1 Hans Kamp and I have been developing versions of this theory independently in a number of papers now. Kamp, H. in ‘Context Thought and Communication,’ Proceedings of the Aristotelian Society 85 (1985) 239–61CrossRefGoogle Scholar, proposes a description of belief and other cognitive states by means of the structures posited by DR theory. He then shows how this thesis helps to explain certain puzzling features about belief–viz. their interconnectedness. This interconnectedness leads toward a solution of certain puzzles about belief, like that in Kripke’s Pierre puzzle. In my ‘Belief in Discourse Representation Theory,’ Journal of Philosophical Logic 15 (1986) 127-89, I develop a theory of belief and a formal semantics for belief reports within the framework of DR theory. It also stresses the interconnectedness of beliefs and treats in detail not only the puzzles of belief underlying Kripke’s and other similar examples but also shows how these belief puzzles affect a theory of belief reports. My contention there is that belief reports are context sensitive in a particular way; their interpretation is sensitive to what the recipient knows about the background attitudes of the agent. This thesis follows from a proper appreciation of the interconnectedness of beliefs. A second paper of mine, ‘A Typology for Attitude Verbs and Their Anaphoric Properties,’ Linguistics and Philosophy 10 (1987) 125-97, extends the semantics for belief to other attitude constructions and develops a treatment of anaphora within various attitude contexts. The present paper attempts to take the central insight of the theory of belief elaborated in these earlier papers and to develop an account of belief formation and acceptance. I also show here how the theory of belief reports as developed in Asher, ‘Belief in Discourse Representation Theory’ arises naturally out of the way I develop an account of belief formation.

2 For details, see Kamp, H. ‘A Theory of Truth and Semantic Representation,’ in Groenendijk, J. Janssen, T. & Stokhof, M. eds., Formal Methods in the Study of Language (Amsterdam, Holland: Mathematisch Centrum Tracts 1981), 277–322.Google Scholar

3 I assume here that attitudes have at least a prima facie causal efficacy in determining action, and so I shall assume that attitudes exist and are components of an agent’s cognitive state. Thus, my ontological commitments will be plainly intentional. This is not to say that I reject a physicalist reduction of intentional entities, but my aim here is not to offer a solution to the problem of intentionality or to argue against some such solution already proposed. Rather, it is to provide a framework within which one can describe precisely intentional phenomena. In effect I am attempting here to analyze some of the observations gathered by phenomenologists with the help of the modern tools of model-theoretic semantics.

4 There may, in fact, be no phenomenological difference between those beliefs containing conceptual individuals standing proxy for real individuals and those beliefs containing conceptual individuals with no real world referent. A unicorn believer thinks in the same way about unicorns as he does about cats, at least from an introspective point of view, an example due to Rapaport, W. ‘Logical Foundations for Belief Representation,’ Cognitive Science 10 (1986) 371–422.CrossRefGoogle Scholar

5 I try to develop this point in ‘Information, Interpretation and Attitudes,’ in P. Hanson, ed., Information and Content: Proceedings of the First British Columbia Conference in Cognitive Science (Vancouver: University of British Columbia Press, forthcoming).

6 Approaches of this kind have been proposed by Fodor, J. The Language of Thought (Cambridge, MA: MIT Press 1974)Google Scholar, Field, H. ‘Mental Representation,’ Erkenntnis 12 (1978) 1–62Google Scholar, and more recently by Boer, S. and Lycan, W. Knowing Who (Cambridge, MA: MIT Press 1986)Google Scholar.

7 Kamp also espouses such a view, I believe. See Kamp, ‘Context, Thought and Communication.’

8 Of course some would argue that this precision is entirely inappropriate. Precision, some would argue, concerning the form of a representation would depend on the future dicoveries of the neurosciences. I would argue that this criticism is entirly misplaced; the structure of information is determined by information-theoretic tasks-the way the structure of the information is realized neurophysiologically is beside the point. I cannot, however, go into any more details here.

9 For much more discussion of the general approach of DR theory, the algorithm for DRS construction and the correctness definition, see Kamp, ‘A Theory of Truth and Semantic Representation,’ Asher, ‘Belief in Discourse Representation Theory,’ Asher, ‘A Typology for Attitude Verbs,’ and Kamp, ‘Situations in Discourse without Time or Questions’ (manuscript, 1983).

10 For a formal specification of DRSs and the construction algorithm for generating them, see Kamp, ‘A Theory of Truth and Semantic Representation,’ and Asher, ‘Belief in Discourse Representation Theory.’ I will in general follow the DRS formulation in Kamp, ‘Situations in Discourse without Time or Question,’ and Asher, ‘Belief in Discourse Representation Theory.’ When appropriate, I will use bold-faced letters of the appropriate type as metalinguistic variables for discourse referents.

11 DR-theory’s treatment of universal quantification is handled quite differently. For a detailed discussion of quantification see Kamp, ‘A Theory of Truth and Semantic Representation.’

12 For a relatively ‘bug-free’ version of the definition of proper embedding that I have in mind here, see my ‘Information, Interpretation and Attitudes.’

13 More precisely, this causal relation obtains between a physical realization of a conceptual individual and real individual.

14 The familiarity theory of definites has been developed within the DR theoretic framework and vigorously defended by Irene Heim in ‘The Semantics of Definite and Indefinite Noun Phrases,’ Ph.D. diss. University of Massachusetts, 1982.

15 For further details see the discussion in Asher, ‘Belief in Discourse Representation Theory.’

16 Barwise, J. and Perry, J. in ‘Semantic Innocence and Uncompromising Situations,’ in French, P.A. Uehling, T.E. and Wettstein, H.K. eds., Midwest Studies in Philosophy VI: The Foundations of Analytic Philosophy (Minneapolis, MN: University of Minnesota Press 1981) 387–404Google Scholar, distinguish between a ‘value-free’ interpretation of a definite description and a ‘value-loaded’ interpretation of a definite description. Something like this distinction (though there are important differences) was noted earlier by Donnellan in Donnellan, K. ‘Reference and Definite Descriptions,’ Philosophical Review 75 (1966) 281–304CrossRefGoogle Scholar. The redundancy in (4) is avoided by supposing that the agent processes the definite according to a ‘referetial’ strategy that employs at the level of discourse referents something like the value-loading strategy of interpretation in Barwise and Perry.

17 Graeme Forbes has suggested to me that this information is perhaps best thought of as an individual sense.

18 Unfortunately, the processes of reinterpretation and paraphrase that underlie Dan’s selective acceptance or ‘pruning’ of my statement are something that I cannot go into here.

19 Clark & Marshall have argued for mutual knowledge in resolving definite reference. I believe a theory like DR theory might be useful for spelling out their ideas on resolution of definite reference. See Clark, H. and Marshall, C. ‘Definite Reference and Mutual Knowledge,’ in Joshi, A. Webber, B. & Sag, I. eds., Elements of Discourse Understanding (Cambridge, England: Cambridge University Press 1982), 10–64Google Scholar.

20 The DRS representation of ‘every man is mortal’ would involve a DRS with no discourse referents in its universe and just one logically complex condition built up our of ‘subordinate’ DRSs. The DRS for ‘there is at least one honest used car salesman’ would contain a discourse referent in its universe for the salesman, but if this DRS were added to an agent’s total cognitive state, the discourse referent for the salesman would remain unconnected to any other discourse referents within the agent’s total cognitive state.

21 Individuals can even share beliefs about fictional objects with each other, if the discourse referents that stand proxy for the individuals get linked by chains of communication (for details see Asher, ‘A Typology for Attitude Verbs’). Of course, this doesn’t answer the question of how to represent those fictional objects that the agent himself takes to be fictional; to handle such cases one may want to mark the discourse referent introduced as standing proxy for something fictional. Exactly how to do this is a much more complicated issue. Also much more here could be said about fictional names, i.e., names of fictional objects. Fictional names get processed in exactly the same way as nonfictional names, except that they don’t generate external anchors for the discourse referents they introduce. Further, depending on whether the agent processing the sentence believes they are fictional names, fictional names may introduce a ‘marked’ discourse referent of the sort alluded to above. Finally, there remains the ticklish problem of truth conditions for sentences involving fictional names, but that is not something I can go into here.

22 Kripke, S. ‘A Puzzle about Belief,’ in Margalit, A. ed., Meaning and Use (Dordrecht, Holland: D. Reidel 1979), 239–83CrossRefGoogle Scholar

23 Another famous example of mistaken identity occurs in Shakespeare’s Twelfth Night.

24 In (7), i is a special indexical discourse referent representing the agent to himself.

25 I have also brushed over certain issues here that are crucial in the recipient’s interpretation of the belief report. The condition named (v, ‘Chernobyl’) within the conditions of the DRS characterizing the discourse referent p in Stage I indicates that the recipient assumes that the agent associates the name ‘Chernobyl’ with some conceptual individual, but this assumption may be questioned in some cases. In general, the construction of DRSs describing Objects of attitudes is a quite delicate matter. For some discussion see Asher, ‘Belief in Discourse Representation Theory.’

26 Certain rules are needed to handle those cases where the context specifies no delineated DRS for the agent whose beliefs are being interpreted. In such a case, one is constructed to yield the required internal anchors for those discourse referents introduced by definite NPs within belief contexts. There is, however, a problem with what conditions should be entered into the delineated DRS on the discourse referents that the recipient supposes to be declared there. That is, the recipient will, given such a context, not know what information the agent associates with what he believes to be the denotations of the definite NPs. What can the recipient assume? Well, not much. For instance, the agent need not even have the same metalinguistic information about the referents as the recipient; for instance, he might associate these discourse referents with linguistic expressions in a language unknown to the recipient. Some rules for such contexts are proposed in Asher, ‘Belief in Discourse Representation Theory.’

27 The details of the approximation of the content and structure of one DRS by another is spelled out in Asher, ‘Belief in Discourse Representation Theory’ and ‘A Typology for Attitude Verbs.’ This notion of approximation predicts a certain natural class of inference patterns to be valid within belief contexts; briefly they are all those inferences that result from the ‘thinning’ of the set of conditions in a DRS, and so I have called them ‘simplification inferences.’ Conjunction elimination and existential quantifier introduction are two rules of first order logic that correspond to the thinning process. There are other ways, however, that one could define the approximation relation-different ones will be appropriate for different types of attitude reports or for rather different agents from normal adult humans. For instance, we might choose a rather laxer notion of approximation, were we to gauge the reporting of beliefs of animals or very small children.

28 The satisfaction definition also predicts such reports given the context as I have set it up to be correct. For according to my definition of ‘determinateness,’ the target portion of the count’s cognitive state is at least as determinate as the DRS derived from the complement of the belief report in either case, and the internal anchors all work as required.

29 I believe that many people share these judgments. If so this shows a difficulty with the direct reference theories of belief such as those proposed recently by Scott Soames and others. As far as I can tell, these theories must predict that the second pair of reports are at least as good if not better than the first pair.

30 See, for instance, Stalnaker, R. ‘Propositions,’ in MacKay, A. & Merrill, D. eds., Issues in the Philosophy of Language (New Haven, CT: Yale University Press 1976)Google Scholar, and Stalnaker, R. Inquiry (Cambridge, MA: MIT Press 1983).Google Scholar

31 Cresswell, M. Structured Meanings (Cambridge MA: MIT Press 1985)Google Scholar; Carnap, R. Meaning and Necessity (Chicago: University of Chicago Press 1947)Google Scholar; Lewis, D. ‘General Semantics,’ Synthese (1970) 18–67CrossRefGoogle Scholar

32 For Cresswell, the Objects of attitudes are more or less structured. Exactly what the structure of the attitude Object is is not a question that Cresswell answers directly, so far as I am aware. But it does appear to be a consequence of his view that the isomorphism that is supposed to obtain between the belief reported and the semantic analysis of the complement clause of a true belief report need not consist in an isomorphism between the belief and the structure which consists in the intensions of the lexical items of the sentence ordered according to the sentence’s syntactic analysis. It may for instance consist in an isomorphism between the belief and a semantic analysis in which only the subject and the intension associated with the verb phrase of the complement are distinguished components.

33 For some problems with the claim of a unique semantic analysis, see n. 26 above. This point is explored in Gupta, A. and Savion, L. ‘Semantics of Propositional Attitudes: A Critical Study of Cresswell’s Structured Meanings,’ Journal of Philosophical Logic 16 (1987) 395–410.CrossRefGoogle Scholar

34 This is an old problem with the Carnap and Lewis account of intentional isomorphism.

35 Adding concept type discourse referents complicates the statement of embedding conditions and the model theory considerably. There is a variety of choices, however. One way is to add DRSs and conditions to the domain of the model as proposed in Asher (1986) and (1987). Then one has to treat the proper embedding of a DRS in effect in a two stage fashion. First we need an embedding function f that maps an n-ary concept discourse referents in K onto a DRS C in the model with n discourse referents bound from the outside by λ operators; when C is applied to its arguments in K, this yields a DRS K′ just like K but with conditions substituted for the concept discourse referents in Con_K. I will write K′ as f[K]. Now we say that K′ has a proper embedding with respect to an embedding function g⊇ just in case g maps all the discourse referrents in U_K′ onto objects in the domain of the model such that all the conditions in Con_K are satisfied in the usual fashion. Going back to K in whose universe concept discourse referents are declared, I will then say that K has a proper embedding with respect to f (and with respect to w, t, K), just in case ∃g⊇ f g is a proper embedding of f[K] (with respect to w, t, K). This would follow the lines of the more restricted interpretation of concept discourse referents in Asher, ‘Belief in Discourse Representation Theory,’ and ‘A Typology for Attitude Verbs.’ The second alternative is simply to include intensions in the domain of the model and treat proper embeddings of DRSs with concept-type discourse referents on a par with those containing individual discourse referents. Of course here there are well-known set-theoretical difficulties in connection with interpreting iterated attitude reports. But there is also a variety of solutions to them. One way of proceeding would be to use Peter Aczel’s theory of non-well-founded sets as a background theory. Yet another would be to use a background set theory in which membership is treated in a semi-inductive way, analogous to Turner’s treatment of predication in R. Turner, ‘A Theory of Properties,’ Journal of Symbolic Logic 52 (1987), 455-73. See also S. Feferman, ‘Constructive Theories of Functions and Classes,’ Logic Colloquium ‘78, M. Boffa et al., eds. (Amsterdam: North Holland 1979), 159-224; S. Feferman, ‘Towards Useful Type-free Theories I,’ Journal of Symbolic Logic 49 (1984), 75-111. A final possibility would be to resort to type-theory in doing the model theory for properties.

36 And the same sort of difficulties involving those familiarity presuppositions. See note 23.

37 See my ‘Semantic Competence, Linguistic Understanding, a Theory of Concepts’ Philosophical Studies 53 (1988) 1-36.

38 Notice that I have not introduced concept discourse referents for logical operators like the DRS negation or second order concepts like named. It would be possible to do so but only at the cost of considerably complicating the underlying conceptual and logical apparatus of the theory. I am not sure such complications are needed.

39 I denote here the intensions of the concept markers in boldface. I assume that the concept of being pretty is not one that has an external anchor; at least it does not have one for the same reason that a concept associated with a natural kind term does. It is an important question how such concepts get a fixed interpretation. It is a question I have addressed in ‘Semantic Competence, Linguistic Understanding and a Theory of Concepts.’

40 The definitions of the notion of one DRS extending another in my ‘Belief in Discourse Representation Theory,’ and ‘A Typology for Attitude Verbs’ are the source for more details about this definition. But they leave out how f would treat function symbols. Also the definition of K extending K’ should be stated relative to two delineated DRSs-one for K and one for K’. I shall call these K and K’ respectively. Finally, we must adapt those definitions to deal with concept discourse referents. Let U*_K be the set of all discourse referents occurring in K. Then,

f is a homomorphic embedding of K in K’ relative to K and K’ just in case f: U*_K → U*_K′, s. th. for any condition φ in Con_K

(i) if φ is atomic and of the form C(x₁, ..., x_n) = y, then there is a condition φ ∈ Con_K′ and φ of the form f(C)(f(x₁), ..., f(x_n)) = f(y).

(ii) if φ is atomic and of the form C(x₁, ..., x_n), then there is a condition φ′ ∈ Con_K′ and φ′ of the form f(C)(f(x₁), ..., f(x_n)).

(iii) if φ is complex and of the form K₁ v K₂, then there is a condition φ′ ∈ Con_K′, and φ′ of the form K₃ V K₄ and (f is a homomorphic embedding of K₁ in K₃ and f is a homomorphic embedding of K₂ in K₄, or f is a homomorphic embedding of K₁ in K₄ and f is a homomorphic embedding of K₂ in K₃).

(iv) if φ is complex and of the form ¬K₁, then there is a condition φ′ ∈ Con_K′ and φ′ of the form ¬K₂ and f is a homomorphic embedding of K₂ in K₁.

(v) if φ is complex and of the form K₁ ℭ K₂, then there is a condition φ′ ∈ Con_K′ and φ′ of the form K₃ ℭ K4, f is a homomorphic embedding of K₃ in K₁), and f is a homomorphic embeding of K₂ and K₄.

(vi) if φ is complex and of the form e-K₁ then there is a condition φ′ ∈ Con_K′ and φ′ of the form f(e)K₂ and f is a homomorphic embedding of K₁ in K₂.

(vii) if φ is complex and of the form p: K₁ and members of U_K1 have internal anchors {y₁ …, y_n] for y₁, ..., y_n ∈ U_K′, then there are z₁,...,z_n ∈ U_K′, and there is a condition φ′ ∈ Con_K′, φ′ of the form p₁:K₂ f is a homomorphic embedding of K₁ in K₂ & f(y_i) = f(z_i) for 1 ≥ i ≥ n).