Anaphora

First published Tue Feb 24, 2004; substantive revision Wed Oct 27, 2021

Anaphora is sometimes characterized as the phenomenon whereby theinterpretation of an occurrence of one expression depends on theinterpretation of an occurrence of another or whereby an occurrence ofan expression has its referent supplied by an occurrence of some otherexpression in the same or another sentence.^[1] However, these are at best very rough characterizations of thephenomena, since things other than anaphoric expressions satisfy thefirst characterization and many cases of anaphora fail to satisfy thesecond. For example, in some sense of “interpretation”,the interpretation of the expression “bank” in thefollowing sentence depends on the interpretation of other expressions(in particular, “of the river”):

(1): John is down by the bank of the river.

But no one would say this is an example of anaphora. And as to thesecond characterization, though all agree that the following is anexample of anaphora (and “he” is an anaphoric pronoun hereon one reading of the sentence), it is not a case of thereferent of one expression being supplied by anotherexpression, (since “he” is not a referring expression onthe reading in question):

(2): Every male lawyer believes he is smart.

Hence, rather than attempting to characterize anaphora generally andabstractly, we shall begin with some examples. There is generallythought to be many types of anaphora, though in some cases there isdisagreement as to whether to classify those cases as anaphora or not.^[2]

Pronominal anaphora:

(3): John left. He said he was ill. (The antecedent is“John” and the anaphoric expression is“he”.)

VP anaphora (also calledVP ellipsis):

(4): Mary Annetook out the garbage. Claudia did too. (The antecedent is “tookout the garbage” and the anaphoric expression a null VP. SeePartee and Bach (1984), Prüst et al. (1994).)

Propositional anaphora:

(5): Oneplaintiff was passed over for promotion three times. But the jurydidn’t believe this. (The antecedent is the propositionexpressed by the first sentence. The anaphoric expression is“this”. Example from Asher and Lascarides(2003).)

Adjectival anaphora:

(6): A kindstranger returned my wallet. Such people are rare. (The antecedent is“kind stranger” and the anaphoric expression“such”.)

Modal anaphora:

(7): John mightgive a presentation. He would use slides. (The antecedent is thepossibility described by the first sentence, and the anaphoricexpression is the modal “would”. Example from Stone andHardt 1999)

Temporal anaphora:

(8): Sheila hada party last Friday and Sam got drunk. (The time at which Sam gotdrunk is anaphoric on the time at which Sheila had the party. Examplefrom Partee 1984.)

Kind-level anaphora:

(9): John gavea presentation. Sarah gave one too. (The antecedent is “apresentation”, and the anaphoric expression is“one”.)

The antecedent also does not always have to precede the anaphoricexpression; when it doesn’t, these are called cases ofcataphora orbackwards anaphora:

(10): If shedoesn’t show up soon, Jane will be disqualified from thecompetition.

Despite there being many kinds of anaphora, this article will focus onpronominal anaphora, since this is the type of anaphora that hasreceived the most attention in the linguistics and (especially)philosophical literature. Some anaphoric pronouns are referringexpressions that inherit their referents from other referringexpressions. For example, on the anaphoric reading of(3), “He” inherits its referent from “John”, whichis said to be theantecedent of the pronoun. Such anaphora issimple and well understood. In cases such as(2) above, the anaphoric pronoun has as its antecedent a quantifier(“Every male lawyer” in (2)), and essentially functions asa variable bound by the quantifier. Again, such cases are wellunderstood. There are some anaphoric pronouns that cannot beunderstood as referring expressions that inherit their referents fromother referring expressions, nor as variables bound by quantifiedantecedents. These cases of anaphora are of interest to philosophersand linguists because formulating proper semantic theories for themhas proved to be a difficult and interesting task. Many theories ofthese cases are currently being advocated.

1. Unproblematic Anaphora

The simplest sorts of anaphoric pronouns are those that “pickup” a reference from a previous referring expression whether inthe same sentence or another. Consider for example:

(3): John left. He said he was ill.
(11): John left his wallet on the table.

on the readings of these sentences on which “he” and“his” co-refer with “John”. In such cases, thepronouns are anaphoric, and the expression “John” iscalledthe antecedent of the anaphoric expression. Thesemantics of such anaphoric pronouns is very simple: the referent ofthe anaphoric pronoun is the referent of its antecedent.

As indicated above, there are also anaphoric pronouns with quantifier(rather than referring expression) antecedents. Examples include(2) above and:

(12): Everymale skier loves his mother.

Again, on the readings of these sentences on which “he”and “his” “look back” to their antecedents forinterpretation rather than being assigned independent reference (e.g.,by pointing to Chris when uttering “his” in (12)). It iswidely held that in such cases, the pronouns function semantically asvariables bound by their quantifier antecedents. Thus, their semanticfunction is just like that of bound variables of first order logic.^[3] The insight that some pronouns with quantifier antecedents functionlike bound variables in first order logic goes back at least to Quine(1960, see chapter IV section 28). Historically, these cases have beenof more interest to linguists than philosophers. For example, onething that needs to be explained is that in a sentence like“Sarah likes her”, “Sarah” and“her” cannot co-refer (in order to get a co-referencereading, we must say “Sarah likes herself”), though we canget the co-reference reading (or not) in a sentence like “Sarahlikes her sister”. Accounting for these types of patterns ofsentence-internal anaphora is the central concern of the area oflinguistics calledbinding theory (see May 1980; Higginbothamand May 1981; Chomsky 1981; Reinhardt 1983a,b; Büring 2005).Though these insights are all important, if examples like(3),(11), and(12) were the only kinds of pronominal anaphora, they currently would notbe of much interest to so many philosophers and linguists.

2. Problematic Anaphora

Significant interest in anaphoric pronouns grew out of the realizationthat there are anaphoric pronouns that cannot be understood as havingtheir references fixed by their antecedents (as in(3) and(11) above) nor as being variables bound by their quantifier antecedents(as in(2) and(12) above). The three sorts of examples of this discussed here havefigured prominently in the literature on anaphora.

First, there isdiscourse anaphora: cases in which ananaphoric pronoun has an antecedent in another sentence, where thatantecedent at least appears to be a quantifier.^[4] Examples include:

(13): Ananthropologist discovered the skeleton called “Lucy”. Henamed the skeleton after a Beatle’s song.

(14): Fewprofessors came to the party. They had a good time.

There are at least two reasons for thinking that the pronouns in (13)and (14) are not variables bound by their quantifier antecedents. Bothreasons are discussed by Evans (1977). The first is that such atreatment clearly yields the wrong truth conditions for examples like(14). If “they” is a bound variable in (14), the twosentences should be equivalent to

(14a): Fewprofessors :x (x came to the party andx had agood time)

(Or, more colloquially, “Few professors are such that they bothcame to the party and had a good time.”) This is clearlyincorrect, since the sentences of (14) entail that few professorsattended the party (i.e., the first sentence entails this), whereas(14a) could be true if many professors attended.^[5]

The second reason for thinking pronouns in cases of discourse anaphoraaren’t bound variables is that it seems committed to the claimthat the following anomalous sentences aren’t anomalous:

*15.: Johnbought no sheep and Harry vaccinated them.
*16.: Every professor came to the party. He had a great time.

If the (apparent) quantifiers in(13) and(14) can bind variables in sentences after those in which they occur, whycan’t the quantifiers in (15) and (16)? If this could happen,(15) and (16) should be fine and should together be equivalent to,respectively:

(15a): Nosheep were both bought by John and vaccinated by Harry.
(16a): Every professor came to the party and had a great time.

But they are not. Thus, pronouns in discourse anaphora are notvariables (syntactically) bound by their quantifier antecedents.^[6]

Furthermore, there are cases of (plural) anaphora in which thedenotation of “they” is derived in a more indirect wayfrom the antecedent, as in (17), an example of complementanaphora:

(17): Fewstudents came to the party. They were busy studying.

Unlike in (14), where “they” picks out the professors whocame to the party, in (17), “they” picks out the studentswhodidn’t come to the party. (For more aboutcomplement anaphora, see Nouwen (2003a), for complement anaphora in thepsycholinguistics literature, see Sanford & Moxey (1993).)

Nor are these like example(3), in which the pronoun simply refers to the same thing as theantecedent. Indefinite descriptions like “ananthropologist” are commonly thought to be quantifiers, andexpressions like “few professors” are certainlyquantifiers, not referring expressions. On most theories of indefinitedescriptions, the first sentence of(13) is true just in case there is at least one anthropologist whodiscovered the skeleton called “Lucy”; its truth does notdepend on any particular anthropologist. Thus there is no referentialantecedent in the first sentence for the pronoun in the secondsentence to be co-referential with.

A further problem with thinking of these pronouns as referential canbe seen by considering a slightly more complex example:

(18): A manbroke into Sarah’s apartment. Scott believes he came in thewindow.

The crucial point is that the second sentence has a reading on whichit attributes to Scott a general belief instead of a belief about aparticular person. This reading would be true, for example, if Scottbelieved that some man broke into Sarah’s apartment by coming inthe window, but had no idea about who might have broken in. This is(prima facie) evidence that the pronoun in the secondsentence is not a referring expression, because if it were, the secondsentence of (18) would only have a reading on which it attributes toScott a belief about the particular person the pronoun refers to. Butthis is incorrect.^[7] (On the other hand, for a treatment of suchde dictoreadings while maintaining that the pronoun is a referring expression,see Elbourne 2005: 99–106.)

Thus, with pronouns in discourse anaphora, we have examples ofpronouns that can neither be understood as picking up their referentsfrom their antecedents nor as being variables bound by theirantecedents. Discourse anaphora provides further interesting examplesto philosophers and linguists when the antecedents are under the scopeof quantifiers, modals, or negation. For example, the pronouns in(19), (20), and (22) are infelicitous, but those in (21) and (23) arefelicitous. This is something further that an account of discourseanaphora needs to explain.^[8]

(19): Bryandidn’t buy a bottle of wine. #It is a pinot noir.
(20): Bryan might buy a bottle of wine. #It is a pinot noir.
(21): Bryan might buy a bottle of wine. It would be a pinot noir. (Thisan example ofmodal subordination. For an introduction tomodal subordination see Roberts (1987, 1989, 1996).)
(22): Bryan bought a bottle of wine at every store in theneighborhood. #It was a pinot noir.
(23): Bryan bought a bottle of wine at every store in theneighborhood. It was always a pinot noir. (This is an exampleofquantificational subordination. For more onquantificational subordination see Brasoveanu 2006.)

A second sort of anaphoric pronoun that cannot be understood as areferring expression or as a bound variable is in fact a special caseof discourse anaphora. However, it deserves separate mention becauseit has generated so much interest. Consider the following discourse,which we shall call aGeach Discourse, adapted from theanalogous conjunction in Geach 1967:

(24): Hobthinks a witch blighted Bob’s mare. Nob wonders whether shekilled Cob’s sow.

There is a reading of this discourse on which both sentences in it aretrue even if there are no witches, so that “a witch” inthe first sentence must take narrow scope with respect to “Hobthinks”. But then the scope of “a witch” cannotextend to the second sentence to bind the pronoun “she”,since the “scope” of “Hob thinks”doesn’t extend to the second sentence. Hence on the reading inquestion, which we shall call theGeach Reading, the pronoun“she” is not a bound variable. Further, since there are nowitches, and “she” is anaphoric on “a witch”,“she” in the second sentence must in some sense being usedto “talk about” a non-existent witch. Thus, it apparentlycannot be a referring term either, since its alleged referentdoesn’t exist. So here again we have an anaphoric pronoun thatcannot be understood as a referring expression nor as a boundvariable. Examples of this sort are sometimes referred to(misleadingly, in our view) as instances ofintentionalidentity.

The third sort of case in which an anaphoric pronoun cannot beunderstood as a referring expression nor as a bound variable is thatof “donkey anaphora”.^[9] Here there are two varieties, which are calledconditionalandrelative clause donkey sentences, respectively:

(25): If Sarahowns a donkey, she beats it.
(26): Every woman who owns a donkey beats it.

On the readings we are concerned with, neither (25) nor (26) istalking about any particular donkey, and so the pronoun“it” cannot be a term referring to a particular donkey.Further, in the case of (25), all independent evidence availablesuggests that a quantifier can’t take wide scope over aconditional and bind variables in its consequent (*“If John ownsevery donkey_i, he beats it_i”). Thissuggests that the (apparent) quantifier “a donkey” in (25)cannot bind the pronoun in the consequent. In addition, even if“a donkey” could magically do this in (25), assuming it isan existential quantifier, we still wouldn’t get the intuitivetruth conditions of (25), which require that Sarah beatsevery donkey she owns. Similarly, the independent evidenceavailable suggests that quantifiers can’t scope out of relativeclauses (*“A man who owns every donkey_i beatsit_i”), and so again the pronoun in (26) is not withinthe scope of its quantifier antecedent and so is not bound by it.Thus, the pronouns in both conditional and relative clause donkeysentences can be neither understood as referring expressions nor asbound variables.

So now we have three cases of anaphoric pronouns that cannot beunderstood as referring expressions nor as bound variables: 1)pronouns in discourse anaphora; 2) pronouns in Geach discourses and 3)pronouns in (conditional and relative clause) donkey sentences.Let’s call these cases ofproblematic anaphora. Therecent interest in anaphora is largely an interest in finding asemantic theory for problematic anaphora. In the next section, weoutline the main theories that have arisen to fill this void.

3. Recent Theories of Problematic Anaphora

Before discussing recent theories of problematic anaphora, a fewcaveats are in order. First, our discussion will not be exhaustive. Wecover what we take to be the best known and most promising theories.Second, because each theory is a formal, sophisticated semantictheory, to describe a single theory in detail would itself be a paperlength project. Thus, we try instead to give a simple, informal sketchof the main features of each theory. The notes and references pointthe interested reader to places where he/she can get more detail.Third, we shall confine ourselves to briefly describing how eachtheory handles simple discourse anaphora of the sort exhibited by(13) above, in which a pronoun in one sentence is anaphoric on anindefinite noun phrase in a previous sentence, and donkey anaphoralike(25) and(26). Readers interested in more details on how these theories deal withembedding under quantifiers, negation, or modals should consult thereadings cited both in the previous section and in the sections below.Readers interested in Geach discourses or “intentionalidentity” should begin by consulting Asher (1987), Edelberg(1986), Geach (1967), Kamp (1990), King (1994), Braun (2012), and theworks mentioned therein.

The first two of the theories discussed below, discourserepresentation theory and dynamic semantics, represent departures fromtraditional semantics, departures which were largely motivated at thebeginning by the problematic anaphora cases. The second two theoriesdiscussed below, d-type theories and the CDQ theory, represent ways inwhich the problematic anaphora data is dealt with within a traditionalsemantic framework.

3.1 Discourse Representation Theory

In the early 1980s, Irene Heim (1982) and Hans Kamp (1981)independently formulated very similar semantic theories that were inpart designed to handle problematic anaphora, particularly donkey anddiscourse anaphora. The theories developed by Heim and Kamp have cometo be known as Discourse Representation Theory or DRT (see entry onDiscourse Representation Theory).^[10] We shall not attempt to describe differences between the formulationsof Heim and Kamp. Indeed, in our exposition we shall combine elementsof the two theories. Readers interested in the differences between thetwo accounts should consult Heim (1982) and Kamp (1981) directly.

We believe it is fair to say that it was the development of DRT thatmade the semantics of anaphora a central issue in philosophy oflanguage. One reason for this was the following bold statement by Kamp(1981):

A theory of this form differs fundamentally from those familiar fromthe truth-theoretical and model-theoretical literature, and thus asubstantial argument will be wanted that such a radical departure fromexisting frameworks is really necessary. The particular analysiscarried out in the main part of this paper should be seen as a firstattempt to provide such an argument. The analysis deals with only asmall number of linguistic problems, but careful reflection upon justthose problems already reveals, I suggest, that a major revision ofsemantic theory is called for. (Kamp 1981: 278)

The problems that Kamp goes on to address are the treatment of donkeyanaphora and simple discourse anaphora. Hence Kamp appears to besaying that these problems cannot be handled within more traditionalframeworks and thus that a DRT approach is necessary. Obviously, theclaim that the semantics of anaphora requires a radical revision insemantic theory got the attention of philosophers of language. Thus,the study of problematic anaphora blossomed during the 1980s and1990s.

The first way in which DRT departs from more traditional approaches isthat it claims that indefinite noun phrases such as “ananthropologist” or “a donkey” are essentiallypredicates with free variables rather than existential quantifiers.Thus, the above indefinites might as well look as follows at the levelof “logical form”:

anthropologist(x)
donkey(x)

In effect, an indefinite introduces a “novel” variable,(i.e., in DRT’s terminology, establishes adiscoursereferent) and a pronoun anaphoric on an indefinite is interpretedas the same variable as was introduced by its indefinite antecedent.Hence a simple discourse such as:

(27): A manloves Annie. He is rich.

in effect can be represented as^[11]

(27a): man(x)
x loves Annie
x is rich

In addition to this, DRT builds in to the assignment of truthconditions default existential quantification over free variables.Thus, (27a) is true iff there is some assignment to the variable“x” that is in the extension of “man”,“loves Annie” and “rich”, that is, iffsomething is a man who loves Annie and is rich. Thus, that indefinitesappear to have the force of existential quantifiers in cases like (27)is not because they are existential quantifiers but because of thedefault existential quantification of free variables.

Let us turn now to the DRT treatment of donkey anaphora. First, notethat both relative clause and conditional donkey anaphora appear tohave a sort of “universal force”: the truth of(25) and(26) above, repeated here, require that Sarah beats every donkey she ownsand that every donkey owning woman beats every donkey she owns.^[12]

(25): If Sarah owns adonkey, she beats it.
(26): Every woman who owns a donkey beats it.

Thus, the indefinite here mysteriously has universal force andexpresses something about every donkey owned by someone. Recall thataccording to DRT, an indefinite is effectively a one-place predicatewith a free variable. The central idea of DRT in the case of bothconditional and relative clause donkey sentences is that the universalforce of the indefinite results from the variable in it being bound byan operator with genuine universal force. In the case of (25), the“conditional operator” has universal force, since it ineffect says that in every case (assignment to free variables) in whichthe antecedent is true, the consequent is true. So (25) claims thatevery assignment to “x” that makes “Sarahownsx” and “x is a donkey” true, alsomakes “Sarah beatsx” true. So (25) is true iffSarah beats every donkey she owns. In (26), by contrast, the universalquantifier (determiner) “every” not only binds thevariables associated with the predicative material “woman whoowns a donkey” (for example, presumably there is such a variablein the subject argument place of “beats”), but it alsobinds the variable introduced by the predicate-with-free-variable“a donkey”. So it is as though (26) has the “logical form”.^[13]

(26a): Everyx,y (woman(x) & donkey(y) &x ownsy) (x beatsy)

Note that this account requires allowing quantificational determiners(“every”) to bind multiple variables. This, again, is adeparture from more classical approaches.^[14]

Now since the DRT approach claims that indefinites get their apparentquantificational force from other elements that bind the variables inthem, it predicts that when different determiners are involved inrelative clause donkey sentences, as in

(28): Mostwomen who own a donkey beat it.

the indefinite should appear to have the quantificational force of thenew determiner (“Most”). So (16) should be true if mostpairs of women and donkeys they own are such that the women beat thedonkeys. Similar remarks apply to conditionals containing“non-universal” quantifiers such as “usually”,as in

(29): Usually,if a woman owns a donkey, she beats it.

This should be true if most pairs of women and donkeys they own aresuch that the women beat the donkeys. But this prediction,particularly in the case of (28), seems clearly false. If there areexactly ten donkey owning women and one woman owns ten donkeys andbeats them all, while the nine other women own a donkey each anddon’t beat them, (28) intuitively seems false: most donkeyowning women fail to beat the donkeys they own. However, the DRTaccount as formulated claims (28) is true in this situation. Thisdifficulty is one of the main criticisms of classical DRT in theliterature and is often calledthe proportion problem (Heim(1990) claims that Nirit Kadmon so dubbed it). The criticism isdamaging, because it appears to refute what was claimed to be acentral insight of DRT: that the apparent quantificational force ofindefinites comes from other elements that bind the variables inthem.

A second difficulty with classical DRT as formulated here involvescases such as(18) above, repeated here:

(18): A man broke intoSarah’s apartment. Scott believes he came in thewindow.

As mentioned above, (18) has a reading on which the second sentence ofthe discourse attributes a general belief to Scott (something like thebelief that a man who broke into Sarah’s apartment came inthrough the window). But as formulated, DRT doesn’t get thisreading. For the default existential quantification of free variablesacts in effect like a wide scope existential quantifier over theentire discourse. Thus, it is as if (18) were as follows:

(∃x)(x is a man &x broke intoSarah’s apartment & Scott believesx came in thewindow).

But this attributes a belief about a specific person to Scott. Henceit can’t capture the reading mentioned. Similarly, consider thefollowing sentences:

(30): Everywomen who has a secret admirer thinks he is stalking her.
(31): If a woman has a secret admirer, usually she thinks he isstalking her

These sentences also appear to have readings on which they attributegeneral orde dicto beliefs to the women in question. Thatis, they have readings on which they attribute to the women inquestiongeneral beliefs to the effect that they are beingstalked by secret admirers. This is why these sentences can be trueeven though the women in question don’t know who their secretadmirers are, and so have no beliefs aboutparticular personsstalking them. For reasons exactly similar to those given for the caseof the analogous reading of the second sentence of(18), these readings can’t be captured by DRT as formulated here. Weshall see below that dynamic approaches have exactly similar problems.Asher (1987) and Kamp (1990) attempt to remedy this problem (amongothers). For further elaboration of the DRT framework, see also Kampand Reyle (1993) and van Eijck and Kamp (1997). For expansions of theDRT framework, e.g., SDRT (segmented discourse representation theory),see Asher and Lascarides (2003), for compositional versions of DRT,see Muskens (1996) and Brasoveanu (2006, 2007, 2008).

3.2 Dynamic Semantic Approaches

As its name suggests, Discourse Representation Theory was designed tocapture the way in which certain features of a discourse, particularlyinter-sentential relations such as inter-sentential anaphora, affectthe interpretation of sentences in the discourse. At the same time,Discourse Representation Theory as originally formulated in Kamp(1981) failed to be compositional, at least in the sense of that termfamiliar from Montagovian approaches.^[15]

The initial motivation for a dynamic semantic (see entry ondynamic semantics) approach to discourse and donkey anaphora was on the one hand topreserve the “dynamic” elements of DRT, that is the viewthat what an expression means is given by the way in which theaddition of the expression to a discourse changes the informationavailable to a hearer of the discourse, (“meaning as potentialfor changing the state of information”). On the other hand,dynamic semantic approaches wanted to adhere to compositionality. Thisis made very clear in the introduction of the classic statement of thedynamic semantic approach to discourse and donkey anaphora, namelyGroenendijk and Stokhof (1991). We shall here discuss their treatmentof discourse and donkey anaphora,Dynamic Predicate Logic(henceforth DPL), and gesture at other treatments in the dynamicsemantic tradition. First generation dynamic semantic theories of anaphora like DPL give an account of singular cross-sentential anaphora as well as donkey sentences. Subsequent work in dynamic semantics has adapted and added to these tools to account for things like plural anaphora, quantificational subordination, and other issues. (See for example van den Berg (1996), Krifka (1996a), Nouwen (2003b), Brasoveanu (2007, 2010), and Keshet (2018).) Of the theories discussed in this entry, this isthe most difficult to explain informally. We shall keep the discussionas informal as possible, and urge interested readers to consult theworks cited directly for more detail.

To begin with, let’s look at how simple discourse anaphora ishandled on DPL. So consider again:

(27): A man loves Annie. He is rich.

Now in DPL, indefinites such as “a man” are treated asexistential quantifiers. Further, DPL treats consecutive sentences indiscourses as being conjoined. So we can think of (27) as follows:

(27b): (∃x)(manx &x loves Annie) &x is rich

Here we have rendered the anaphoric pronoun “He” as thevariable “x”, the same variable that is thevariable of its quantifier antecedent. This represents the anaphoricconnection. The important point to notice is that the anaphoricpronoun/variable in (27b) is not within the syntactic scope of itsquantifier antecedent. This corresponds to the fact that in DPL, thesyntactic scopes of quantifiers are confined to the sentences in whichthey occur, as current syntactic theory tells us they should be.

The key to understanding the DPL account of discourse anaphora lies inunderstanding its semantics of the existential quantifier andconjunction. Let’s begin with existential quantification. Thebasic idea here it that when we interpret an existential quantifier,the output of that interpretation may affect the interpretation ofsubsequent expressions. In standard predicate logic, theinterpretation of an existential quantifier is a set of assignmentfunctions. In DPL, it is a set ofordered pairs of input andoutput assignment functions. The output assignment functions act asthe input to subsequent formulas. Take for example the simple formula“\((\exists x)(\mbox{man } x)\)”. In DPL, such a formulatakes all the input functionsg, and for each one outputs allthe possible assignment functionsh such that they differ fromg at most in that they assignx to an object in theinterpretation of “man” (i.e., they assignx to aman). More generally, accounting for possibly more complex formulas inthe scope of the existential (including another quantifier), a pair ofsequences \(\langle g, h\rangle\) is in the interpretation of anexistential formula “\((\exists x)\Phi\)” just in casethere is an assignment functionk differing fromg atmost onx such that \(\langle k,h\rangle\); is in theinterpretation of“\(\Phi\)”.^[16] So note how interpreting the existential quantifier results inshifting from the input functiong tok, wherekis now the input to “\(\Phi\)”. This makes the existentialquantifierinternally dynamic, capable of affecting theinterpretation of expressions within its syntactic scope. Further, thefact that the output assignment functions of interpreting the wholeexistentially quantified sentence are allowed to be different from theinput to the interpretation means that the processing of theexistentially quantified formula may affect the interpretation ofexpressionsafter the existentially quantified formula, andhenceoutside the scope of the existential quantifier. Thisis to say that the existential quantifier isexternallydynamic, capable of affecting the interpretation of expressionsoutside its syntactic scope. As we will see, an expressioncan be internally dynamic and externally static (as well as internallyand externally static). At any rate, putting things very roughly, theidea here is that once the existential quantifier “resets”the value of “x” so that it satisfies the formulathe quantifier embeds, that value stays reset (unless there is asubsequent existential quantifier attached to the same variable) andcan affect the interpretation of subsequent formulas.

Turning now to conjunction, the idea here is similar. Again, thefundamental idea is that the interpretation of the left conjunct canaffect the interpretation of the right conjunct. A bit more formally,a pair of assignment functions \(\langle g,h\rangle\); is in theinterpretation of a conjunction just in case there is an assignmentfunctionk such that \(\langle g,k\rangle\); is in theinterpretation of the left conjunct and \(\langle k,h\rangle\); theright conjunct.^[17] So note how interpreting the left conjunct changes the input sequencefor the interpretation of the right conjunct. Again, this means thatconjunction is internally dynamic, possibly affecting theinterpretation of expressions in its scope. And again, that the outputof interpreting a conjunction, hereh, can differ from theinput, hereg, means that a conjunction is capable of affectingthings outside of it and hence outside of the scope of thatconjunction sign. Again, this is to say that conjunction is externallydynamic.

To go through an example, we also need to understand the semantics ofan atomic formula like “manx”. Atomic formulas actlike a test on the input assignments, allowing those assignments thatsatisfy the condition to pass through and act as input to subsequentassignments and rejecting the rest. However, atomic formulas do notchange assignment functions. More specifically, an inputoutput pair \(\langle g,h\rangle\) is in the interpretation of anatomic formula “\(Rt_1 \ldots t_n\)” just in case \(h=g\)andh assigns “\(t_1\)”…“\(t_n\)” to something in the interpretation ofR.

Putting these elements all together, we are now in a position to seehow DPL accounts for (27b). Informally speaking, the first sentence of(27b) takes all the input assignment functionsg and outputsall those assignmentsh in that they differ at most fromg in assigning “x” to a man who loves Annie.Thus the output of the first sentence is all (and only) the possibleassignments of “x” (given the model) to men wholove Annie. The output of the first sentence is the input to thesecond. The second sentence tests these assignments, allowing onlythose through which also assign “x” to something inthe interpretation of “rich”. The output of the secondsentence includes all and only the assignments of“x” to rich men who love Annie. As long as themodel includes at least one rich man who loves Annie, there will be atleast one such output assignment. Hence the discourse is true iffthere is at least one rich man who loves Annie. Since conjunction isexternally dynamic, we can keep adding sentences with anaphoricpronouns to similar effect. Thus in a discourse such as

(27c): A manloves Annie. He is rich. He is famous.

the discourse is all true iff some rich famous man loves Annie.

Thus the dynamic semantic treatment yields a truth conditionalequivalence between \[(\exists x)(\Phi) \mathbin{\&} \Psi \] and \[(\exists x)(\Phi \mathbin{\&} \Psi) \] even when“\(\Psi\)” contains free occurrences of“x”. Hence it is often said that in DPL quantifierssemantically bind free variables outside their syntacticscope. This doesn’t encounter the same problems as the syntacticbinding treatment rejected insection 2, since it allows quantifiers to provide values for subsequentanaphoric pronouns without actually binding them in a way that falselypredicts, e.g., that “Exactly one man loves Annie. He isrich” is truth-conditionally equivalent to\(\mbox{“}(\exists !x)(\mbox{man } x \mathbin{\&} x \mbox{loves Annie} \mathbin{\&} x \mbox{ is rich})\mbox{”}\).

Because the treatment of donkey anaphora is a bit more complicatedtechnically, and because some of the main ideas of DPL are now on thetable, we will be more suggestive here. Again, we urge the interestedreader to consult Groenendijk and Stokhof (1991) directly.

First, consider conditional donkey anaphora:

(32): If afarmer owns a donkey, he beats it.

(32) gets regimented in DPL as follows:

(32a): \((\exists x)(\mbox{farmer } x \mathbin{\&} \exists y(\mbox{donkey} y \mathbin{\&} \mbox{own }x,y)) \rightarrow \mbox{beat }x,y\)

There are three crucial points to the DPL treatment here. (1) Theexistential quantifier is externally dynamic and hence may affect theinterpretation of variables outside its scope, and in particular“x” in the consequent of (32a). (2)“\(\rightarrow\)” is internally dynamic and allows theinterpretation of its antecedent to affect the interpretation of itsconsequent (just as is conjunction). 1 and 2 together mean that thequantifier in the antecedent of (32)/(32a) can semantically bind thevariable in the consequent, even though it is not in the syntacticscope of the quantifier. But without doing anything further, we wouldbe left with (32a) having the truth conditions of

(32b): \((\exists x)(\mbox{farmer } x \mathbin{\&} \exists y(\mbox{donkey }y \mathbin{\&} \mbox{own } x,y)) \rightarrow \mbox{beat }x,y)\)

where “\(\rightarrow\)” is the standard materialconditional. This doesn’t give the intuitive truth conditions of(32) on the reading that concerns us, i.e., that every donkey-owningfarmer beats every donkey he owns. The third and final element we needto get the truth conditions to come out right is to say that a pair ofassignments \(\langle h,h\rangle\) is in the interpretation of aconditional iff for allk such that \(\langle h,k\rangle\)satisfies the antecedent, there is aj such that \(\langlek,j\rangle\) satisfies the consequent.^[18] This says, roughly, that for any output assignmentk of a pairof assignments satisfying the antecedent of the conditional(assignment of a donkey-owning farmer tox and a donkey ownedbyx toy in the case of (32)/(32a)),k is theinput of a pair \(\langle k,j\rangle\) that satisfies the consequent,for somej. Since the consequent of the conditional in(32)/(32a) is an atomic formula,j=k. So the accountclaims that any output of a pair of sequences that satisfies theexistentially quantified antecedent also satisfies “xbeatsy”, and so also assigns to “x”and “y” to something that stands in the beatingrelation. That is, the truth of (32)/(32a) requires everydonkey-owning farmer to beat every donkey he owns.

Turning now to our relative clause donkey sentence, (repeatedhere)

(26): Every woman who owns a donkey beats it.

we shall be even more schematic. This gets regimented in DPL asfollows, (giving the predicate letters here the obvious meanings):

(26a): \((\forall x)((Wx\mathbin{\&} (\exists y)(Dy \mathbin{\&} Oxy)) \rightarrowBxy)\)

Note in particular that the “y” in“Bxy” is not in the scope of the existentialquantifier. Now given a quite straightforward treatment of theuniversal quantifier, on which it allows dynamic effects in its scope,^[19] in all essentials, the example works like (32)/(32a). For strippingthe universal quantifier away, we have:

(26a′): \( ((Wx\mathbin{\&} (\exists y)(Dy \mathbin{\&} Oxy))\rightarrowBxy\)

And overlooking the free variables left by stripping away theuniversal quantifier (which anyway were in its scope and bound by it),we simply have another conditional with an existential quantifier inits antecedent and a formula in the consequent containing anoccurrence of the variable of that existential quantifier. So thetreatment goes essentially as it did for (32)/(32a) itself, with theexternally dynamic existential quantifier, internally dynamicconditional, and universal quantification over assignments in thesemantics of the conditional all working their magic so that(26)’s truth requires every donkey owning woman to beat everydonkey she owns.

Though DPL cannot handle relative clause donkey sentences such as:

(33): Mostwomen who own a donkey beat it.

since it is working within the framework of a first order logicwithout generalized quantifiers, this is only a limitation of thisparticular formulation and not of dynamic approaches generally. Othershave formulated systems of dynamic semantics with generalizedquantifiers that are capable of dealing with examples like (33).^[20]

On the other hand, DPL and dynamic approaches generally do face aproblem. Put crudely, DPL (and dynamic approaches generally) solve theproblems of discourse and donkey anaphora by formulating semantics forquantifiers that allows quantifiers to semantically bind variablesthat aren’t in their syntactic scopes. In this they(self-consciously) resemble DRT. But then they face a problem similarto one faced by DRT and mentioned above. Consider again our discourse(18), repeated here

(18): A man broke into Sarah’s apartment. Scott believeshe came in the window.

As mentioned above, (18) has a reading on which the second sentence ofthe discourse attributes a general belief to Scott (something like thebelief that a man who broke into Sarah’s apartment came inthrough the window). On a dynamic approach to (18), the quantifier inthe first sentence semantically binds the variable in the secondsentence. But then this semantically amounts to quantification intothe verb of attitude, and so will not result in a reading of thesecond sentence on which it attributes a general belief to Scott.Hence, dynamic approaches need to invoke some other mechanism to getthe reading of the second sentence in question.^[21]

Similarly, again consider the following sentences discussed inconnection with DRT above :

(30): Every woman whohas a secret admirer thinks he is stalking her.
(31): If a woman has asecret admirer, usually she thinks he is stalking her.

As mentioned there, these sentences also appear to have readings onwhich they attribute general orde dicto beliefs to the womenin question. That is, they have readings on which they attribute tothe women in questiongeneral beliefs to the effect that theyare being stalked by secret admirers. This is why these sentences canbe true even though the women in question don’t know who theirsecret admirers are, and so have no beliefs aboutparticularpersons stalking them. For reasons exactly similar to those given forthe case of the analogous reading of the second sentence of (18),these readings can’t be captured by DPL or dynamic approachesgenerally.

Paul Elbourne (2005) reviews three other serious problems for dynamicapproaches. The first is the problem of disjunctive antecedents(discussed in detail in Stone 1992). The problem is with sentenceslike the following:

(34): If Maryhasn’t seen John lately, or Ann misses Bill, she calls him.(Elbourne 2005: 19)

This is problematic because the pronouns cannot co-refer with theantecedent (since it is disjunctive), but the antecedent also does notintroduce any suitable variables or quantifiers to provide values forthe pronouns, since they are definites (names) and not indefinites orother quantificational expressions.

The other two problems involve anaphoric pronouns that don’thave a proper linguistic antecedent. The following example, originallyfrom Jacobson (2000), is one in which there is no linguisticantecedent for the pronoun “it”, though the pronoun has acovarying interpretation with the quantifier “most facultymembers”:

(35): Anew faculty member picks up her first paycheck from her mailbox.Waving it in the air, she says to a colleague: Do most facultymembers deposit it in the Credit Union? (Elbourne 2005:20)

The second kind of example involves what is commonly called apaycheck pronoun:

(36): Johngave his paycheck to his mistress. Everybody else put it in the bank.(Elbourne 2005: 21)

The problematic (salient) reading is the one is which everybody elseputtheir own paychecks in the bank. The first sentence onlyintroducesJohn’s paycheck, hence “it”doesn’t have a proper antecedent. Standard dynamic accountsdon’t have the machinery for dealing with pronouns without theproper linguistic antecedent, since it is the antecedent’seffect on the context that accounts for the anaphoric pronoun’s interpretation (but see Keshet (2018) for a recent dynamic semantics of anaphora that includes an account of paycheck pronouns).^[22]

3.3 Descriptive Approaches

There have been many accounts of the semantics of anaphora accordingto which anaphoric pronouns in some sense function like definitedescriptions. Though there are important differences between suchtheories, examples of theories of this sort include Evans (1977),Parsons (1978, Other Internet Resources), Davies (1981), Neale (1990),Heim (1990) and Elbourne (2005). Theories of this sort are oftencalledE-Type orD-type approaches. Though it is beyond the scope of thisarticle to compare all the different accounts, some of the maindifferences in types of accounts are as follows. E-type accounts aresometimes distinguished as ones in which a definite description fixesthe referent of an anaphoric pronoun, whereas D-type accounts areones in which the pronoun itself has the semantics of a definitedescription. However, it is common to describe the latter as 'E-type' as well. These are further sub-divided into those that treatpronouns as definite descriptions merely at the level of semantics andthose that also treat them as descriptions at the level of syntax.Finally, accounts differ in how the descriptive material is recovered.Some accounts hold that the descriptive material has to be recoveredlinguistically, from prior discourse. Others hold that it can be anycontextually salient description.

We will discuss two of the best known versions of the view, Neale(1990) and Elbourne (2005). We should add that though Neale developedthe view in question in greater detail, Davies (1981) had earlierdefended essentially the same view in all crucial respects.^[23] Thus, the view we go on to describe should probably be calledtheDavies-Neale view. But since we shall focus on Neale’spresentation of the view, we shall talk of Neale’s view.

On Neale’s view, in all instances of problematic anaphora,anaphoric pronouns “go proxy for” definite descriptionsunderstood as quantifiers along roughly Russellian lines. First,consider discourse anaphora. Neale’s view is that in a discoursesuch as:

(37): Johnbought a donkey. Harry vaccinated it.

the pronoun “it” “goes proxy for” the definitedescription “the donkey John bought.” Hence the secondsentence of such a discourse is equivalent to the sentence“Harry vaccinated the donkey John bought” with thedescription understood in the standard Russellian fashion. Within ageneralized quantifier type framework, where “the” istreated as a determiner that, like other determiners, combines with aset term to form a quantified NP, the evaluation clause for sentencescontaining a singular description (with wide scope) can be given asfollows

(38): “[The \(x:Fx](Gx)\)” is true iff \(|\mathbf{F}|=1\) and\(|\mathbf{F-G}|=0\)

So the second sentence of (37) is true iff Harry vaccinated the uniquedonkey John bought. Thus far, then, the view is that pronounsanaphoric on singular indefinites are interpreted as Russelliandefinite descriptions.

There is, however, a further complication in Neale’s theory thatis invoked in the explanation of donkey anaphora. In particular, Nealeintroduces what he calls a “numberless description”: adescription that, unlike semantically singular descriptions, puts nocardinality constraint on the denotation of the set term that combineswith the determiner to form the quantified NP (other than that it mustbe nonempty—note above how in the singular case \(|\mathbf{F}|\)is constrained to equal one.) Following Neale, let “whe”be the determiner (corresponding to “the”) used to form“numberless descriptions.” Then the evaluation clause forsentences containing numberless descriptions, analogous to (38) above,would be

(39): “[whe \(x: Fx](Gx)\)” is true iff \(|\mathbf{F}| \ge 1\)and \(|\mathbf{F-G}|=0\)

Thus numberless descriptions are in effect universal quantifiers.

In addition to going proxy for Russellian singular descriptions in theway we have seen, Neale claims that anaphoric pronouns sometimes goproxy for numberless descriptions. In particular, Neale holds thatpronouns anaphoric on singular existential quantifiers (but outside oftheir scope) can be interpretedeither as standard Russelliandescriptionsor as numberless descriptions. Now if thepronouns in our conditional and relative clause donkey sentences(repeated here)

(25): If Sarah owns a donkey, she beats it.
(26): Every woman who owns a donkey beats it.

are interpreted as a numberless description, (25) asserts that ifSarah owns a donkey, she beats all the donkeys she owns and (26)asserts that every donkey owning woman beats every donkey she owns.Thus, Neale’s account of donkey anaphora requires the pronounshere to be interpreted as numberless descriptions.

Having seen how Neale’s theory handles discourse anaphora anddonkey anaphora, we turn to difficulties with the account. An obviousquestion concerning an account like this that allows pronounsanaphoric on singular existential quantifiers to go proxy for bothRussellianand numberless descriptions is: what determineswhether such a pronoun is going proxy for a Russellian, as opposed toa numberless, description? This question is pressing for Neale’saccount, since there will be a substantial difference in the truthconditions of a pronoun-containing sentence depending on whether thepronoun receives a numberless or Russellian interpretation. In hismost explicit statement about the matter (1990: 237) Neale makes clearthat it is primarily whether the utterer had a particular individualin mind in uttering the indefinite description that determines whethera pronoun anaphoric on it receives a Russellian or a numberless interpretation.^[24]

If this is correct, then discourses of the form

(40): A(n)F isG. He/she/it isH.

generally ought to display both readings (in the suitable contexts),depending on whether the utterer of the discourse had a particularindividual in mind in uttering “A(n)F”. So thesecond sentences of discourses of the form of (40) ought to havereadings on which they mean the uniqueF that isG isH (Russellian)and on which they mean everyFthat isG isH (numberless). But this does not seem tobe the case. In particular, such discourses do not have readingscorresponding to the numberless interpretation of the pronoun.Consider the discourse anaphora analogue of the donkey conditional(25):

(25a): Sarahowns a donkey. She beats it.

It seems clear that this discourse has no reading on which the secondsentence means that Sarah beats every donkey she owns, even if weimagine that the utterer of the discourse had no particular donkey inmind when she uttered the first sentence. Suppose, for example, thatthe Homeland Security and Donkey Care Bureau comes to town and wantsinformation about local donkey ownership and beating. The speakertells them that she really don’t know how many donkeys anybodyowns, and has never seen or had any other contact with particularlocal donkeys. But she tells them that she has received someinformation from reliable sources and it has been deemed“credible”. Asked what she has heard, she responds:“Sarah owns a donkey and she beats it”.

Even though she has no particular donkey in mind in uttering thesesentences, we simply don’t get a numberless reading here. IfSarah beats some donkey she owns, the speaker has spoken truly even ifshe owns others she fails to beat. Or again, suppose we are debatingwhether anybody has an eight track tape player anymore, and one of ussays “I’ll bet the following is true: some guy with a‘68 Camaro owns an eight track player and he still usesit.” Again, there is no numberless reading for the pronoun inthe second sentence, even though the speaker clearly has no particulareight-track player in mind. If some ‘68 Camaro driving guy ownsand uses an eight-track player, the sentence is true even if he ownsother eight track players that aren’t used.^[25]

So it appears that Neale’s account has no explanation of why thepronouns in discourses like (25a) never have numberless readings.Neale’s account has similar problems with sentences like:

(41): Somewoman who owns a donkey beats it.

Here again, Neale’s theory predicts that this sentence has areading on which its truth requires that some woman beats every donkeyshe owns. And again, even if we imagine the sentence being utteredwithout any particular woman or donkey in mind, we don’t getthis reading of the sentence predicted by Neale’s theory, (saywe are discussing women’s tendencies towards animals they own,and one of us utters (41) simply thinking it is statistically likelyto be true). So Neale’s account has no explanation as to why thesecond sentence of discourse (25a) and sentence (41) lack the relevantreadings assigned to those sentences by his theory.^[26]

Elbourne (2005) proposes a different D-type theory. The main thesis ofthe book is that pronouns of all types, proper names, and definitedescriptions have a unified syntax and semantics: they are all of type\(\langle s, e\rangle\) (functions from situations to individuals) andare syntactically comprised of a definite determiner that takes twoarguments: an index and an NP (noun phrase).

His theory of unbound pronouns isNP-deletion theory.NP-deletion is when an NP at the level of syntax is (felicitously)unpronounced at the surface level as in:

(42): I likeBill’s wine, but Max’s is even better.

On Elbourne’s theory, pronouns undergoobligatoryNP-deletion. That is, a sentence like(25), at the level of syntax is actually (25b):

(25): If Sarah owns adonkey, she beats it.
(25b): If Sarah owns a donkey, she beats [it donkey].

Following Elbourne, we’ll suppress mention of the index, sinceit doesn’t do any work here (anaphoric pronouns have a nullindex on his view, though he does provide arguments for why this nullindex is present—see Elbourne (2005: 118–126)). Pronounshave the same semantics as the determiner “the”(abstracting away from the phi-features of pronouns) so that (25b) hasthe same semantics as (25c):

(25c): IfSarah owns a donkey, she beats the donkey.

This is motivated by the insight that pronouns pattern withminimal definite descriptions rather than long ones, as otherD-type theories have it. For example, a theory like Neale’spredicts that (43a) has the semantics of (43b):

(43a): A manmurdered Smith, but John does not believe that he murderedSmith.
(43b): A man murdered Smith, but John does not believe that the man whomurdered Smith murdered Smith.

But this is problematic, because (43a) clearly has a salient, truereading, whereas (43b) does not. However, Elbourne observes that (43c)has the same salient true reading as (43a):

(43c) A manmurdered Smith, but John does not believe that the man murderedSmith.

Treating pronouns as determiners is motivated more generally by Postal(1966)’s argumentsthat they at least sometimes have the same semantics as determinersbased on examples such as:

(44): Youtroops will embark but the other troops will remain.

Finally, positing an NP-deletion theory provides an elegant solutionto the problem of the formal link, which is that any good account ofanaphora has to explain why (45a) is felicitous but (46b) is not:

(45a): Everyman who has a wife is sitting next to her.
(46b): #Everymarried man is sitting next to her. (Heim 1982, 1990)

Since NP-deletion generally requires a linguistic antecedent, ifpronouns are determiners that have undergone NP-deletion, thisexplains the contrast.

As mentioned above, pronouns have the semantics of determiners.Specifically, Elbourne proposes a situation semantics (situations in natural language semantics), where the semantics of pronouns (and determiners) are treated in aFregean way, as follows:

\[[[\mbox{it}]]^g = \lambda_{\langle\langle s,e\rangle\langle s,t\rangle\rangle}. \lambda s: \exists!x(\lambda s'. x)(s) = 1. \iota x\ f(\lambda s'. x)(s)= 1\]

That is to say, pronouns come with presuppositions that there is aunique individual in each situation that satisfies the predicate, and(when that presupposition is satisfied), they refer to that individual(in that situation). Conditional donkey anaphora works as follows. Asentence like (47) has the structure at LF of (48):

(47): If a manowns a donkey, he beats it.
(48): [[always[if [[a man] [\(\lambda\)6 [[a donkey][ \(\lambda\)2 [t6 ownst2]]]]]]][[he man] beats [it donkey]]] (Elbourne 2005: 52)^[27]

The semantics of “always” is crucial to getting the truthconditions right:

\([[\mbox{always}]]^g = \lambda p_{\langle s,t\rangle}. \lambdaq_{\langle s,t\rangle}. \lambda s\). for every minimal situation\(s'\) such that \(s' \le s\) and \(p(s') = 1\), there is a situation\(s''\) such that \(s'' \le s\) and \(s''\) is a minimal situationsuch that \(s' \le s''\) and \(q(s'') = 1\)

Basically, “always” takes two sentences, and returns trueiff every minimal situation that satisfies the first sentence has aminimal extension that satisfies the second sentence. A minimalsituation is one that contains one or morethinparticulars—an individual abstracted away from itsproperties—and one or more properties or relations that the thinparticular(s) instantiate(s). An extension of a minimal situationincludes all those same particulars and properties and relations, with(possibly) some more particulars, properties, or relations inaddition. On Elbourne’s account “if” doesn’tplay any role in contributing to the truth conditions of a donkeyconditional; it is semantically vacuous. It is the (sometimes silent)adverb of quantification along with the semantics of the antecedentand consequent that do the work in yielding the truth conditions. Thefollowing are the truth conditions for (47) on Elbourne’saccount. (We won’t go through the derivation for relative clausedonkey anaphora, but it works similarly. See Elbourne 2005: 53.)

\(\lambda s_1\). For every minimal situation \(s_4\) such that
\(s_4 \le s_1\) and there isan individualy and a situation \(s_7\) such that \(s_7\) is aminimal situation such that \(s_7\le s_4\) andy is a man in\(s_7\), such that there is a situation \(s_9\) such that \(s_9\les_4\) and \(s_9\) is a minimal situation such that
\(s_7\le s_9\) andthere is an individualx and a situation \(s_2\) such that\(s_2\) is a minimal situation such that \(s_2\le s_9\) andxis a donkey in \(s_2\), such that there is a situation \(s_3\) suchthat \(s_3\le s_9\) and \(s_3\) is a minimal situation such that \(s_2\le s_3\) andy ownsx in \(s_3\),
there is a situation \(s_5\) such that
\(s_5\le s_1\) and \(s_5\) is a minimal situationsuch that \(s_4\le s_5\) and \(\iota x\ x\) is a man in \(s_5\) beats in \(s_5\) \(\iota x\ x\) is a donkey in \(s_5\). (2005: 52)

Thus on Elbourne’s account (47) is true iff each donkey-owningman beats every donkey he owns.

Elbourne surprisingly never goes through a derivation of a case ofcross-sentential anaphora as in:

(49): A womanwalked in. She sat down.

His view is that this has the same semantics as (49a):

(49a): Awoman walked in. The woman sat down.

But he doesn’t provide an account of how this works, neither indescription nor detailed derivation. One worry about this is that inthe conditional and relative clause donkey sentences, the fact thatthe pronoun(s) co-varies with its antecedent is accounted for by“always” and “every”. These expressionsquantify over situations in a way that guarantees that the man whobeats the donkey is the same man who owns that same donkey,effectively acting as (semantic) binding. But there is no suchmechanism in place to guarantee that “the woman” in (thesituation in) the second sentence of (49) in any sense co-varies withthe woman (in the situation) in the first. It is not clear howElbourne’s view can accomplish this without employing either adynamic notion of binding or a more traditional d-type account withcomplete descriptions.

However, Elbourne’s account doesn’t encounter the sameproblem as Neale’s in predicting numberless readings where thereare none, as he doesn’t posit a numberless interpretation of thepronoun at all. This highlights a difference between the way thatNeale’s theory approaches the truth conditions of conditionaldonkey sentences and the way DRT, dynamic semantics, the CDQ theory(discussed in the next section) and other D-type theories likeElbourne’s and Heim (1990)’s do (Heim 1990 also employs asituation semantics to account for conditional donkey anaphora). Inthese other theories, the requirement that all the donkey-owning menbeat all the donkeys they own for (47) to be true arises due to theinteraction of the semantic of indefinites, the semantics of anaphoricpronouns and the semantics of conditionals.^[28] Indeed, it is the latter that is primarily implicated in (47)’struth requiring thatall donkeys owned by donkey-owning menbe beaten (since the theories posit some sort of universalquantification in the semantics of conditionals). By contrast, onNeale’s view, the requirement that the men beat all the donkeysthey own for (47) to be true (on one of its readings) essentiallyfalls out of the semantics of the anaphoric pronoun alone, since onone of its readings, it expresses universal quantification overdonkeys Sarah owns (the numberless description reading).

One problem that D-type theories face is that pronouns come with a uniqueness requirement (either as a presupposition or part of the asserted content). But it has been observed that pronouns anaphoric on indefinites do not have a uniqueness requirement; it seems that the truth conditions for such sentences are existential. This observation is nicely captures by Discourse Representation Theory, File Change Semantics, dynamic semantics, and the Context Dependent Quantifier approach (discussed in the next section). For example, consider (49) again. This seems true even if many women walked into the contextually salient place at the contextually salient time, and regardless of whether they sat down or not, so long as at least one woman walked in and sat down. Mandelkern & Rothschild (2020) call this phenomenon "definiteness filtering" and Lewis (forthcoming) calls it "the problem of non-uniqueness". Both of the cited works argue that there is evidence of uniqueness requirements on definites more generally, and the non-uniqueness is specific to the kind of constructions in (49). Mandelkern & Rothschild tentatively propose a D-type theory that employs situation semantics, while Lewis (forthcoming) argues for a D-type theory that takes definite descriptions to be ambiguous between presupposing worldly uniqueness and discourse uniqueness.^[29]

Another problem that all D-type theories must address is the problem ofindistinguishable participants. Since on D-type theories,pronouns in one way or another have the semantics of definitedescriptions, they come with uniqueness presuppositions. When it comesto conditional donkey anaphora, the way to meet these uniquenesspresuppositions is by employing minimal situations—the definitedescription then picks out the unique object satisfying thedescription in the minimal situation. (With the exception ofNeale’s theory: since he employs numberless pronouns, thepronouns have no uniqueness presupposition.) Thus uniqueness issatisfied within the situation, even if it can’t be satisfied inthe larger world. But in examples of indistinguishable participants,uniqueness cannot even be satisfied within a minimal situation.Consider the typical example, (50):

(50): If abishop meets a bishop, he blesses him.

In the minimal situation that satisfies the antecedent, there aretwo bishops that have the same property (meeting anotherbishop). Thus descriptions like “the bishop” or“the bishop who meets a bishop” do not denote uniquely.DRT and dynamic theories don’t have any problem at all withthese examples because pronouns are treated as dynamically boundvariables, not definite descriptions, and each instance of “abishop” in the antecedent of (50) is associated with a differentvariable, which prescribe the anaphoric links to the two pronouns inthe consequent. For D-type solutions to this puzzle see Heim(1990),Ludlow (1994), Elbourne (2005, 2016), Lewis (forthcoming).

Finally, it should be mentioned that there are some who proposemixed approaches, wherein some pronouns are treated asdynamically bound variables whereas others are treated as D-type (seeChierchia 1995; Kurafuji 1998, 1999). On these views, some pronounsare ambiguous between the two readings, while others have only thedynamically bound variable or D-type reading. This type of theoryavoids many of the problems raised for each type of account, sincethey use dynamic semantics for the examples most amenable to a dynamicexplanation and d-type pronouns for example most amenable to that sortof explanation. However, the theory comes at a considerabletheoretical cost in that it predicts a systematic ambiguity inpronouns that is (arguably) not explicitly marked in any language.(See Elbourne 2005 for further criticisms of these views.)

3.4 The Context Dependent Quantifier Approach

The Context Dependent Quantifier, or CDQ, account of anaphora wassuggested in Wilson (1984) and subsequently developed in King (1987,1991, 1994).^[30] The idea underlying the application of CDQ to discourse anaphora isthat these expressions look like quantifier-like expressions ofgenerality, where the precise nature of the generality they express isdetermined by features of the linguistic context in which they occur.On the CDQ account, anaphoric pronouns with quantifier antecedents indiscourse anaphora are contextually sensitive devices ofquantification. That is, these anaphoric pronouns expressquantifications; andwhich quantifications theyexpress is partly a function of thelinguistic environmentsin which they are embedded. Consider the following discourses:

(51): A manfrom Sweden climbed Mt. Everest alone. He used no oxygen.
(52): Most students passed the exam. They didn’t get scores below70%.

Looking at (51), suppose that in fact at least one Swede has soloedMt. Everest without oxygen. Then it would seem that the sentences of(51) are true. If this is correct, then it appears that the secondsentence of (51) expresses a (existentially)general claim.CDQ claims that the pronoun “He” in the second sentence isitself a (existential) quantifier, and this explains why the secondsentence expresses a general claim: the generality is a result of thepresence of this quantifier in the sentence. Similar remarks apply to(52), (except that “They” expresses a universalquantifier). Further, consider the following example, which is similarto our example (18) above:

(53): A mankilled Alan last night. Michelle believes he used a knife to killhim.

The second sentence of this discourse appears to have two differentreadings. On one reading, it asserts that concerning the man whokilled Alan last night, Michelle believes ofthat very manthat he used a knife. This would be the case if, for example, Michelleknew the man who killed Alan, believed that he killed Alan and basedon his well-known fondness of knives, believed he used this sort ofweapon. But the second sentence has another reading on which itascribes to Michelle the general belief to the effect that a mankilled Alan with a knife last night. On this reading the sentencewould be true if e.g., on the basis of conversations with personnel atthe hospital and having no particular person in mind, Michellebelieved that a man fatally stabbed Alan last night.

Again, CDQ claims these facts are to be explained by holding that thepronoun in the second sentence is a quantifier. For then we shouldexpect that, like other quantifiers, it could take wide or narrowscope relative to “Michelle believes”. On the wide scopereading of the pronoun/quantifier, the second sentence attributes toMichelle a belief regarding a particular person. On the narrow scopereading, it attributes to Michelle a general belief.

Occurrences of “ordinary quantifiers”, such as“every man” have what we might call aforce, inthis case universal; what we might call arestriction, inthis case the set of men; andscope relative to otheroccurrences of quantifiers, verbs of propositional attitude, and soon. CDQ claims that the anaphoric pronouns in question also haveforces (universal, existential, etc.),restrictions(“domains over which they quantify”) andscopesrelative to each other, verbs of propositional attitude, etc. However,unlike “ordinary” quantifiers, these anaphoric pronounsqua quantifiers have their forces, restrictions and relative scopesdetermined by features of their linguistic environments. King (1994)lays out how the forces, restrictions and relative scopes of theseanaphoric pronouns are determined, and we shall not describe thosedetails here.

As to donkey anaphora, without going through the details, let me justsay that CDQ assigns to a relative clause donkey sentence such as(26) above (repeated here)

(26): Every woman whoowns a donkey beats it.

truth conditions according to which (26) is true iff every woman whoowns a donkey beats some donkey she owns (see King 2004 for detailsand discussion). Some think that the truth of (26) requires everywoman who owns a donkey to beatevery donkey she owns, and aswe saw, DRT, DPL, and the D-type theories discussed assign these truthconditions to (26) (though this is not an essential feature of DRT ordynamic semantic approaches more generally). The truth conditions CDQassigns to (26) correspond to what is often called theweakreading of donkey sentences (Chierchia (1995) calls this the\(\exists\)-reading) and the truth conditions the accounts discussed thus farcorrespond to thestrong reading of donkey sentences(Chierchia calls this the \(\forall\)-reading). There actually has been a debatein the literature as to which truth conditions sentences like (26)have. There are sentences that are exactly like (26) except for thedescriptive material in them that clearly seem to have (only) the weakreading. An example is:

(54): Everyperson who had a credit card paid his bill with it.

It seems clear that the truth of this sentence does not require everyperson with a credit card to pay his bill with each credit card hehas. We will discuss these matters further insection 4, but for now let us simply note that CDQ differs from the otheraccounts discussed on what truth conditions should be assigned tosentences like (26) and (54) and that it is simply unclear which truthconditions are the correct ones.

As for conditional donkey anaphora, the CDQ account is rathercomplicated and we are only able to provide the briefest outline ofthe account here (interested readers should consult King 2004). As wesaw above, a conditional donkey sentence such as(25)

(25): If Sarah owns adonkey, she beats it.

is true iff Sarah beats every donkey she owns. Thus, “adonkey” somehow seems to have ended up with universal force. TheCDQ account holds that this illusion of universal force for theindefinite is really the result of the interaction of the semantics ofthe conditional, the indefinite, understood as an existentialquantifier, and the CDQ “she”, understood as acontext dependent quantifier with existential force ranging overdonkeys Sarah owns. Roughly, the account goes as follows. Theantecedent of (25) is equivalent to

(25a): \((\exists x)(x\mbox{ is a donkey} \mathbin{\&} \mbox{Sarah owns }x)\)

Given the CDQ “it” and its context in (25), the consequentof (25) is equivalent to

(25b): \((\exists x)(x\mbox{ is a donkey} \mathbin{\&} \mbox{Sarah owns } x\mathbin{\&} \mbox{Sarah beats } x)\)

The semantics of the conditional involves universal quantificationover minimal situations. In particular, a conditional claims that forevery minimal situation \(s_1\) in which its antecedent is true, thereis a situation \(s_2\) that \(s_1\) is part of in which its consequentis true. In the case of (25), a minimal situation in which theantecedent is true consists of Sarah and a single donkey she owns. Thefinal element here is that the definiteness and/or anaphoricness ofthe CDQ “it” in the consequent of (25) makes a differenceto its truth conditions. The definiteness and anaphoricness of“it” in (25) induces a sort of “familiarity effect”.^[31] In particular, for any (minimal) \(s_1\) in which the antecedent istrue, there must be an \(s_2\) that \(s_1\) is part of in which theconsequent (understood as expressing the claim that Sarah beats adonkey she owns) is true. Butin addition, because of the“familiarity” condition induced by the anaphoric definite“it”, there must be a donkey in \(s_2\) that is also in\(s_1\) and that makes the consequent true. In other words,familiarity requires that a donkey that makes the CDQ-containingconsequent true in \(s_2\) also be present in \(s_1\). In this sense,the donkey is “familiar”, having been introduced by theantecedent and the situation \(s_1\) in which it is true. To see whatthis means, consider a situation \(s_1\) that is a minimal situationin which the antecedent is true. \(s_1\) consists of Sarah owning asingle donkey. If e.g., Sarah owns ten donkeys, there are ten suchminimal situations. For (25) to be true, each such \(s_1\) must bepart of a situation \(s_2\) such that \(s_2\) is a situation in whichSarah beats a donkey that she owns and that is in \(s_1\). Now theonly way that every minimal \(s_1\) in which Sarah owns a donkey canbe part of an \(s_2\) in which Sarah beats a donkey she owns in\(s_1\) is if Sarah beats every donkey she owns. Thus, the CDQ accountclaims that (25) is true iff Sarah beats every donkey she owns.

Turning now to difficulties with CDQ, a main difficulty is that itisn’t clear whether the use of the notion offamiliarity in the account of conditional donkey sentencescan be ultimately upheld. Recall that the idea was that because“it” is a definite NP, and because definite NPs generallyare thought to involve some sort of familiarity, the pronoun in thedonkey conditional induces a sort of familiarity effect. There arereally two distinct problems here. One is that though the pronoun“it” is “syntactically” definite in that thepronoun “it” is thought to be a definite NP, according toCDQ it is “semantically” indefinite in (25), since itexpresses an existential quantification (over donkeys owned by Sarah).But then if “it” really is semantically indefinite in(25), why should it induce familiarity effects at all? (Jason Stanley(p.c.) raised this difficulty). One might reply that it is the factthat “it” is “syntactically” definite thattriggers the familiarity effects CDQ posits. But familiarity probablyis not well enough understood to allow us to assess this response. Asecond, and perhaps more pressing, difficulty is this. Generally,familiarity has something to do with whether what an expression isbeing used to talk about is familiar or salient to the audience beingaddressed. This is vague, of course, but the idea is that if one says“The dog is hungry” to an audience who isn’t evenaware of any dog that is around or relevant to the conversation, theremark is somewhat infelicitous. That is because the definite NP“The dog” was used to talk about something not familiar tothe audience. Now the question is: is it plausible to claim that thisand related phenomena are related to the rather complex effect CDQclaims is induced by the anaphoricness/definiteness of“it” in donkey conditionals? In the latter case, CDQclaims the effect of familiarity is to make the CDQ “it”in the consequent of donkey conditionals quantify over donkeys in theminimal situations introduced by the antecedents of the conditionals(in the case of (25), situations consisting of Sarah and a singledonkey she owns). The CDQ can only quantify over“familiar” donkeys—those introduced by theantecedent. One may well wonder whether the effect CDQ posits here canreally be seen to be a manifestation of phenomena that havetraditionally been explained in terms of familiarity.

4. How Many Readings Do Donkey Sentences Have?

We have already mentioned that there is some disagreement regardingthe truth conditions of sentences like

(26): Every woman whoowns a donkey beats it.

Some think that the truth of (26) requires every woman who owns adonkey to beatevery donkey she owns. As mentioned above,this is called thestrong reading of a donkey sentence.Others think that the truth of (26) requires that every donkey owningwoman beatssome donkey she owns. As above, this is theweak reading of (26). As we mentioned above, there aresentences that are exactly like (26) except for the descriptivematerial in them that clearly seem to have (only) the weak reading.The example we gave was:

(54): Every person whohad a credit card paid his bill with it.

It seems clear that the truth of this sentence does not require everyperson with a credit card to pay his bill with each credit card hehas, but merely with some credit card he has. Our comments to thispoint have suggested that the debate with respect to (26)/(54) andweak vs. strong readings is over which one of the two sets of truthconditions (26)/(54) have. Each of the theories discussed in thisentry only assignone of the existential or universal truthconditions to relative clause donkey sentences (though this may bemore of an artifact of the specific implementations of the theoriesthan the theories themselves).

But some think that (at least some) donkey sentences haveboth weak and strong readings. Chierchia (1994) and Kanazawa(1994b) are examples. In their favor, for a given determiner, one canfind pairs of relative clause donkey sentences fronted by thatdeterminer such that one has the existential truth conditions (on itsmost natural interpretation) and the other has the universal truthconditions (on its most natural reading). For example, consider thefollowing pairs:

(55)

Weak Readings:

a.: Every person who had acredit card paid his bill with it.
b.: Most women who have a dime will put it in the meter.
c.: No man with a teenage son lets him drive the car on the weekend.

(56)

Strong Readings:

a.: Every student whoborrowed a book from Peter eventually returned it.
b.: Most parents who have a teenage son allow him to go out on theweekend.
c.: No man with an umbrella leaves it home on a day likethis.

Elbourne, for example, explicitly addresses this issue, since hissemantics captures only the strong reading. He claims that while thismay present a problem for his semantics, it is not a problem forNP-deletion theory more generally, since replacing the pronoun in atypical weak reading example with a minimal definite description alsoyields a weak reading, e.g.:

(57): Everyonewho has a dime put the dime in the meter. (Elbourne 2005:84)

However, he doesn’t present an account of how this reading mightbe captured.

These examples and others suggest that whether a given relative clausedonkey sentence appears to favor the strong reading or weak reading isinfluenced by a variety of factors, including the monotonicityproperties of the determiner on the wide scope quantifier, the lexicalsemantics of the predicates occurring in the sentence, and generalbackground assumptions concerning the situations in which we are toconsider the truth or falsity of the sentences. However, it is veryhard to find significant generalizations regarding under whatconditions a given reading is favored.^[32] Further, it is very hard to find sentences that clearly allow both astrong and a weak reading.^[33] This makes the view that the sentencesactually possess both readings as a matter of their semantics at leastsomewhat suspect. If they really do possess both readings, why is itso hard to find sentences that clearly allow both readings? Andfinally, relative clause donkey sentences fronted by the determiner“some” seem always to only have the existential truthconditions:

(58): Somewomen who own a donkey beat it.

Obviously, the facts here are quite complicated.

Brasoveanu (2006, 2007, 2008) points out that there are alsomixed readings of donkey sentences, such as:

(59): Everyperson who buys a book on amazon.com and has a credit card uses it topay for it.

Sentence (59) intuitively is true iff forevery book that acredit-card owner buys on amazon.com, there issome creditcard or other that she uses to pay for the book. Hence the mixedstrong and weak reading. Brasoveanu accounts for these readings, alongwith the weak/strong ambiguity in general, within his system of PluralCompositional Discourse Representation Theory (PCDRT) by positing anambiguity at the level of indefinites. In his account, indefinites areunderspecified as to the presence of a maximization operator (which ispresent in the strong indefinite but not the weak); the decision ofwhich indefinite to use in a specific case is a “context-drivenonline process”.

Theories that assign both sets of truth conditions to relative clausedonkey sentences generally do so by positing some sort of ambiguity,either in the quantifiers, the pronouns, or the indefinites.^[34] Though the matter isn’t entirely clear, it seems plausible thatthe theories discussed in this entry also may be able to assign boththe universal and the existential truth conditions to relative clausedonkey sentences by positing some sort of ambiguity. These mattersrequire further investigation.^[35]

A recent theory that does not rely on any ambiguity is presented in Champollion, Bumford & Henderson (2019). Champollion et al. argue for a trivalent semantics that allows for truth-value gaps for donkey sentences, along with a pragmatic theory that both fills in the gaps and predicts when hearers get a strong or weak interpretation. This explains the different readings of donkey sentences in terms of underspecification rather than ambiguity. The (dynamic) semantics delivers that a sentence like (26) is true iff every female donkey-owner beats every donkey she owns, false if at least one female donkey-owner does not beat any donkey she owns, and otherwise neither true nor false. Relying on Križ (2016)'s framework for plural definites, speakers can use a sentence to address the question under discussion (QUD) that is true enough at a world w even if it lacks a truth value at w, so long as it is not false at any world equivalent to w. If the QUD is such that it requires that every female donkey-owner beat every donkey she owns, then worlds in which (say) some female donkey-owners who own multiple donkeys only beat one of their donkeys will be equivalent to worlds in which some female donkey owners do not beat any of their donkeys. However, if the QUD is such that it requires that every female donkey-owner beat some donkey she owns, such worlds will be equivalent for conversational purposes to worlds in which each female donkey-owner beats all the donkeys she owns, and thus speakers will judge the weak reading true in this scenario.

5. Anaphora in Sign Language

Another recent development in the study of anaphora comes from aseries of papers by Philippe Schlenker on anaphora in sign language,particularly ASL (American Sign Language) and LSF (French SignLanguage) (2010, 2011, 2012a,b, 2013a,b, 2014, 2015). In signlanguage, an antecedent is associated with a particular position insigning space called alocus, and an anaphoric link to theantecedent is obtained by pointing at that same locus. Unlike spokenlanguages, which have a limited number of lexically encoded pronouns,in sign language there seems to be no upper bound on how many loci cansimultaneously be used, aside from limitations of performance (sincesigners have to remember what the loci are assigned to, and be able todistinguish one from another). Schlenker (2015) gives an example of ashort discourse that involves 7 distinct loci. Given their unboundednumber and their overt connection to antecedents, Schlenker (as wellas others) posits that they are the overt realization of formalindices, i.e., the variables that mark anaphoric connections intheories like DRT and dynamic semantics. Despite their differences,sign language and spoken language pronouns have enough in common thata uniform theory is desirable, and Schlenker argues that sign languageprovides evidence applicable to at least two debates in the anaphoraliterature. First, there is good evidence that in sign language, thereis a single system of anaphora using loci for denoting individuals,times, and worlds. This provides evidence in favor of those who thinkthat there are temporal and modal variables and pronouns in spokenlanguage. Second, Schlenker argues that the use of loci, which looklike an overt use of indices, very much resembles the dynamic semanticaccount of pronominal anaphora since antecedents introduce variables(loci) and anaphoric connections are made by repeating the samevariables (loci). Just as in spoken language, this occurs even whenthe anaphoric pronouns are outside the syntactic scope of theirantecedents. Furthermore, according to Schlenker one of the mostdecisive examples is the bishop example(50), repeated here:

(50): If a bishop meetsa bishop, he blesses him.

In sign language, the only way to obtain the intended reading of thesentence is for the pronouns to index different antecedents. Thisshows that a theory need not only get the truth conditions right (assome D-type theories can), but must account for the formal linkbetween each antecedent and pronoun. For criticism of the thesis thatloci are overt variables see Kuhn (2016).

The second major conclusion from Schlenker’s research is thatsign language pronouns have aniconic element. For example,the verb “ask” is signed near the chin/neck area of alocus. If the locus denotes a personstanding on a branch,“ask” is signed at a fairly high spot in the locus. If thelocus denotes a personhanging upside-down from a branch,“ask” is signed lower in the locus. This and many otherexamples of iconicity in pronouns provides evidence that there needsto be an account of iconicity integrated into the formalsemantics.

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Parsons, Terence, 1978, “Pronouns as Paraphrases”,unpublished ms., Philosophy Department, UCLA. [Parsons 1978 available online]

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