3.2.1 Outline of MSDRT

MSDRT has inherited from DRT the overall architecture of a logical form approach to natural language semantics. In a logical form approach semantic representations are assigned to expressions of the natural language L under study. These semantic representations belong to a formal representation language that comes with its own syntax and a model-theoretic semantics for that syntax. Sentences and multi-sentence texts and discourses of L get their semantics via the semantic representationsFootnote ² assigned to them: their semantics is given by definition as the model-theoretic semantics of those representations. I assume that the reader has some basic familiarity with DRT and will focus on aspects of MSDRT in which it extends beyond DRT.Footnote ³

The extension of DRT to MSDRT was motivated by the observation that attitude reports – sentences and bits of discourse in which speakers describe the beliefs, desires and other attitudes of one or more agents (the ‘attributee(s)’) – are much more diverse and complex than had been assumed implicitly in semantic treatments of such reports. More often than not, attitude reports are not restricted to a single attitude – a single belief or desire or other type. And reports involving more than one attitude often convey semantic connections between the different attitudes of which they speak that are crucial to the meaning of the report as a whole. A proper theory of attitude reports must account for those connections. Furthermore, attitude reports are not limited to describing an attributee’s mental state at just one time, but also serve to describe how attitudes change in the course of time – how people change their minds is often just as important to us as what states they are in at any one particular moment. Attitude reports with such more complex contents can take a wide and open-ended range of different forms, and they often consist of several sentences rather than just one.

In the light of these considerations, the nearly exclusive preoccupation with simple single sentence reports of the form ‘x believes/desires/… that φ’ (where φ is typically some that-complement of the attitudinal verb), which has dominated the literature for most of half a century, seems curiously parochial. And the method mostly used for the semantics of these simple reports does not seem capable of dealing with the much wider and diverse linguistic repertoire regularly and naturally used by speakers of English and other natural languages.Footnote ⁴

In MSDRT propositional attitude reports are analyzed as descriptions of the mental states of the attributees. These descriptions assume that mental states have much more structure than has been assumed by analyses based on modal logic, in which propositional contents are identified with sets of possible worlds. This is so in more than one respect. As noted, attitude reports often describe their attributees’ mental states as consisting of several attitudes of distinct ‘attitudinal mode’, for instance as consisting of both beliefs and desires. Furthermore, the contents of attitudes of distinct attitudinal mode are often ‘referentially connected’.Footnote ⁵ To account for such reports, which attribute several referentially connected attitudes of different modes, the mental state descriptions of MSDRT have to be fairly complex. Details will follow as we go along. Since ‘mental state description’ is somewhat of a mouthful, I will use the abbreviation ‘MSD’ for the mental state descriptions of MSDRT.

When MSDRT is used in the semantics of attitude reports, its MSDs occur as parts of DRSs that serve as the logical forms of attitude reports. These DRSs constitute a ‘second level’ of MSDRT, so to speak. But MSDs also have a different application, viz. as characterizations of the mental states of language users. In this application utterances are analyzed as vehicles employed by speakers and authors to transfer information represented in their own minds to the minds of the recipients of their utterances: The producer has, as part of her mental state, a representation of a certain thought or complex of thoughts, and the utterance she produces as expression of that thought or thought complex will produce a representation of a thought or thought complex in the mental state of the interpreter; there is communicational success when the representation constructed by the interpreter suitably matches that of the producer. It is in this second way, as a formalism for describing the mental states of language users, that MSDRT will be used in this paper.

The assumptions that are made in MSDRT about the form of MSDs vary somewhat between its different applications. But in all applications it is assumed that among the constituents of MSDs are (i) descriptions <MOD,K> of Propositional Attitudes (PRs, for ‘Propositional representations’) and (ii) Entity Representations (ERs). A PR <MOD,K> consists of (a) a Mode Indicator MOD, which indicates the ‘attitudinal mode’ of the represented attitude, i.e. whether it is a belief (in which case MOD is BEL), a desire (MOD = DES), an intention (MOD = INT), and so forth (the list of Mode Indicators may vary between applications); and (b) a DRS K from the DRS language of MSDRT that has been adopted for the application at hand.Footnote ⁶ The MDS formalism used in this chapter will eventually go beyond this basic repertoire, in Section 3.3.2.

In the application of MSDRT to the analysis of the referential–attributive distinction ERs play a central part.Footnote ⁷ Since their form and role is central to this application, the next section has been set aside for a more detailed discussion of these.Footnote ⁸

3.2.2 Form and Role of Entity Representations

The form we adopt for Entity Representations is given in Definition 1.

1. (1)

   Definition of ‘Entity Representation’
   An Entity Representation (‘ER’, for short) is a triple
   $<\left[\mathit{ENT},x\right],K_{\mathit{\text{descr}}},{𝒦}_{\mathit{\text{anch}}}>$, where
   (i.a) ENT is a Mode Indicator, indicating that the MSD constituent to which it belongs is an Entity Representation (and thus not a propositional attitude of any mode);
   (i.b) x is a discourse referent, the distinguished dref of the ER.
   (ii)	$K_{\mathit{\text{descr}}}$ is a DRS, which contains certain kinds of information about the entity represented by the ER.
   (iii)	${𝒦}_{\mathit{\text{anch}}}$ is a set of internal anchors. Internal anchors will be defined below.

Before saying more in general terms about the form and role of ERs and about the MSDs that contain them as constituents, let me show an example of an MSD – one that describes a mental state that consists (among other things, presumably) of (i) an ER for Smith and (ii) an ER for his murderer, together with (iii) the belief that the entity represented by the second of these ERs is insane.

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As this simple example illustrates, one role of ERs is to serve as a kind of interface between the propositional contents of thoughts and the outside world. On the one hand ERs can enter into the representations of such propositional contents. In the formal implementation of this adopted in MSDRT they do this via their distinguished drefs. Thus the distinguished dref x of the second ER in (2) occurs as an argument term in the content representation of the belief in (2). Because of this the propositional content of this representation is a singular proposition, which is true in any possible world w iff the person represented by the ER (in the actual world, via its anchor set) is insane in w.Footnote ⁹

Which entity is represented by an ER depends on the process responsible for its formation and sometimes also on its subsequent use. The first example, used as illustration in the early days of MSDRT, was that of an agent who observes an unfamiliar entity and forms, as part of her perception, an ER representing this entity. This ER has a perceptual anchor, which acts as a record of the visual experience to which the ER owes its existence – an anchor of the form ‘I am seeing α’, where α is the ER’s distinguished dref.Footnote ¹⁰

A second type of anchor are vicarious anchors. According to MSDRT, ERs can also be formed when the recipient of an utterance that contains a referring expression α takes the producer of the utterance to have used α to refer to an entity for which she, the producer, has an ER ${\mathit{ER}}_{\mathit{\text{prod}}}$. The ER ${\mathit{ER}}_{\mathit{\text{recip}}}$ that the recipient can then form for the entity to which the producer has referred will have a vicarious anchor to record that the ER represents whatever it was that the producer referred to by using α on the given occasion, and thereby makes ${\mathit{ER}}_{\mathit{\text{recip}}}$ to a representation of this referent.Footnote ¹¹

Once a PR or ER has become a constituent of an agent’s mental state, it will tend to persist there, though it may fall into oblivion at some later point or even be razed from memory altogether. While such a constituent is part of the agent’s mental state, it can partake in various kinds of mental processes. One important use of previously acquired ERs is in entity recognition: When the agent encounters an entity represented by an ER in his mental state and he recognizes this entity as one that is familiar to him, then according to MSDRT this will take the form of reactivating this ER and recording the present recognition through the addition of a new anchor to the ER’s anchor set. (In this way the anchor sets of ERs can keep growing after the ER has first been formed.) Among the new encounters with an entity that is already familiar, in the form of an ER representing it, there are on the one hand those where the agent meets the entity face to face, so that he can see the entity (or directly perceive it in some other way, e.g. by hearing the sounds it makes). In such cases the new anchor will be a perceptual anchor. But there are also the cases where a familiar entity is mentioned by someone else. In this case the new anchor will be a vicarious one. This second kind of recognition will be central to our discussion of referential uses of descriptions in Section 3.3.

It is important to keep in mind that the internal anchors of ERs are ‘records’, available to the agent at a mind-internal level, of her exposures to the entities they represent. The real link between an ER and the entity it represents resides in the ER’s actual causal history, starting with the occasion on which it was first formed and then subsequently enhanced on the later occasions when it was reactivated in new encounters with the referent. Indeed, it is possible for an anchor to give a false account of the history of its ER, for instance when an ER with a perceptual anchor is the result of an optical illusion.Footnote ¹²

3.2.3 Entity Representations and Articulated Contexts

Entity Representations also play a pivotal role in another extension of DRT, the Entity Representations and Articulated Contexts framework of Kamp (Reference Kamp, Alden Pepp and Almog2021a, Reference Kamp2022). The ER & AC framework was developed to deal with a very different problem from that which gave rise to MSDRT. One objection to DRT in its original form is that it only makes room for anaphoric interpretations of definite descriptions. In its original formulation (see in particular Fraurud Reference Fraurud1990) the objection targeted Heim’s File Change Semantics (FCS) (Heim Reference Heim1982, 1988), but this is just as much an objection to DRT, as soon as DRT is extended to cover definite descriptions as well as pronouns. Heim analyses the difference between definite and indefinite descriptions as that between familiarity and novelty: indefinite descriptions introduce new entities into the discourse, definite descriptions refer back to entities that have already been introduced. The problem that Fraurud and others pointed out is not one for Heim’s novelty–familiarity distinction as such, but for the particular way in which it is implemented in her File Change Semantics. In this setup the only entities that are available as anaphoric antecedents for definite descriptions at any given point in the course of semantically processing a text or discourse are the ones that have been made available in the text or discourse itself. But that is highly unrealistic. Many of the definite descriptions found in actual texts (such as newspaper articles, for instance) refer to things that have not been previously mentioned in the text. (For many texts this is true for well over 50 percent of all the definite descriptions that can be found in them.) Nevertheless the reader may have little difficulty in understanding the text, and the reason for that is clear enough: Authors and readers are immersed in the same culture, with its large repertoire of widely known people, places, events, and so on. As a member of this cultural community the reader will come equipped with representations for these various entities, as part of the large ‘ER libraries’ that most of us carry around with us as we make our way through life. In terms of the ER & AC framework this means that his entity library will have ERs for those various entities, which he can use when those entities are mentioned by name, and also by definite descriptions that make use of properties of their referents that are generally known. This entity library will enable him to make sense of all or most of the discourse-new definite descriptions he will encounter.

It is more or less obvious how this problem should be tackled within the formal setting of a framework like FCS or DRT: the theory has to adopt a more comprehensive notion of context, which includes besides the ‘discourse context’ – in DRT this is the discourse representation that has been constructed for the part of the text that has been read so far – additional sources of contextual information, with something like an ‘entity library’ as part of it. Other kinds of contextual information may be needed too. For instance, discourse and text processing often require various kinds of world knowledge for the verification that an entity which has been selected as possible referent of a definite description does have the properties that the description attributes to it and that competing candidates do not.

These considerations have led to the following notion of an Articulated Context.Footnote ¹⁵

1. (5)

   Definition
   An Articulated Context (AC) is a 4-tuple $<K_{\mathit{dis}},K_{\mathit{enc}},K_{\mathit{gen}},K_{\mathit{env}}>$, where
   (i)	$K_{\mathit{dis}}$ is the representation of the discourse context;
   (ii)	$K_{\mathit{enc}}$ is a set of representations of “known entities”;
   (iii)	$K_{\mathit{gen}}$ is a set of representations of items of “nonepisodic world knowledge”;
   (iv)	$K_{\mathit{env}}$ is a set of representations of elements from the immediate environment, perceptually accessible to the discourse participants.

So far this definition is only a shell. To make the ER & AC framework useful in formal semantics we need to say more about what the four components $K_{\mathit{dis}}$, $K_{\mathit{enc}}$, $K_{\mathit{gen}}$, and $K_{\mathit{env}}$ of an Articulated Context are like. Here follows what we will need for the purposes of this paper.

The two AC components of special importance for what follows are $K_{\mathit{enc}}$ and $K_{\mathit{env}}$. As definition (5) indicates, these are both collections of entity representations. And in the ER & AC framework, as in MSDRT, entity representations take the form of ERs. But ERs are mental entities, so these two components of ACs must be understood as parts of agents’ mental states. Since the discourse contexts of ACs – their $K_{\mathit{dis}}$-components – are constructed with the help of $K_{\mathit{enc}}$ and/or $K_{\mathit{env}}$, and thus often contain the distinguished drefs of ERs belonging to these components, they too should be seen as constituents of mental states, for instance as the content representations of beliefs, which is what I will assume here, simplifying somewhat.Footnote ¹⁶ About the remaining AC component, $K_{\mathit{gen}}$, little will be said in this paper. But in this case too, a psychological interpretation is plausible. After all, the general knowledge that an agent makes use of when interpreting a linguistic input must be available to him. I assume that it is available to him in the form of his $K_{\mathit{gen}}$, whatever the precise form this part of his mental state may have (something about which not much has been said in MSDRT up to now).

The upshot of this is that ACs are to be considered parts of mental states. More specifically, they are parts of the mental states of agents that process verbal inputs when they start the interpretation process and also while this process is going on, changing the AC – mostly its $K_{\mathit{dis}}$, but often other components as well – and therewith the interpreter’s mental state as a whole. Whether a psychological conception of ACs, of the sort that I will assume when using them in my analysis of the referential–attributive distinction in Section 3.3, is inevitable, or whether a user-neutral, nonpsychological conception is possible as well, will be briefly discussed in the final section of this chapter.

This concludes the formal background to our explorations of referential and attributive description uses in the next section.

3.3.1 The Man with a Martini

Recall the situation: A and B are standing in one corner of a room in which a party is going on, A says to B, looking or gesturing in the direction of the opposite corner,

In this utterance A is using the man with a martini to refer to some particular person on whom her vision is focused. In the terms of our approach this means that A has an ER for the person whom she is looking at, with a current perceptual anchor as witness of the visual contact. Since A is in a position to say of this person that he is a Formula 1 driver, her ER for him must date from an earlier time, at which she acquired this information. (This also means that the ER’s anchor set will have besides the mentioned current perceptual anchor some other anchors as well. About what these other anchors might be there is no need for us to speculate.) Since A refers to the referent of her ER as ‘the man with a martini’, she will presumably also believe of him that he is holding a martini. If so, then the relevant part of her mental state must be as in (7).

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Footnote ¹⁷

If A is in a mental state of the kind described in (7), then it is legitimate for her to use the man with a martini to refer to the entity represented by the ER of (7). That she actually chooses this description as device for referring to the person she intends to refer to is a further matter. We will assume that this choice takes the form of a referential intention, the intention to refer to the entity represented by the given ER by means of the chosen expression. This intention is a PR that gets introduced as a constituent of A’s mental state when the intention is formed, and that remains there until it is discharged by its execution (in the present instance: through A’s utterance of (6)). We assume further that the propositional content of this PR is as in (8).Footnote ¹⁸

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The predicate ‘ref’ in (8) is the same as that occurring in (4) of Footnote note 11 for the general form of vicarious anchors. Furthermore, in the instance of (8) that is part of A’s intentions when she utters (6), α is the description the man with a martini, i is once again the special dref used for the mind-internal representation of the self (see Footnote note 10) and x is the distinguished dref of the ER in (7).

A's use of the man with a martini in (6) to refer to the person represented by her perceptually anchored ER in (7) is our first example in this section of the referential use of a definite description.

We now turn to the interpretation of (6) by B. First, let us assume that B already has an ER for the person to whom A has used the man with a martini to refer, that B is also looking at this person when A is saying (6) to him and that B also believes that this person is holding a martini. In other words, the relevant part of B’s mental state when he starts his interpretation of (6) looks much like the corresponding part of A’s state:Footnote ¹⁹

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In the situation in which A says (6) to B, it is plausible for A to assume that she is referring to someone that they can both see. But that assumption he can only make if B has an ER for the person A is referring to. If he does have such an ER, he will then make use of it in his interpretation of A’s utterance of the man with a martini. This will lead him to the construction of a representation of A’s utterance in which the dref introduced by its grammatical subject phrase the man with a martini is set equal to the distinguished dref $x_B$ of the ER described in (9). The resulting DRS is shown in (10).Footnote ²⁰

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The use and interpretation of the man with a martini in the communication just described are examples of the deictic use and interpretation of definite descriptions. Deictic uses and interpretations of noun phrases are those in which the phrase is used or interpreted as referring to an entity in the physical environment within which the communication takes place. In MSDRT deictic noun phrase uses are distinguished by the fact that the ERs involved in use and interpretation belong to the $K_{\mathit{env}}$ components of the ACs of speaker and recipient; in other words, these ERs must each have a current perceptual anchor. Evidently this condition is satisfied in the case just considered: Both A’s ER in (7) and B’s ER in (9) have such an anchor at the time when (6) is uttered and interpreted.Footnote ²¹

The analysis just presented makes it easy to see and state why referential uses of definite descriptions can be successful even when they misdescribe the intended referent – that was one of the central points that Donnellan used the man with a martini to illustrate. Suppose that A and B are both mistaken about what is in the glass held by the man jointly represented by their respective ERs displayed in (7) and (9). Then A will think that using the man with a martini is a legitimate and helpful way to refer to this person and B can be expected to zero in on this person and employ the ER of (9) to interpret A’s use of it and to construct as Logical Form for (6) the DRS in (10), which correctly captures the content of what A wants to say: both this DRS and the first belief DRS in (7) express the singular proposition about the person represented by his ER that this person is a Formula 1 driver. That is what A wanted to convey to him. So the communication is a success, in spite of the fact that the description the man with a martini has done its work in a way that it wasn’t meant to do it. In fact, A and B will go on to be wrong about what the man is drinking, but for the success of what A wanted to accomplish this is irrelevant.

This is not the only scenario in which A can use the man with a martini successfully to refer to the person represented by the ER described in (7) in spite of the fact that the description isn’t uniquely satisfied by the man. Another scenario is that in which A thinks that the man does satisfy the description, but B does not. In that case it might well be that the circumstances in which A utters (6) make it clear to B which individual she is trying to refer to – e.g. because in the direction in which she is looking there is only one person who is holding a glass of any kind. If so, B may once again use the ER of (9) in his interpretation of A’s words and once again correctly capture the propositional content of A’s assertion. He may then consider whether he should point out to A that the man she has referred to isn’t drinking a martini. But since this is irrelevant for what he has concluded she wants to tell him, he may decide that correcting her on this point would just be pedantic.

There are further scenarios that illustrate the point as well. A may know that the man she wants to refer to is drinking water, but have good reasons to assume that B thinks he is drinking a martini, since that is the kind of glass the man is holding. So she decides to refer to the man as the man with a martini as the most effective way of drawing B’s attention to him. And her strategy may work: B identifies the person she wants him to, makes use of the ER described in (9) to interpret her words and is thereby led to the correct understanding of them (see also Footnote note 18).

These three scenarios may not exhaust the list, but they suffice for Donnellan’s general moral: Referential uses of descriptions can work even when they misdescribe what they are being used to refer to. Furthermore, as our discussion has made plain, this is possible either because speaker and hearer are victim to the same misconception about the intended referent, which the communication will not reveal to them in spite of its success, or because one of the interlocutors compensates for the misconception of the other.

3.3.2 Smith’s Murderer I: Referential Use and Utterance Motive

In the second Donnellan example mentioned in Section 3.1 the speaker A and her interlocutor B are attending the trial for Smith’s murder. Donnellan uses this example to illustrate the difference between the referential and the attributive use: A can make both a referential and an attributive use of Smith’s murderer in the setting he considers, where at some point A addresses B with the words:

We start with what Donnellan presents as an example of the referential use of Smith’s murderer: A uses Smith’s murderer to refer to the man in the dock, motivated to make her statement (11) by the bizarre behavior he is displaying while she and B are watching. What A wants to express by uttering (11) in this case is the singular proposition about the man in the dock that he is insane, a claim that is independent of whether this man really is the one who murdered Smith or isn’t.

From the perspective of the present chapter this case is closely similar to the one discussed in the last section. Once again, and in line with what Donnellan says about this use of Smith’s murderer, we can assume (i) that both A and B have ERs for the man in the dock, with anchors reflecting their current perception of him, (ii) that A uses Smith’s murderer to refer to the man represented by her ER and (iii) that B makes use of his ER for the man to interpret her use of the description. Note that the current perceptual anchors of the ERs involved make A’s use of Smith’s murderer and B’s interpretation of it instances of the deictic use and interpretation of definite descriptions, just as the use and interpretation of the man with a martini in the last section. And that makes the use and interpretation of Smith’s murderer we are considering also instances of the referential use and interpretation.

What distinguishes Donnellan’s discussion of this example from the the man with a martini case is his bringing up of A’s motive. This was no doubt a good way to make it clear to his readers that A’s use of Smith’s murderer is referential: A wants to say something about the man in the dock and uses Smith’s murderer to draw B’s attention to this man, so that he will interpret her statement as expressing a (singular) proposition about this man. We should keep firmly in mind, however, that having a motive of this sort isn’t a necessary precondition for the referential use. We will see this more plainly when we come to Donnellan’s presentation of an attributive use of Smith’s murderer in the next section.

But first, let us reflect more closely on why A’s motive in the present case seems to add so much force to the claim that her use of Smith’s murderer is referential. The intuitive reason for that, I take it, is that the motivating belief – that the behavior of the man in the dock is of the sort one would expect from someone insane – does not depend on whether the man in the dock is the one who murdered Smith. Therefore, the statement that is motivated by that belief should presumably be one that does not depend on this question either. And that condition is satisfied by the proposition which asserts of the man in the dock that he is insane (and not by a proposition in which the descriptive content of Smith’s murderer is logically included; see the next section).

How can we articulate this intuitive explanation in the formal terms of our MSDRT-based approach? Let us approach this problem indirectly, by first considering an analogous one for A’s addressee B. B, who has also observed the strange behavior of the man in the dock, can be expected to see that behavior as an explanation for what he takes to be the content that A communicates to him by uttering (11), much as A’s observation of that behavior was her motive for making her utterance. That is, the mental state that B is in as a result of interpreting A’s statement and concluding that what A is saying is plausible given the man’s behavior in the dock (and accepting what A is saying as true on account of this), can be described by the following MSD:

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Footnote ²²

Most of the notation used in (12) is by now familiar ground: The three ERs are (i) for the person A sitting next to B at the trial, who has just said (11) to him, (ii) for Smith and (iii) for the man in the dock. The BEL constituent describes the belief B has formed by accepting the assertion that A has just made, according to B’s interpretation of her words, which is given by the content DRS of the BEL constituent. But the final constituent of (12), beginning with ‘EXPL’, requires comment.

EXPL (for ‘Explanation’) is a Mode Indicator of a novel type, which wasn’t mentioned in Section 3.2.1. EXPL links two propositions (once again represented as DRSs). The attitudinal mode EXPL in (12) is a generalization of the Explanation relation of SDRT (Asher & Lascarides Reference Asher and Lascarides2003) and other theories of rhetorical structure.Footnote ²³ It is a generalization of that relation in that it is not restricted to contents of clauses and other parts of a given discourse or text, but may be applied also to propositions of other provenance. The application of EXPL in (12) is an example of this insofar as one of its relata is the content of a bit of discourse in this case – all of A’s utterance (11) – but the other relatum, the content of B’s observation of the behavior in the dock, is not.Footnote ²⁴ But from a cognitive perspective EXPL is just the same as the corresponding discourse relation. The first relation is nothing but an extension of the second to a larger application domain.

What is it for a proposition p to provide an explanation for some other proposition q? One way in which p can do this is to logically entail q. If this is the relation that holds between the propositions expressed by the two DRSs of the EXPL constituent of (12), then we have the basis for an account of why B should interpret A’s utterance of (11) as a singular proposition about the man in the dock and interpret, as part of that, Smith’s murderer referentially. By interpreting (11) in this way B assigns it a propositional content that doesn’t say anything about Smith’s murder. That makes the content one that can be explained by the behavior of the man in the dock which B has been observing. (That content may not strictly speaking entail B ’s interpretation of (11) on its own, but it would in conjunction with the belief that his behavior could only be that of someone insane, a reasonable belief for B to hold in the given circumstances.) Furthermore, these circumstances may impel B to take the goings-on in the dock as an explanation of what A is saying to him (assuming that A speaks to him just after they have watched a particularly absurd piece of behavior by the accused). But if these goings-on are to provide explanatory support for what A says, then her words should be interpreted in such a way that these goings-on do explain it. And for that to be the case B’s interpretation shouldn’t entail anything about the murder; for if it did, then it couldn’t be entailed by a proposition about the man in the dock, which doesn’t entail any such thing. (In the next section we will see reasons for thinking that just such a content would result if B would not interpret Smith’s murderer referentially, but attributively.)Footnote ²⁵

Below I will return to the argument of the last two paragraphs. But first let us go back to our point of departure: A’s motive for the utterance of (11). If A’s utterance is motivated by the behavior she observes in the dock, then the relation between that and the proposition she wants to express is like the relation between B’s observation of it and his interpretation of her words. So, by analogous reasoning, the proposition she wants to express shouldn’t entail anything about the murder. But such a proposition is expressed by the words she has chosen only when her use of Smith’s murder is referential. (I will not provide an MSD here for the mental state of A in which the motivation relation is explicitly represented, as little would be gained from that for the point that is at issue – the reason why mentioning A’s motive strengthens the case for the claim that she is using Smith’s murderer referentially).Footnote ²⁶

Unfortunately, this account of why the goings-on in the dock motivate A to use Smith’s murderer referentially, and why B’s taking them as explanation for A’s words induces him to interpret Smith’s murderer as referentially used, is no more than a first stab. Logical entailment may be a sufficient condition for explanation and motive, but it surely isn’t a necessary one. As regards explanation, it isn’t just that p can provide an explanation for q without entailing q on its own; the entailment may rest on a number of additional premises: q isn’t entailed by p but by p together with tacit premises $r_1$, …, $r_n$. But even such a more relaxed notion of logical entailment is almost certainly too strong for what we want. In order that p can be seen as explanation for q, especially in the sense in which Explanation functions as discourse relation, all that seems to matter is that p can be seen to render q more plausible than it would be without p, or raise q’s probability, or something along such lines – I am speaking vaguely because I do not know what the right explication of Explanation as discourse relation is. Likewise for the relations expressed by EXPL and MOT (see Footnote note 26).

Whatever such a logically weaker definition of explanation and motive may be, it is far from obvious that it will enable us to account for why motive can guide intended utterance content, and explanation guide utterance interpretation, in the way they can when motive and explanation involve strict logical entailment. Perhaps a truly persuasive reconstruction of the relation between utterance motives and the kinds of use that utterers make of definite descriptions will prove illusory. But even if this should turn out to be so, there may be enough to the story I have sketched to explain why Donnellan found it useful to bring motive into play and why that seems to have worked well enough.

3.3.3 Smith’s Murderer II: The Attributive Use

A could also make an attributive use of Smith’s murderer, Donnellan observes, and she would do so when her utterance of (11) is motivated by the horrific details of the way in which the generally beloved Smith has been killed. For instance, she could say (11) to B in reaction to some of these details that they had to listen to during the trial when the prosecution presented them as part of their case. The intuition here is that (11) is true in part by virtue of how its grammatical subject Smith’s murderer describes its referent. One way in which this might be made more precise is to say that attributive uses of descriptions lead to general rather than singular propositions. For instance, the proposition that is expressed by (11) when its description is used attributively might be represented by the Logical Form in (16) assigned to it by B.Footnote ²⁷

(16)

While the content determined by (16) is a singular proposition with respect to Smith, represented by the distinguished dref ${\mathit{sm}}_B$ of B’s ER for Smith, it is not singular with respect to Smith’s murderer, which is what matters: (16) says that there is a unique individual who murdered Smith, and that that individual is insane. This DRS is thus a close approximation of a Russellian Logical Form for (11) (modulo its treatment of the name Smith), which I take to be the distinctive mark of the attributive use of Smith’s murderer: by representing (11) as (16) B treats A’s use of Smith’s murderer as attributive. Likewise, if A’s own representation of what it is she has chosen (11) to express has the form of (16), then her use of Smith’s murderer is an instance of the attributive use of definite descriptions.

This then is one way in which the notion of attributive uses of definite descriptions can be defined within our MSDRT framework:

Is this the correct definition of the notion attributive use, or at least a defensible one? That is a delicate question, for one thing because it is to a large extent a matter of Donnellan exegesis. According to my own perception, (17) succeeds in capturing Donnellan’s intentions insofar as it conforms to the received view of definite descriptions at the time when he introduced the distinction between referential and attributive uses. New to that distinction was that descriptions have referential as well as attributive uses – the attributive use was the one that everyone was familiar with, from the work of Frege, Russell, and many others. According to those authors descriptions always make their contributions via unique satisfaction of their descriptive content.Footnote ²⁸

That the use of Smith’s murderer by A we are currently discussing is attributive in the sense of (17) is supported by A’s motive for uttering (11) in the scenario described at the beginning of this section. The motive, recall, was that whoever murdered Smith must be insane given what is known about the details of the crime. That thought, evoked or rekindled in A’s mind by the prosecution’s exposition, has a Logical Form which speaks of the unique satisfier of the predicate ‘murdered Smith’. And just as that thought is A’s motive for uttering (11) in the present scenario, it can serve B, who has also been listening to what the prosecution has had to say, as explanation of why A is saying what she is saying, and saying it at this particular time. And just as in the last section, B’s explanation will be valid only when the two propositions – the one expressed by his Logical Form for (11) and the one explaining it – are suitably related. For this to be the case, and since the explaining proposition is to the effect that the unique satisfier of ‘murdered Smith’ committed the atrocities described by the prosecution, the proposition it explains should also be about the unique satisfier of this predicate; that is, it should be the proposition that the unique satisfier of ‘murdered Smith’ is insane (and not the proposition that the man in the dock is insane). This will be a reason for B to interpret (11) by constructing the Logical Form shown in (16). And in this case too, what goes for the Explanation relation that B may be assumed to infer from what A says, and the conditions under which she says it, also goes for the relation between A’s motive and the proposition she wants to express by (11). That proposition too should not be a singular proposition about the man in the dock, but a nonsingular proposition about whoever murdered Smith.

The reconstructions I have offered of the referential use in Sections 3.3.1 and 3.3.2 and of the attributive use in the present section appear to entail that these uses are mutually exclusive: no description use can be referential and attributive at the same time. The reason for this assumption should be clear enough: In any sentence S containing a definite description δ, δ will fill an argument position of some predicate P. In a Logical Form for S the translation P′ of P will have some discourse referent x in the corresponding argument position. When δ is used referentially, then x will be the distinguished dref of some ER. When δ is used attributively, x will be a dref internal to the Logical Form, of which the Logical Form says that it is the unique satisfier of δ’s descriptive content.

But should we conclude from this that description uses can’t be both referential and attributive at the same time? Not necessarily. The conclusion would follow only if sentences with definite descriptions must always have either one of the two Logical Forms we have so far considered for such sentences and that is something we shouldn’t take for granted.

3.3.4 Are the Referential and the Attributive Uses Mutually Exclusive? And Are They Jointly Exhaustive?

It is, I believe, a widespread if mostly tacit assumption that ‘referential’ and ‘attributive’ are mutually exclusive. Sections 3.3.1–3.3.3 may have come across as carrying such an implication too, although it was never explicitly stated that the referential uses of 3.3.1 and 3.3.2 weren’t also attributive uses or that the attributive use of 3.3.3 wasn’t also a referential one. But is the mutual exclusiveness of ‘referential’ and ‘attributive’ really supported by the criteria so far suggested? The answer to that question is ‘no’.

True, there are referential uses that are not attributive and attributive uses that are not referential. For an example of the latter consider the situation of Section 3.3.3, where A utters (11) as a reaction to the horrors of Smith’s murder detailed by the prosecution. But now, let us assume in addition that there is a common understanding between A and B that they got the wrong man: the accused is not the one who murdered Smith. So when A is prompted to say (11) by the prosecutor’s presentation, she doesn’t intend to speak of the man she can see in the dock. What she is saying is about whoever it was that murdered Smith and not about anyone for whom she has an ER with a current perceptual anchor. The Logical Form she associates with her utterance may therefore be assumed to be like (16) (with the distinguished dref ${\mathit{sm}}_B$ of B’s ER for Smith replaced by the distinguished dref ${\mathit{sm}}_A$ of her ER for Smith). There is no further ER in her mental state that plays a part in this Logical Form. So, by our criteria (see (15)) A’s use of Smith’s murderer as part of her utterance is in this case not a referential one.

Similarly it will be clear that the referential use of Smith’s murderer discussed in Section 3.3.2 won’t be an attributive use according to the criteria in (17), if we make the following assumptions: Once again A doesn’t believe that the man in the dock is the murderer, but now we also assume that she thinks B is convinced of the contrary. In this situation A may use the description Smith’s murderer as an effective way to convey to B that she is referring to the man in the dock: it is about the man in the dock that she wants to say something and not about someone that satisfies the content of the description she uses. In this case the Logical Form she will associate with her utterance of (11) is like the content DRS of the belief in (12) (once again with ${\mathit{sm}}_A$ in lieu of ${\mathit{sm}}_B,$ and now also with ${\mathit{md}}_A$ in lieu of ${\mathit{md}}_B$). The descriptive content of Smith’s murderer plays no part in this Logical Form, so by our criteria her use of the description is not an attributive one.Footnote ²⁹

But the scenarios of these last two paragraphs seem quite special. Indeed, they were chosen carefully to make sure that A’s use was not referential in the one case and not attributive in the other. For other scenarios these negative conclusions do not follow. Assume for instance that A and B both take it for granted that the man in the dock is the murderer.Footnote ³⁰ In this situation it is possible for A to utter (11) for the two reasons considered in Sections 3.3.1 and 3.3.2: the present behavior of the man in the dock or the prosecution’s details about the murder. But how should we classify A’s uses of Smith’s murderer in this scenario? Consider the case where A reacts to the details about the murder, the one that Donnellan gives as his example of the attributive use. Since A wants to express in this case that it is the man who murdered Smith who is insane – as that is what she is reminded of by the prosecutor’s presentation – the Logical Form she associates with her utterance will predicate insanity of the unique satisfier of Smith’s murderer; so by criterion (17) her use of Smith’s murderer is indeed attributive. But can we also assert that it is not a referential use?

There are two sides to this question, an intuitive side and a more formal one, which has direct connections with the MSDRT-based analysis of the referential–attributive distinction of this chapter. Intuitively, when A is convinced that the man in the dock is the murderer, then even if her utterance is prompted by facts about the murder, she could hardly fail to conceive of what she says as being about the man she can see in the dock. Therefore, it might be claimed, her utterance is about the man in the dock, whatever her reasons for asserting it, and therewith an instance of the referential use. But if this is to be a referential use in the sense of our criteria in (15), then A’s Logical Form for her utterance of (11) should contain an occurrence of her ER for the man in the dock. (16) (once more with ${\mathit{sm}}_B$ replaced by the distinguished dref of A’s ER for Smith) does not have such an occurrence and therefore doesn’t capture the intuitive idea that A cannot fail to see her statement as one about the man in the dock. To do justice to this, A’s Logical Form for her utterance should rather be as in (18).

(18)

In (18) the description Smith’s murderer has left two traces, (i) as the unique satisfaction specification that (18) shares with (16) and (ii) as the distinguished dref ${\mathit{md}}_A$ in the final DRS Condition ‘$s^{\prime }$: insane’(${\mathit{md}}_A$)’. By the criteria (15) and (17), if A’s Logical Form for her utterance of (11) is as in (18), then her use of Smith’s murderer is referential as well as attributive.

What should we conclude in the light of (18)? Was it wrong after all to think of the referential and the attributive use as mutually exclusive? There are two points to consider. First, is it really possible for an utterance of (11) to give rise to a Logical Form like (18)? Second, does the possibility of representations like (18) as Logical Forms for utterances like (11) show that the distinction is not mutually exclusive?

An objection to the possibiliy that (18) could be the Logical Form for (11) might be that the referential–attributive distinction is about ambiguity: definite descriptions can be used (and interpreted) in the one way or in the other, but never in both ways at once.Footnote ³¹ This objection may sound a bit like begging the question: The issue raised by (18) is precisely, it may be countered, whether the referential–attributive distinction is a case of ambiguity thus understood. But on the other hand I have, as things stand, no better argument in favor of (18) as a possible Logical Form for utterances of (11) than the intuition I appealed to above. Whether utterances can have Logical Forms in which definite descriptions are interpreted ‘twice over’, in the way that Smith’s murderer is interpreted twice over in (18), is a question that will require further work.Footnote ³²

But assume that (18) is the correct Logical Form for some utterances of (11). Are we then forced to admit that the referential and the attributive use are not mutually exclusive? No, not necessarily even then. There could be something wrong with the ways in which we have defined the referential or the attributive use (or both). It might be thought, for instance, that the term ‘attributive’ should be reserved for those description uses that are ‘merely attributive’, in the sense that they are attributive according to our criteria for the attributive use, but not referential according to our criteria for the referential use. Such a partly negative definition of ‘attributive’ might be justified insofar as it was the referential use that was novel in Donnellan’s introduction of the referential–attributive distinction; the attributive use was supposed what had thus far been thought to be the only way that definite descriptions could be used.

In this light a natural and simple redefinition of the notion ‘attributive use’ might be one according to which attributive uses of descriptions are those that are not referential. Given the commitments we have made up to this point, this definition will identify the attributive uses as those that satisfy criterion (17) but do not satisfy criterion (15). Note well, however, that this definition will do only on the assumption that the referential–attributive distinction is exhaustive in the sense that each description use is either in accordance with criterion (15) or with criterion (17). If the distinction is exhaustive in this sense, then a description use that is not referential must be attributive in the sense of satisfying (17) and therefore qualify as (merely) attributive.

But is the referential–attributive distinction exhaustive in this sense? Discussions of the distinction often read as if this were assumed. But I am far from persuaded that this assumption can be sustained. One worry has to do with the anaphoric uses of definite descriptions, those which pick out an entity that has been previously introduced in the text or discourse to which the description itself belongs. There is a substantial literature on anaphoric descriptions,Footnote ³³ but to my knowledge discussions of these uses have thus far been divorced from discussions of the referential–attributive distinction. Perhaps it is possible to apply the distinction also meaningfully to the anaphoric domain. But to decide this matter we need a unified theory of definite descriptions, which covers both their anaphoric and their nonanaphoric uses.Footnote ³⁴

Here is where I must end. It will have become increasingly clear in the course of this chapter that its explorations form a stage in an ongoing investigation. I hope that the distinctions to which these explorations have led us will prove robust enough to be of further use in a deeper and more comprehensive account of all the different ways in which descriptions and other definite noun phrases can refer.

4.2.1 Frege/Russell/Strawson

The modern debate on the semantics of definite descriptionsFootnote ³ begins with Frege (Reference Frege1892), who introduced the distinction between sense and reference (Sinn and Bedeutung in German), in order to solve what came to be known as ‘Frege’s puzzle’: Why aren’t the following equivalent?

1. (1)

   a.	The morning star is the evening star.
   b.	The morning star is the morning star.

The morning star is identical to the evening star, but these expressions denoting them are not interchangeable, since (1a) is informative and (1b) is not. For Frege, the two expressions share a referent, but not a sense. He wondered if an expression could have a sense without a referent, and thought of several good examples, including the least rapidly convergent series, for which there is a proof that it has no referent, although it clearly has a sense. Such descriptions would later come to be known as ‘empty definite descriptions’, The king of France being the most famous representative. According to Frege, use of a definite description is generally “permitted” only when there is exactly one object that falls under the description, and he surmised that any use of what he called ‘proper names’ (a category that also includes definite descriptions, for him) always presupposes a referent.

Frege himself was not committed to the actual existence of a referent; he just said we speak as if there is a referent. He acknowledges that skeptics would object as follows (p. 214): “You talk, without further ado, of the moon as an object; but how do you know that the name ‘the moon’ has any referent? How do you know that anything whatsover has a referent?” His reply is that “we presuppose a referent,” continuing:

If the skeptics are right and the presupposition is always mistaken, then we go around speaking nonsense all the time, but Frege did not seem particularly bothered by that possibility.

The question whether the presupposition is perhaps always mistaken was one that Russell (Reference Russell1905) took very seriously, as he was someone who viewed direct acquaintance with an object as a precondition for knowledge of its existence. (See the chapter by Sharvit and Moss in this volume for further discussion of this point.) To do so, he set out to give a treatment of the definite article that does not presuppose the existence of entities with which the interlocutors have no direct acquantaince. He treated English the on a par with quantificational determiners like some and no, so that ‘The F is G’ makes an existential claim: ‘There is an F such that: nothing else is an F, and F is G’. A sentence containing an empty description, then, such as the following:

1. (2)

   a.	The least rapidly convergent series consists of integers.
   b.	The king of France is bald.

is perfectly ‘permissible’ for Russell; it’s just false. (Frege would deem the usage impermissible.) One of Frege’s arguments against a view like Russell’s comes from negation. If Russell were right, then the negation of The king of France is bald should be equivalent to: Either there is no king of France, or there is and that individual is not bald. But that disjunctive type of proposition is evidently not what the negated sentences express:

1. (3)

   a.	The least rapidly convergent series does not consist of integers.
   b.	The king of France is not bald.

According to Frege, these sentences presuppose existence and uniqueness just as much as their positive forms do (and are hence just as impermissible). Russell admits that neither (2) nor (3) is generally felt to be true. But Russell can actually explain this fact, using the assumption that (3) is ambiguous between two readings: one true one, where the negation takes scope over the existential quantifier introduced by the definite article, and one false one, where the scoping is the other way around. He argues that a true reading for the negated sentences is in fact available, and that is a reading that Frege’s theory does not immediately capture.

This is not the only argument Russell gives in favor of his own theory; he adheres to the dictum that “it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.” In this spirit, he asks how Frege could account for sentences like The king of France does not exist, if definite descriptions presuppose existence. Neale (Reference Neale1990) discusses this problem among others, and advocates a Russellian approach from a modern perspective.Footnote ⁴

Despite the cleverness of Russell’s argumentation, Strawson (Reference Strawson1950) disagrees mightily with him (and totally ignores his aim of avoiding existence presuppositions for objects that one does not have direct acquaintance with). Strawson advocates a more Fregean view, one on which existence is presupposed. For Strawson, this isn’t just about definite descriptions; this is about whether the sorts of logical methods that Russell applies to natural language were appropriate. Russell’s entire approach fails to situate language in contexts of use, where acts of referring take place. Dropping the proverbial microphone with this epic one-liner, Strawson concludes, “Neither Aristotelian nor Russellian rules give the exact logic of any expression in ordinary language; for ordinary language has no exact logic.” But the only tangible piece of evidence Strawson gave was an intuitively compelling argument that the question of the truth of sentences like (2) did not arise. It is easy to construct a logic in which a sentence containing an empty definite description is neither true nor false. If that is the goal, then it can be achieved within the range of the logician’s methods, as it has been. The story of presupposition is told in greater detail in Márta Abrusán’s contribution to this volume.

A great number of modern formal semanticists take a broadly Fregean view, incorporating Strawson’s intuition that the question of truth for a sentence with a failed presupposition does not arise (Heim Reference Heim, von Stechow and Wunderlich1991; von Fintel Reference von Fintel, Bezuidenhout and Reimer2004; Elbourne Reference Elbourne2005, Reference Elbourne2008; Glanzberg Reference Glanzberg2007). In their exposition of this view, Heim and Kratzer (Reference Heim and Kratzer1998) cite the following passage from Frege, on the negative square root of four:

To flesh out Frege’s analysis of this example further, Heim and Kratzer (Reference Heim and Kratzer1998) suggest the following structure (presented here in the style of Coppock & Champollion Reference Coppock and Champollionin preparation), where natural language expressions are translated into corresponding logical expressions):

(4)

Here the is translated into a logical representation using the iota operator $\iota$. The iota-expression denotes the unique individual satisfying the indicated condition, if there is one, and otherwise has no referent, at least no referent in the domain of entities that might be actualized in any possible world. Semantic definitions of iota-expressions sometimes appeal to a special ‘undefined individual’ for use in the case that there is no actual satisfier of the description. Notations for this include Kaplan’s (Reference Kaplan, Almog, Perry and Wettstein1977) $†$, standing for a ‘completely alien entity’ not in the set of individuals, Landman’s (Reference Landman2004) 0, and Oliver and Smiley’s (Reference Oliver and Smiley2013) O, pronounced ‘zilch’. Coppock and Champollion (Reference Coppock and Champollionin preparation) use the notation #_e in the metalanguage to denote it, and give the following characterization of its semantics:

This says that $\mathit{\iota u}.\varphi$ denotes the unique individual k that satisfies the condition on u given by $\varphi$, if there is one, and otherwise denotes the ‘undefined individual’, that ‘completely alien entity’. The latter case is invoked for the least rapidly convergent series. An empty description like this generallyFootnote ⁵ prevents the sentence as a whole from having a truth value, as most predicates fail to produce a classical truth value (true or false) when given the undefined individual as an argument. This result accords with Strawson’s intuition that sentences like The king of France is bald are neither true nor false (against Russell’s (Reference Russell1905) intuition that it is plainly false). The definite article can then be translated into a typed lambda calculus as according to the following lexical entry, where $⇝$ signals a translation relation from English to the formal representation language.

Another option is to take iota-expressions to be entirely undefined, completely bereft of meaning, when the condition does not hold of one and only one object in the domain. In either case, the expression only has a proper referent when there exists a unique satsifier of the description, and in that sense is only ‘permissible’ in such a case. In other words, use of an iota-expression presupposes that existence and uniqueness obtain.Footnote ⁶

4.2.2 Challenging Uniqueness

While Russell’s theory of descriptions has largely been set aside in modern research on definiteness, another theory – the familiarity theory – has taken over as a competitor. In a paper advocating a kind of familiarity theory, Roberts (Reference Roberts2003) discusses the following example, adapted from Heim (Reference Heim1982):

This example could felicitously and truthfully be used to describe a scenario in which two wine glasses broke. It does not carry a presupposition that there was only one glass, or even that there was only one that broke (although it does carry such an implicature). Heim (Reference Heim1982) proposes that a glass introduces a new discourse referent constrained by the property ‘glass’. On the familiarity theory of definiteness, the glass is licensed in virtue of this fact, picking up this now-familiar discourse referent. The meaning of a definite article, then, crucially involves the concept of familiarity (previously being introduced in the discourse). Dynamic semantics, in which meanings are instructions for updating a context, and discourse referents are introduced and picked up, provides a way of implementing that idea. In Heim’s file change semantics, contexts are viewed essentially as sets of variable assignments, where the variables correspond to discourse referents, and the values they are assigned to are individuals in the model. The fact that the context consists of sets of variable assignments allows for the possibility that it is not fully narrowed down exactly which individual a given discourse referent picks out. As more information comes in through successive updates, the set of possible values for a given discourse referent may be whittled down. A definite description is a device for identifying an already-introduced discourse referent, a key step in being able to say more about it.

But this example alone does not prove the familiarity theory of definites. It is uncontroversial (so far as I know) that there is independent need for so-called ‘domain restriction’, where the overt descriptive content of a nominal is apparently enriched. A particularly telling case (due to Soames Reference Soames1986, building on an example from Barwise & Perry Reference Barwise and Perry1983) is the following:

Clearly, everyone must be interpreted relative to a domain that excludes the research assistants, and yet the indefinite a research assistant requires that they be part of the domain. This type of example can be accounted for by using a contextually-provided variable over predicates C that is intersected with the descriptive content of the nominal that the determiner combines with (Westerståhl Reference Westerståhl, van Benthem and ter Meulen1984; von Fintel Reference von Fintel1994). Perhaps, then, what is going on in (7) is just domain restriction. For example, glass could be interpreted as ‘glass in C’, where C is the set of objects the speaker cares about, for instance.

A more challenging case comes from the use of definite descriptions in donkey sentences like the following:

A dynamic semantic theory, in which indefinites introduces new discourse referents and definites pick them up, and conditionals ‘execute’ the meaning of the consequent after ‘executing’ the meaning of the antecedent, provides an elegant account of this type of phenomenon. A dynamic analysis avoids overly strong uniqueness implications, captures the quantificational dependence of the definites on the indefinites, and accounts for the potentially universal force of these sentences. It does so by treating both indefinites and definites as variables that can potentially be bound by the same operator, effectively. The relevant analysis of definites can be approximated by the following lexical entry, in which $v_i$ is a variable, the ith variable in the sequence of variables recognized in the formal representation language. The variable $v_i$ is free in the expression below; its value is expected to come from context.

A pure Fregean analysis would make the false prediction that a sentence like (9) presupposes that there is exactly one farmer and exactly one donkey. A Fregean analysis augmented with a simple predicate-intersection theory of domain restriction also comes up short, as it fails to capture the systematic covariance in the way that the indefinite and definite descriptions are interpreted.

To capture the type of quantificational binding observed in donkey sentences using domain restriction, it has been proposed that the relevant set be determined by a contextually given function f, which maps a sequence of individual variables to an appropriate set (von Fintel Reference von Fintel1994; Chierchia Reference Chierchia1995). A mechanism for letting the domain of a quantifier (or a definite article) covary with the choice of witness for another quantifier seems to be independently needed:

1. (11)

   Everyone answered every question.

   (Stanley & Szabó Reference Stanley and Szabó2000)

1. (12)

   Only one class was so bad that no student passed the exam.

   (Heim Reference Heim, von Stechow and Wunderlich1991)

Example (11) could be verified by a scenario in which the questions differed for each participant, and the interpretation of the exam in example (12) varies according to which class is under consideration. But observe that such an approach to domain restriction has a lot in common with the familiarity theory of definites: It involves a locally free variable ranging over individuals that can be interpreted as a bound anaphor. So the general inventory of interpretive mechanisms required in the grammar is the same, whether one adopts the familiarity view of definites or this relational approach to domain restriction, be it through dynamic semantics or some other way of binding the variable.

Substantially different mechanisms are required on the situation-based approach to definite descriptions, where they are interpreted relative to a given situation (Heim Reference Heim1990; Cooper Reference Cooper and Lappin1996; Schwarz Reference Schwarz2009; Elbourne Reference Elbourne2013). The lexical entry for the definite article on this type of view might look more like the following:

For Elbourne (Reference Elbourne2013), a definite description always carries a locally free situation pronoun, which can either be bound by a special quantifier over situations or interpreted as anaphoric to a salient situation in the discourse. For the case in (7), the situation made salient in the first sentence could serve as the antecedent for the silent situation pronoun hiding in the glass. Relative to that situation, there is perhaps only one glass: the one that the speaker cares about. Elbourne (Reference Elbourne2013) shows that there is a viable, nondynamic alternative in the face of data like (7) and (9), one that is fundamentally Fregean, with the principal difference being that a situation pronoun is posited inside the definite description.

What, then, is at stake in the choice between these two theories? In the debate over donkey pronouns, one type of data that is presented as potentially problematic for a situation-based view is the following type of sentence, attributed to Hans Kamp by Heim (Reference Heim1990), though the original observation is apparntly due to Jan van Eijck (Hans Kamp, p.c.):Footnote ⁷

If the pronoun he is interpreted as a disguised definite description (the bishop), and uniqueness for this description is calculated relative to the minimal situation characterized by the antecedent (a bishop meeting a bishop), then the pronoun should not be felicitous, because there are two bishops in this situation. Elbourne (Reference Elbourne2005) calls this ‘the problem of indistinguishable participants’. It’s easy to account for this type of example on a dynamic view, as long as the pronouns’ discourse referents can be identified with those of their antecedents. As Heim (Reference Heim1990) discusses, Kadmon (Reference Kadmon1987) has a situation-based view that can account for some bishop-type sentences. But Heim argues that in general, it has uniqueness presuppositions that are too strong. This comes out in examples like the following:

The first should presuppose that each man has at most one namesake, under Kadmon’s proposal. Similarly, the second should presuppose that each man has at most one roommate. Elbourne (Reference Elbourne2005) offers another situation-theoretic approach, where in (14), there is an asymmetry between the two bishops such that one is part of a relevant situation that does not involve meeting another bishop and the other is not.

Elbourne argues furthermore that the situation-based view is capable of making a distinction that the dynamic view misses, one that can account for the contrast in acceptability between sentences like (14) and ones like (17).

According to Elbourne, there is no relevant situation involving one bishop but excluding the other for this sentence, so the pronoun is correctly predicted to be ruled out.

It is crucial for Elbourne that only a restricted set of situations be considered relevant, or else the asymmetry would disappear (Elbourne Reference Elbourne2005: 149–153). The exclusion of these situations does not strike me as particularly well motivated, so this is an unfortunate corner for the situation-based theory to be backed into. Furthermore, Barker and Shan (Reference Barker and Shan2008) argue that this contrast can in fact be accommodated under a dynamic theory, and they blame the infelicity on the difficulty of finding an antecedent for the pronouns. Elbourne (Reference Elbourne2009) expresses skepticism about this argument, arguing that (14) is likewise ambiguous. I leave it to the reader to adjudicate; suffice it to say that the issue is not clear-cut.

Bishop sentences can also be formed with definite descriptions (Schwarz Reference Schwarz2009: 244):

The same kind of question arises here. This kind of example can easily be accommodated under a dynamic view, because the two indefinites are associated with distinct discourse referents, yielding distinct antecedents for the two definites. Prima facie, it poses a problem for a situation-based view, because the uniqueness requirement is violated in the situation where the two bishops meet. But notice that intransitive cases with definite descriptions like the following are just as unacceptable as ones with pronouns:

To the extent that the contrast between (14) and (17) militates in favor of the situation-based view on pronouns, the contrast between (18) and (19) does the same for the situation-based view on definite descriptions. Perhaps a retort in the style of Barker and Shan (Reference Barker and Shan2008) can be upheld here as well.

What other evidence can be brought to bear on the issue, as it concerns definite descriptions? According to Schwarz (Reference Schwarz2009), the strong/weak distinction among definite determiners in German dialects reflects the fact that strong determiners mark familiarity, while weak determiners mark situation-based uniqueness. Implicit in this reasoning of course is that the two analyses make different predictions about the range of uses that an article should have. Let us turn to this next.

4.2.3 A Both-And Solution

Schwarz (Reference Schwarz2009) takes a statesman-like approach, where the familiarity-based (dynamic) view and what he calls the ‘uniqueness view’ (a Fregean view enriched with situation variables à la Elbourne) are both needed, albeit for different purposes. He focuses on the distinction between two types of definites in German, strong and weak. For Schwarz, the weak definites are ‘uniqueness’ definites, but the strong ones are familiarity definites.

The weak article in German undergoes reduction after a preposition, yielding vom ‘by the’ rather than von dem ‘by the’. The former is used in cases involving so-called ‘situational uniqueness’, such as the following:

1. (20)

   Der	Empfang	wurde	vom / *von dem	Bürgermeister	eröffnet.
   the	reception	was	by-theweak / by thestrong	Mayor	opened
   ‘The reception was opened by the mayor.’

There may be more than one mayor in the world, but there is only one mayor in the situation being described here; in that sense, we have ‘situational uniqueness’ here. As Schwarz shows, the weak articles are used when uniqueness is presupposed with respect to what Hawkins (Reference Hawkins1978) calls an ‘immediate situation’ (e.g. the dog), a ‘larger situation’ (e.g. the priest), or a ‘global situation’ (e.g. the moon), and in certain types of bridging anaphora, namely ‘part–whole’ bridging (e.g. the tower, after a church has been introduced).Footnote ⁸ In all of these cases, the situation-relativized Fregean article would be expected to be possible, as the relevant property is unique, relative to the given situation. Weak articles also have what Schwarz calls ‘covarying uses’, as in:

1. (21)

   At every train station that our train entered, a letter …
   a.	vom		Bürgermeister
   	from.theweak		mayor
   b.	*von	dem	Bürgermeister
   	from	thestrong	mayor
   	… was handed to me.

For these kinds of uses, he posits a type-shifting operation that allows the situation argument to be bound.

The strong form, on the other hand, is what is found in an anaphoric context:

1. (22)

   Hans	hat	einen	Schriftsteller	und		einen	Politiker			interviewt.
   Hans	has	a	writer	and		a	politician			interviewed
   Er	hat	*vom / von dem			Politiker			keine	interessanten
   He	has	from.theweak / from thestrong			politician			no	interesting
   Antworten		bekommen.
   answers		gotten
   ‘Hans interviewed a writer and a politician. He didn’t get any interesting answers from the politician.’

Here, the referent of the politician is previously introduced into the discourse, so a familiarity article should be felicitous. The strong article in German occurs here as well as in ‘product–producer’ bridging (e.g. the author, after a book has been introduced). The latter type of usage is not immediately predicted by the familiarity account, and Schwarz introduces a relational version of the definite article in order to account for it (p. 271).

We certainly expect a uniqueness article (in Schwarz’s sense) to be felicitous for ‘the mayor’ in (20) and we certainly expect a familiarity article to be felicitous for ‘the politician’ in (22). And it is certainly not obvious that we would expect them to be able to switch places. But what exactly is the distribution that we expect? Should a familiarity article be infelicitous with ‘the mayor’? Should a situation-relative Fregean article be infelicitous with ‘the politician’? Let us consider these questions in turn.