Three Alternatives on Contexts1 Carlo Penco Dipartimento di Filosofia, Università di Genova penco@unige.it Context is a concept used by philosophers and scientists with many different definitions. Since Dummett, we speak of the "context principle" in Frege and Wittgenstein: "An expression has a meaning only in the context of a sentence". The context principle finds an extension in some of Wittgenstein's ideas, especially in his famous passage where he says that "to understand a sentence means to understand a language" (Philosophical Investigations, §199). Given that Wittgenstein believes that "the" language does not exist, but only language games exist, we should conclude that he is speaking of the need always to consider a sentence in the context of some language game.2 This general attitude is certainly attuned to the contemporary tendency to place contextual restrictions on the interpretations of our sentences. However, we find so many kinds and forms of restrictions that such a general attitude does not suffice to provide us with a viable tool to find an order in the web of the many different theories of context. To look for an order, or at least for some clarification, w e may start with two contrasting theoretical paradigms: the "objective" theory of contexts, where a context is a set of features of the world, and the "subjective" theory of context, where a context is a speaker's or agent's cognitive background with respect to a situation.3 We have here not only two different ways of using the term 'context', but also two different 1 I would like to thank the many people who commented on this paper: Horacio Arló Costa, Margherita Benzi, Paolo Bouquet, Gilles Fauconnier, Marcello Frixione, Michael Green, Diego Marconi, Marina Sbisà. Special thanks to the Pittsburgh Center for Philosophy of Science, where I first presented the schema of this paper, and to the Giunchiglia research group in Trento, which set up the great opportunity for discussing such topic at Context 99. 2 Penco 1998 and 1999a provide an interpretation of Wittgenstein's remarks in this direction. 3 We have to take into account another general distinction given by Perry 1997, among presemantic, semantic and postsemantic context (the term "presemantic" is used by Kaplan 1977, par.XXII). The presemantic context is what gives an ambiguous epression its linguistic meaning (in "I saw her duck under the table" we have to decide whether "her" is a pronoun or an adjective, or whether "duck" is a noun or a verb). The semantic context is what gives the evaluation of the terms once their linguistic role has been disambiguated ("her" is a particular person – "if" a pronoun; etc.). The post-semantic is some kind of presupposed encyclopedia which is taken for granted and never made explicit (when I say "it is one o' clock" I normally assume to refer to my time zone, unless the contrary is explicitly stated). Both pre-semantic and post-semantic contexts can be interpreted as cognitive contexts, i.e. as assumptions or explicit information for what is going on in the relevant situation. The semantic context is the "objective" context, the features of reality given in the semantic evaluation (however odd this may sound in the face of the limitation of semantic theory as far as the interpretation of lexical items is concerned see Thomason 1991, Marconi 1997. In this paper we will not deal with this aspect of the matter). conceptions of semantics and philosophy. Such different conceptions are normally associated, respectively, with the classical paradigm of model theoretic semantics (Kaplan, Lewis, Stalnaker) on the one hand and with the A.I. paradigm (McCarthy, Buvac, Giunchiglia) on the other hand. For the sake of simplicity I will mainly restrict my attention4 to Kaplan 1989 and to McCarthy 1993 and Giunchiglia 1993. The two different conceptions can be summarised by means of the following schema: a) context as: b) context as: set of features of the world set of assumptions on the world (+ rules) <time, place, speaker,...> <axioms, rules> "context is a package "context is a group of whatever parameters of assertions closed are needed to determine (under entailment) the referent ... of the about which something directly referential expressions" can be said" Kaplan 1989 McCarthy 1993 "each parameter has an "a theory of the world interpretation as a natural which encodes an feature of a certain individual's perspecregion of the world" tive about it" Kaplan 1989 Giunchiglia 1993 In "Afterthouhgts", Kaplan explicitly speaks of the "metaphysical" point of view in describing contexts, while in "Notes on formalizing contexts" McCarthy uses a notion of context which leads to the idea of "microtheory" (Guha) or to the idea of a subjective point of view on the world (Giunchiglia). Given these differences, I will distinguish the two conceptions of contexts as: (a) "objective" or "metaphysical" (ontological), and (b) "subjective" or "cognitive" (epistemic). 4 Hints at a comparison between these two theories has been given by Thomason and Moore (1995), where the authors stress the fact that "there are difficulties with the view that contextual effects in natural language are confined to Kaplan-like effects". Also referring to these two theories Giunchiglia and Bouquet (1997) speak of a contrast between "pragmatic" and "cognitive" context, and Bouquet (1998) speaks of the contrast between metaphysical and cognitive context. We have here two very different interpretations of what a context is: features of the world, or representation of features of the world. Apparently, the concern of the cognitive theory is wider than that of the metaphysical theory: the cognitive theory is concerned with any feature of the world, not just with the limited set devised by Kaplan (however enlarged by Lewis5). An inviting picture is often tacitly assumed: the two theories seem to correspond to two contrasting philosophical stances and two different kinds of formalism: (a) the metaphysical theory is an expression of realism or objectivism, and goes hand in hand with model theoretic semantics (particularly with direct reference theory and with the double indexing); (b) the cognitive theory is the expression of an anti-realistic attitude typical of cognitivism and subjectivism; it goes hand in hand with computational, mostly syntactic, solutions (with predicates of belief that take names of propositions as arguments). I don't think this pairing of theoretical interpretations and kinds of formalism is correct. On the contrary, it seems to give an oversimplifying and misleading picture. To link multicontext theories with a subjectivist view represents a dangerous step which would cast a useless restriction on such theories. On the other hand, it would be possible to use model theoretic semantics to represent a subjective point of view (think also of autoepistemic logics). However, to make the contrast simpler, I will keep this general oversimplification as a starting point. Eventually, the discussion should be carried out at a logical level. From this point of view, we may think of the contrast between model theoretic semantics and local model semantics.6 Which formalism can better express our basic intuitions on the working of our language and reasoning? Shall we have a radical opposition or can we find an equivalence relation between the two paradigms? After all, alternative paradigms sometimes do converge. In this paper, however, I will not carry out the confrontation at the logical level; I will discuss instead some philosophical aspects of the contrast between Kaplan's theory of 5 In the 1981 postscript of Lewis 1970, Lewis says that the package of features of context should be extended. However, Lewis 1980 suggests that, besides the choice of building richer and richer indexes, we might leave most of the aspects implicit and at the same time extend double indexing (restricted by Kaplan to possible world and time) to include location and standard of precision. The criterion concerning which features should be packed into an index is: give only features that can be shifted. 6 We have to distinguish a semantic level, where model theoretic semantics may face the challenges of inferential semantics of local model semantics, and a syntactic level, where a modal logic with belief operators is just an alternative to other syntactic solutions, such as a non-modal logic which uses predicates of belief on names of sentences. For a general discussion of these different solutions see Frixione 1994. Generally speaking, we may see two alternative directions: (i) extending modal logic to include further cognitive aspects; see for instance Fagin and Halpern 1983, Thomason 1998 and Thomason (forthcoming); (ii) leaving the predicate calculus as it is (even first order, if we like) and enrich the structure, giving more relations among different logical systems, as in multi-context systems; see for instance Giunchiglia, Serafini and Frixione 1993 and Giunchiglia and Serafini 1994. See also McCarthy (b) demonstratives and McCarthy's theory of commonsense reasoning. Contrasting the two kinds of theories, we are offered different possible strategies: (1) The two theories deal with different problems, and should be developed separately; (2) The two theories have a large intersection, and should co-operate to solve problems which are not solvable by each theory separately. (3) The two theories are reducible to each other, and it is to be decided which direction is the most promising. As it often happens, probably no one of these possibilities is the right one; a more realistic and promising alternative could be a work of convergence which composes the best of each approach. The three alternatives, however, deserve a careful study because the problems posed by each of them can help to enrich our understanding of the possibility of the future research. 1. Separation A separatist vision stresses the difference of aims and problems to be solved by the two kinds of theories. The theory of the metaphysical context has been devised in order to treat the peculiar logical behavior of indexicals (expression like "I", "here", and so on). In classical semantics it was impossible to give a correct semantic value to sentences with indexicals because of their dependence on context. The classical example given by David Kaplan: "I am here now" is a sentence which is always true; however, it is not a necessary truth, because we cannot say that it is true in all possible worlds. I might have been somewhere else. Kaplan 1977 (parr. VI-VII) proposed a solution for the formal treatment of this kind of sentences (which, following Kripke's terminology, we might call "contingent a priori "). We have to distinguish between two indexes at which sentences are to be evaluated: on the one hand, we evaluate them at all circumstances (pairs of a moment of time and a possible world); on the other hand, we evaluate them at contexts of utterance (speaker, time and location). From this work onwards logicians began to speak of "double indexing"7 to indicate this novel treatment of semantical evaluation. Double indexing is a tool to evaluate two different aspects of indexicals: one aspect deals with the objective context of utterance, and it evaluates the linguistic meaning of the indexicals, the "character", intended as a function that given the 7 Actually, double indexing was "invented" by Kamp in 1971 for a treatment of "now", and rediscovered by Kaplan for treating indexicals and demonstratives in general (see Kaplan 1977, par.VII).