225 Jaakko HINTIKKA and Jack KULAS: (G. 3) The game G(3xS(.{)) begins with a Anaphora and Definite Descriptions. Tho choice by Myself of an individual from do Applications of Game-Theoretical Sem• (M), i.e. the domain of a model which antics. DordrechtiBostoniLancaster: G(3xS(x) is played on. If "b" is the name D. Reidel 1985 (Synthese Language of this individual either in L or in an Library 26), XIV + 250. extension L(l) of L, then the game in question is continued with respect to S(b), This is an original and ambitious book where S(b) is the result of replacing every that gives a new theory of definite descrip• free occurence of "x" in S(x) by "b". tions and anaphora phenomena via game• theoretical semantics. (G. V) The game G(VxS(x) begins like• The book is divided into three parts. wise as the game G(.FlxS(x), except that the Part I, the shortest of all, presents an individual is chosen by Nature, and is overview of game-theoretical semantics continued likewise. (GTS) as a basis for further considerations on definite descriptions and anaphoric The authors state that any G(S) is finite, pronouns. GTS invented by Hintikka in i.e. it "will come to an end after a finite early 70's and subsequently developed by number of moves" (p. 5). Moreover, they himself and his students is a sort of truth• sketch a proof that GTS for first-order conditional semantics. Its basic concept is language is equivalent with Tarski-type that of the semantic game. Semantic games semantics. are two person zero-sum games played by The authors claim that GTS has explicit Myself and Nature. Let L will be a first advantages over the standard semantics. order applied lan~age. Now, one can as• Hintikka in his Introduction to the whole sociate a game 61 S) with each sentence S book writes on GTS: "What game-theoret• of L. If G(S) ends with a true atomic ical semantics provides is a theoretical sentence in some extension L(l), which is model of the right sort. It is roughly com• obtained by supplementing L with a finite parable to such familiar frameworks of set I of individual names of objects which semantical representation as first-order G(S) is played on, then Myself wins and logic. However, the earlier theoretical Nature loses; if G(S) results with a false frameworks offered by contemporary logic sentence, Nature wins and Myself loses. are simply far too distant from the realities Intuitively speaking, Myself tries to show of natural languages to be what linguists that sentences are true and Nature's aim is really need" (p. XI). Thus, on Hintikka's to falsify them. This determines strategies view, the rule associated with particular logical constants, providing that a sentence S is false if there (G. some) If the game has reached a sen• is a winning strategy in G(S) for Nature tence of the form and S is a true sentence if Myself has a winning strategy in G(S). For instance, if S x - some Y who Z - W = Sl A S2' the semantical game for S is regulated by the following rule then Myself chooses a person from do (M) with respect to which the game is being (G.A) The game G(S, A S2) begins with a played. If the name of the individual is choice by Nature of a conjunct Sj (i = 1 or "b", then the game is continued with 2). The rest of the game is as in G(Sj). respect to

The rules for quantifiers are further exam• x - b - W, b is a Y, and b Z, ples: is more adequate for the meaning of Of- 226 dinary "some", than its counterpart gen• X - B - W, b is a(n) Y, b Z, but d is not erated by first-order logic; for instance, (G. a(n) Ywho Z. some) is applicable to the sentence "some man to whom he had spoken saw Tom". Perhaps the following comment concerning Part II is devoted to definite descriptions. the relation of (G. anaphoric the) and (G. The authors distinguish three uses of the Russellian the) is important: "It is thus phrases: Russellian ("the present king of possible to see in pragmatic terms how the Italy is wise"), anaphoric ("if Bill owns a Russellian use of the-phrases can be con• donkey, he beats the donkey") and generic sidered as a variant of the anaphoric use. ("the tiger is a dangerous animal"). Al• Briefly, since there is no non-empty set [in though Hintikka and Kulas declare them• the sense of (G. anaphoric the) available, selves as followers of Russell in the descrip• the hearer interprets the the-phrase by tion theory, they regard the anaphoric use making the next obvious choice, that is as basic. It is regulated by the following setting [ equal to the whole domain of rule discourse (strictly speaking, to the relevant category)" (p. 67). This treatment of the• (G. anaphoric the) When a semantic game phrases is supplemented by considerations has reached a sentence of the form which try to show that GTS meets various problems connected with Russellian theory X-the YwhoZ- W, of definite descriptions. The authors discuss i.a. Bach-Peters sentences, primary and then an individual, say b, may be chosen secondary occurences, Donnellan's distinc• from a set of individuals [ by Myself, tions and Strawson's criticism of Russell. whereupon Nature chooses a different in• Part III, the most extensive of all, con• dividual, say d, from the same set [ (the tains a detailed analysis of anaphora phe• choice set). The game is then continued nomena in natural language. The authors with respect to compare the GTS-oriented theory of ana• phoric pronouns with other contemporary X - b - W, b is a(n) Yand b Z, but dis approaches: pronouns as placeholders for not a(n) Y who Z their heads, repeated reference account of pronouns, bound-variable account, and ap• If I is a unit set, the game is continued proaches via coreference assignments. Hin• with respect to a sentence of the form tikka and Kulas argue that these accounts are limited by obvious counterexamples X - b - W, b is a(n) Yand b Z. and try to show that GTS offers here satisfactory solutions. G-rules for anaph• The Russellian use is governed by the oric pronouns look like this rule (G. he) When a semantic game has reached (G. Russellian the) When a game has reach• a sentence of the form ed a sentence of the form X-he- Y, X - the who Z - W, an individual of the appropriate kind (a an individual, say b, is chosen by Myself, person or an animal), say b, may be chosen whereupon a different individual, say d, is by Myself from [, whereupon Nature chosen by Nature. If these individuals do chooses another individual, say d from [. not already have names, the players give Then the game is continued with respect to them names, which are assumed to be "b". The game is then continued with respect to x - b - Y, b is male, but d is not male.