3.1 Referential Pronouns

In the tradition originating in the work of Cooper (1983), pronouns are seen as variables encoding presuppositions that constrain their values. I will lay out the main parts of one way of developing this kind of framework, which is a simplified version of the kind of theory that is found in Heim and Kratzer (1998); von Stechow (2003); Heim (2008); Sauerland (2004, 2008b), and other work in this area.

We think of a pronoun as associated with a variable, written as a numerical index, call it i. So I\(_i\) is an occurrence of I whose variable component i needs to be given a value by an assignment. In turn, I\(_i\) presupposes that i is the speaker. Similarly, she\(_i\) presupposes that i is female.

Formally, we take \(\llbracket \rrbracket ^c\), as always, to be a function that assigns denotations (meanings) to logical forms (LFs), relative to a context c. A context c is a tuple \(\langle s_c, h_c, t_c, l_c, w_c, g_c \rangle \) of a speaker \(s_c\), a hearer \(h_c\), a time \(t_c\), a location \(l_c\), a world \(w_c\), and an assignment \(g_c\). We then give the following semantics for I and she:Footnote 5

(9)   a. \(\llbracket _}\rrbracket ^c \)= [\(\lambda x: x = s_c\). x](\(g_(i)\))

b. \(\llbracket _}\rrbracket ^c\)= [\(\lambda x: x\) is female. x](\(g_(i)\))

The function

\(\lambda x: x = s_c\). x

is a partial identity function that takes an individual x as argument and returns the same individual x if and only if x is \(s_c\), the speaker in c.Footnote 6 If x is not \(s_c\), the function is undefined: it returns nothing. And analogously for she\(_i\):

\(\lambda x: x\) is female. x

is a function that maps any x onto itself if and only if x if female.

We think of \(g_c\) as representing the factors of an utterance situation that determine reference. Depending on one’s preferred theory, one might think that \(g_c\) represents the speaker’s intentions, or the audiences’ idea of what is referred to, or the result of a complex, perhaps inscrutable interplay of factors. We do not have to take a stand on this here. (I will comment briefly on this again later.)

To illustrate how this system works, consider (10), as uttered by Malwina.

(10)   Malwina: I\(_1\) teach karate.

In this case we assume that the context determines Malwina as the value of 1. She is certainly the intended referent, and presumably also who the audience think the referent is. So in this case \(g_(1)\) is Malwina. But moreover, Malwina is the speaker in c: Malwina is \(s_c\). So the presupposition is satisfied, and \(I_1\) refers to Malwina.

By contrast, consider

(11)   Trump pointing to Giuliani: She\(_1\)’s a genius.

In this case the context determines Giuliani as the value of 1: \(g_(1)\) is Giuliani. He is clearly the intended referent and is also most likely who the audience would take to be the referent. However, since Giuliani is not female, the presupposition is not satisfied, and so she\(_1\) is undefined (has no referent). In turn, therefore, (11) is equally undefined, that is, neither true nor false.

As seen from this, we are here theorizing about what is typically called semantic reference, that is, the sense of reference that is relevant to truth conditions. Even so, one can agree, if one is sympathetic to such views, that Trump speaker-referred to Giuliani, corresponding to the observation that audiences will most likely be able to recover that Trump meant to say that Giuliani is a genius. Indeed, one might see \(g_c\) as representing speaker reference, and cases like (10) as ones in which semantic and speaker reference coincide. Yet we set these issues aside here.

There is a central difference between these two pronouns. The presupposition triggered by I requires that its value be identical to the speaker of the context, whereas the presupposition triggered by she requires that its value be female. The former is a presupposition that imposes a constraint in terms of a parameter of c, the Kaplanian context of utterance. As it is often said, this is an indexical presupposition.Footnote 7 By contrast, the presupposition that the value of she be female is not a presupposition concerning a Kaplanian parameter, and is therefore not an indexical presupposition. This difference will play a central role in what follows.

3.2 Bound Pronouns

We now turn to how this framework explains the possibilities for binding pronouns that we reviewed in 2.2. In particular, why can she be bound in (5a) but I cannot be bound in (6a)?

(5)a. [Every karate teacher]\(_1\) thinks \(\underline\)\(_1\) is the best.

(6)a. #[Every speaker]\(_1\) has difficulty stopping when I\(_1\) should.

On the approach we are considering here, binding possibilities are explained by the projection behavior of the presuppositions triggered by pronouns. By "presupposition projection," we mean the phenomenon by which the presuppositions of compound sentences are determined by those of their parts.

As a rough generalization, presuppositions under universal quantifiers usually project to the domain of quantification. For example, (12) usually presupposes that all the students used to smoke.

(12)   Every student stopped smoking.

So if there were a bound reading of (6a), we should expect the presupposition of the bound first person pronoun to project across the domain, in this case all the speakers quantified over. In other words a bound reading of (6a) would presuppose that each of the speakers is identical to \(s_c\), the speaker of (6a). But since this is an incoherent assumption, there is no bound reading. By contrast, (5a) only presupposes that each of the karate teachers is female, which is arguably the correct result.

Next, consider the cases in which the first and second-person pronouns can be bound, e.g. (7c).

(7) c. I\(_1\) did my\(_1\) homework, and so did you. [sloppy reading]

As we noted, according to the standard treatment, my in (7c) is bound by I to form the property

\(\lambda x.\) x did x’s homework

This property is applied to you under ellipsis to get the sloppy reading on which both the speaker and hearer have this property. But why does the indexical presupposition of my not project? Why does (7a) not presuppose that the referent of you is the speaker?

The central thought of the theories in von Stechow (2003), Heim (2008); Sauerland (2004, 2008b), and many others is that when a feature of a binder and a bindee match, the latter is not interpreted: it is semantically inert. So, for instance, when both the binder and the bindee are 1st person, the 1st person indexical presupposition of the bindee is semantically inert. In other words, it will not be presupposed that the bindee is 1st person.

There is disagreement about the correct theory of this phenomenon. (See also below.) For our purposes, we can assume the following formulation:

Feature Deletion

A feature \(\alpha \) is deleted at logical form (LF) from a variable if \(\alpha \) is also present on the variable’s semantic binder. (After Heim (2005))

Since my is bound by I in (7a), their 1st person features match. Hence, Feature Deletion entails that the 1st person presupposition of the bound my is inert: it is not seen by the semantics. So when we apply \(\lambda x.\) x did x’s homework to you in the second conjunct, we do not trigger the unwanted presupposition that the referent of you is the speaker. By contrast, the presupposition of the 1st person is left in place for I, which is not bound, and (7a) does presuppose that the referent of I is the speaker, which is the right result.

By contrast, consider (6a). Since every speaker is not 1st person, but 3rd person (as can be seen from agreement), the features of every speaker and I do not match. Hence, the indexical presupposition on I remains operative: it is not deleted from the bound I. In other words, the bound reading incoherently presupposes that every speaker is identical to \(s_c\).

This explains the difference in binding possibilities. Indeed, it also explains (5c).

(5c) c. She\(_1\) did \(\underline\)\(_1\) homework, and so did Mike. [sloppy reading]

Since the gender features of her and she match, the presupposition that the referent be female is deleted from the bound her. So when the property \(\lambda x.\) x did x’s homework is applied to Mike under ellipsis, we do not trigger a presupposition to the effect that Mike is female. This is how the sloppy reading is made possible.

Yet there are reasons to think that not all cases of presupposition triggers in the scope of quantifiers generate presuppositions concerning the entire domain of quantification.Footnote 8 Consider, for example, (13).

(13) A student stopped smoking. (Sudo 2012)

Sudo (2012, 45 notes that (13) does not presuppose that each student in the relevant domain used to smoke. Instead, following Sudo, let us assume that sentences such as (13) generate existential presuppositions: roughly, (13) presupposes (14).

(14) There is at least one student who used to smoke.

In support of this, we can note that (13) is felicitous in a context in which more than one student has been smoking but only one stopped, as well as in a context in which only one student has been smoking.

Now consider (15).

(15)A student did my homework.

No bound reading of my is available in this case. It might seem that the kind of explanation we sketched above for cases like (6a) is not applicable here. Given what we assumed for (13), a bound reading of (15) presupposes (16).

(16) There is at least one student who is \(s_c\).

But if (16) is all that would be presupposed, then why is there no bound reading of (15)? After all, (16) is clearly true in the relevant context: the speaker of (15) is herself one of the students.

(16) is arguably a deviant presupposition, even if it is not incoherent like that generated by (6a). In particular, there are independent reasons to follow Heim (1991, 2008); Percus (2006); Sauerland (2004, 2008a, 2008b), and others, in assuming a principle, similar to the Gricean maxims of Quantity, admonishing speakers to make their utterances presuppose as much as possible.Footnote 9 This kind of principle can be formulated in different ways. Here we appeal to Sauerland (2008a) formulation, adapted from Heim (1991):

Maximize Presupposition (Heim 1991; Sauerland 2008a)

Make your contribution presuppose as much as possible!

Maximize Presupposition helps explain some observations concerning indefinites. Consider (17).

(17)A father of the victim arrived at the scene. (Sauerland, 2008a)

Maximize Presupposition explains the oddity of (17), in that (17) does not presuppose that the victim has a unique father. Hence, “the speaker must either assume that the victim does not have a unique father or the speaker must be violating [Maximize Presupposition]." Sauerland (2008a, 585–586) Either way, the utterance is pragmatically deviant.

An analogous explanation can be given for the unavailability of a bound interpretation of (15). If such an interpretation presupposes (16), the speaker does not presuppose that there is a unique student who is \(s_c\), that is, who is herself. The latter is a stronger presupposition than (16), and is of course readily available. Hence, the speaker is violating Maximize Presupposition. At the same time, Maximize Presupposition does not predict that (13) is deviant, since there is nothing problematic in the inference that the speaker of (13) assumes that there is no unique student who used to smoke.

In other words, given a principle like Maximize Presupposition, there are good reasons to think that we can explain the possibilities for binding pronouns at least in a very wide range of cases. Yet before moving on to the spatial indexicals, we should note that the approach just outlined is not the only competitor for explaining these binding facts.

Most prominently, Kratzer (1998, 2009) has proposed another theory according to which some bound pronouns are "fake indexicals" in that they are born without the relevant features to begin with:

when otherwise indexical pronouns end up with a bound variable interpretation, they start their life in syntax as mere indices that pick up the features that make them visible or audible via binding relations in the PF [i.e. phonological form] branch of syntactic derivations. (Kratzer, 2009, 189)

In other words, on this view, at the level of LF, my in (7c) is just a variable (or index), while the reason it is pronounced as my at PF is due to its having picked up some features of its bindee, simply in order to make it audible at all. But since this is not a phenomenon at the level of LF, there is no need for a story of how an indexical presupposition of my can "disappear" semantically under binding.

Yet what I want to point out here is that, given the parallels in the data, whatever one’s theory of the binding facts we have noted above, one should apply the analogous theory to the spatial indexicals. If the binding facts of the 1st and 2nd person are to be explained in terms of fake indexicals, so are the binding facts of here and there. I will continue to conduct the discussion in the simplified version of the framework that employs Feature Deletion sketched above.Footnote 10

3.3 Spatial Indexicals

It is relatively straightforward to give a parallel treatment of spatial indexicals. The central idea is that here mirrors the 1st and 2nd persons in triggering an indexical presupposition in terms of \(l_c\), while there mirrors the 3rd person pronouns in triggering no indexical presupposition. We spell this out as follows:

(18)a. \(\llbracket _i}\rrbracket ^c\) = [\(\lambda x: x = l_c.\) x](\(g_(i)\))

b. \(\llbracket _i}\rrbracket ^c\)= [\(\lambda x:\) x is a location. x](\(g_(i)\))

Given this, we can explain (8a) vs. (8b):

(18)a.Whenever Fred goes to [a new restaurant]\(_1\), he leaves his jacket \(\underline\)\(_1\).

b. #Whenever Fred goes to [a new restaurant]\(_1\), he leaves his jacket \(\underline\)\(_1\).

In particular, if there was a bound reading of (8b), it would presuppose that each of the restaurants is \(l_c\), i.e. the location that (8b) is uttered. This is incoherent. By contrast, (8a) only presupposes that each restaurant is a location.

And parallel to the pronouns we also explain (8c).

(8)c. Fred had a special speech prepared for each town on his campaign trail. But he got confused. Here\(_1\) he gave the speech he was supposed to give here\(_1\). In Manchester he didn’t. [sloppy reading]

Since here is bound by here, their features match, and the presupposition of the bound here is deleted. Hence, (8c) does not presuppose that Manchester is \(l_c\).

There are arguably other features of the spatial indexicals that should ultimately be taken into account. Most conspicuously, both here and there are singular, as is seen from agreement:

(19) a. Here is/#are where I want to live.

b. There is/#where I want to live.

The focus of the present discussion is on the contrast between indexical presuppositions and the absence of such presuppositions, as in (18). In the next section, we will see how indexical presuppositions influences referential uses of spatial indexicals.