Pras hant Parikh
The MIT Press Cambridge,
Massachusetts London, England

6 2010 Massachusetts Institute of Technology
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Library of Congress Cataloging-in-Publication Data
Parikh, Prashant. Language and equilibrium /
Prashant Parikh.
p. cm. Includes bibliographical references and index. ISBN
978-0-262-01345-1 (hardcover : alk. paper) 1. Pragmatics. 2. Grammar,
Comparative and general
— Syntax. 3. Game — theoretical semantics. 4.
Semantics (Philosophy) I. Title. P99.4.P72P365 2010 401'.43
— dc22
2009015862
1 0 9 8 7 6 5 4 3 2 1

1
I learned very early the di¤erence between knowing the name of something and knowing something. —
Richard Feynman, The
Making of a Scientist
In th is book , I presen t a new account of mean ing fo r nat ural lan guage.
The acco unt has three level s. Most concre tely, it o¤ers a tool to derive and comp ute the meanings of all possib le ut terances, at least in prin ciple. M ore gen erally, it provides a method to produ ce variant theor ies of mean ing and to addres s t h e many proble ms and puzzl es that beset its stu dy. Most abs tractly, it advan ces a way to think a bout meaning and lang uage through the lens of a broad and powerful idea a n d imag e.
At th e first level th e account is a theory, at

the seco nd a framewo rk, and at th e t h ird a par adigm.
The par adigm embodi es the leading idea and imag e o f equil ibrium
—or bala nce amo ng mu ltiple interact ing forces.
The framew ork draws primarily upon game th eory and situati on th eory. These are the best tools available at presen t t o impl ement the idea of equi librium in our conte xt of lang uage and meaning. The th eory use s t h e const raints that arise from game theory and situati on theory to capture the mean ings of utterances. Thi s render s t h eir der ivation a m o r e o r less straig htforwa rd comp utation al task.
The resulti ng account is called e quilibrium seman tics
.
1.1 Brief Background
Alt hough the study of meaning goes back to classical times in mu ltiple cultu res,1 there have bee n two broad trad itions in the phi losophy of
1. See, for example,
Deutsch and Bontekoe
(1997) and Raja (1977).

2 Chapter 1 language th at have addres sed mean ing in the twentieth cen tury. One is the ideal lan guage trad ition and the ot her is the ordina ry language tradition. 2 Fre ge, Russell, Whiteh ead, and the early Wittgen stein were amon g the first contr ibu tors to the former, and the later W ittgens tein,
Austin, Grice , and Straws on were amon g the first contr ibuto rs to the latt er. In the seco nd hal f o f the twe ntieth centur y, both trad itions have borrow ed a great deal from each other and hav e partly even merged , albeit uneasily.
From all the details of both traditio ns, it is possi ble to e xtract two cen tral ideas, one fro m each traditio n. The firs t traditi on has contribu ted th e idea of referenc e , o f language’ s bei ng about the worl d (or abou t extral inguisti c entities in par ticular); th e seco nd traditio n has contr ibuted the idea of use or communi cativ e activity in a broad sen se. The first trad ition tried to underst and reference or the aboutnes s o f language; the seco nd tradition tried to underst and use or the commu nicative funct ion of langu age. Both ideas, inciden tally, ar e nicely captu red in the happy phrase the flow of informati on , a compos ite idea th at und erlies and undergi rds the a c count of meaning in th is book .
Ideal language phi losophy originat ed in the study of mathe matics and the logic of math ematical statem ents, which led to its emphasis on the idea of reference. In the main, it did not see mathem atics as a situa ted activity , partly on account of its abs tract and formal nature. Thi s led to its igno ring the dimensi on of use and to its focus on formal logic and especial ly on tran slating natu ral langua ge utteran ces into logica l lan guages. 3
In fact, in th e early day s, the often inconven ient facts of use were treated as a kind of defect that would be removed by ideal izing language. W hile this traditio n has yiel ded many insights of c ontinuin g relevance including, cru cially, its use of mathem atica l method s — exp ressed perhaps most of all in what is called formal semanti cs after Monta gue (1974b) — its attem pt to exten d its ideas fro m mathem atica l langu ages to natur al langu ages has led to many di‰cult ies as elaborated in section 1.4. 4
2. See the collection of essays in Rorty (1988). 3. Perhaps the classic example of this is Russell (1905, 1919). To be fair to these philosophers, their interest in semantics was secondary to their interest in the philosophical problems they were attempting to solve. Semantics was a means to a philosophical end.
4. Indeed, there are problems with its account of the semantics of mathematical activity as well such as the problem discussed in section 7.3.

Introduction 3
The practitio ners of ordina ry langu age phi losophy, reacti ng to this arti ficia l and ersatz 5 view of natu ral langua ge, started from th e visi on that nat ural language was an inheren tly situate d activity and that the use of lang uage in communicat ion should be at the heart of its stu dy.
Unfortunat ely, they also appea red to bel ieve in the main that this attribut e o f natura l langu age mad e f o rmal method s relat ively inap plicable .
This traditio n to o has a¤orded man y insights into th e nature of linguis tic mean ing, alth ough its lack of a mathem atica l approach has often mad e its arguments impreci se and vagu e.
The a wkward state of a¤ai rs that exist s a t pre sent can be best seen in th ere being the two distinct discipl ines of seman tics and pragmati cs, each concer ned with meaning, one pri marily with its referenti al aspect and largel y formal a n d convent ion al, the other primarily with its use-rela ted or commun icative aspect and largely informal and contextu al. 6 While both disciplin es have drawn upon each other and have dev eloped a great dea l since their originat ing ideas were establi shed, in the mainst ream view , seman tic meaning is still generally identi fied wi th a senten ce’s convention ally given and formally represen ted tru th-condition s, and pra gmatic mean ing is gen erally iden ti fied with som e combinati on of contextu ally inferred and in formally represented Gric ean implicature and
Austi nian illo cutiona ry force. 7 These two types of meaning typ ically coexist and may coincide or diverge in ways best exempli fi ed perhaps in
Gric e (1975, 1989 ) and Kripke (1977) .
Kap lan (1969) , building on Monta gue’s index semanti cs and Lewis’s
(1972) conte xtual coordi nates, introdu ced conte xt into seman tics proper via his two- dimensi onal notio n o f characte r but th is was intended for just a limited set of expression s, primari ly ten se and prono uns. Stalnaker
(1970, 1978, 1998, 1999b), noting the ubiqui ty of conte xt-sensi tive
5. This word is used to indicate that the notion of an ‘‘ideal’’ language was an inferior substitute for natural language and is not meant pejoratively.
6. In the literature, there are many di¤erent ways of drawing the distinction between semantics and pragmatics. Two of the most important are: between the formal representation of meaning and the communicative aspect of meaning, and between literal meaning seen as conventional and rule-based and implicature and illocutionary force seen as contextual and inferential. These two di¤erent distinctions can be and are often merged. A third related distinction is that between the truth conditions of an utterance and the felicity conditions of an utterance.
7. The origins of the idea of force go back to Frege, so the neat picture presented above should be seen as a vast schematic oversimpli fication for expository purposes.

4 Chapter 1 expression s i n langu age, generalized the concep t o f a conte xt from an index to a context set — a n entire ‘‘body of informat ion ’’ — for lit eral meaning, whic h i s e s sentially the underl ying idea of conte xt that is pre valent toda y, including rough ly the one used in th is boo k, except th at
Stalnaker’s noti on is couched in the framew ork of possi ble worl ds. The quest ion of exactly how conte xt obtruded into the sphere of semanti cs, whether convent ionally or inferen tially, or a comb ination of both, was largely unadd ressed.
Barwi se and Perry (1983) tried to reorgan ize these insights in a radical rather than moderate way by extend ing mo del-theoret ic or referenti al method s t o accommo date Austi n’s fo cus on use by inventing th e key idea of a situa tion , som ething Aus tin had used informal ly 8 and someth ing that cap tures Stalnak er’s idea of a body of informat ion dir ectly rath er than c ircuitousl y via possi ble worl ds. 9 Among other advan ces, th is led to a b l urring of th e boun daries between th e two traditions a n d betwee n semantic s and pragmati cs, althou gh not in a n y very pre cise way. One problem was that s ituation s emantics, as their ac count was called, involved an overly abstract and impoveri shed notion of use, as did the earli er e¤orts
8. See, for example, Austin (1979a). 9.
To quote from Stalnaker (1999b):
My central assumption was that a context should be represented by a body of information that is presumed to be available to the participants in the speech situation. A context set is de fined as the set of possible situations that are compatible with this information
— with what the participants in the conversation take to be the common shared background. The contextual factors relevant to interpreting John’s utterance of ‘‘I love Mary’’ will then be, not simply the index, but the fact that the relevant body of information includes the information that John is speaking and that the utterance is taking place on June 14, 1998.
Stalnaker’s (1998) context set plays a dual role: it provides both the initial body of information within which an utterance takes place as well as the final body of information that results from the utterance. So there is a single entity (a set of possible worlds) that changes through a discourse. An utterance situation and the resulting described situation, in Barwise and Perry’s sense, are more general than this, as they need not be fully shared by the participants in the discourse (a point I discuss in detail in section 3.3.4 on common knowledge and section 5.7 on the indeterminacy of contexts) and the relation between them is di¤erent. As I see it, the described situation resulting from an utterance then a¤ects the succeeding utterance situation in an ongoing discourse. I say more about this in section 2.6 and section 7.2.
Situation theory also transcends situation semantics and has been applied to areas other than language.

Introduction 5 by M ontague , Lewi s, Kaplan, and Stalnak er 10 : they had no theory of use , just some nota tional ‘‘st and-ins’’ for broad a spects of use. 11 Nevert heless, I hav e found Barwi se’s dev elopment of a theor y o f informat ion
— call ed situati on theory — a s wel l a s a few asp ects of their attem pt to com bine th e two trad itions to be of great value in develop ing my own approa ch to language and meaning. Part of the reaso n for this is the convi ction th at if things are done cor rectly there ough t t o b e just one uni fied th eory of mean ing rather than two uneasily juxtaposed account s. Thi s Hegel ian auf hebung of th e two traditions and the two discipl ines is what will be attem pted in Lan guage a n d Equ ilibrium . 12
The e rosion of the barrier sep arating semanti cs from pra gmatics has bee n und erway from other quart ers as wel l. Recana ti (2004b , 2004c) as wel l a s the Rel evance Theo rists (see Sperber and Wils on 1986a,
1986b, 2004 ; and Carsto n 2004 amon g other s) hav e also been chippin g away at th is distinct ion (most striki ngly with example s o f so-c alled free enr ichment 13 ) and o¤eri ng a more imbricated picture of mean ing.
The view th at many linguis tic phenomen a tha t were pre viously seen as belong ing to semanti cs in fact belong to pragmati cs has com e t o b e c alled radica l prag matics though, of course , i n m y view , t h ese are all part of a ra dical seman tics that I hav e chosen to call equi librium seman tics.
10. It is notable that Stalnaker (1996, 2006) has himself turned to game theory more recently.
11. Like ‘‘speaker connections,’’ for those familiar with their account. 12. Despite the dynamic turn of Kamp (1981), Heim (1982), and Gronendijk and
Stokhof (1991), most of these developments remain squarely within the tradition of
Montague-inspired formal semantics where the focus is on finding appropriate meaning representations rather than on deriving intended and optimal meanings through use. Discourse representation theory, file change semantics, and dynamic logic are concerned more with the results of the communicative process than with communication itself, with the what rather than with the how. They address what
Austin (1979b) called the perlocutionary act and e¤ects of communication, not the locutionary and illocutionary acts and the securing of uptake and understanding. As such, they do not appear to question the syntax-semantics-pragmatics trichotomy and pipeline view of meaning bequeathed by Morris (1938) and Grice (1989) despite their undoubted technical accomplishments.
13. For example, when an utterance of a sentence such as ‘‘ Casablanca is playing’’ is being interpreted, it has to be enriched or completed with a partial content such as in New York this evening . This enrichment is part of the literal content of the utterance. See Parikh (2006b) and section 4.4.1 for a detailed game-theoretic analysis of this phenomenon.

6 Chapter 1
Typicall y, follow ing Charl es Morris’ s (1938) original tricho tomy syntax
– seman tics – pragm atics , seman tics is identified with what comes fro m the linguistic rep resentati on or with the conven tional meaning of the rep resentati on and pra gmatics is iden ti fied wi th th e contr ibution s o f the ambient circums tances . Lin guists especially use th e term un derspeci fi cation to describe th is — semanti cs first underspec ifies c ontent that is later filled in by pra gmatics. It is bet ter to iden tify seman tics wi th the prob lem of inferring the ent ire conte nt,14 regard less of what contr ibutes to th is conte nt, the linguis tic represen tation or th e context. Indeed, it has often been a s sumed in the pas t t h a t conven tions su‰ce for getting at conte nt so th ere is an ambigui ty in th e original iden ti ficatio n o f semanti cs with convent ion since it was implicit that convent ion wou ld yield conte nt. This per haps explai ns th e origin of the term lit eral content. That is, it is not clear whether the commi tment should be to the literal, purpo rtedly c onventional source of conte nt or to conte nt per se. The mainst ream view
15 of semanti cs has iden ti fied with the former, but I a m urg ing the latt er, esp ecially since even literal c ontent is in eluctabl y conte xtual.
A major adv antage of the iden ti fication of semanti cs wi th the determi nation of conte nt rath er than with conven tion is that it allows a unifo rm view of all represe ntations and symbo ls, whether th ey are linguis tic, or belong to other mo des such as the visual or gestural , o r whether the y a re mental rep resentati ons. The uni form view is that conte nt of a n y kind is a function of two variabl es, the rep resentatio n j and its embedd ing ambience u . That is, the content can be written as C рj ; u Ю , where j stand s f o r any represen tation, whether it is linguis tic, visual, gestural , o r men tal. Indeed, j can stand for any sign as wel l, inc luding tree rings, foot prints, or black clou ds.
Secondly , this view of a single discipl ine for mean ing pre vents an arti ficial divisi on into two subfiel ds — semanti cs and pragmati cs — o f all the factors that should jointly contr ibute a uni fied theor y o f conte nt. The former v iew tak es th e r e presentati ons themsel ves as primary and more or less exclusive (th e firs t variabl e i n C р j; u Ю ) and as the starti ng poi nt for scienti fic inquiry, the latter view tak es th e flow of info rmatio n and commu -
14. ‘‘Meaning’’ and ‘‘content’’ are used interchangeably in most places in this book.
When ‘‘meaning’’ is used di¤erently, as it will be later in certain contexts, it will be pointed out explicitly.
15. Even Austin (1979c) assumed that demonstrative conventions correlated utterances (statements) with historic situations. Perhaps Grice (1989) is ultimately responsible for the mainstream view.

Introduction 7 nica tion and th ought as primary (C itself ) and as the startin g point fo r scient i fic inquiry. If the field of langu age and mean ing is seen as falling within the larger dom ain of info rmatio n flow wi th hum an behav ior as one cen tral com ponent of it, then we ought to be more incline d t o the second view . Languag e t h e n become s just a part of all that makes mean ing possible. As Dretske (1981) wri tes, ‘‘In the beg inning there was informat ion. The word came later.’’ An e xclusive focus on langu age takes hold of the wron g end of th e stick a n d make s g r ammar primary , and meaning seconda ry and an afterthough t. This leads to a par allel exclusi on of context by focusin g o n ‘‘se mantic meaning’ ’ (mean ing derived almost entirel y fro m the linguis tic rep resentatio n) as primary and
‘‘pragm atic mean ing’’ (mean ing arising fro m conte xtual factors) as secondar y. Restorin g the cen trality of informat ion and its flow enables a balanced view of the source s o f meaning a s such. And , a s w i l l b e seen later in this chapter as wel l a s througho ut the book, the subject matt er, includ ing even syntax, 16 is best viewed not as a linear ‘‘stick’’ but as a circle instead.
Thi rd, Austi n (1975, 1979b ) o¤ered a criti que of the se mantics – pra gmatics distinct ion th at appea rs to have bee n largely igno red. His dialecti cal argu ment started by making a persuasive case that the meaning of at least some ut terances is not a matter of tru th condit ions alone. While asser tions require tru th conditio ns, performati ve utterances req uire felicity condit ions. Semantic s would th en be concer ned with truth condit ions and pragmati cs with felicity condition s. But th is argu ment places us on a slipp ery slope. Austi n argu ed th at truth condit ions are themsel ves just par t o f the feli city condit ions for uttering a sen tence. This sug gests that seman tics is reall y a par t o f pragmati cs or, to put th e t h esis in its most rad ical form, that there is no principled di stinction betwee n semanti cs and pra gmatics. If illocution ary force is taken as an aspect of the conte nt of an ut terance, then once again this leads to a uni fied view of seman tics and pragmati cs.
Of c ourse, to be convin cing, the viewp oint bein g adv anced requires a hom ogeneou s framewo rk that actu ally ena bles a uni form derivati on of th e full conte nt of an ut terance. I s how it is possib le to cre ate suc h a framew ork from firs t prin ciples. 17
16. See section 7.1.1. 17. As will be seen later, content will be divided into locutionary and illocutionary content, but because context will play an essential role in the derivation of both types of content, this distinction is quite d i¤erent from that between semantics and pragmatics.

8 Chapter 1
An added adv antage to o¤eri ng a compreh ensive and detaile d math ematical framework for meaning is tha t many argu ments o¤ered today for or agains t a the ory of particul ar phenomena remain inco nclusive because th eir propo nents of ten presuppo se di¤eren t views of semanti cs and pragmati cs and also give nonu niform account s for di¤er ent classes of phenome na. For example , i n the fasci nating argumen ts ove r the last centu ry for or a gainst Ru ssell’s (1905) theory of defin ite des criptions, di¤eren t theor ists of ten assu me di¤er ent and inco mpatibl e position s o n the notion of mean ing itsel f and then adv ance a very par ticula r theor y o f de finite descripti ons th at may be at odds with theor ies of other , even adj acent, phenomen a.18 Such argu ments may be seen as o¤eri ng a perspe ctive at two level s simul taneous ly, both an impl icit argument fo r a n idea of mean ing and an explicit one for a particul ar theor y. In contr ast, th is boo k provides a unifo rm approach to the der ivation of the full conte nts of more or less all ut terances, couch ed within an explicit and uni fied framew ork for meaning that syn thesizes semanti cs and pra gmatics. Thi s does not obvi ate the need fo r par ticular theor ies but it makes these account s reasonab ly unifo rm acro ss pheno mena.
Besides com bining the cen tral ideas of reference and use stemm ing from ideal langu age and ordinary langu age phi losophy, I also depart fro m both traditio ns in fu ndamen tal ways . I see conte nt as indet erminate in a number of speci fic ways, a facet of mean ing that has not bee n seriou sly addres sed bef ore. Finall y, of course , I introdu ce the idea of equilibri um to exp lain its man y aspects, both trad itional and new, in a manner th at uni fies them and provid es a single idea and image of the system of language and meaning.
Thus, in a simpl i fied and abs tract way, it would be accurate to say that equilibri um semanti cs, the account of mean ing pre sented her e, comb ines four dis tinct ideas in a sin gle uni fied framew ork: referenc e , use , indetermi nacy , and equilibri um .
1.2 The Origins of Symbols
Observat ional cos mology sug gests that th e universe is roughly fourteen billion years old. By contr ast, it appea rs that a little over sixty thousand years ago the hum an race broke in to a symbo lic conscio usness , a new kind of consci ousness th at allowed it for th e first tim e t o use objects and even ts
18. See, for example, the papers in Reimer and Bezuidenhout (2004). Not all views
— even in the collection cited — are so fragmented of course.

Introduction 9 to represent other objects and even ts. The expe rience of death or the experienc e o f play may have been amon g t h e first events that trigg ered this fatef ul break wi th our ‘‘prehu man’’ pas t. Until th en, pre sumab ly, man 19 was subm erged in a kind of presym bolic awarene ss that allowed hi m just ‘‘di rect’’ percep tion and ‘‘direct’ ’ action s and interact ions in the worl d, not unlike the conditio n o f o t her animal s. See Terr ence Deacon
(1997) fo r one account of what is involved in man ’s ach ievemen t o f a symbo lic consci ousness. 20
It is di‰cult fo r u s t o imag ine th is presymbo lic s tate because this new cog nitive abili ty must have suddenly transforme d the universe into a mira culous ly di¤eren t place, one with myri ad ind ividuals, propert ies, and relat ions. Of course , these entities had bee n t h ere all alon g, and had bee n per ceived, rea soned abou t, and acted upon in direct and unme diated ways , but their richer existenc e a s w e know it to day required the ability to name them, to form discrete mental and public symbols corr esponding to the m, to pluck them out of the relat ively undi¤erenti ated store of the worl d. Overni ght, the worl d must hav e bec ome a r epository of information , a novel ontol ogical spa ce in place of the old continu um. It seems reaso nable to surmise that it was this fresh and unfa miliar power to represen t the worl d t o ourselv es and commun icate it to others, esp ecially th rough lan guage, th at mad e u s hum an. 21
19. This word and its cognates are used in their gender-neutral sense. 20.
See also the book by Ian Tattersall (2002). I quote two paragraphs:
If the modern human brain, with all its potential capacities, had been born along with modern human skull structure at some time around 150 to 100 kyr ago, it could have persisted for a substantial amount of time as exaptation, even as the neural mass continued t o perform in the old ways. We have much less evidence than we would like that directly bears on the origin and spread of Homo sapiens. However, we do know that our species originated in this general time frame, probably in Africa. And we know as well that it quite rapidly spread Old
World-wide from its center of origin, wherever that was.
Further, if at some point, say around 70 to 60 kyr ago, a cultural innovation occurred in one human population or another that activated a potential for symbolic cognitive processes that had resided in the human brain all along, we can readily explain the rapid spread of symbolic behaviors by a simple mechanism of cultural di¤usion.
21. The presymbolic Neanderthals were able to build beautiful stone tools, and, as far as we know, communicate like many other mammals, but they do not appear to have possessed language as we know it (see Tattersall, 2002). The dramatic experience of Helen Keller in modern times may also throw some light on this transformation, although in her case she clearly had private representational capabilities
— what she discovered was public symbolic communication.

10 Chapter 1
In th is boo k, I take as my starting point th is info rmationa l space of individual s, propert ies, relation s, and other entiti es, and s tudy how we use langua ge to talk about the world and do thin gs in the worl d.
I now describe in broad terms my concept ion of mean ing a n d langu age and how th ey fit into th e larger scheme of things.
1.3 Information and Meaning
The breakth rough transforma tion described above allow ed reali ty, that is, the worl d, to be const rued as a spa ce of entities. Thi s space is what we call informati on . I t conta ins ind ividuals, propert ies, and relation s; it also contain s ent ities involvi ng individual s having propert ies and standi ng in relat ions as well as collect ions of suc h states of a¤airs.
Intuiti vely and epistem ological ly, it is perhaps such collect ions th at people first learn to disc riminate and iden tify, chunk s and slic es of reali ty called situa tions . I t i s from situati ons, from these parts of the world that agents may observ e o r find th emselves in, that th ey isolat e individu als stand ing in relat ions.
An ancestor who had emerged into a symbo lic awarene ss of the world may have noticed fo otprints in th e snow or may have fo und himsel f fashioning a t o ol: both are situati ons the ancesto r encountere d and iden ti fied. Equal ly, modern man may read a rep ort on a compan y o r find himsel f i n a restaur ant: again, both circums tances are situati ons in our special sen se of the term.
Beyond th ese rudimentary ind ividuatio ns, the ancesto r may have realized that s uch footpr ints meant that a bea r had passe d b y recently or that the hardness of the piece of stone he was usin g t o fashion a tool meant that he could use it to chip away at vario us rocks. Simi larly, the modern man in question may also have dra wn th e concl usion th at the com pany report meant that its s tock price was about to rise or that his bein g i n a restauran t meant th at he coul d order some food. Such observ ations point to another type of basic entity in our informat ional space: link s bet ween situatio ns th at allow one situati on to carry informat ion about another . This kin d o f link, c alled a constrai nt , i s the essence of meani ng . Put metaphoric ally, meaning is the flow of informati on . 22
22. As I wrote above, ‘‘meaning’’ also refers to content or, in other words, to information itself. Thus, it can stand for both the flow of information from one situation to another and for the information that flows. It is useful to have this dual sense for our central concept.

Introduction 11
Sm oke means fire, black clouds mean rain, foot prints in the snow mean th at a bear has pas sed by there recently . The natural pre symbo lic order th at exist s prio r t o man is full of const raints that enable one par t o f the worl d t o b e system atically linked to another and to carry info rmatio n abou t anot her. 23
Of course , i f t h ere is no one aro und to observ e these nat ural regulariti es, th ey remain undisc overed and unexpl oited. But it was an essen tial par t o f man’s s urvival that he was able to regist er these constrain ts and choo se his actions on their bas is. Man y suc h causal const raints were instinct ivel y r ecognized by pre symbo lic man and even ot her animal s and lowe r forms, but it was th e a bility to mental ly rep resent and manipu late suc h system atic links and commun icate them to others that ena bled Homo sapien s to succeed so spectacula rly.
Thu s, the info rmatio nal univ erse conta ins not just individual s stan ding in relation s and situatio ns but also const raints. My th eory of this space is call ed situation theory , firs t inven ted by Bar wise (1989b ), who was in fl uenc ed by Dretsk e’s (1981) acco unt of info rmation flow, and who in turn was insp ired by the classic theory of info rmation transmi ssion develop ed by Shan non (1949) . The version of situatio n theory presen ted in this book is very mu ch my own , t h ough it draws a great deal from
Bar wise and Perry (1983) and Barwis e (1989b ).
An other way to describe the cau sal links that are part of the natural order is to say that smok e i s a sign of fire , black clou ds a sign of rain, and footpr ints a sign of a bea r’s pre sence. The term ‘‘sign’’ will be use d to refer to constraints that do not invo lve hum an agency in a bas ic way.
Onc e man broke into a symb olic conscio usness, a new type of e ntity arose th at I w i l l call a symbol . Sym bols are arti fici al constru cts that involve hum an intenti on and agency in a bas ic way and that are at least partly soc ial. Our mo dern man’s comp any report is a collect ion of symbo ls. Sym bols are org anized in system atic ways and such structures are call ed symbo l systems . The system of tra‰c lights is one example of a symbol system , but the major symbo l s y stems are those of langu age.
Once again, see Ter rence Deacon (1997) for one acco unt of the distinct ion.
The object of a theory of mean ing should be symbols and symbol system s and how they are used by agents to bring about a flow of
23. All these constraints are causal and causality is therefore the basic cement of the universe. If causality implies regular succession of causally related events, then this statement would need to be modi fied to take account of the nondeterministic implications of quantum mechanics. See chapter 1 o f Dretske
(1981) for an illuminating discussion of the connection between causality and

information.

12 Chapter 1 informat ion. For an entity to be a symbol, it must stand for , be about , refer to ,or represent some other entity in the worl d and this relat ion must owe its existenc e ultim ately to hum an intenti on and agency. Both signs and symb ols in volve ‘‘abo utness,’ ’ but th e r equirement of hum an intention and agen cy is what distingui she s symbols from signs. The relation of a symb ol to its referent is the relat ion of r eference or represent ation . 24 This relatio n c a n be exp ressed as a const raint betwee n two situati ons and th us enables one situatio n t o carry informat ion about another , the hallm ark of meaning. A red light means you hav e t o sto p and a green light means you can go. The unive rse of symbo ls and symb ol system s i s very wide bec ause it includ es not only verbal language s, but also imag es, gestures, and other symbo l system s.
Peirce (1867 – 1913/1991 ) and Saussure (1916/ 1972) were per haps the firs t figures to build exp licit semiot ic theor ies of th is generali ty, but this kind of attempt has since fragmented into the sep arate study of each symbol sy stem with little underl ying unity. 25
While the r elation of reference or rep resentati on may be said to be th e central aspect of meaning , i t i s also in some ways its most obvi ous attri bute. 26 A less obvious aspect, indeed one that still eludes man y, is the equally central relat ion of use . Thi s i s the asp ect connect ed with the requiremen t o f hum an intenti on and agenc y. It would perhaps not be an exaggerat ion to sa y that the subtl ety of the relat ion of use is what makes semanti cs (or what many call pragmati cs toda y) di‰cult . This is not to dimini sh the great strides that made referenti al seman tics possib le, but once th e bas ic ideas of Tar skian mod el theor y were in place, th e r e s t has
24. Usually, the term ‘‘reference’’ is reserved for the relation between a symbol and an individual and ‘‘representation’’ is used more widely. I will use ‘‘reference’’ more or less interchangeably with ‘‘representation.’’
25. Interestingly, some semblance of unity prevails in the so-called Continental tradition in the work of figures such as Jakobson, Barthes, Derrida, and Eco because they all draw upon Saussure. See, for example, Colapietro (1993). While my book is entirely in the analytic tradition, readers more inclined to Continental semiology may also find it of interest as problems of common concern to both traditions are addressed. An explicit connection with the Continental tradition and
Derrida is made in section 5.7.
26. Some philosophers deny this referentiality altogether while some others — like most Continental thinkers — assert that the relation of meaning is one between a symbol and a mental entity. I will simply take reference as the starting point of our study. This is not to deny that language has mental signi ficance of course.

Introduction 13 bee n a matter of working out details, however innova tive they may be. A simi lar revoluti on has yet to occ ur in the dom ain of use , altho ugh part of th e di‰cu lty is that its subtlety makes many phi losophers and linguis ts deny its importan ce and someti mes even its existenc e. The main reaso n fo r this skeptici sm is that there is as yet no system atic th eory and mathemati cal appara tus to model use ; this is a lacun a I hope to fill in th is book in a comp elling way.
In addition to the two central asp ects of referen ce and use, a third equal ly fundam ental attribut e o f nat ural langu age and many other symbol system s i s the ind etermin acy of meaning. Excep t for the relat ively copio us literature on vague ness, this propert y has also remaine d largely unexp lored in its ot her dimen sions. It is primari ly this attri bute of meaning that has allowed writers such as Derri da (1988) to make some amazingly outland ish clai ms about lang uage and meaning. But if approach ed system atica lly and mathem atica lly, this vital but amorp hous attribut e bec omes easier to g rasp and allows one to underst and s ome rath er commo nsensical facts about language th at have been ignored by many. It also mak es clear why, alon g with the relat ion of use, this propert y o f mean ing is responsib le for many of the di‰cult ies faced by com putational lingu ists.
Fi nally, the fourth ent irely new featu re of nat ural lan guage that appea rs to hav e gone almost complete ly unnotic ed is th at of equi librium. W hile Lewi s (1969) was a pre cursor , Parik h (1987b, 2001) may hav e bee n th e first to bring this aspect squarel y in to the re alm of meaning. The generati ve idea in phi losophy, linguis tics, and arti fici al intell igence, the idea of starti ng with a sto ck of simpl e objects and comb ining th em acco rding to formal rules to derive more complex obj ects, was enorm ousl y fruitful, but per haps too much has been attem pted with this single idea. W hat seman tics (and language mo re widely) needs in addi tion is the equally powerfu l idea of equilibriu m. Essent ially, equi librium allows one to consi der th e inter actions of objects a t multip le levels, something that gen erativity pre cludes. Earlie r, I considere d Language and Interaction for the title of th is book . There was a del iberate a mbiguity in th is title:
‘‘interact ion ’’ was mean t t o refer not onl y t o the interact ion s betwee n agents in volved in the flow of info rmation, but also to th e interact ions among v arious ent ities at multi ple levels in th e s y stem of langua ge and meaning.
Equ ilibrium semanti cs rests on the four fundamen tal ideas of referenc e, use, indeterm inacy, and equilibriu m bec ause these featu res inhere
I in mean ing; they are not impo sed on it by the framewo rk. The acco unt

14 Chapter 1 const ruct is like any other emp irical th eory in th e science s; in addition, a science of meaning is a social science. 27
Situated games of parti al infor mation play a central role in cap turing all four of these ideas in a uni fied math ematical framework .
1.4 Language
The focus in this book is on language altho ugh th e meth ods dev eloped will also be applicabl e t o other s ymbol system s. Languag e i s possib ly our most sophis ticat ed symb ol system and is certai nly the most intricately stru ctured. Mean ing is also almost comp letely social: th e relation betwee n a word a n d its referen t i s i n the main not fixe d b y a
‘‘nat ural’’ relatio n such as resembl ance. The relat ion is, in a specific sen se, arbit rary . ‘‘Tabl e’’ coul d hav e meant ‘‘chair’’ and vice versa if English had evo lved di¤er ently. 28
I now discu ss the four key ideas intro duced above in some more det ail.
1.4.1 Reference
The concept of reference came to be bet ter appreciate d and more pre cisely underst ood in mo dern times. Sin ce this happen ed via the work of logician s such as Fre ge, Russel l, and Tarski work ing with formal languages, and s ince these methods were then extended to natural langu ages, it seems best to start with a long quote from one of the mor e elegan t mod ern texts on formal semantics by L. T. F. Gamut (1991a, 1991b).
The semantics of standard logic can be seen as a referential theory of meaning
(and thus as a correspondence theory of meaning). When de fining a model for predicate logic, the first thing we do is choose some set of entities 29 as our domain. The set is independent of the expressions which collectively form a predicate-logical language. We then specify a relation between the predicatelogical language in question and the domain. By means of an interpretation function, the constant symbols are assigned individual domain elements, and the predicate symbols are assigned sets of domain elements (or sets of ordered se-
27. It is a social science for two reasons: because both speaker and addressee are integrally involved in communication and meaning and because the entire society plays a part in contributing to meaning. The first point is discussed throughout the book, the second brie fly in section 1.5 and section 7.1.2.
28. This arbitrariness of conventional meanings is dealt with partially in section
7.1.2.

29. Here ‘‘entity’’ stands for ‘‘individual’’ in our sense. For us, ‘‘entity’’ is used to refer to any object in the ontology introduced in section 1.3.

Introduction 15 quences of n domain elements in the case of n-ary predicate letters) as their references. With this as a basis, we are in a position to de fine the reference relative to this model of all sentences in our language (that is, their truth-values), in the socalled truth de finition.
The semantics of predicate logic is indi¤erent to the kinds of things we choose to put in the domains of our models. And whatever the domain may be, the theory of meaning is always a referential one: the meanings of the symbols are always their references.
One important characteristic of the semantic interpretation process, a characteristic which also happens to be shared by the nonstandard systems we shall meet up with, is that a strict parallelism is maintained between the syntactic constructions and their semantic interpretations. The truth de finition mirrors the syntactic de finition of the formulas of the language in question. There is a methodological consideration underlying this practice, one which can be traced back to Frege. This German logician and mathematician gave the first satisfactory analysis of sentences with relational predicates and multiple quanti fication in 1879, in his Begri¤sschrift . Now the fundamental insight behind his solution to these age-old problems is that every sentence, no matter how complex, is the result of a systematic syntactic construction process which builds it up step by step, and in which every step can receive a semantic interpretation. This is the well-known principle of semantic compositionality .
Thi s extract exp lains clearl y how r eference is concept ualized and set up fo r formal lan guages. The framework of formal seman tics for nat ural langua ge has largely taken over th is c onceptual ization and added to it more com plex entities to handle the more com plex devices of nat ural language. M ontague Gram mar and its derivativ es such as Disc ourse
Representa tion Theory 30 represen t i n s ome sen se the pinnac le of this approach to mean ing.
But som e aspects of the underl ying concept ualiza tion that formal seman tics shares with the seman tics of pre dicate logic ar e proble matic for nat ural lan guage for the following reaso ns:
Rest rictio n o f the domain to individu als
Ho lism of truth values
Refe rence as assignm ent
Compo sitional ity
Ext ensionali ty and intension ality As we have a lready seen in sec tion 1.3, and will see in greater det ail in th e next chapter , there are a plu rality of entiti es in the informat ional spa ce. It is this sign i ficantly r icher s pace that will be s een to be req uired fo r the seman tics of natural langu age becaus e natu ral language is much
30. See Kamp and Reyle (1993).

16 Chapter 1 richer than ( first-order ) formal langu ages. Indi viduals and sets of
(sequences of ) individu als may be a dequate for pre dicate logic but they are far too impoveri she d t o handle the complexi ties of nat ural langu age. Some of these inadequa cies have bee n addres sed in formal semanti cs by bringing in propert ies and relat ions as entities in their own right (as opposed to mod eling them as sets), but what is needed is a t h oroughgo ing revisio n o f the ontolog y. Thi s i s provided by situatio n theory, both in its original fo rm and especial ly in the version pre sented here.
The se cond assu mption of the hol ism of truth values is a par ticular instance of the pre vious assu mption. Instead of supply ing approp riate structured entiti es to play th e role of th e conte nts of utteran ces, formal semanti cs and philoso phy have contin ued to deal with truth values as their (referent ial) ‘‘meaning s.’’ Bar wise and Perry (1975, 1983) hav e criticize d this hol ism in very thoroug h ways and there is little point in repeating this criticism here. Un fortunately , situati on theory and situation semanti cs have falle n out of favo r 31 and so their sol ution to the proble ms posed by th is holism have been largel y ignored .
Third, referen ce has bee n treated simpl y a s assignment , a move that is perfectl y legi timate for formal languages, but leaves mu ch to be desired for natur al languag es. This is one reaso n for the split in the study of meaning: fo rmal se manticists hav e conte nted themsel ves with simply addres sing the problem of represe nting meanings and hav e left the messy facts of use th at lie at the core of reference to pra gmatics and the phi losophy of langu age. Unfo rtunately , b y and large, th ese latt er disc iplines have simpl y replaced assignm ent by co nvention , that is, ( literal) contents
31. Partee (2005) identi fies two reasons why this may have happened: Barwise avoided the notion of possible situations and Barwise and Perry never gave a satisfactory account of quanti fied noun phrases such as ‘‘every student.’’ While this may be true from the viewpoint of the Montague grammar community, I believe the reason for their falling out of favor is more fundamental, one that plagues even the formal semanticists: as I said above in section 1.1, they had no theory of use, and so failed to deliver the breakthrough of incorporating Austin into model theory bruited by situation semantics. They could not develop such a theory partly because of fundamental gaps in situation theory, something I rectify in chapter 2, and partly because they had no access to the ideas of game theory.
This led to an inability to carry the entire program forward, not just to a lack of solutions to the particular problems posed by possibility and quanti fiers. I address noun phrases in chapter 6 and I have no objection to possible situations when required as long as they do not lead to a modal realism. Indeed, they arise in a natural way in the situation-theoretic construction of games described in chapter 3 and sections A.2 and A.4 of Appendix A.

Introduction 17 are generally taken as conven tionally given . W hat is required is both an ade quate ontolog y and an ac count of reference in its full comp lexity that mesh es with these rep resentati ons. I attem pt to do this via a comb ination of game theory and situati on theory that allows one to actu ally const ruct a formal de finition of re ference. 32
The fourth sha red assumpti on is Frege’s ven erable p rinciple of compo sitiona lity . 33 Again , this is per fectly valid fo r formal langu ages because it is alw ays assu med that such languages are per fectly pre cise and unam biguous. But nat ural languages are notorio usly ambiguo us and vague and th en Fregean com positionali ty bre aks down. This is bec ause the meaning of one word (an d phrase) in a n ut terance of a senten ce can a¤ec t and be a¤ec ted by the meanings of the other word s (and phrases) in the senten ce.34 When no amb iguity or vaguen ess are prese nt, th ese interdep endenci es and interact ions of meaning are otiose and super fluou s. But when they are presen t, as they almost always are in nat ural language, th e s imple gener ative idea of Frege an compos itional ity falls short . A s I said earlier, gen erativity prohibi ts the inter actio ns of variou s objects. Equ ilibrium semanti cs o¤ers a gen eralizati on of the Freg ean principle of compo sitio nality , called th e fixed point principle or fixed point compositiona lity , that is able to a ccommoda te the se per vasive attribut es of natural lan guage; when they a r e absent , the fixed po int p rinciple red uces to the spe cial case of Fregean com positionali ty.
Fi nally, Fre ge’s (1980) classi c paper appeared to make it clear that referen ce could not be direct , that th ere had to be some in tervening layer suc h a s that of his ‘‘sense .’’ These issues have bee n hotly conte sted after Kripk e’s (1972/198 0) dra matic work on direct referen ce for a subcl ass of word s. I will side with Fre ge and o¤er a picture of word meaning that is a gen eralizati on and re finemen t o f the traditio nal observation th at the ordinar y word ‘‘mean ing’’ is ambiguou s and nee ds to be spl it into two parts
32. I d o not actually give this de finition of reference in the book because it is messier than similar de finitions. It follows the general line of definitions discussed in chapter 6 o f Parikh (2001) with appropriate modi fications to accommodate the more general framework for meaning presented here. It is analogous to De finition 2 i n section 5.10 of this book.
33. Frege himself may or may not have put forward this principle, but it is widely known as such and I will stick to this appellation.
34. In an utterance of ‘‘The waiter is rude,’’ all four words are ambiguous as will be seen in chapter 6, and their intended meanin gs a¤ect and reinforce one another. Indeed, it will be seen in section 7.1.1 that meaning and grammar are

also interdependent.

18 Chapter 1 that hav e var iously bee n c alled connotat ion and denotat ion , sense and reference, and intension and extension . I ca ll th ese two tiers conven tional meaning and referenti al meaning. 35 In this book , I do not o¤er any argu ment for this posi tion, as it would mean a l o n g detour and require addres sing a large literature including, mo st prom inently, Kripke (1972/
1980) himsel f. I hope to do this on another occasio n but some inkling of my v iews may be gleaned from cha pter 6 o n noun phrase s where I brie fl y addres s proper names and where I o¤er detailed counter arguments to
Kripke’ s (1977) criti que of Don nellan (1966) bas ed on my theory of de finite des criptions. In any case, I hope th e theor y w i l l b e immune to th e kinds of criti cisms Kripke (1972/198 0) and Putnam (1975) (amon g man y other s) have made. A somew hat surprising consequ ence of my acco unt is that while ev ery word in a nat ural langu age has at least one conven tional meaning, phrase s and sentences hav e n o convent ional meanings; on the other hand, when use d i n a n u t terance, words, phrase s, and sen tences all receive r eferential meanings or conte nts. Each word in an utteran ce of a senten ce such as ‘‘Th e waiter is rude’ ’ has at least one convent ion al mean ing, but th e variou s phrase s and the entire sentence have no conven tional meaning. On the ot her hand, all words, phrases , and sen tences acquire conte nts when uttered . This again is a failure of compos itionality at the level of sense or inten sion or convent ional meaning.
Despit e thes e depart ures from the many assumpti ons shared by the stand ard seman tics of formal and natu ral languag es, equilibri um seman tics does share its foundati onal assu mption that language requires a referential th eory of meaning. Indeed, my acco unt requi res th at every word , phrase , and s entence in an utteran ce have a reference, even appare ntly syncatego rematic words such a s the and or .
1.4.2 Use
There a r e a t least two reaso ns why the concept of use is subtle and has resiste d ana lysis. One is that it involves a number of other concept s t h a t are often poorly underst ood. The other is that it is di‰cu lt to dev elop a mathem atica l apparatu s that can ac commodate all these concept s and that does justice to interact ion s bet ween agents. With formal langu ages, it is possi ble to abs tract from use and pre tend we are dealing ju st with inert s ymbols rather than with their use. W ith nat ural langu ages, th is
35. When the context is clear, I will use just the term ‘‘meaning’’ instead of the longer ‘‘referential meaning.’’ This sense of ‘‘meaning’’ is identical with that of
‘‘content.’’

Introduction 19 bec omes imposs ible as we will see below. Tho se who have tried to ignore th e relat ion of use as cen tral to seman tics have had to reso rt to many awkw ard c ontortion s such as posi ting all kin ds of entities at mu ltiple layers of sen tential rep resentati on, whose connect ion with empiri cal reality becom es increasin gly ten uous and ad hoc, remi niscent of the epicycl es of pre -Coperni can astron omy. 36
M inimally , the follow ing concept s are intimatel y relat ed to , i f not inclu ded in, th e concep t o f use :
Belief , des ire, intenti on, and age ncy
Sente nce and utterance
The situate dness of langu age
The e‰cienc y o f language
Ambi guity
Comm unication a n d informat ion flow
36. A single example should su‰ce: Recanati (2004b) cogently confutes the
‘‘representationalist’’ analysis of an utterance of ‘‘It is raining.’’ I quote:
John Perry (1986) and many others after him have argued as follows. Even though nothing in the sentence ‘‘It is raining’’ stands for a place, nevertheless it does not express a complete proposition unless a place is contextually provided . The verb ‘‘to rain,’’ Perry says, denotes a dyadic relation — a relation between times and places. In a given place, it doesn’t just rain or not, it rains at some times while not raining at others; similarly, a t a given time, it rains in some places while not raining in others. To evaluate a statement of rain as true or false, Perry says, we need both a time and a place. Since the statement ‘‘It is raining’’ explicitly gives us only the two-place relation (supplied by the verb) and the temporal argument (indexically supplied by the present tense), the relevant locational argument must be contextually supplied for the utterance to express a complete proposition. If Perry is right, the contextual provision of the place concerned b y the rain is an instance of saturation like the assignment of a contextual value to the present tense: both the place and the time are constituents of what is said, even though, unlike the time, the place remains unarticulated in surface syntax.
But is Perry right? If really the contextual provision of a place was mandatory, hence an instance of saturation, every token of ‘‘It is raining’’ would be unevaluable unless a place were contextually speci fied. Yet I have no di‰culty imagining a counterexample, that is, a context in which ‘‘It is raining’’ is evaluable even though no particular place is contextually singled out.
Then Recanati (2004b, 9 – 10) goes on to provide an irrefutable counterexample and thereby argue against the representationalist view. I should add that the main thr ust of Perry’s (1986) paper is antirepresentationalist, so even his failing to avoid this tendency is especially revealing of the pervasiveness of the mainstream view that can ultimately be traced back to logicism.

20 Chapter 1
It is aston ishing that mainst ream lingu istics in th e twent yfirst centu ry has no the oretically grounded concept ion of agen cy.37 Wha tever our innate endowmen t may be, langu age (its dimensi on of meaning in par ticular) is surely a social institu tion and a s such superv enes on use and human agency. Ever since Gric e, th e phi losophy of langu age has had recour se to the concept of rational agency, but it has remai ned informal.
The onl y framewo rk to day th at has a n appara tus with a mathem atically formu lated and philo sophicall y sound concept ion of agency is that of game and decision theory. Thi s concept ion has underg one exciting cha nges since the work of Tversk y and Kahn eman (Kahn eman, Slo vic, and
Tve rsky 1982) and is stil l evo lving. In this sense, my earlier work (Pa rikh
1987b, 1992, 2000, 2001; Fehl ing and Parikh 1991) and other s’ subsequent contribu tions (e.g., th e volu me edited by Benz et al. 2006 and the volume edited by Pie tarinen 2007) to th e now burgeon ing field of gametheor etic semanti cs and pra gmatics have bee n the only approach es th at involve the c oncept of agency in a full-blo oded way. Belief , desire, and intenti on are integral to action and it is th e singular virtue of decision and game theo ry that they o¤er a way to integrat e these component factors that res ult in action. Any system atic approach to question s o f use must dra w upon a theor y o f a ction and especial ly interact ion that includes its const ituents of belief , desire, and intenti on. I ndeed, we will see in th e par agraph s that fo llow that all the other elem ents of use listed above can be addres sed adequat ely only becaus e w e hav e recour se to game theory and situati on th eory.
Perhaps equal ly asto nishing is the insiste nce of many phi losophers and linguis ts on dealing with sen tences rather than ut terances despite the contributi ons of ordina ry language philoso phy. A sign or symbo l seldo m carries informat ion by itself. It is only when we take account of the circumstances in which the sign or symbo l occurs th at we can infer a referential mean ing. 38 Likewise, a senten ce by itself does not hav e a mean ing. It is only an utterance, an act invo lving the produ ction of a sen tence (o r other symbo l) in some situatio n, that carries informat ion. While words and sen tences appear to mean things in the abstract, onl y a momen t’s reflection is required to see th at a name suc h a s H arvey or commo n noun
37. Even Optimality Theory does not, just as it does not have many of the other concepts listed above. See Blutner and Zeevat (2004).
38. This observation is in fact a little subtler for images and similar symbols than for words.

Introduction 21 suc h a s bank can only carry their convent ional mean ings 39 when abs tracted fro m their circums tances of use . Withou t a n embedd ing utteranc e, a nam e cannot possibly refer (which one of c ountless Harvey s i s bein g referred to?) nor can a noun , verb, pre position , o r a r ticle. 40
Ident ifying ut terances with sentenc es may be per missible onl y for formal langua ges. The circums tances of ut terance simpl y can not be igno red in the case of nat ural lan guage. Put di¤er ently, a senten ce a n d its com ponent par ts cannot ever connect with reality, cannot ever be about any thing wi thout bein g ens conced in an utterance. I suspect the reaso n for the reluc tance to deal square ly wi th utterances is that, as hinted above , there simpl y appea rs to be no mathem atical or otherwi se solid appara tus to dea l with the messi ness and unruliness of contex ts . Sente nce s are wel lbehav ed, rule-go verned objects and so we feel more comfortab le wi th th em and have ways of manipu lating them. I hope th at equilibri um seman tics, wi th its use of game th eory and situatio n t h eory, will disp el these doub ts.
I hav e already referred to the situate dness of langu age when talking abou t conte xts and circums tances, just alter native words for what will tech nically be called th e utteran ce situa tion . Indeed, agen ts are always in situati ons of one sort of anot her, and not just our utteran ces, but all our action s a s well as th eir const ituents — beliefs, desires, and intenti ons — are situate d. In the case of ut terances, as wi th all actions, this situate dness impl ies that meaning is a result of both the sen tence uttered and the ut terance situati on. In fact, a s already mentioned earlie r, we will write
C рj ; u ЮјCр j Ю fo r the conte nt of a s e ntence j uttered in situatio n u .
The conte xt mak es many contr ibutions to th e meaning of an ut terance in general unl ike the case of formal languages where one can e¤ec tively write C uu р jЮ 1 C р jЮ fo r all situatio ns u . This situatedness occurs more widely th an just with natu ral language. When someon e waves his hand to extend a greeting , there is a situati on in whic h h e perfo rms the action and thereby convey s a greeti ng. In a di¤eren t situatio n, the same action could have mean t a goodb ye.
Int imately relat ed to this situate dness is th e e‰cienc y o f langu age.
The fact that the same sen tence can be used to convey di¤er ent conte nts in di¤er ent circums tances is pre cisely what makes languag e e‰ci ent. Part ly,
39. That is, the suitably indexicalized properties and relations corresponding to what one might find in a dictionary for a common noun as explained in section
7.1.2; the case of names is a little di¤erent and is dealt with in sections 3.2 and 6.3.
40. In the extended sense of reference I a m using.

22 Chapter 1 e‰cie ncy is purely linguis tic, th at is, it resides in th e lexi cal ambigui ty of words and structural ambigui ty of se ntences, thereby allow ing one word or one senten ce to carry mu ltiple seman tic values via lingu istic mech anisms, but by and large it is contextu al. Context is central to e‰ci ency as it provides th e ambient informat ion that gets added to the purel y linguisti c informat ion a sen tence provi des to produce mean ing. In these two ways , e‰cie ncy is an ent irely observab le and empiri cal fact about language and mean ing. However, when we beg in to bui ld theories of language and mean ing, then anot her di mension of e‰cienc y enters the picture. Agency is central to contexts and agency itself is more or less e‰cient bec ause it is more or less ratio nal . While few agents (includ ing human beings) a r e always perfectl y ration al in ways sometimes required by game and decision th eory, they are not entirel y irratio nal either. I n any case, whateve r our variabl e degre e o f rational ity, it is argu able that it lies at the center of the e‰cienc y o f language, not onl y i n its contextu al aspect, but even in its purely linguis tic asp ect. Indeed, it is at th e cen ter of all hum an instit utions, let alon e just the institu tions of langu age and meaning. (That is why g ame and dec ision theory have such wi de applicability.) Un til it is kno wn bet ter and more empiric ally how we make choices, one aspect of e‰cienc y then is that it provid es a way of idealizi ng language and meaning via the idea of ration ality, just as earlier th e predicate calculus had provid ed a way to regim ent th e messine ss of natu ral language. Howe ver, this time it is not language itself that is being idealized but its use. Moreov er, becaus e game and dec ision theory are increasingly open to all kinds of behavi oral mod es of choi ce, not just per fectly rational ones, the degree of ideali zation involved can be ‘‘tuned ’’ fo r greater or lesser realism in our theor y-buildi ng. These two dimensi ons of e‰cie ncy, one purel y empirical (involvi ng both langua ge and conte xt), the other more or less theoretica l (involvin g agency ), are both what mak e semanti cs di‰cult and what make language an extraord inarily r ich symbol system .
I hav e alluded to ambigui ty in language a few times in the foregoing . I see ambigui ty in an extended sen se as an essentia l par t o f lang uage. Gen erally, linguis ts and phi losophers think of amb iguity as bein g either lexi cal or structu ral; I use the term ver y wide ly to cover any and all cases where more than one possi ble interp retation of a n utteran ce may exist . This includes not just lexical and structura l ambigui ty, but all those c ases that resu lt from the e‰ci ency of language. It turns out, as show n esp ecially in Parikh (2001, 2006b ) and
Clark and Parik h (2007) , that more or less the same game- theor etic mo dels can be applied to disambi guating all

Introduction 23 mu ltiple possible interpreta tions. It is because of this uniformit y o f appl ication th at I feel that ‘‘ambiguit y’’ should be broadened to encom pass all th ese varied c ases. 41 In section 7.1.1, the notion of a mbiguity will be generali zed even furth er.
The essence of use lies in com municati on and informat ion flow betwee n agen ts. Gric e (1957, 1969) was the firs t per son to introd uce and exp lore th e related concept of nonnatural mean ing. St rawson (1964) and
Schi ¤er (1972) refi ned Gric e’s attempts at definit ion. Parik h (2001) expan ded this exp loration into an in fini te latt ice of concept s o f com municati on and info rmation flow as well as relat ed infi nite lattices of concep ts associat ed wi th spe aker meaning and a ddressee interpreta tion, a n d gave rigoro us game- theor etic de finition s o f these concept s.
W e will see in sec tion 5.10 th at these game- theor etic de finit ions nee d t o b e gen eralized to account fu lly for the indeterm inacy of meaning.
The six interloc king notions above a r e all integral parts of th e concept of use . I t i s t h e comp lexity of thes e const ituent noti ons that makes it dif ficul t t o incorpora te the concept of use into semanti cs in a smooth way and this is why it has been consi gned to the ‘‘dustbi n o f pra gmatics.’ ’ I t is for tunate that th e situate d game th eory I w i l l pre sent is ideally suited to tackle each of these com ponent notio ns in a t h orough way th at allows a seaml ess uni fication of seman tics and pragmatics .
To sum marize, by and large, meaning in volves utterances a s actions and is situate d. Di¤erent situatio ns with the same signs or symbo ls typ icall y carry di¤er ent info rmatio n. In one situati on, smoke may mean fire, in anot her, a cigare tte smoker. Or, as remark ed above , a hand wave may mean hello or goodbye. To paraphra se W ittgenstein (1953/196 8), an utteran ce of ‘‘This chair is brow n’’ coul d mean a variety of th ings in di¤erent circu mstances . Thi s situate dness of mean ing goe s hand-in
hand with th e e‰cienc y o f language who se flip side is a pervasive ambigui ty in signs and symbo ls, particul arly th ose of language. All of th ese to gether make com municati on and the flow of in formatio n betwee n agents possib le.
1.4.3 Indeterminacy
A consequ ence of the fact that mean ing depends on use is that it may be ind etermin ate in a number of ways. 42 Three of these are:
41. This extended applicability of my games of partial information has sometimes been misunderstood as applying only to the narrower, traditional concept of ambiguity.

42. An extended discussion of this feature of meaning can be found in Parikh
(2001, 2006b).

24 Chapter 1
1. Content is not alw ays fully intend ed. 2. Content is not alw ays determin istically given. 3. Content is not alw ays the same for spe aker and addres see.
Overwh elmingly in the literatu re of the last centu ry, both in linguis tics and in the philoso phy of language, the negations of these statemen ts hav e been the shared beliefs. Even Wittgen stein, Aus tin, and Grice, three phi losophers who were very sen sitive to aspects of the use of language, and their many followers, appear to hav e mad e t h ese assu mptions.
At least part of the meaning of an utterance is e xplicitly intende d b y speake rs bec ause they are eng aged in purpo sive activ ity. Indeed, there are correspond ing inten tions on the side of the hea rer as well. 43 But inten tions a r e themsel ves situa ted so that spe akers do not need to exp licitly intend every thing. For example , did Dostoe vsky explicitl y intend th e entire literal and impl icate d conte nt of Crime and Punishm ent ? I t i s per haps even physicall y impossi ble to do so becaus e, even minimall y, there wou ld be so mu ch impl icit informat ion bein g convey ed. The way to think about conte nt is to allow for som e o f i t not to be explici tly inten ded and to inq uire if the spe aker might assent to the unint ended par t o f the content . This will be show n i n detail once our game- theoretic mo dels are in place. However, since in practice we are seldom in a position to ask such quest ions of speake rs and a ddressees about th eir utterances and interp retations, we have to reconc ile oursel ves to sayin g that content is partly inde terminate in this sen se, since it may hav e partly not been explicitl y intend ed and we cannot kno w whether it has been cor rectly inferred. Of course, since in tentions are invisible, it is not possi ble to be sur e even a bout the intend ed par ts of the conte nt. Perhap s Gric e
(1989) , who introd uced intenti on-base d derivati ons of conte nt, exp ected too much to be r esolved by intenti ons.
Gric e was also probably the first philoso pher to allow that conte nt may be par tly ind eterminate in a direct sen se, but he restri cted this indeterm inacy just to implicature, assuming that literal conte nt was always determinate ly given in com municati on. It is nat ural to extend this type of indeterm inacy to all asp ects of meaning. The prin cipal insight her e i s t h a t linguis tic commun icatio n and informat ion flow can be probabi listic , s omething that does not seem to hav e bee n noted before at this ge neral level . 44
43. See Strawson (1964) and Parikh (2001). 44. Except in Parikh (2001, 2006a,
2006b). More recently, probabilistic approaches to particular phenomena such as conditionals have appeared in

Kaufmann (2005). See Cohen (2003) as well. Probabilistic methods have, of course, been common in computational linguistics.

Introduction 25
Prob abilistic commun ication is importan t i n t h e det erminat ion of both lit eral content and impl icature as wel l a s illocution ary force. Once we tak e note of th is fact, we beg in to see it everyw here, even in the simplest info rmatio n flows. This makes the nee d for prob abilistic approach es to interp retatio n suc h a s that used in game and decision th eory even mo re appare nt. That is, all aspects of conte nt may be probabil istic and indeterm inate, and an addres see may not infer just propo sitions fro m a n u t terance, but also the probabil ities with whic h they are being convey ed.
Fi nally, in practica lly all the releva nt literatur e, it has been assu med th at com municati on and informat ion flow consi st in just an iden tity betwe en a propos ition convey ed and a propos ition grasp ed. Closer exami nat ion of this assumpti on shows th at this is the simpl est case, and in a sen se th at will becom e clear later , i t i s a n ideal case that is s eldom reali zed in pra ctice. Essential ly, content s w i l l usually be di¤eren t f o r di¤er ent partici pants in a commu nicative interact ion. This fact introdu ces yet anot her asp ect of ind etermin acy into meaning.
Other sources of indeterm inacy, some of a more tech nical ki nd, will be intro duced in cha pter 5.
1.4.4 Equilibrium
Our final and central uni fying idea and imag e i s that of equilibriu m. This idea has a long history: it goes back to Newto n’s mech anics, and th en, espec ially via Adam Sm ith in the eighteent h centu ry and the math ematician Cou rnot in the nineteen th, finds its way in to eco nomics and later into game theory in the twe ntieth. Today, the idea of equi librium occurs in pra ctically every natur al and social science. Indeed , i t i s argu able that Saussu re (1916/197 2) had an inkling of th is noti on in his idea of phono logy (an d semiolo gy, gene rally) as a system of d i¤erences .
Whi le I i n itially saw equilibri um in language and meaning via the applicat ion of game th eory, it is possi ble to abstract from th e g a m e theor y and see equilibri um as an inh erent and emp irical par t o f t h i s system .
Equ ilibrium simply means balanc e amon g multiple interact ing elemen ts. In each conte xt where th e idea of equi librium is applicabl e, we hav e t o determi ne what th ese elem ents are and what the nature of their interact ion s is. Once we have these, all that remai ns is to des cribe the con dition s under whic h these mu ltiple interact ions ‘‘bal ance.’’ In some contexts, the only observ able states of a system are those in equilibriu m; in ot her conte xts, disequ ilibrium may also be observ able. Equil ibrium may also be dynam ic and evolve over time.

26 Chapter 1
For langu age, equilibri um enter s essentia lly through th e elem ent of choice : the spe aker must choose his utteran ce and th e addres see mu st choose her interpreta tion and these choices mu st be in balanc e .As we will see, the speake r and addres see particip ate in multiple games at mu ltiple level s i n a single utterance — a t the level of words, phrase s, and the senten ce itsel f — and so the re are mu ltiple equilibri a that occur in com municati on. Not only does each equilibriu m involve a balance amo ng the choices and strateg ies availa ble to th e spe aker and addressee in each game, but th e m u ltiple equilibria are themsel ves in balan ce: an equi librium of e quilibria!
Saussure (1916/197 2 ) view ed langu age as a system of oppo sing elements th at underl ay a proces s o f choice. ‘‘What idea or phon ological material there is in a sign matt ers less th an what there is around it in the other sign s.’’ 45 Saussure’ s position seems to be that a sign has signi fican ce not simply becaus e o f t h e associat ion between sound and meaning but because this associat ion is embedd ed in a larger system of sound-me aning associat ions. 46 The signi fican ce of this notio n bec omes appare nt in the conte xt of making a lingu istic choice; it is worth quoti ng Saussure (1916/ 1972) at length :
Our memory holds in reserve all kinds of more or less complex phrases, regardless of their type or length so that, when we employ them, associated groupings can be called upon to fix our choice. When someone says marchons!
(‘‘Let’s walk!’’), he thinks unconsciously of a divers group of associations in the midst of which the phrase marchons! finds itself. On the one hand, it is part of the series marche ! (‘‘Walk!’’ [familiar]) marchez! (‘‘Walk!’’ [formal, plural]), and it is the opposition of marchons! with these forms that determines the choice; on the other hand, marchons! evokes the series montons! (‘‘let’s go up/get aboard!’’) mangeons!
(‘‘let’s eat!’’) among which it is chosen by the same process. For each series, we know what must be varied to obtain the correct contrast with the desired unit. If we change the idea to be expressed, then other oppositions will be needed to make the correct value appear; we say, for example marchez! or perhaps montons! .. .
This principle applies to phrases and to sentences of all kinds, even the most complex. At the point where we say the sentence fque vous ditil?g (‘‘What does he say to you?’’), we vary an element in a latent form, for example: fque te ditil?g
(‘‘What does he say to you [familiar]?’’) —fque nous dit-il?g (‘‘What does he say to us?’’), etc., and it is in this way that our choice is fixed upon the pronoun vous. S o i n this operation, which consists in mentally eliminating anything that
45. ‘‘ Ce qu’il y a d’ide ґ e o u d e matie ` re phonique dans un signe importe moins que ce qu’il y a autour de lui dans les autres signes .’’ (Chapter VI, section 4) Note that all translations in this section are by Robin Clark.
46. Thus, changing one part of a system should ramify throughout the system,

causing all the other associations to change as well.

Introduction 27 does not lead to the desired di¤erentiation at the desired point, associative groupings and phrasal patterns are both in play.47
Acco rdingly, Saussure’ s insight is that a language is defined by a system of choices that can bea r meaning, and th e fact of choosi ng one sign instead of another is, in itself, a criti cal act that is an inheren t par t o f the lingu istic system . The content of th is insight has bee n far from clear, however , and most th eoretica l linguis tics has shied away from usin g a n action suc h a s choice as par t o f its th eoretica l machinery in favor of th e study of lingu istic representati ons, a static obj ect that seems more amenab le to formal investigati on.
Phil osophers in fl uenced by th e ordinary lan guage traditi on, on the ot her hand, hav e alw ays had recour se to the idea of an utteran ce and th erefore of an actio n and even impl icitly of an interactio n . While Gric e
(1989) may have bee n the first to introdu ce the idea of interact ion into th e philoso phy of language, it remaine d relat ively impl icit in his ana lysis of speake r meanin g. Strawson (1964) was perhaps the first to explicitl y consi der the interact ion betwee n a spe aker and addres see by noting that th ere were reciprocal intenti ons and a ctions on the addres see’s side in com municati on, but his insight has been ignored in subsequ ent work by phi losophers and linguis ts. By a n d large, the addresse e remains a ghost in mainst ream semanti cs, at mo st a pas sive recipie nt of the spe aker’s action s.
47. ‘‘ Notre me ґ moire tient en re ґ serve tous les types de syntagmes plus ou moins complexes, de quelque espe ` ce ou e ґ tendue qu’ils puissent e € tre, et au moment de les employer, nous faisons intervenir les groupes associatifs pour fixer notre choix. Quand quelqu’un dit marchons!, i l pense inconsciemment a ` divers groupes d’associations a ` l’intersection desquels se trouve le syntagme marchons!
Celui-ci figure d’une part dans la s’erie marche! marchez! , e t c’est l’opposition de marchons! avec ces formes qui de ґ termine le choix; d’autre part, marchons! e ґ voque la se ґ rie montons! mangeons! etc., au sein de laquelle il est choisi par le me € me proce ґ de ґ ; dans chaque se ґ rie on sait ce qu’il faut faire varier pour obtenis la di¤e ґ renciation propre a ` l’unite ґ cherche ґ e. Qu’on change l’ide ґ ea ` exprimer, et d’autres oppositions seront ne ґ cessaires pour faire apparai € tre une autre valeur; on dira par exemple marchez! , o u bien montons! ...
‘‘Ce principe s’applique au syntagmes et aux phrases de tous les types, me € mes les plus complexes. Au moment ou ` nous pronon cons la phrase: fque vous ditil?g, nous faisons varier un e ґ le ґ ment dans un type syntagmatique latent, par exemple fque te dit-il?g
—fque nous dit-il?g, etc., et c’est par la ` que notre choix se fixe sur le pronom vous . Ainsi dans cette ope ґ ration, qui consiste a ` e ґ liminer mentalement tout ce qui n’ame ` ne pas la di¤e ґ renciation voulue sur le point voulu, les groupements associatifs et les types syntagmatiques sont tous

deux en jeu .’’ (Chapter VI, section 2)

28 Chapter 1
Furt her, except for the singular work of Davi d Lewi s (1969), neither linguis ts nor philoso phers have quite concei ved of utterances and interactions with in a system of choices. Unfortu nately, Lewi s thought of game theor y a s mere ‘‘sc a¤oldi ng’’ th at was ultimatel y dispen sable. 48
More importantl y, he concei ved of spe aker meaning as entirel y conven tional becaus e his primary aim was to analyze the concept of convent ion and he believe d Gric e’s concept of nonnatu ral or spe aker meaning fell with in his concept of c onventio n. The particul ar types of game models he considered, based on the work of Schel ling (1960) , were also fairly basic and lacked the com plexity req uired for mod eling commu nication that was ambiguo us and conte xtual and costly. (The first work to dev elop appropriate game mo dels was Parikh 198 7b.) 49
Thus, Saussure consid ered choice but not interact ion between speake rs and addres sees, and phi losophers with the exception of Lewi s consi dered action and interact ion but not choice. Both the se element s o f choi ce in th e conte xt of strateg ic interact ion need to be brough t together in a way that results in an equilibri um, a com posite idea that neither componen t idea by itsel f suggests. To the best of my knowledge, the only mathem atica l framewo rk th at does this adequat ely is game theory, par ticularly situate d games of par tial informat ion , t h e kinds of games inven ted in Pari kh (1987b) and dev eloped th roughou t this book. The kin d o f system th at emerges from taking choice and strateg ic interact ion as fundam ental
48. To quote from Lewis’s (1969) introduction:
My theory of convention had its source in the theory of games of pure coordination — a neglected branch of the general theory of games of von Neumann and Morgenstern, very di¤erent in method and content from their successful and better known theory of games of pure con flict. Coordination games have been studied by Thomas C. Schelling and it is he who supplied me with the makings of an answer to Quine and White.
Yet, in the end, the theory of games is sca¤olding. I can restate my analysis of convention without it. The result is a theory along the lines of Hume’s, in his discussion of the origin of justice and property.
49. The key insight required was the modeling of communication by representing the relevant interactions and choices via games in so-called extensive form as initially developed by Kuhn (1953) and as elaborated by Kreps and Wilson
(1982) for games of incomplete information. The extensive form enabled making explicit certain crucial information involving ambiguity, something that is obscured in the so-called strategic form representations Lewis used. These ideas are introduced in chapter 3 and in Appendix A. Lewis also never considered the costs of communication.

Introduction 29 prop erties of linguis tic and commun icatio n system s i s r ather di¤er ent fro m what has emerged in the past.
To tak e just one impo rtant example , the a pproach tak en her e i s very di¤er ent from the appro ach that Monta gue (1974b) took in ‘‘The Proper
Tre atment of Quanti fica tion in Ord inary English.’ ’ There, Montagu e gave a meth od of tran slating an interestin g fragm ent of Engl ish into the lang uage of Intension al Logi c ( IL). Sin ce th e interp retatio n o f I L relative to a m o del is a straig htforwa rd a¤ai r, Engl ish could then be interp reted ind irectly by piggyback ing on IL. M ontague ’s acco mplishme nt is an impre ssive one, stand ing as the culmi nation of the ‘‘lo gicist’’ appro ach that has its origins in the work of Fre ge and Russel l. Thi s type of approach, whic h remains th e dom inant par adigm in ( linguis tic) semanti cs, maps sur face linguis tic forms into an abs tract logica l represen tation,
Logical Form . Logi cal Form is a s yntactic level of represe ntation that sha res man y propert ies with an arti ficial logica l langu age such as First
Order Logi c. Thi s abs tract langu age can the n b e i n terpreted relative to a mod el.
Ho wever, unl ike an arti fici al lan guage — such as standard First Order
Logi c o r a compute r programmi ng lan guage, both of whic h can be interpre ted directl y — Logical Form neces sarily conta ins elem ents tha t can onl y b e interp reted relat ive to a conte xt. Thus, Logi cal Form req uires a pra gmatic comp onent th at wi ll fill in detail s fro m the conte xt a n d yield th e conte nt of the utteran ce. Thus, these th eories give the linguist
(an d phi losopher) tw o degre es of freedom: firs t, there is the unseen level of Logi cal Form , whic h can be quite remote from observab le sen tences; 50 seco nd, the fact that one then map s Logi cal Form s t o conte nts means th at Logical Form can be remo te from inten ded contents as well. While th is situati on is not, in itsel f, a fatal one, these two deg rees of freed om wi th an unob servable and re latively r emote Logical Form in th e center do mean that theor ies of this sor t will be relat ively unconstrai ned by empirical factors. Any eviden ce contra dicting such a theory coul d, in prin ciple, be fixed by ad hoc adju stments to the interm ediate layer of
Logical Form . I t seems therefo re th at concept ually simpl er theories res ponsive to th e emp irical facts of languag e use might be preferred . 51
50. Notice that surface syntax is already quite remote from what we can observe directly since it involves abstract objects such as constituents and grammatical categories. Logical Form adds another level of unobservable structure.
51. It appears that the neuroscienti fic evidence also indicates that choices are actively considered in the brains of interlocutors during communication (see
Glimcher, 2004, and more recent books on neuroeconomics); interactions

30 Chapter 1
The approach deve loped here shares som e propert ies with the analysi s found in M ontague ’s (1974a) ‘‘En glish as a Form al Languag e .’’
There, he tried to interp ret a fragm ent of English directly relative to a model. However, th e obj ects he chose to tran slate were sen tences and their par ts, not utterances. My appro ach is similar though I connect utteran ces directly to mode l-theoret ic structu res, that is, to situatio n theor y, and give a method for com puting the interp retatio n o f complex expressions and their par ts in a non-Frege an way via the fixed point principle . A s will be shown, because my obj ects of analysi s are utterances and not senten ces, and becaus e utterances invo lve both choice and strateg ic interact ion , game theor y plays a fundam ental rol e i n this comput ation.
I a m thus advan cing an empirical hypoth esis about choice, strateg ic interactio n, and equilibri um, and th e nature of linguis tic mean ing and communicati on as well as develop ing a set of math ematical to ols fo r linguis tic and phi losophi cal exp loration. A consequ ence of the ana lysis will be th at there is no principled distinct ion between seman tics and pragmati cs. There are cur rently many views about the relation ship betwee n semanti cs and pragmati cs, but they all appea r t o sha re the view th at certai n thin gs are inherently semanti c — fo r examp le, convent ional meanings — and ot her things are inheren tly pra gmatic — for ex ample, th e role of context. This startin g point originat ed perhaps in
Grice’s (1975) pionee ring work on implicature , but it has now become almost an a pri ori commitmen t f o r researchers .
My suggesti on is that it is worthw hile to start afresh fro m first principles and see what kind of framewo rk emerges bef ore we draw a line between the two sub fi elds, if any such line needs to be drawn. In the end, it is the techn iques and ana lyses of natural langu age meaning th at are interesting, not some putativel y inh erent distinct ion betwee n sub fiel ds.
Game theor y and equilibri um seman tics allow us to loo k a t ‘‘t he proble m o f meaning’ ’ i n a new way.
To return to the main theme of equi librium, the detail s o f this idea in the framew ork wi ll bec ome clear as we develop it. It incorp orates the other th ree principal features we hav e discussed: reference, use, and indetermi nacy. Below I des cribe a glob al view of the idea.
Languag e and its use may be viewed as a system of const raints in the speci fic sen se of ‘‘con straint’’ in troduce d earlier. I w i l l not bother to conamong agents are of course obviously observable. So the elements underlying equilibrium
— choice and strategic interaction — appear to have empirical validation.

Introduction 31 vert a relation ship th at obtains in to a formal const raint in this sen se, but when this word is used, my in tention is that the relat ionshi p c a n be so exp ressed. In other word s, equilibri um semanti cs will itself be expressibl e as a system of const raints within situati on theor y.
M y concer n i n this boo k w i l l b e with the following fo ur s ets of const raints:
1. Synt actic const raint ( S ) 2.
Conven tional constraint ( C) 3.
Infor mational const raint ( I ) 4.
Flo w constr aint ( F )
Equ ilibrium semanti cs may be descr ibed compactl y via its system of const raints SCIF . When spe ech is consi dered, a fi f t h set of phono logical const raints P would have to be a dded. This last const raint wi ll be addres sed very brie fl y i n cha pters 5, 6, and 7.
S conta ins some account of the syntax of the language bei ng consi dered . I will not adopt any particul ar approach to gramm ar, but will use th is const raint informal ly as it is not my chief concern. Synt ax interact s wi th and is in fl uenced by meanin g, that is, the ot her th ree const raints in
SCIF , but we will simply take it as given, except in chapter 7. S plays a criti cal rol e i n the derivati on of content . A s a n asid e, we observ e that it is primari ly with resp ect to this const raint that di¤er ent symbo l s y stems differ: language is the symbo l system wi th th e m o s t elabora te and det erminat e syn tax.
C is a set of convent ional const raints th at maps every word into one or more propert ies or relat ions. This map is called the convent ional map and can be largely extract ed fro m a diction ary,52 excep t for a relativel y smal l class of syncatego rematic word s such as determi ners and conjunction s. The conven tionality of the meanings implies that th ey are inde pendent of conte xt. 53 Again , t o a lesser deg ree, di¤er ent symb ol system s di¤er with respect to this constraint as well: som e symb ol sys tems such as language are mo re or less fully convent ional whereas ot hers suc h a s imag es may be par tly natu ralistic. The exact role and place of conven tional meanings in commun ication will be exami ned from cha pter 3 onw ard.
52. With appropriate modi fications to take account of the kinds of criticisms Kripke
(1972/1980) and Putnam (1975) have made. See section 7.1.2.
53. This independence is actually partial in a sense that is made precise in section 7.1.2.

32 Chapter 1
I maps the prop erties and relat ions obta ined from th e conven tional map into cer tain special situati on-the oretic obj ects introd uced in the nex t chapt er. Which par ticula r obj ects th ey get mapp ed into is in par t det ermined by S and in part by our informat ional space or ontol ogy relat ive to a conte xt or ut terance situati on u . This map is called the infor mational map . The gen eral form of this constraint is by and large the same fo r all symbo l system s, but as S in fluence s its behavior, its det ails vary from system to system .
Finall y, F is in some sen se the main constraint, the one that embo dies much of the framework of equilibri um semanti cs. Ess entially, a system of situate d games provi des a mod el of the utteran ce situatio n u , s o t h a t together with the sentenc e and its phrase stru cture, we can infer its mean ing. Again , t h i s const raint works in the same way for di¤er ent symbo l system s a t a general level, but di¤er s i n particul ars.
At this stage, th is very brief descripti on of SC IF will necessari ly be rather abstract. The rest of the book will spe ll it out. 54
The general idea of equilibri um in equi librium seman tics is that all four sets of const raints are in equilibri um — within each constraint and acro ss const raints, both in the c ontext of the system of meaning and gramma r and in the conte xt of utteran ces. In this book , w e exp lore the cen tral part of this ide al concept ion.
1.5 The Scope of Game Theory in Language
As explai ned in Parikh (2007) , there are broad ly two levels at whic h game theor y can addres s the proble ms posed by lan guage, a situatio nal level and a structu ral level . A t the situati onal level , the interest is in solving the proble m o f content in situate d com municati on. At th e stru ctural level, the interest is in solving the proble m o f how the variou s structu res — convent ional meaning, seman tical rule s, linguis tic variation
— emerge to enable commun ication. Of course , both th ese levels coexist and codet ermine each other , a s discussed in section 7.1.2, but this boo k will try to offer a m o r e o r less comp lete account at th e situati onal level since this is th e central prob lem of semanti cs in philoso phy and lingu istics. I hope to address th e s tructural level and also relat e the two level s elsewh ere. In analogy with the field of econom ics where the main divisio n i s betwee n microec onomi cs and macroeco nomics, th ese two levels could well be called mic rosema ntics and macro seman tics since the first deals wi th com -
54. See Parikh and Clark (2006, 2007) for a short introduction to this framework.

Introduction 33 mu nication bet ween and amon g ind ividuals and the sec ond deals wi th attri butes of langu age th at emerge in entire populat ions.
As I have arg ued in this chapt er, a new framew ork that reo rganizes and reconc eptualiz es semanti cs and pra gmatics is badl y required . The mainst ream consensus has re ached an impasse . The account of equilibrium semanti cs does three things: it provid es a new theor y, a new framework , a nd a new paradigm for lang uage and meaning. It would therefore be a fatal mist ake to view th e g a me-theoret ic a n d relat ed appara tus dev eloped in Lan guage and Equilibr ium as simply graftin g a piece of mathemati cal machinery onto a mainstream, largel y Grice-insp ired framewo rk in order to formal ize relat ively informal areas of the field such as impl icatu re or lexical disambi gua tion. It is a great dea l more than this: I a m seek ing a rad ical reframing of the proble m o f meaning and, indeed , a m prom ising a who le new way to think about it.
In contrast, much ot her recent game- theor etic work pri marily in the field of linguis tics, especially by Arthur Me rin, Rob ert van Roo ij, Gerhar d
J a Ё ger, Anton Benz, and ot hers, 55 while nota ble in its own right, has generall y taken the mainst ream view of seman tics and prag matics as given and so work s primarily with in what has come to be called formal prag matics as there is relat ively lit tle that can be don e w i thin the sphere of lit eral mean ing if it is assumed to be given by c onventio nal r ules. As a result, much though perhaps not all such work has focused on th e formali zation of received pra gmatic factors ( like the Gric ean maxi ms and vario us types of implicature) invo lved in commun icatio n rather th an attem pting som ething more fundam ental to tran sform our very v iew of mean ing and, in par ticular, the relat ion betwee n seman tics and pragmati cs. In all of this work, the idea of equilibri um is simpl y a com putation al techn ique to solve games rather than a pervasive empiri cal fact abou t lan guage. For such work, game theory is, in a sen se, everything . W ithout it, there would be nothing to say. Readi ng such work, a phi losopher or linguist could be reaso nably secure that not mu ch wi ll need to cha nge in his or her broad picture of langu age. But, of course , t h i s i s a serious proble m bec ause man y (e.g. , those favoring a more radical
55. See Merin (1999) and Benz et al. (2006) for instance. The title of the latter collection of papers — Game Theory and Pragmatics — indicates that their contributions are viewed as belonging only to pragmatics and, indeed, this is what they have been in the main. The corresponding semantics is left primarily to researchers in formal semantics and the combination of the two to a Gricean view of the whole.

34 Chapter 1 pragmati cs) feel that th is foundati onal mainst ream view of language is breakin g dow n.
For my a ccount, on the other hand, game the ory (an d situati on theor y) are merel y the best cur rently availab le to ols to forge th is new way of think ing about langu age and meaning that I hav e call ed equi librium semantic s. M y primary interest is not in the appara tus but in th e refram ing and transforma tion it makes possi ble. Indeed, I hav e added signi fican tly to the tools where they fell s hort of the task.
As such, I urg e the read er to be open to this omn ipresent but largely unnotic ed idea and imag e o f equilibri um in langu age.
1.6 A Note to the Reader
Mean ing is central to life. It is what makes us hum an. As suc h, this book is intend ed for a wide read ership in the cog nitive sciences: philoso phers in fluence d b y either Anglo-A meri can or Continen tal or non-Wes tern thought, linguis ts, arti fici al intellige nce researchers, comp uter scienti sts, neurosci entists , psychol ogists, eco nomists and other soc ial scientists interested in language and commun ication, and even formally incli ned theorists in the arts, esp ecially literary and visual.
Readers will brin g t h eir own proj ects and philoso phical com mitments to th e book and I want to alert them to one overriding principle as a guide to the ir read ing: while th e materi al is presen ted largely as a tightl y knit and almost seaml ess framewo rk, it has in fact many s eparable a n d interact ing par ts and level s that can be disce rned. I have selected the se const ituents bec ause I believe they are th e comp onents bes t suited to th e ends I had in mind, but people with di¤er ent goals or wi th di¤er ent tastes may mak e di¤er ent choices for these individual element s. A read er may accept my view of a foundati onal issue wi thout being per suaded by som e particul ar analysi s o r vice versa. I natura lly hope that read ers will find th e entire structu re credible and appea ling, but some may pick and choose from the o¤ering s and build their own wholes. I want rea ders to keep such varian t arch itectonic possi bilities in mind as they read the book .
It is also usefu l t o brie fl y g o over what is bac kground and what is new. There are three prin cipal elem ents that form the c ontext for this book .
Forem ost is the rich backdro p o f the last centu ry of seman tics itself. I have tried to iden tify some weaknesse s i n mainst ream approach es to meaning and to relate my propo sals to this setti ng in cha pter 1. Some

more discu ssion is pre sented later , especial ly in chapter 5 where I consid er the issue of ind etermin acy and the Gric ean challenge of de fining mean ing

Introduction 35 and commun ication, and in cha pter 6 where I addres s especial ly Kripke’ s argu ments for a Russel lian view of de finit e descripti ons. I hope to attem pt a more detail ed com parative analysi s with other seman tic ac counts in the fu ture.
The second has to do with the per spective of situatio n theor y, the req uired parts of whic h I have recount ed in chapt ers 1 and 2 for the uniniti ated reader. I hope this backg round will a lso hel p those who are familiar with its history to bre ak free of some of th e prejud ices th at have sur rounded its dec line. As I have argued, especial ly in cha pter 2, it proved inad equat e becaus e some key pieces were missi ng, and I hav e tried to supply these item s i n what follows. Amon g these are a new perspe ctive on info ns (and th erefore on par tiality and fine-g rainedn ess, two of situatio n th eory ’s impo rtant strengths) and a new operation of uni fication
.
The last is the conte xt of game theor y whic h has now been around for almost a cen tury. 56 I have presented its bas ic ideas fro m scratch in cha pter 3 but from my own per spective of situa ted choice. I t is di‰cu lt to separate the bac kground fro m t h i s viewp oint but th e exp erienced read er will hav e n o tro uble di¤er entiating bet ween the two. For newcome rs,
I hav e provi ded referen ces to stan dard texts in the field.
Cl assical game th eory is also concer ned largely with single games (or wi th rep etitions of a single game) . A key inn ovation is the idea of interaction s betwee n and amon g games. This has led to man y new elem ents, not least the prod uct operat ion on g ames, conceiving the initial prob ability distri butio ns as strateg ic variabl es, and interd ependent ga mes with a double fixe d point solu tion — all introd uced in chapt er 4 — but, again, it is not easy to produce a comp lete list of additions and alter ations. Appendix A also contains an elabo ration of my perspe ctive on situate d games and th eir solution that exploits an analogy made possi ble by the uni versality resu lt of chapt er 4.
I hav e followed a certai n convent ion throughou t t h e book: unless display ed, linguis tic exp ressions are almost alw ays men tioned in double quotes or smal l cap italization , and meanings or content s are italici zed.
The use of di¤er ent alphab ets or styles for th e man y symbols also follows a pattern th at is harder to des cribe but should bec ome fami liar as the read er progress es th rough th e book .
56. Zermelo (1913) was probably the first person to publish a theorem in the theory of games.