of Possible Worlds
p Talk about coreference only makes sense in relation to the specification of a definite possible world or set of possible worlds. The external linguistic sign that a sentence must be treated from the standpoint of possible worlds, is the presence in it of modal terms, i.e. of terms that fix modal concepts. Understanding the latter means understanding a definite relation (depending on the content of the modal concept concerned) of alternativity to a definite set of possible worlds. When it is a matter of concepts that express propositional attitudes of a speaker of the language (his knowledge, belief, opinion, conviction, desire, striving, etc.) the relation of alternativity is treated in relation to this speaker, and possible worlds compatible with the given propositional attitude of the given speaker as a member of world W are understood as corresponding alternative worlds in relation to W.
p In other words it is then a matter of worlds compatible with what a definite speaker of the language knows or believes, what he wants, what he is striving for, etc., in the given world W. The sentence ’John lost a black pen yesterday and Bill found it today’ differs from this standpoint from ’John lost a black pen yesterday and Bill believes that he has found it today’ in that in the second case it is a matter of the identity of the black pen that John lost yesterday and the pen that Bill found today, from the standpoint of possible worlds compatible with Bill’s given prepositional attitude and alternatives to the world described in the sentence under consideration; it is not excluded that Bill is mistaken in his opinion and has not found John’s pen at all.^^35^^ Analysis of the sentences containing a coreference across several contexts of belief (for example, in the sentence ’John thinks he has caught the fish he wanted to catch yesterday, but Bill thinks he has caught it’), i.e. sentences that contain a reverse reference to a possible world 154 mentioned earlier, are constructively analysed in terms of ’backwards-looking’ operators.
p The following explanation is suggested in terms of this approach for cases in which coreferentiality takes place independently of the referentiality (in Hintikka’s understanding, as reference to an object existing in the real world). Thus the coreferentiality in the sentence above ’John wants to catch a fish and eat it for supper’ is that in each possible world compatible with what John wants, he will catch a fish and eat that fish for supper. There is coreference although different objects will be subjected to this operation in different possible worlds. The explication of the difference between the attributive and referential uses from the position of the approach is correspondingly based on understanding of a sentence with the form ’Fa’— (in which ’a’ is a singular term and ’F’ is a predicate expression containing one, or more than one, modal concept), for example, ’John believes the Prime Minister of Denmark is a Social Democrat’,—as a sentence about different objects that are referred to by the singular term in different possible worlds; in this case it is a matter of de dicto interpretation.
With this interpretation the sentence concerned is
understood as expressing John’s belief that, whoever is the
Prime Minister of Denmark he is a Social Democrat. John’s
belief may be based, for example, on information that the
Danish Cabinet consists exclusively of Social Democrats.
In that case John’s belief refers to different Danish
politicians who are Prime Ministers of Denmark in different
possible worlds. These worlds are those that are
compatible with what John believes. It is by virtue of that
reference to different objects belonging to different possible
worlds that it is not allowed to deduce the truth
from the truth of ’Fa’ (as is prescribed by the classic rule of existential generalisation), i.e. affirmation of the existence of an object about which ’Fx’ is true), i.e. to conclude that ’Fx’ is true about a certain definite object.
It can be a matter, in addition, of understanding the
sentence ’Fa’ as one about a definite object that is re-
ferred to (selected) by a singular term in a number of
possible worlds, including the actual world. In this case it is
a matter of interpretation de re, or formally: 3 xFx, in
which ’Fx’, for example, ’John believes that x is a Social
Democrat’. In other words, John has in mind a definite
Danish politician who, he knows, is the Prime Minister of
Denmark, because, to have belief about who is what, means,
according to Hintikka, to have belief about a definite
individual who satisfies the predicate under consideration.
Hence it follows that the rule of existential generalisation is
not valid for any interpretation of singular terms; its
application calls for meeting an additional condition, which
consists in guaranteeing that V selects one and the same
individual in all possible worlds as a member of which ’a.’
is treated in ’Fa’, i.e. depending on what prepositional
attitude is ascribed to the given speaker of the language in
’Fa’. If, moreover, this individual is presupposed to exist
in the actual world, we have
p The explanation of the reasons for the possibility, or conversely the impossibility, of employing an existential generalisation, in other words, the possibility of quantifying over a modal context, comes down to examination of the possibility of making a cross identification of individuals existing in different possible worlds, i.e. to whether one can say about a definite member (of the set of individuals) of one possible world that he is or is not identical with a member of another possible world.^^37^^
p The uses de dicto and de re, according to Hintikka and in opposition to Donnellan’s point of view, are not treated as not irreducible. It is a peculiarity of this ambiguity, which distinguishes it from other structural (syntactic or semantic) ambiguities, that the two interpretations under consideration ’merge’ when there is certain additional information, i.e. information not contained in the sentence itself. The gap between a statement about several referents in a number of possible worlds and a statement about an actual referent, which is indicated by a singular term, disappears as soon as this term picks out one and the same object in all these worlds. Thus, in relation to our exam- 156 ple, the definite description ’Prime Minister of Denmark’ ’singles out’ one and the same individual in this case in all the alternatives to the actual world compatible with John’s belief. That is interpreted, in turn, as meaning that John has an opinion about who Prime Minister of Denmark is.^^38^^
p Analysis of the ambiguities of this kind raises a number of questions of a methodological order relating to the explicating possibilities of certain logically oriented linguistic theories of the ’semantics of language’. The possibility of the coincidence of de dicto and de re interpretations when there is supplementary information means that the ascription of a definite logical form to an expression depends, in the general case, on the context of use of the linguistic expression. The problem of exposing this ambiguity is solved of course by theories in which the meaning of the appropriate expressions is explicated in intensional concepts (for example, in Montague’s grammar), i.e. in those in which the concepts of intensional logic are employed to define the meaning of the linguistic expressions and not just to establish their reference and coreference, as in generative semantics. At the same time, one must stress, when noting the great explicating possibilities of theories of that kind, that these possibilities are exhausted by demonstration of a definite set of interpretations of the linguistic expressions. These theories do not contain an explanation of the procedure for resolving these ambiguities,—choice, according to the context, in the broad sense, and according to the speaker’s knowledge contained in his conceptual system, and according to a definite interpretation of the linguistic expression from the set of possible interpretaions. It is this moment, moreover, that is essential for speakers’ understanding and use of natural language.
p At the same time one cannot conclude from the fact that a sentence does not contain terms that express modal concepts, that this sentence cannot be paraphrased in a disjunction of several sentences when there is a certain situation or context that contains definite additional informations. In other words, it does not follow from the fact that an expression is, when it is taken by itself, i.e. out of context, that it will remain such when put into a certain con- 157 text. The relativisation of concepts of a possible world suggested by Hintikka, and of the concept of the object in relation to the speaker’s prepositional attitudes, is undoubtedly a contribution to analysis of the problem of reference and coreference. The scope of the phenomena embraced by this analysis, together with acceptance of a specific doctrine of possible worlds, promotes adoption of the conception of language, or semantic, games, to a considerable extent as the theoretical basis of this analysis, or of game-theory semantics as a definite system of rules for the semantic analysis of sentences of natural language.
p The concept of a language-game correlates methodologically with Wittgenstein’s concept of ’language games’,^^39^^ and theoretically with the analogous rigorous concept of the mathematical theory of games. From the standpoint of the approach being considered understanding a sentence is knowledge of what is happening in the language-game correlative with this sentence as a definite rule-governed activity of speakers of the language that links the language with the world about which it speaks.^^40^^ The game itself is a consistent procedure of verification of the sentence (in particular the transformation of quantified sentences into atomic sentences governed by the rules of the game). One of the two players, called T and ’Nature’ respectively, tries to show that the sentence concerned is true (in the traditional sense), and his opponent, observing the rules prescribed for playing the game, tries to show that it is false. In other words, truth of the sentence signifies that the player called T has a winning strategy in the game corresponding to the given sentence. Falsity of the sentence correspondingly implies that the other player, i.e. ’Nature’, has a winning strategy.
p The basic idea thus consists in determining the truth of a sentence by reference to a semantic game correlated with it. Since the verification of existential statements, for example, comes down to a search for and (when successful) finding of a definite object, semantic games connected with quantifiers (the main means of reference and coreference) are at bottom games of hide-and-seek in which the semantics of the quantifier expressions of natural language not 158 embraced by certain logical calculi, for example of first order logical theory, is brought out.
p Without going deeper into analysis of this process, let me note that, in spite of a certain opposition of the truth- theoretic approach (as descriptive) and the game-theoretic approach (as one of activity) to analysis of the semantics of linguistic expressions, one canot help ultimately seeing their fundamental link, which consists, from my standpoint, in the following. In one case it is considered that knowledge of the meaning of a sentence implies knowledge of how the world should be for the sentence to be true, i.e. what objects we can come across when we know the meaning of a sentence. In the other case it is supposed that knowledge of the meaning of a sentence implies knowledge of the way it is realised, i.e. knowledge of the procedures for finding the appropriate objects. In short, while it is a matter in the first case of a representation (description) of the truth- conditions of a sentence, in the second it is a matter of establishing their availability, in the terminology of linguistic philosophy of how the truth of a sentence is established ( substantiated) in practice in face of its possible refutation.^^41^^
p An essential feature of the game-theoretic approach is that by the semantic interpretation of a sentence is not meant relating it to some sort of deep structure (from which it can be obtained syntactically), but a sequence of operations performed on the surface form of the sentence that step by step bring out its meaning. The point concerns application of the set of rules of the game to the sentence as rules of its semantic interpretation rather than syntactic deduction of the surface structure of the sentence from different postulated representations of it. Although the semantic analysis of a sentence is determined by search for its concealed semantic structure (i.e. the structure discoverable during application of the rules of the game), the result of each such application is a definite meaningful (propertly constructed) sentence of the natural language, i.e. a definite surface form. Regarded conversely this analysis can naturally be understood as a process of the generation of the given sentence.
p The semantic interpretation of a sentence is thus not 159 determined directly by its surface form. Although each rule of the game operates on this structure, it converts it into another surface structure for subsequent applications of the rules. The semantic interpretation of the initial sentence is determined by the game as a whole and not by some part of it. With that understanding semantic analysis can be characterised as semantic prevision of what can happen in language games correlated with the sentence. The semantic representations formulated in a certain logical theory, for example in epistemic logic, are themselves treated at best as products of this analysis. They do not figure at any stage whatsoever of the semantic analysis. Finally, because semantic games refer to the use (application) of natural language, it is concluded that questions of its use cannot be excluded from semantics.
p This approach, which combines in one theory the relativised (in relation to speakers of the language) doctrine of possible worlds with a game-theoretic interpretation of sentences of natural language, not only lays the foundation for systematic investigation of the logical behaviour of a class quantified expressions of natural language but also raises a number of questions relating to the methodology of its analysis in contemporary formal theories.
p The inadequacy of this analysis is due to its end result being treated as a function of analysis of parts of some whole in accordance with ’Frege’s principle’—both syntactically and on the semantic plane—and so is determined ’from the inside-outside’ while the factor of context is always characterised in the opposite direction. A number of semantic ambiguities, including the de dicto | de re distinction, are resolvable when there is definite additional, extralinguistic information.
p What is important in principle here, however, is that in the theories being examined the feedback of the context to linguistic expressions coming within its scope (which also resolves the ambiguity of the linguistic expression) is not provided for, rather than that the function of determining the ambiguity of the linguistic expression is ascribed to the context. In that sense both Frege’s principle of analysis and the thesis of the recursiveness of the set of 160 grammatically correct sentences of natural language, the ascribing of logical form, irrespective of the context of the use of a linguistic expression, and the postulate of the universality of deep linguistic structures, seem questionable. In short, there are sufficient grounds for casting doubt on the relation of syntactic and semantic structures that they are given in modern formal theories of natural language as theories of the logical form of its expressions, and so to question the substantiation of the relevant analogy of natural and formal languages on presupposition of which this understandinfi of the relation of the syntactic and semantic aspects of this language is based.
p It is of fundamental importance for the theory of coreference, which is based on employing the concepts of the semantics of possible worlds, to substantiate the methods of identification, or the methods of cross-identification, of objects that exist in different possible worlds. The complexity of the problem of establishing these methods naturally corresponds to the complexity of all the possible situations, including counterfactual ones, described by natural language. In the end, in order to analyse these situations, concepts are often resorted to that correspond to speakers’ intuition only as an approximation. McCawley’s example, well known in the literature, ’I dreamt I was Brigitte Bardot and that I kissed me’, which is not amenable to analysis in terms of the coreference of the objects of the real world, is treated in terms of the semantics of possible worlds as describing a situation in which it is a matter of there being two of his doubles, or analogues, in the speakers ’dream worlds’ (i.e. in worlds like that he dreams about), and these being analogues, moreover, in a different sense.^^42^^ One of the speaker’s doubles, is the one whose experience he shares in a given ’dream-world’, the other, obviously, is his double in another respect. The problem is to establish the methods of identification of these objects, the more so that a breakup of one and the same object into several is sometimes presupposed in the other possible world.
p True, the criteria by which speakers in fact make a cross-identification and decide whether or not objects belonging to different possible worlds are identical, are problematic- 161 al, since there are no clear structural properties of what called the ’world lines’ linking the various ’manifestations’, ’roles’, ’doubles’, or ’analogues’ of one and the same object in different possible worlds. Hintikka treats the concept of the meaning of singular terms as a definite individuating junction from possible worlds to their objects or individuals.^^43^^ The identity of the individuals is understood in that connection as something establishable, not by means of certain absolute logical principles, but by a comparison of various possible worlds made by speakers by the principles of the continuality and similarity of the objects. The form of the continuality may be selected by different means, i.e. it does not eliminate speakers’ choice of different ’world lines’.
p It is supposed that speakers are constantly dealing in their actual conceptual and linguistic practice with at least two different systems of world lines, depending on whether they depend, when examining objects, on their descriptive (physical) or perspective (contextual) characteristics. One of these systems is correspondingly based on methods of descriptive identification that start mainly from the continuality of the objects in space and time, and the other on an identification of objects that consists in the same perceptual, or other directly cognisable, relations in various worlds with the given speaker, and is called perceptual identification.^^44^^ Both the one and -the other are treated ’as explications of Russell’s epistemic dichotomy of knowledge by description and knowledge by acquaintance.^^45^^
p Since the referents of connected variables must be objects identical in all the possible worlds concerned, the duality of the methods of cross-identification is reflected on the logical plane in a duality of the corresponding pairs of quantifiers. ’Ex’, ’(y)’, are employed as descriptive quantifiers and ’gx’ and ’Ay’ as perceptual ones. On the intuitive plane the variables of the first pair cover ordinary physical objects, while the variables of the second pair cover perceptual objects characteristically individualised by their location in the speaker’s perceptual field.
p The difference between the methods of cross- identification in many natural languages are already manifested on the surface level and expressed by different types of lin- 162 guistic constructions. The logic of descriptive identification can thus be regarded as the logic, or theory of logical form, of complex, interrogative sentences containing, as the main verb, the epistemic verbs ’to know’, ’to think’, ’to understand’, while the logic of cross-identification ’by acquaintance’ is treated as the logic, or theory of logical form, of constructions of direct object with appropriate epistemic verbs.^^46^^ The de dicto | de re distinction obviously passes through the distinction between cross-identification by description and by acquaintance; it belongs to both. Thus, although both the sentences ’John knows who the girl is that is standing in front of him’ and ’John knows the girl standing in front of him’ are de re, it is a matter of employing different criteria of identification in them, viz., descriptive and perspective.
p As I noted above, one of the fundamental problems pertaining to the structure of ’world lines’ is that of whether they can be divided, ’split up’ during the transition from one world to its possible alternatives. An affirmative answer would mean that several ’manifestations’ or ’doubles’ of the object under study are assumed to exist in some of the alternative worlds, which would introduce ambiguity into both the understanding of the modus de re, and consequently the de dicto | de re distinction as well. One can therefore agree with Hintikka’s viewpoint; what is regarded as division of ’world lines’ is rather an indication that we are dealing with the functioning of different principles of cross-identification. The question of continuity or similarity as the basis of cross-identification depends, as further study has shown, on the type of intensional context in which the object liable to identification is regarded.^^47^^ Namely: in impersonal modal contexts (such as, for example, ’Maybe my brother will resemble me, as I am now, more than I will resemble myself), and also in counterfactual situations (as described in the sentence ’If John gave a big enough bribe to Senator X, he could manage Carswell’ the principle of the continuity of the object and of the criteria of the descriptive identity of the object has priority; it is a matter of examining what we call ’ objective’ modalities that are not relativised in reference to what- 163 ever perspective of the examinatiaon, i.e. in contrast to personalised modalities such as prepositional attitudes (see Ch. V).
p Delimitation of the two aspects of the concept ’possible world’ furthers theoretical substantiation of this approach: viz., that which is called ’the possible course of events’ and that which is called ’the possible state of affairs’. The latter can be treated autonomously, i.e. as not connected by any course of events whatsoever. Preference is given to considerations of continuity when an object is being examined in terms of the possible course of events, i.e. in terms of possible states of affairs connected by a definite course of events. When, however, the object is examined in terms of autonomous states of affairs that are not stages in a definite possible course of events, considerations of similarity figure as the basis of its cross-identification. In actual semantic practice a speaker is concerned, as a rule, with possible courses of events, although that may not be clearly expressed in the surface forms of the corresponding sentences.
p There is thus justification for the conclusion that one of the most significant criteria of transworld comparison is provided by the different principles of continuity employed by speakers rather than by any doctrine of essentialism by which cross-identification is treated in terms of privileged attributes of the objects being studied. As Hintikka has remarked,
you may of course propose to call these continuity properties ’essential attributes’, but they are by any token a far cry of Aristotelian essentialism.^^48^^
What has been said leads to a consideration of knowledge or information on the basis of which the speakers of a language identify real or possible objects. From my point of view this information is part of what I call the speakers’ ’conceptual systems’. It should correspondingly be a matter of deciding the problem of the identification of objects from the angle of a speaker’s conceptual system in view of the definite concepts he has at his disposal about real or possible objects, in view of the appropriate information about them.