2.5 An alternative proposal for a unified account
2.5.2 A formal account inspired by Nunberg (1993)
Nunberg(1993) does not provide a full formalization for his three-component account.
For some of the examples he discusses, he suggests truth-conditions, though. For instance, for (107-a) he argues that we contributes a contextually determined kind, and sketches the formula in(107-b).
(107) a. We don’t talk with our mouths full.
b. ¬Talk-with-their-mouths-full(ιxR(cs)(x)) where x ranges over kinds
(adapted with minor changes from Nunberg 1993:16f)
Inspired by Nunberg’s account,Elbourne (2008) proposes a formal account to analyze demonstratives. He argues that pronominal expressions should be analyzed as definite descriptions60, and that, once formalized, Nunberg’s proposal can also account for
60This view goes back to at least Elbourne(2005) and the observation that E-type uses of third person singular pronouns require an analysis as definite descriptions. Elbourne generalizes this idea to all uses of third person pronouns.
deferred reference uses of third person singular personal pronouns and bare and complex demonstratives.
Elbourne proposes a syntacticized version of Nunberg’s account; for pronominal ex-pressions, he introduces the complex syntactic representation in (108).
(108) [ pronoun [ R1 i2 ] ]
R . . . models the contextually determined relation i . . . models the index
(cf. Elbourne 2008:421)
The variablesiandRmodel the index and the contextually determined relation holding between the index and the referent. Both variables are a fixed part of the syntactic representation of personal pronouns, and are left unbound.61
The paraphrases given by Nunberg for the deferred reference examples fit in with Elbourne’s previous work on pronouns as definite descriptions (cf.Elbourne 2005,2008).
Although Nunberg at some point suggests that the referent of a personal pronoun can be either an individual or (essentially) an individual concept, Elbourne aims for maximal generality, and argues that a pronoun always contributes an individual concept, i.e. a function from worlds/situations to individuals.
To generate the individual concept interpretation compositionally, Elbourne proposes thatR1is a variable of typehe,hse, stii(i.e. an intensional relation between individuals and individual concepts), andi2 is a variable of typee. The values of the free variables R1 and i2 are specified contextually by the variable assignment g. The denotation of the subtree [ R1 i2 ] is R(i), which is of typehse, sti.62
The pronominal forms are interpreted as definite determiners that takeR(i) as their argument, and return the individual concept λs.ιx[R(i)(λs0.x)(s) = 1]. This is the concept that returns the unique individual x such that the “variable concept”, [λs0. x], stands in relation R to the index i in a given situation of evaluation s.63
61Elbourne (2008) states that i and R correspond to the deictic component and the relational component, respectively. This does not correspond to Nunberg’s original proposal. The relational component does not provide the relation in which the index and the referent stand to each other, but only general constraints on possible relations. Furthermore, the indexical component acts like a func-tion from contexts to individuals, and cannot be equated with its output. Consequently, to stay true to Nunberg’s original account,Rcan only be meant as the relation that was determined contextually and/or through speaker intentions, and is constrained by the relational component. Similarly, i has to be seen as the index.
62For reasons of simplicity and readability, I useRandifor both the variables and their contextually assigned valuesg(1) and g(2), respectively.
63Compare the meaning proposed for it in (109) to the meaning usually assigned to the definite determinerthe in (i).
(i) JtheK
g,w,c=λfhse,sti.λs. ιx[f(λs0.x)(s) = 1]
(Elbourne 2008:416)
(109) JitK
g,w,c =λfhse,sti.λs. ιx[f(λs0.x)(s) = 1]
(Elbourne 2008:421)
The interpretation of an “indexical structure” is computed from its complex under-lying structure as shown in the following example.
(110) J[ pronoun [ R i ]]K
g,w,c = J pronoun K
g,w,c (J R K
g,w,c(J iK
g,w,c)) =
λfhse,sti.λs.ιx[f(λs0.x)(s) = 1] (R(i)) =
λs.ιx[R(i)(λs0.x)(s) = 1]64
Depending on the contextually determined value for R, the semantic contribution of a pronoun corresponds to a deferred reference reading or to a standard referential reading.
Elbourne (2008) does not apply the above formalization to first and second person singular pronouns. Given his inspiration, however, an account of these pronouns can be given by straightforwardly assigning the values proposed in Nunberg (1993) to the variables R and i. The non-deferred referential reading for I, for example, is derived by contextually assigning the identity relation to R:
(111) λye.λxhse,sti.λs.y=x(s) in s
The indexiis fixed by the lexical entry ofI to be the speaker of the utterance,cs. The result for the referential use ofI without deferred ostension is given in (112).
(112) λs. ιx[cS = [λs0.x](s) in s] = λs. ιx[cS =x in s]
Elbourne does not explicitly formalize the classificatory component. He suggests, how-ever, that presuppositionalφ-features could be included in his account, i.e. morphosyn-tactic features that trigger presuppositions on the final semantic value of a pronoun (cf.Heim and Kratzer 1998 and Section1.5.3).
Notably in Elbourne’s account, the lexical pronominal expression is only one of three parts featuring in a complex structure. The final semantic value that Nunberg proposes as the semantic contribution of a pronominal expression is therefore not the meaning of the lexical pronominal expression, but the meaning that is assigned to the entire complex tree structure in (108).65
One problematic aspect of Elbourne’s formalization in general is his choice to fully syntacticize Nunberg’s original account. Introducing the variablesRandiinto the
syn-In Elbourne’s system, the definite determiner takes properties of individual concepts as arguments.
Elbourne assumes that each nominal element is evaluated with respect to a situation variable.
64Compare this denotation with Nunberg’s suggestion in (107-b).
65For reasons of space, I do not give Elbourne’s analysis of demonstratives as definite descriptions based on his formalization. The interested reader is referred toElbourne(2008:423ff).
tax is a major conceptual departure from Nunberg’s original proposal. Nunberg argues, in fact quite forcefully, that for none of the components, the values are contributed to the truth-conditions of the sentence. So, even though the semantic values contributed by an indexical may be similar to the contribution of a descriptive nominal expres-sion, the indexicals’ lexical meaning is strictly indicative. In Elbourne’s formalization, on the other hand, personal pronouns always contribute descriptive content—even in their standard referential uses that do not involve deferred ostension. As discussed in Section 1.5.2, Kaplan and Nunberg argue against analyzing I as the speaker (of this utterance) since definite descriptions in contrast to indexicals interact with operators on worlds/situations of evaluation. The descriptive content derived in Elbourne’s for-malization of Nunberg’s account for the standard referential use of I, i.e.being identical to cS, is different from the descriptive content argued against by Kaplan and Nunberg.
Nevertheless, this proposal runs into similar problems. The following sentence is in-tuitively true, but since definite descriptions involve a uniqueness presupposition that cannot be satisfied in the accessible worlds (because of the antecedent), the sentence is predicted to be truth-valueless.
(113) If no one were to exist, I would not exist, either.
Another unfortunate aspect of Elbourne’s proposal regarding the aim of this thesis is that his formalization cannot be used to capture the impersonal uses of personal pronouns: singular personal pronouns in all of their uses come out as singular definite descriptions. In the following section, I modify Elbourne’s semantic proposal for my purposes, and build on it to propose a unified account of a different kind to capture the impersonal and referential uses of personal pronouns. The complex syntactic structure proposed in (108) is, for now, adopted as it is.