Abstract
Both definite descriptions and pronouns are often anaphoric; that is, part of their interpretation in context depends on prior linguistic material in the discourse. For example: (1) A student walked in. The student sat down. (2) A student walked in. She sat down. One popular view of anaphoric pronouns, the d-type view, is that pronouns like ‘she’ go proxy for definite descriptions like ‘the student who walked in’, which are in turn treated in a classical (neo-) Russellian or (neo-) Fregean fashion. I argue for a novel version of the d-type view in which anaphoric definites are restricted existential quantifiers that presuppose discourse uniqueness, which is uniqueness of discourse referent in the context, rather than uniqueness of object in the world. In other words, the anaphoric definites ‘the student’ and ‘she’ in (1) and (2) presuppose that there is a single object under discussion that is a student who walked in. I further argue that, by contrast, non-anaphoric definites are restricted existential quantifiers that presuppose worldly uniqueness, that is, that there is a unique object in the world that satisfies the descriptive information. The semantics for anaphoric and non-anaphoric definites accounts for the differences in truth conditions in discourses involving the two different types of definites, improving on existing accounts. It is further supported by crosslinguistic data. The semantics is formally implemented in a static system employing quantifier domain restriction in the style of Stanley and Szabo (Mind Lang 15(2–3):219–261, 2000) and extended to account for bridging definites and donkey sentences.
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Notes
I will treat indefinites in the classical way—as existential quantifiers. An anonymous reviewer suggested that if indefinites are treated as singleton indefinites, i.e., existential quantifiers whose domain is restricted to a single object, pronouns could be treated referentially while maintaining that indefinites are not referential terms. I do not think it is plausible for all indefinites that license anaphoric pronouns to be treated as singleton indefinites because this gets the truth conditions wrong, and because there are in general insufficient contextual grounds for determining a singleton extension. These are the similar to the considerations I raise against traditional d-type theory’s treatment of pronouns in Sects. 2.1.2 and 2.1.3 below.
I’m following Neale (1990) in this terminology. It is also often called e-type theory.
Though it does feature in, for example, Evans (1977) and Neale (1990), it is entirely absent from Heim (1990) and the most well-developed recent view, that of Elbourne (2005), which does not contain a single example of this sort of discourse anaphora (nor is there one in his book on descriptions, Elbourne 2013).
I use “anaphoric definites” as a term that includes both anaphoric pronouns and anaphoric definite descriptions.
This is one problem with the context dependent quantifier (CDQ) view defended by King (1991, 1994, 2004). King treats pronouns as going proxy for quantifiers; exactly which quantifier is context-dependent. This is all well motivated, but the same truth-conditional considerations that motivates the treatment of pronouns anaphoric on indefinite antecedents as themselves indefinite motivates thinking of anaphoric definite descriptions as having indefinite truth conditions. But I don’t think there are good reasons to treat definite descriptions as context dependent quantifiers. So King needs a different treatment of two things that appear to be very similar phenomena.
Some might protest that ‘the student’ sounds odd here. This is not due to uniqueness restrictions, but rather the oddity of using the full definite where one is not required. To see this, note the felicity of the following:
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a. A student and a professor came to Fred’s office. b. The student asked questions about the upcoming assignment while the professor took notes. c. The student was one of many students to come to his office that day, but the professor was the only professor to come.
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Continuations (c’) and (c”’) are evidence against any kind of homogeneity requirement for multiple witnesses for an anaphoric definite.
Of course, sometimes the descriptions will happen to be complete, e.g. (6) in a context in which only one student came to Fred’s office hours (on the day in question). Or, e.g. if context makes it clear that I’m talking about Fred’s Introduction to Philosophy students and only one Intro student came to Fred’s office hours that day. My claim is just that this is not universally or even standardly true of such discourses.
I am making no claims here about logical form, just truth conditions. The d-type description might be “the student who came in during Fred’s office hours who the speaker had in mind just now”, “the student x... s.t. x = Elissa”, restricted to a situation in which Elissa is the only student, or something else.
Kadmon’s (2001) uniqueness requirement is a unique individual or uniquely identifying property that doesn’t have to be available to the hearer, so the comparison with quantifier domain restriction and demonstratives would not be an apt one on her view. However, this raises the question why the restrictor on anaphoric definite descriptions works so differently from these other kinds of context-sensitivity. Furthermore, Roberts (2003) makes the point that such a uniqueness criterion is too weak:
For any object I could imagine and intend to refer to by uttering some definite description, there seems to be some (possibly complex) unmentioned property of it that I could have in mind which would make the NP semantically unique relative to my private information, but which, because it was not mentioned, would not be in the common ground of the interlocutors in the conversation. If this is adequate to satisfy the uniqueness condition, then the condition seems too easy to satisfy, leaving it unclear how any examples could be infelicitous because of a failure of uniqueness. (pp. 293–294)
Heim (1982, p. 28) raises a related worry (the complementary one) about whether there is actually the contrast d-type theory predicts between anaphoric and existential sentences like (12) and (13)
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A wine glass broke last night. It/the glass that broke had been very expensive.
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A wine glass which had been very expensive broke last night.
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Mandelkern and Rothschild (2020) discuss this kind of contrast extensively, showing that time and again, the presence of an indefinite as an antecedent to an anaphoric definite results in there being no uniqueness requirement on the definite, whereas in cases that lack an antecedent, as in (11), there is a uniqueness requirement. They call this phenomenon definiteness filtering. One way they argue for it, which makes a similar point to mine here, if that examples like (10) are fine if the context explicitly sets up that there are (possibly) many students who came to Fred’s office hours but examples like (11) are not.
Propositions are evaluated relative to Austinian topic situations, that is, the situation that is of concern in the discourse. This doesn’t really matter for our purposes, and we could very well think of p and q as being evaluated relative to a whole world (in fact, sometimes the actual world is the topic situation).
Some (but not all) problems with a simpler definition could potentially be avoided if a persistence condition (for everything but anaphoric definites) was built into the theory, that is, that propositions true in a situation s are also true in all larger situations that contain s. See Zweig (2006) for an interesting examination of the complications inherent in persistence, situation semantics, and donkey sentences.
This is not the same as, but perhaps related to, Mandelkern and Rothschild’s own worry that this mechanism for definiteness filtering (as they call it) is completely distinct from any general method of presupposition filtering. So again, it requires its own mechanism and is not independently motivated.
Mandelkern and Rothschild see this as the most serious challenge to the proposal. They do not consider the possibility of treating discourses as consisting of a series of conjunctions.
It satisfies the two generally agreed upon constraints on accommodation, as noted by Roberts (2003), retrievability (the hearer has to be able to easily infer the accommodated material) and plausibility (the accommodated material is unobjectionable).
See also Coppock and Beaver (2015, p. 393), in addition to the sources cited below.
For Roberts, definite descriptions presuppose weak familiarity (that the existence of the object has to be entailed by the context) and informational uniqueness (that there is a unique discourse referent among both the strongly and weakly familiar ones that is contextually entailed to satisfy the description). The Gricean explanation is given for definites where both weak familiarity and informational uniqueness fail.
Roberts deals with 3 different cases of strong uniqueness effects: titles and directions, those in which weak familiarity is satisfied (but strong familiarity fails), and those in which weak familiarity fails. The Gricean explanation just applies to the last case, but I take it to cover most of the non-anaphoric cases. In cases of bridging definites and other weakly familiar definites, worldly uniqueness is implicated because if it is well known that there are multiple objects that satisfy the descriptive material, informational uniqueness automatically fails. I think bridging definites are more complicated than this, and deal with them in Sect. 4.2 below. In any case, I find it difficult to accept both that Gricean considerations lead to robust worldly uniqueness implicatures in the cases described above and that cases in which weak familiarity but not informational uniqueness is satisfied are so robustly infelicitous. Gricean cooperativity and quantity considerations in particular would lead one to expect that informational uniqueness could be accommodated, i.e., hearers could accommodate that there is some distinguished witness among the possible witnesses for the description. Roberts explains the titles and directions cases epistemically: they involve definite descriptions that are meant to be employed in a variety of environments in which hearers may have a lot of information. So the only way to ensure informational uniqueness is to have worldly uniqueness. I have nothing to say against this.
Thanks to an anonymous reviewer who suggested this version of the sage plant sentence as more problematic for my view than Heim’s original one.
There are two other technicalities I am glossing over here which will become clear in Sect. 4.3. One is that one of the theories I propose for quantified sentences like (25) involves situation semantics, and like in classical d-type treatments, quantifiers then quantify over individual/minimal situation pairs, which solves the uniqueness problem for examples like (25) (following Heim 1990). This doesn’t directly help with bishop sentences though. The second is that I employ quantification over minimal situations for conditional donkey sentences like (26) in all versions of my theory of conditional donkey sentences. Uniqueness of referents and discourse referents is relative to minimal situations.
Examples from Elbourne (2005). His judgments are that these are ungrammatical, not infelicitous. I do not share the ungrammaticality judgments, for reasons that will soon become clear.
Thanks to an anonymous reviewer for pressing me on this point.
Elbourne (2009) also makes this point. Chapter 9 of Barker and Shan (2014) addresses Elbourne (2009) but doesn’t say anything further about why (27) should be pragmatically unresolvable but (26) perfectly fine. One might argue that there is a preference for syntactic parallelism and so this is some indication of how the pronouns are to be resolved. Still, there is no strong parallelism requirement in these constructions, as indicated by the perfect felicity of examples like:
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If a woman is friendly to a man, he asks for her number.
This stands in contrast to some other constructions, such as Kehler (2001)’s (33):
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#Margaret Thatcher admires Ronald Reagan and George W. Bush absolutely worships her.
(33) is generally judged to be bad despite strong pragmatic reasons for taking ‘her’ to refer to Margaret Thatcher. The point is, even if there is a preference for parallelism, both interpretations (i.e. ‘he’ and ‘him’ each picking out the subject or the object) are easily accessible. It’s not clear the parallelism preference is strong enough for there to be a default interpretation that privileges it completely out of the blue.
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In a small informal survey, the sentences in (34) were judged to be infelicitous by those surveyed, and follow-up questions indicated there was no preference for resolving the anaphora according to syntactic parallelism.
Of course, they are not strictly speaking exactly the same in their dynamic effect, as one will update one discourse referent and the second the other, but since discourse referent indices are arbitrarily assigned, this doesn’t actually affect the discourse information being tracked.
Elbourne (2013) also suggests that Ludlow’s theory can explain the contrasting data, though Elbourne (2005, 2013, 2016) argue for a different d-type solution to the problem of indistinguishable participants. Elbourne derives a distinguished and undistinguished bishop by a syntactically derived situation structure. I have nothing to say against Elbourne’s solution here.
See Chomsky (1981).
Or proto-agent and proto-patient, or meeter and meetee, or whatever the right way of thinking of these roles turns out ot be.
I think a similar thing is going on in the sage plant sentence. Of course, there is no natural way to describe one sage plant as the agent and another as the patient, but their roles are similarly syntactically distinguished in a way that matters for what is communicated: there is the first “primary” sage plant bought and then the “secondary” one bought along with it. Compare:
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a. Everyone who invited a friend to come invited another friend along with her.
b. Everyone invited two friends to come.
If someone said (38a) to me, I’d want to know which friends were the afterthoughts.
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In many languages (unlike English) definite articles co-occur with demonstratives.
For a detailed discussion of the German and Fering data, see Schwarz (2009).
Gray (2017) argues that an ambiguity view of definite descriptions along anaphoric/non-anaphoric lines solves a problem for the predicativist theory of names. He argues that the unpronounced definite determiner that is present in bare uses of names according to the-predicativists is marked as non-anaphoric.
See Abbott (2008), Hawthorne and Manley (2012), Ludlow and Segal (2004), Szabo (2000) for some defenses of existential treatments of definites. Hawthorne and Manley defend an existentialist semantics given very different sorts of considerations than the ones that occupy the current paper. They argue that it is a natural and elegant position to hold once one gives up a strong acquaintance requirement, which is what they do. I take it to be some further support for the present proposal that similar ones are motivated on independent grounds.
An anonymous reviewer for this journal suggested that a neo-Fregean account could be implemented if I included identity with a particular discourse referent in the semantics of definites at LF. E.g., suppose an indefinite ‘a student’ introduces a discourse referent 1 into the context, then ‘the student’ could be treated along the lines of ‘[the x: (student, identical to 1) x]’, which is then treated in a neo-Fregean way such that it refers to the unique individual that is a student and identical to 1, since for any particular assignment function g in the context, only one individual is identical to g(1). This suggestion is not so straightforward to implement. The problem is that context doesn’t provide us with a particular assignment function for the discourse referent. So although for any particular assignment function we get a referent, since we don’t have a particular assignment function, what we do in fact get is a function from assignment function to referents. I suppose this is all well and fine if we want to treat propositions as functions from world/assignment pairs to truth values, and then define truth in a context as true at all possible assignment functions, but this seems to make adopting a d-type theory pointless. If we are happy with this kind of result, then we could just treat pronouns as free variables. We would then have open propositions that would be true if they were true relative to all possible assignment functions in the context. In any case, as I will argue, the account I adopt below does not require a novel view of what propositions are or an unusual definition of truth.
The proposed semantics can be extended quite naturally to plural definite descriptions if we employ plural quantification and take the uniqueness presupposition to be about a maximal plurality rather than a single individual.
This is not to say it couldn’t be implemented as a dynamic semantics—I see no obstacle to doing so.
I am suppressing a treatment of tense here as well as contextual restriction to a particular time for the sake of simplicity, but the discourse referent will actually contain a property like came to Fred’s office hours on March 20, 2018.
I follow Hawthorne and Manley (2012) in this simplification for presentational purposes.
Including the pseudo-singular restrictor would make discourse uniqueness trivial, since by definition there is only one discourse referent identical to 1.
A complete theory of context tracks more than just discourse referents. Minimally, it also tracks the common ground, but perhaps also the questions under discussion, domain goals, and other things.
See also the Appendix of Lewis (2021).
In the intensional version, the model also contains W, the set of all worlds. The interpretation function assigns a predicate to a set of pairs where the first element is a w \(\in \) W and the second is a member or n-tuple of members of D\(_e\), as applicable.
In an intensional version of the theory, the context also contains CG, the common ground, modeled as a context set. While it will not play a role in the explanation that follows, it is relevant to the bigger picture of update with discourse referents and a full theory of what makes a discourse referent accessible. A necessary (but not sufficient) condition on accessibility is that the discourse referent is satisfied in every world in the context set. And of course it is necessary to model how the context tracks informational content. Furthermore, on the intensional version, instead of G, there is WG, the set of all possible pairs \(\langle w, g \rangle \), where w \(\in \) W and g is one of the possible assignment functions for the elements of DR in w. Note that w are the elements of W and not restricted to CG. This is because the information G encodes are the properties associated with the discourse referents; this has nothing to do with which worlds are still considered open according to the conversation. Of course, if certain assignments to individuals are only associated with worlds that have been eliminated from the CG, they won’t be live possibilities as witnesses for the discourse referent. But that doesn’t matter because the set of pairs \(\langle w, g \rangle \) is not supposed to track live possibilities (that is the job of the CG). It is supposed to track properties that are associated with discourse referents. Keeping these separate is helpful in maintaining the ordinary notion of truth at a world in the system. E.g. Sentences will still have truth values relative to worlds which have been eliminated from the CG. This is particularly helpful if the actual world has been eliminated from the CG, which in practice, it often is.
Technically, they don’t have to be treated separately. But I find it more perspicuous to do so.
Deictic pronouns are treated as non-anaphoric pronouns with singular restrictors. Deictic pronouns are not the only non-anaphoric pronouns on my view. Bound pronouns (see footnote 74), and possibly donkey pronouns (see Sect. 4.3), are also treated with the non-anaphoric clause. Some non-deictic discourse pronouns are also so treated (see for example the discussion in Sect. 5.2 below).
An anonymous reviewer raised an example that is problematic for a view that accepts that a definite description is always licensed when a pronoun is, even if the reverse does not hold.
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A student came to Fred’s office hours. She asked for a higher grade. In fact many students came to Fred’s office hours. But she/ ??the student was the only one to ask for a higher grade.
Here the pronoun is felicitous but the overt anaphoric definite less so. I think this shows that we do need to take word choice—following Grice’s Maxim of Manner—into consideration when judging for felicity. Using an overt anaphoric definite is already dispreferred to using a pronoun when one is possible. Not only do we here have an overt definite where a pronoun is possible, but it follows the use of a pronoun to pick up on the intended antecedent, as well as intervening information about other students, which makes the descriptive information associated with the definite not only superfluous, but downright confusing. I do think the example is much improved, if not perfectly fine, with ‘the student’ replacing the initial ‘she’.
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The informal theory presented in the previous section could be implemented in a multitude of ways. However, this is not to say nothing rests on this choice; certainly much of the way I work out the theory rests on the formal choices made, though it is beyond the scope of the present paper to argue for all of them.
Though Stanley and Szabo do not discuss this, there is no reason to think that the variable has to be limited to a function that takes only one individual variable. In principle, it can take as many individual variables as it requires (i.e. as need to be bound). Von Fintel (1994, [31]), who has a similar quantifier domain restriction theory to that of Stanley and Szabo, defines the QDR variable as taking an indefinite number of variables. Cooper (1979, pp. 78–79) whose paycheck pronouns have the same structure as QDR variables also defines them as taking as many individual variables as necessary.
In an intensional theory, these are properties, i.e. functions from worlds to sets.
For example, consider the sentence ‘every student got an A’ in a particular context of use. We can represent this using the notation of generalized quantifier theory as [every x: \(\langle \)student, f(i)\(\rangle \) x] (x got an A). In a particular context, f might be the function from classes to their participants, and the value for i might be Fred’s Introduction to Philosophy Fall 2018 course. Hence, f(i) yields the set of all the participants in Fred’s Intro course from Fall 2018 (perhaps including auditors, TAs), and intersecting that with the set of students, we get the students in Fred’s Introduction to Philosophy Fall 2018 course as the restrictor. Thus we get the restricted universal claim that every student in Fred’s Introduction to Philosophy Fall 2018 course got an A.
On the other hand, Jacobson (2014, p. 378) posits that all hidden variables can have this kind of complex form, which she calls the paycheck generalization.
I.e. ‘the x: \(\langle \emptyset \), f(1)\(\rangle \) x’.
Again, in our extensional version, this is equivalent to a set of individuals. In the intensional version this would yield a property, or a function from worlds to sets of individuals.
In an intensional version we would of course include reference to a world.
The part of the context I have described here, DR and G, only goes so far in determining the content, because it determines the content of anaphoric definites once they have been resolved to a particular discourse referent, but it does not explain how salient QDR functions are contextually determined, or how the contextual assignment function h gets determined. The present theory is compatible with many possible answers to this question. One such possible answer is that it is determined by the common ground.
Compare this to a case of a gradable adjective like ‘tall’. The general statement of truth for such a sentence might be ‘John is tall’ is true relative to a context c and model M iff John has greater height according to M than the c-determined standard for ‘tall’. A context determines the value for the standard for tallness and the LF in context is something equivalent to tall(John) \(\ge \) 6ft, which is true or false relative to a model in a straightforward way.
Since the theory of anaphoric definites crucially employs discourse referents, it can account for the data from sign languages like American Sign Language (ASL) and French Sign Language (LSF). In ASL and LSF, anaphoric connection works by setting up a locus in the signing space the first time an object is introduced. Anaphoric links are achieved by pointing subsequently to the same locus. Schlenker (2010, 2011, 2013, 2015) has argued that this is evidence for needing indices or discourse referents in a correct semantics of anaphora, since loci are overt realizations of indices. On the present view, discourse referents are not ordinary indices in the semantics, but the loci of sign language can be construed as an overt realization of the quantifier domain restriction (where the discourse referents do appear at LF) or the pseudo-singular restrictors.
Thank you to Shane Steinert-Threlkeld for suggesting this idea.
That is, the pronoun is not in the syntactic scope of its antecedent.
We also find cases of bound QDR variables in pronouns in the form of ordinary in-scope binding. In the case of in-scope binding, the non-anaphoric definition for the pronoun is typically in play, as discourse referents play no role. The higher quantifier binds the individual QDR variable and the QDR function is the identity function.
The theory of adverbs of quantification that does not mesh well with this account, however, is treating them as unselective quantifiers, as first suggested by Lewis (1975). DRT theories of donkey anaphora employ this account of adverbs of quantification.
Or is it? I must admit I am of two minds here. I am attracted to a modest situation semantics, in which most sentences deal only in maximal situations, i.e. worlds, while only operators that so to speak “look inside” worlds, such as adverbs of quantification, actually require smaller situations as part of their semantics (and thus require situation variables at LF). On this type of view, to think that quantifiers require smaller situations would require evidence that they look inside worlds. Elbourne (2001) argues in favor of a modest situation semantics, as well as arguing that quantifiers sometimes, but do not always, quantify over situations. I will not evaluate these arguments here.
This is the kind of pragmatic contribution that King and Stanley (2005) call weak pragmatics.
For some recent empirical work demonstrating that particularized quantity implicatures are calculated incrementally rather than at the end of the sentence, see Breheny et al. (2013). There are relevant parallels between the sort of quantity implicatures tested in the experiment and my preferred account of the introduction of discourse referents; both are involve quantity reasoning based on alternatives determined by a Hirschberg set (see Hirschberg 1985). See Lewis (2021) for more about my preferred account.
There is a problem here in the extensional version of the view. Since farmers with multiple donkeys appear in more than one situation, there is more than one discourse referent with exactly the same possible witnesses. For example, if situation 1 contains Alex and Dobbin and situation 2 contains Alex and Eeyore, then we also have 2 distinct discourse referents in the (subordinate) context that have Alex as their only possible witness and discourse uniqueness is not satisfied. But this is just an artifact of the extensional system. The discourse referents associated with farmers in situations 1 and 2 have different properties associated with them, and the possible witnesses will differ across worlds (e.g. consider a world in which Alex has only one donkey).
If one preferred that the term minimal situation be defined in a way that larger situations could never count, we could alternatively define adverbs of quantification as quantifying over relevant situations, where what situations are relevant is context dependent.
For example, (42) seems to be a case of the anaphoric definite in a donkey construction in German. But this is just one example. More extensive cross-linguistic data would have to be examined.
Technically, the situation containing Greg, the property of being the agent of the meeting, Howie, the property of being the patient of the meeting, and the meeting relation.
They are:
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a.
The antecedent determiner must be existential in force.
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b.
The antecedent-containing sentence must be affirmatively embedded relative to the minimal sentence that contains the pronoun.
The definition of affirmative embedding is a little hard to apply here, because 1) Evans is only thinking about sentences rather than discourses when he defines affirmative embedding and 2) he is thinking of pronouns as referring expressions, the reference being fixed by a definite description. The definition is as follows: Let \(\Sigma \)(\(\sigma \),\(\sigma \) \('\)) be a sentence embedding an existential sentence, \(\sigma \), and a sentence \(\sigma \) \('\) that contains a pronoun anaphoric on the indefinite in \(\sigma \). \(\sigma \) is affirmatively embedded in \(\Sigma \) relative to \(\sigma \) \('\) iff when the truth of \(\Sigma \) turns on the truth or falsity of \(\sigma \) \('\), \(\sigma \) is true. Intuitively, the idea is that whenever a sentence’s truth turns on the truth or falsity of the pronominal sentence, there is something that the pronoun refers to. We can extend this idea to discourses by thinking of the discourses as the conjunction of the sentences within them, and we could tweak the definition to better suit d-type theories so that the requirement is that there is a unique object that satisfies the description. So, for example, the determiner “no” is not existential in force, and so there is no well-formed d-type pronoun anaphoric on sentences like “No woman walked in”, and “a woman” is not affirmatively embedded under negation relative to “she sat down”, hence “It is not the case that a woman walked in” also doesn’t license anaphora.
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a.
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Acknowledgements
Thanks are due to Chris Barker, Simon Charlow, and to two anonymous reviewers for this journal for helpful comments and questions. Thanks also to the audiences at the Vendler Group Workshop on Reference and Pronouns at the University of Calgary in March 2017, the Jerrold Katz Memorial Lecture at the CUNY Graduate Center in March 2017, the New York Philosophy of Language Workshop in May 2017, the Nova Scotia Meaning Workshop in July 2017, the Meaning as Action Conference at Oxford in March 2018, the Rutgers Semantics Workshop in April 2019, and philosophy department colloquia at MIT (May 2017), Notre Dame (November 2017), Northwestern (March 2018), and the University of Maryland (February 2019) whose comments and questions on parts of and predecessors to this paper helped improve it vastly.
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Lewis, K.S. Descriptions, pronouns, and uniqueness. Linguist and Philos 45, 559–617 (2022). https://doi.org/10.1007/s10988-021-09325-y
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DOI: https://doi.org/10.1007/s10988-021-09325-y