil never reach the ful meaning of the original expresion.</Paragraph>
      <Paragraph position="7"> The second objection claims that similarity does not make metaphor, but metaphor makes us realize the similarity. As Eisenstein created the 'flow' of story by montage sequence in his film 'Batleship Potemkin', people try to find semantic conection when some information is given in a line. Especialy, if it is presented as a sentence, we almost automaticaly try to find 'meaning' in it. 'Colorles gren ideas slep furiously' is a famous meaningles sentence writen by Chomsky. He made up this sentence as nonsensical sentence, but he himself admits that it can be interpreted as a metaphor. It can be a headline of newspaper that tels Grenpeace members who lost their livelines to stop their political activities.</Paragraph>
      <Paragraph position="8"> Those objections above to pragmatic aproach  to metaphor sugest that there are elements in the study of metaphor that are to be left for the semantic aproach. In the next sub-section, I wil revise the semantic aproach in Richards and Black.</Paragraph>
    </Section>
    <Section position="4" start_page="3" end_page="3" type="sub_section">
      <SectionTitle>
2.4 Richards' Interaction Theory
</SectionTitle>
      <Paragraph position="0"> Richards introduces interaction theory that insists the meaning of metaphor is the tension betwen two thoughts (literal meaning and metaphorical meaning) in a sentence. Before him, metaphor had ben studied at word level. Richards brought the viewpoint of semantics which focus on meaning at sentence level.</Paragraph>
      <Paragraph position="1"> Another character of his theory is to demand unlikelines betwen literal meaning and metaphorical meaning. This unlikelines is the source of the tension, literal, artistic value that the metaphor has. Richards says, 'as the two things put together are more remote, the tension created is, of course, greater'.</Paragraph>
    </Section>
    <Section position="5" start_page="3" end_page="3" type="sub_section">
      <SectionTitle>
2.5 Black's Interaction Theory
</SectionTitle>
      <Paragraph position="0"> Black develops interaction theory to more rigid theory that covers not only figurative language but the whole of language. He introduces the idea of 'focus' and 'frame'. For Black, metaphorical expresion 'Man is a wolf' is an expresion that has a  Here, I would like to state what I mean by 'pragmatics'. I interpreted Aristotle as a pragmatist. In Aristotle, language use is judged as rhetoric when the use is understod. It is a context-conscious theory. Semantics caries a diferent task. It should give the foundation of meaning. It should give other property diferent from the condition of language use.</Paragraph>
      <Paragraph position="1"> focus 'a wolf' in a linguistic frame of 'man is'.</Paragraph>
      <Paragraph position="2"> This frame is literal, but it wil be contradictory when 'a wolf' is also literal (principal subject). We realize this categorical mistake and find 'focus' metaphorical meaning (subsidiary subject) led by asociation of comonplaces. Asociated commonplaces enable us to share the same metaphorical meaning for the same expresion. Literal meaning is infered first, then after realizing its categorical mistake, metaphorical meaning is infered. This inference model is often used in the semantic aproach after Black.</Paragraph>
    </Section>
    <Section position="6" start_page="3" end_page="3" type="sub_section">
      <SectionTitle>
2.6 Problems in Interaction Theory
</SectionTitle>
      <Paragraph position="0"> In the two previous sub-sections, I have revised the main characters of Richards and Black's interaction theory. These are more sophisticated than Aristotelian substitution theory for admiting the dynamics of meaning. However some problems also remain in interaction theory.</Paragraph>
      <Paragraph position="1"> Firstly, Black suceds to explain why we understand the so-caled 'dead metaphor' in the same way, why we se similarities in metaphor by introducing the idea of 'asociated comonplaces'. But this also weakens the creativity of new metaphorical expresions. If 'asociated comonplaces' gives us stable understanding of meanings, this also prevent us not to have a new metaphorical meaning out of the system.</Paragraph>
      <Paragraph position="2"> Secondly, although Black strongly insists the necesity of semantics in his study of metaphor, Black's theory uses the inference model which is very pragmatic. What he tries to expres in his semantics was the meaning which is understod in context. Therefore he neds inference model and asociated comonplaces. I do not deny the inference model. We use our inference in our language use to determine one meaning for an expresion.</Paragraph>
      <Paragraph position="3"> But semantics, which gives the foundation of meanings to language use, should avoid such a pragmatic proces. We should separate semantics and pragmatics as clearly as posible.</Paragraph>
    </Section>
  </Section>
  <Section position="4" start_page="3" end_page="5" type="metho">
    <SectionTitle>
3 Tasks for the Semantics of Metaphor
</SectionTitle>
    <Paragraph position="0"> In the previous section, we have overloked some major theories for metaphor. I sorted them into two types, the pragmatic aproach and the semantic aproach. What is characteristic in the pragmatic aproach is that what maters in a metaphor is its use and efect. In Davidson, he even denies metaphorical meaning and replaces it with the psychological efect of literal meaning. The semantic aproach like Black criticizes Aristotelian paraphrasing and admits metaphorical meaning delivered though inference. This also means that metaphorical meaning is subsidiary meaning.</Paragraph>
    <Paragraph position="1"> These two are very complex and we canot se a clear confrontation betwen them. The pragmatic aproach canot avoid refering to metaphorical meaning when we consider the reason of metaphorical language use. The semantic aproach also canot evade using inference model, which may belong to pragmatics.</Paragraph>
    <Paragraph position="2"> Let's be naive, and remember how we read a new metaphorical expresion.</Paragraph>
    <Paragraph position="3"> (ex.6) 'She was a swan floating on the sea; alone swan on the sea of sorow blue sea, nor blue sky could not hold her.' Do we think about their literal meanings? No  . We understand the metaphorical meaning of 'sea of sorow' before thinking of its literal meaning. And when we enjoy its literal value, we read (or hear) it again and again, may think about its metaphorical meaning and literal meaning. We do enjoy these two thoughts in an expresion, and the tension that those thoughts create. In this acount, I folow interaction theory that Richards insists.</Paragraph>
    <Paragraph position="4"> What I have argued in this section are;  1. A metaphorical expresion has some meanings including literal meaning and metaphorical meaning.</Paragraph>
    <Paragraph position="5"> 2. Metaphorical meaning canot be paraphrased. Repeating paraphrasing canot give the original metaphorical meaning.</Paragraph>
    <Paragraph position="6"> 3. Semantics is a description of language ex- null presion, not language interpretation, so it  I have received some inspiring comentary on this point. Some argue that they gain mental image of a literal sea imediately after reading it. My answer to this claim is what they gained is actualy a metaphorical meaning of the expresion. Literal 'sea' has a contradiction to 'of sorow'. The image may resemble to its literal meaning though.</Paragraph>
    <Paragraph position="7"> should exclude the inference proces as a part of it.</Paragraph>
    <Paragraph position="8"> The four theorists we have reviewed canot satisfy these thre conditions. To met the demand, we ned to have a semantics, which alows the plurality of meanings in an expresion.</Paragraph>
    <Paragraph position="9">  oped as an alternative semantics where major semantics have ben based on Tarski's definition of truth. As the name shows, GTS is a semantics that models the idea of game theory. Most GTS theorists use zero-sum games betwen two players, Myself (Verifier) and Nature (Falsifier) for in Hintika, for example. Verifier tries to make a sentence true and Falsifier does the oposite. Whether the sentence is true or false is known by knowing who wil win the game. It is to state one meaning for a sentence, and the meaning is compared with an equilibrium in a game. However, if we kep using zero-sum games, we canot represent more than two meanings in a sentence.</Paragraph>
    <Section position="1" start_page="4" end_page="4" type="sub_section">
      <SectionTitle>
4.1 Cordination Problem Game
</SectionTitle>
      <Paragraph position="0"> Cordination problem game, which is analyzed and defined by Lewis (1961), is a game with at least two equilibria. Supose we are talking on the telephone and in the midle of the conversation, the line is sudenly cut of. I wil wonder whether I should cal back because if you cal me while I cal you, the line wil be busy and we canot reach each other. At the same time, you must be wondering if you should cal me. This is a problem.</Paragraph>
      <Paragraph position="1"> In this telephone line case, it can be a problem because there are at least two equilibria in this situation; one is the caler cals back and the receiver waits, and another is the caler waits and the receiver cals back. Which to chose is not a problem. The important thing is that there are two equilibria, which are indiferent for the caler to chose, so they wonder. Lewis cals this kind of problem 'cordination problems', and equilibrium 'cordination equilibrium'. Players of these games wish to cordinate acording to their expectations about what the other is going to do to gain a beter outcome comparing to not cordinating.</Paragraph>
      <Paragraph position="2"> The cordination problem games have at least two cordination equilibria by definition. Therefore using GTS with a cordination problem game, we can represent a sentence having more than two meanings.</Paragraph>
      <Paragraph position="3"> A metaphorical sentence coresponds to a cordination problem game which has two equilibria that corespond to literal meaning and metaphorical meaning. Since both cordination equilibria are same in its role as equilibrium, none of the meanings is superior or inferior (Figure 1).</Paragraph>
      <Paragraph position="4">  Interestingly, this cordination problem game also has 'tension'. A player of this game has to make a choice which wil be meaningles if his choice difers from another's. We do not wonder when we have only one choice. e have to take it.</Paragraph>
      <Paragraph position="5"> But the players in cordination problem game have at least two choices. This presence of two choices itself is the 'tension' of the metaphorical expression. Being of one afects the other. They interact. The reason of enjoyable uneasines of metaphorical expresion is in this interaction in this polysemy.</Paragraph>
      <Paragraph position="6"> With GTS extended by cordination problem game, we gain the folowing thre points.</Paragraph>
      <Paragraph position="7"> Firstly, semantics that alows more than two meanings for a sentence is posible. The semantics also promises us to find both literal and metaphorical meanings in a sentence.</Paragraph>
      <Paragraph position="8"> As a result of the first point, metaphorical meaning does not remain in its subsidiary position infered from primary meaning. It is a meaning as important as literal meaning.</Paragraph>
      <Paragraph position="9"> The being of two equilibria represents 'tension' that Richards insists as the character of the meaning of metaphorical expresions.</Paragraph>
    </Section>
    <Section position="2" start_page="4" end_page="5" type="sub_section">
      <SectionTitle>
4.2 Diference from Hintika's GTS
</SectionTitle>
      <Paragraph position="0"> This cordination problem game is very diferent from what Hintika and his folowers use. In Hintika's GTS, game directs the logical operation of logic of a sentence in order to state truth and falsehod of the sentence. It is because the meaning of the expresion is to be one.</Paragraph>
      <Paragraph position="1"> On the contrary, cordination problem game itself canot be operated as Hintika's does because the game has two equilibria and this is the point of the game.</Paragraph>
      <Paragraph position="2"> However Lewis starts his analysis from the game and ends in convention. Acording to Lewis, people in the il telephone line area start making convention that one of them (caler or receiver) should cal back. After the convention spreads over the area, the game has a unique equilibrium and the residents find the problem solved  .</Paragraph>
      <Paragraph position="3"> In the proces of building up convention, the elements to determine which equilibrium to fal in are out of the game. In the case of metaphor, I let them belong to the area of pragmatics. Though context, we use our inference system to determine, to grasp what is meant by the expresion when it is polysemous. We may know what is the subject, what is the intention of the uterer, which meaning should be apropriate in the time and place when it is expresed. These are the problems to be left in the consideration of the inference proces.</Paragraph>
    </Section>
    <Section position="3" start_page="5" end_page="5" type="sub_section">
      <SectionTitle>
4.3 Problem of 'Dead Metaphor'
</SectionTitle>
      <Paragraph position="0"> What makes the diference betwen literal meaning and metaphorical meaning? I think this is just a mater of frequency of use.</Paragraph>
      <Paragraph position="1"> 'Dead metaphor' is a type of metaphor of which metaphorical meaning is rigid and most of us understand it in same way so that often we find its metaphorical meaning in dictionary. On the other hand, we have very new, poetic metaphors that may be understod in various ways. Also there are metaphors of which metaphorical meaning became its literal meaning and do not have original literal meaning as you se in 'leg of chair'.</Paragraph>
      <Paragraph position="2">  It may remain as a cordination problem game because any new resident moves to the area, they may have same problem until he finds out the convention or is told by someone. The potential posibility of the problem is always there.</Paragraph>
      <Paragraph position="3"> The diferences betwen those types of metaphors are mater of frequency of use. If a very new metaphorical expresion is used, its metaphorical meaning may be ambiguous, can be paraphrased but posibly misunderstod. But as the expresion is used again and again, its metaphorical meaning grows to gain comon interpretation in the used language. As the metaphorical meaning becomes comon understanding of the expresion, the metaphorical expresion starts losing its tension betwen literal meaning and metaphorical meaning.</Paragraph>
      <Paragraph position="4"> This is how a metaphorical expresion is born and dies.</Paragraph>
      <Paragraph position="5"> This is stil just a sugestion of the life of a metaphorical expresion. One of the bigest problems to this acount is that it does not explain how we understand very new metaphorical expresion which we had never heard of. We ned the study of other level of meaning to explain it. But stil, if we understand those diferent types of metaphorical expresions are on a same line, continuous being, it may be fruitful of the semantics of metaphorical expresion.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="5" end_page="6" type="metho">
    <SectionTitle>
5 Why More Than Two Meanings?
</SectionTitle>
    <Paragraph position="0"> In this section, I wil spread my idea of the meanings in metaphorical expresions through some observations of the usage.</Paragraph>
    <Section position="1" start_page="5" end_page="5" type="sub_section">
      <SectionTitle>
5.1 Meanings in a Polysemous Expresion
</SectionTitle>
      <Paragraph position="0"> One of the main points of this paper is that it is aiming to expres the state of meaning of an expresion, not the meaning that is understod. In everyday conversation, we often asure what is the meaning of the expresion that we use with phases like 'you know what I mean.' 'the meaning of this term is..'. This is necesary when we come acros some polysemous expresion.</Paragraph>
      <Paragraph position="1"> If the meaning of the sentence is clear in its context, then uterer does not ned to asure its meaning, but when the uterer asure its meaning with other words. Here, we se two characters of polysemous expresion. Firstly, a polysemous expresion has more than two meanings. Secondly, a polysemous expresion ned to be defined its meaning in the usage by context.</Paragraph>
    </Section>
    <Section position="2" start_page="5" end_page="6" type="sub_section">
      <SectionTitle>
5.2 Metaphorical Meanings in an Expresion
</SectionTitle>
      <Paragraph position="0"> Let's go back to our familiar example.</Paragraph>
      <Paragraph position="1"> (ex.2) 'Man is a wolf' This is often understod as a metaphor to expres man's hunger and brutality. However 'wolf' has diferent aspects in its image. In Mongolia, wolf is the divine animal and the Mongolian hero, Chinggis Khan is caled 'blue wolf'. Other East Asian myths regard Sirius as wolf and atributes lonelines and rationality to the star. In this context, 'man is a wolf' may means 'man is a creature which has clear eyes to se and judge with his own evaluation, holds his own view even others are against him'. This image may also be found in 'lone wolf' in English.</Paragraph>
      <Paragraph position="2"> What I intend to do here is not insisting multiculturalism. What I do is to insist that metaphorical expresions are polysemous expresions. And as I wrote above, the meaning of polysemous expression is determined in its context (if it is sucesful). As the name 'polysemy' tels, we atribute more than two meanings to an expresion. Why can't we do same treatment to metaphors? The 'man is a wolf' expresion has at least one literal meaning which is a false expresion in our world, and two metaphorical meanings. When we say we understand the meaning of an expresion, this means that we chose a meaning of the expresion sucesfuly. The meaning of a metaphorical expresion is infered and one of them is chosen.</Paragraph>
      <Paragraph position="3"> Metaphorical expresions are often found in poetical expresions.</Paragraph>
      <Paragraph position="4"> (ex.7) 'my love wears forbiden colors' What is 'forbiden colors'? How 'love' wears color? As the expresion is newer, we consider what is realy meant and try to grasp its metaphorical meaning through its literal meaning, we come and go betwen those two meanings  . In this proces, we se both meanings in a metaphorical expresion. When we 'taste' a poetic expresion, we often go through this proces and this proces itself is a part of the 'tasting' of the poem. When we enjoy poems, we enjoy how the literal meaning and  'grasp its metaphorical meaning through its literal meaning' sounds as if I admit to use the inference model for semantics. But here, I am talking about how e understand, not about semantics.</Paragraph>
      <Paragraph position="5"> metaphorical meaning are related. This is what Richards caled 'tension' and this is the meaning of metaphorical expresion. In order to expres this 'tension', we should admit both literal and metaphorical meanings in a sentence.</Paragraph>
    </Section>
    <Section position="3" start_page="6" end_page="6" type="sub_section">
      <SectionTitle>
5.3 The Meanings of 'meaning'
</SectionTitle>
      <Paragraph position="0"> The semantics with cordination problem game have diferent meaning of 'meaning' from the one in traditional understanding of metaphor.</Paragraph>
      <Paragraph position="1"> When they ask 'what metaphor mean?', they have a presuposition that there is a semantic property that coresponds to a metaphorical expresion. With cordination problem game, what coresponds to a metaphorical expresion is a game that has two equilibria. The meaning of a metaphorical expresion is a game that has two 'meanings', which are two choices with the tension caused by the coexistence of the two meanings.</Paragraph>
    </Section>
  </Section>
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