Other anaphoric approaches - Anaphoric approaches

3.3 Anaphoric approaches

3.3.2 Other anaphoric approaches

Adopting Heim’s (1992) idea that the semantics of additivity involves an anaphoric component that is very similar to pronouns, Geurts and van der Sandt (2004) propose that sentences with additives involve two presuppositions. The first is specifically due to the lexical semantics of

ad-ditives, while the other is due to the focus structure of the host sentence (see also Ruys 2015, section 3.2.1; Szabolcsi 2017, section 3.2.3). Specifically, Geurts and van der Sandt (2004, p. 23) propose that the additive-specific presupposition corresponds to the requirement that there be some dref y distinct from the focus x in the context (i.e. in the DRS, or discourse representa-tion structure; Kamp, 1981; Kamp and Reyle, 1993). The general focus-related presupposirepresenta-tion in turn requires that the scope predicateφapplies toy. The latter presupposition is due to the Background Presupposition Rule(BPR) (Geurts and van der Sandt, 2004, p. 11):

(136) Background Presupposition Rule (BPR)

Whenever focusing gives rise to a backgroundλx[φ(x)], there is a presupposition to the effect thatλx[φ(x)]holds of some individual

The account of Geurts and van der Sandt (2004) is built on the binding theory of presupposi-tion, itself formulated within discourse representation theory (DRT; Kamp, 1981; Kamp and Reyle, 1993). On this approach, presuppositions are bound much like pronouns; in other words, pre-suppositions search for an antecedent within the DRS-structure. Without going into the details of DRT, in (137) I show how the two additive presuppositions – each doubly underlined – are bound in Geurts and van der Sandt 2004.

(137) Binding additive presuppositions (Geurts and van der Sandt, 2004, p. 23)

a. If Herb comes to the party, the boss comes, too (Kripke, 1990/2009) b. [u: Herb(u),v: boss(v),[: comes(u)]⇒[x: x6=v, comes(x), comes(v)]]

c. [. . .u: . . . .Herb(u),v: boss(v), . . . .u6=v,[: comes(u)]⇒[comes(x), comes(v)]]

d. [u: Herb(u),v: boss(v),u6=v,[: . . . .comes(u)]⇒[comes(v)]]

First, the DRT-translation of the sentence in (137a) is given in (137b), where brackets delimit the DRSs. The main DRS contains two discourse referents,u andv. The embedded DRS encodes the conditional; ifucomes, thenvcomes – with the additive presuppositions shown doubly un-derlined. The first presupposition to be bound is the distinctness-encodingx: x6=v. A suitable antecedentu is found in the main DRS; hence,x is bound there, as shown in (137c) (signaled with . . . .dotted. . . .underlining). After this step, the second presupposition comes(x) is bound by the antecedent that is located in the protasis of the conditional (signaled with dotted underlining).

(137d) shows the final DRS where both presuppositions have been bound. The meaning con-tributed by this DRS is the conditional statement that if Herb comes, then the boss comes, and Herb is not the boss.³⁰

The separation of the additive presupposition into two parts – one specific to additives, and another to focus structures in general – allows Geurts and van der Sandt (2004) to argue that the

30As the DRT-approach of Geurts and van der Sandt (2004) explicitly assumes that additive presuppositions are bound like pronouns, it becomes important to define when this binding is possible. As Zeevat (2002) notes, additives are generally able to refer back to drefs in positions that are otherwise unreachable for e.g. definite descriptions:

3.3. Anaphoric approaches

reason why additive presuppositions cannot be accommodated is that they are ‘descriptively at-tenuate’, i.e. do not have much semantic content (cf. section 3.1.7.2). Additive presuppositions thus belong to the same natural class with pronouns. Beaver and Zeevat (2007) note that this proposal has at least two weak spots. First, such a proposal is hard to motivate; in essence, saying that descriptively attenuate presuppositions cannot be accommodated amounts to saying that the rescue strategy for securing presupposition satisfaction does not work for presuppositions that donothave much content. Intuitively, it should instead be hard to accommodate presuppo-sitions withrichcontent. Indeed, there are other classes of presupposition triggers which resist accommodation (e.g. politeness markers; see Beaver and Zeevat, 2007), but do not have poor descriptive content.

Second, Beaver and Zeevat (2007) argue that Geurts and van der Sandt (2004) make a false prediction: the additive-specific presupposition – the one requiring that some salient dref be accessible in the context for purposes of presupposition binding – should be satisfied whenever such a dref is made salient. This prediction is not borne out, however, as (138) shows:

(138) False prediction for accommodation

??Jane, a New Yorker, likes Bill. Bill is having dinner in New York, too

In (138), a salient individual distinct from Bill –Jane– is introduced in the context before the host sentence oftoois uttered. Hence, the additive presupposition that is supposedly not accom-modatable is satisfied in (138). Moreover, the focus-related additive presupposition is arguably

(i) Inaccessible antecedents (Geurts and van der Sandt, 2004, p. 26) a. ? The Swissmayhave a navy. The Swiss navy is stationed on Lake Geneva

b. Fredmaybe staying at the Ritz, and Barney is at the Ritz, too

In (i-a), the antecedent of the definite descriptionthe Swiss navy– namely,a navy– is embedded under a possibility modal, and therefore it is not accessible. In (i-b), however, the same modal embedding seems to have no effect on the felicity oftoo, as the discourse is natural. Geurts and van der Sandt (2004) propose that this is because the DRS of (i-a) is ill-formed due to the occurrence of a free drefxin the final DRS, shown in (ii-c) (after the underlined presupposition is bound within the scope of the modal), while in (i-b), no such ill-formedness arises, as (iii) shows.

(ii) Ill-formedness of (137a) (Geurts and van der Sandt, 2004, p. 26)

a. [:◊[x: Swiss-navy(x)]] [first part of (137a)]

b. [u: Swiss-navy(u),uis stationed on Lake Geneva] [second part of (137a)]

c. [:◊[x: Swiss-navy(x)],xis stationed on Lake Geneva] [resolved presupposition]

(iii) Well-formedness of (136b) (Geurts and van der Sandt, 2004, p. 26) a. [x: Fred(x),◊[: stay-at-Ritz(x)],

u: Barney(u), stay-at-Ritz(u),v:v6=u, stay-at-Ritz(v)] b. [x: Fred(x),◊[: stay-at-Ritz(x)],

u: Barney(u),x6=u, stay-at-Ritz(u), stay-at-Ritz(v)]

c. [x: Fred(x),◊[: stay-at-Ritz(x)], u: Barney(u),x6=u, stay-at-Ritz(u)]

satisfied as well, given that there are individuals that dine in New York (for example, we can in-fer that Jane the New Yorker is such an individual). Nevertheless, the use oftoois infelicitous in (138). Therefore, the resistance of additives to accommodation remains unexplained under the approach that Geurts and van der Sandt propose.

The second approach that relies on pronominal anaphora that we will discuss here is that of Abrusán (2014). Abrusán proposes that additive presuppositions begin their life as entailments, and they become presupposed (in addition to being entailed; Stalnaker, 1974; Abrusán, 2011) because they fail a specific requirement for being at-issue. In particular, Abrusán argues that the presuppositionality of additive meaning is closely related to itstense-insensitivity.

For Abrusán, additives thusentailthe truth of an alternativeqto the prejacentp. Informally, this entailment becomes a presupposition as well becauseqis never "paid attention to"; in other words,qis always backgrounded (Abrusán, 2011). Formally, Abrusán (2014) proposes that back-grounded information is not necessarily about themain eventdescribed inp, i.e. the asserted proposition. To avoid problems related to event semantics, Abrusán assumes that presupposed information concerns events whoseruntime is (unaccidentally) independent from that of the main event.

To see what this means, consider the sentenceSin (139). Abrusán notes that among the many entailments ofS, there are two –φandψ– that differ in whether they are independent of the main event inSin (139a), i.e. the knowing event that takes place att₁. Whileφin (139b) is aboutt₁,ψin (139c) is not (although it could, of course,accidentallycoincide with it). Thus, asφis necessarily about the event time of the matrix predication inS,φis an entailment ofS; asψis not necessarily about the same event time,ψis a presupposition (as well as an entailment) ofS.

(139) Independence of main event (Abrusán, 2014, p. 7)

a. S =John knows (att₁) that it was raining (att₂) b. φ=John believes (att₁) that it was raining (att₂) c. ψ=It was raining (att₂)

For additives, the simplest cases follow easily. First, Abrusán (2014) proposes to model the ad-ditive meaning as in (140). Abrusán follows Heim (1992) and assumes that additivity involves anaphoric pronouns that are resolved in the context.³¹In (140), the anaphoric pronoun is repre-sented as F’_C. In a familiar way, the entry requires that the anaphoric pronoun and the associate F of the additive are distinct (last conjunct). It also states that the predication that is stated to hold of the associate in the host sentence (first conjunct) holds of the anaphorically determined alternative (second conjunct).

31Abrusán’s approach there faces the same problems as were discussed in section 3.3.1; first, one must explain why the anaphoric pronoun that is introduced in the additive semantics is able to find antecedents that other, normal pro-nouns cannot, and second, one must explain how things that do not correspond to drefs can function as antecedents (in the case of e.g. focus on a verb).

3.3. Anaphoric approaches

(140) Additive semantics (Abrusán, 2014, p. 14)

ADD₁[(φ(F₁)] =φ(F) ∧[φ(F’_C)∧ F’_C 6=F]

Abrusán argues that additive meaning is presuppositional for the same reason thatψis a presup-position ofSin (139). In (141), the main event inSis aboutt₁. The focus alternative that satisfies the additive presupposition (i.e. φ(F’C), which corresponds toψin (141b)), may be aboutt₂, which is distinct fromt₁. Therefore,ψis presupposed (and entailed).³²

(141) Additive presuppositions may be independent of main event runtime a. S =Mary likes spaghetti (att₁), too

b. ψ=John likes spaghetti (att₂)

Additionally, Abrusán proposes that entailments that are about the main event time can still avoid becoming presuppositions if they directly address secondary pragmatic main points, introduced in the form of a Question Under Discussion (cf. Beaver, 2010). For example, whilediscover is a factive predicate and as such presupposes the truth of its complement, in (142a), the F-marking pattern connects the assertion to the Question Under DiscussionWhat will the TA realize?, and given that the factive complement directly addresses this question, its content is not presupposed (i.e. the addressees work is not presupposed to be plagiarised in (142a)). A small change in F-marking brings back this presupposition in (142b).

(142) Effect of focus on presupposition (Beaver, 2010)

a. If the TA discovers that your work is plagiarised, I will be forced to notify the dean b. If the TA discovers that your work is plagiarised, I will be forced to notify the dean For additives, Abrusán argues that such a situation never arises, because additive meaning does not directly address QUDs. To illustrate this point, Abrusán proposes the example in (143) (p. 19):

(143) Additive meaning cannot address QUDs directly A: Bill ate the beans. What did John eat?

B: John ate the beans too [ x ate beans andx6=John]

In (143), the QUD is given explicitly in A’s assertion. Crucially, the additive component of B’s re-sponse – wherexis resolved to Bill – does not address this question. However, there are examples

32Note that although additivity is argued to be tense-insensitive, some tense-pairings are not as felicitous as others, as shown in (i) (with a future-past pairing). Abrusán does not discuss the source of such effects (see Abrusán, 2014, p.

15).

(i) ? John will invite Mary for dinner, and yesterday Peter invited Mary for dinner, too

where additive meaning directly address a QUD. Consider, for example, (144) from Kaplan (1984) (see section 3.1.7):

(144) (Who ate what? What did Jo eat? What did Mo eat?)

Jo had fish, and Mo had soup too [ Mo had fish]

In (144), the presence of the additive leads to the inference that Mo had fish (as well as soup, as is asserted). This piece of information directly addresses both the superquestionWho ate what?

and the subquestionWhat did Mo eat?. Nevertheless, the timing of the two eating events re-lated to Mo may be different, and therefore the additive component is indeed presupposed under Abrusán’s definition of presupposition triggering, which is summarised in (145).³³

(145) Presupposition triggering (Abrusán, 2014, p. 9)

Entailments of a sentenceSthat can be expressed by sentences that are neither necessarily about the event time of the matrix predicate ofSnor about the event time of the sentence expressing the most direct answer to the (grammatically signalled) background question are presupposed

As the discussion makes clear, Abrusán’s main goal is to account forwhythe meaning contributed by additives has a double status as presuppositions and entailments of the host sentenceS. The main argument for this duality comes from the following example:

(146) Additive inferences as entailments (Abrusán, 2014, p. 13) a. # Mary went to the shop, but it is not the case that somebody went there

b. Mary went to the shop, but it is not the case that somebody went thereas well Example (146a) does not contain an additive, and the meaning is contradictory; both conjuncts cannot be true at the same time. In (146b), an additive is added at the end of the second conjunct, and the contradictoriness seemingly disappears. For this reason, Abrusán argues that the seman-tic import of the additive in (146b) cannot be restricted to being presuppositional; if it were only presuppositional, (146b) should be felt to be as contradictory as (146a).

The contradictoriness of (146a) clearly comes about due to the clash between stating that Mary went to the shop while maintaining that the negation of the existential claim in the second conjunct is true: it cannot be thatthat Mary went to the shopis true ifthat no one went to the store is true as well (Ahn, 2015). The felicity of (146b), on the other hand, seems to involve an inter-pretation ofsomebodyassomebody else, and not simply an existential; the latter is interpreted as excluding Mary. Indeed,that Mary went to the storeandthat no one other than Mary went to the storecan be true at the same time (Abrusán, 2014; Ahn, 2015), and adding the overtelsein (146b)

33For Abrusán (2014), the fact that additives are hard presupposition triggers (which means that additive meaning cannot be suspended) follows from the fact that additive entailments never fail to be presuppositions by (145).

3.3. Anaphoric approaches

makes the example feel more natural. In (146a), too, addingelseremoves the contradiction. The question, then, is whysomebodyis rather interpreted as a ‘normal’ indefinite in (146a), and as an else-indefinite in (146b). I leave this question open, but note that given that there is an alterna-tive explanation in terms ofelse, (146) does not warrant the claim that the additive meaning must (also) be part of the at-issue content of the second conjunct.

The idea that additive presuppositions are entailments is taken slightly further by Ahn (2015).

Ahn proposes that additives denote two-place operators. Of the two arguments, one corresponds to the host sentence of the additive p (the prejacent), and the other is a silent propositional anaphorqwhich, as usual, requires a contextual or textual antecedent. The additive comes with a presupposition requiring thatqis a focus alternative ofp, but the two are distinct. In terms of at-issue content,tooasserts the conjunction ofp andq.

Ahn’s semantics fortooare shown in (147a). When applied to a sentence such as (147b), the presuppositional and assertive meanings come out as shown in (147c). The meaning of the host sentence of the additive depends on the identity ofq: ifq is resolved toMary left, for example, the whole sentence denotes the conjunction ofJohn left(prejacent) andMary left(antecedent).

(147) Conjunctive semantics oftoo(Ahn, 2015, p. 26) a. J^tooK^(q⁾⁽J^pK∼C)=λw:q∈C − {J^pK

o }.q^w∧J^pK

b. John left too J^pK=John left c. J^tooK^(q⁾⁽J^pK⁾

(i) presupposes thatq is a distinct focus alternative ofJ^pKand thus has the formx left

(ii) assertsq∧J^pK

One of the main points of innovation in Ahn’s (2015) approach lies in the analysis ofeither: Ahn proposes thateitheris polarity-sensitive (paceRullmann, 2003) and that its polarity-sensitivity is rooted in its lexical semantics and the semantics of exhaustification (e.g. Chierchia, 2013, and references therein), and not in a stipulated licensing condition. Specifically, Ahn (2015) proposes that whiletooasserts the conjunction ofp and the anaphorq,eitherasserts their disjunction.

(148) Disjunctive semantics ofeither (Ahn, 2015, p. 29)

a. J^eitherK^(q⁾⁽J^pK∼C)=λw:q∈C− {J^pK

o}.q^w∨J^pK

b. John did not leave either J^pK=John left

c. ¬J^eitherK^(q⁾⁽J^pK⁾

(i) presupposes thatq is a distinct focus alternative ofJ^pKand thus has the formx

left

(ii) asserts¬[q ∨J^pK] = [¬q∧ ¬p]

As (148c) shows, Ahn assumes thateithertakes scope under negation (Rullmann, 2003). There-fore, the prejacentp and the focus alternativeq both have positive polarity. The additive pre-supposition is exactly as withtooin (147). What changes is the assertion: as (148c) shows, the assertion amounts to the negation of the disjunction ofp andq, which by De Morgan’s law is equal to the conjunction of the negation ofpand the negation ofq.

Assuming that the semantics ofeitherinvolves disjunction allows Ahn to argue that the re-striction on the distribution ofeither– namely, that it has to occur in the scope of negation, as is assumed in polarity approaches to additivity – follows from general principles related to exhaus-tification (Krifka, 1995; Lahiri, 1998; Chierchia, 2006; Chierchia et al., 2011; Chierchia, 2013). As Ahn assumes that the semantics ofeitherinvolves disjunction, she takes the relevant alternatives evoked byeitherto be those of disjunction: this set includes the scalar alternative[p∧q]as well as the domain alternativespandq(Sauerland, 2004).³⁴

(149) Alternatives ofeither p, i.e.[p∨q] (Ahn, 2015, p. 32) a. Scalar: {p∧q,p∨q}

b. Domain: {p,q}

Ahn proposes that the exhaustification operatorO(i) asserts the prejacentp, and (ii) negates all alternatives thatp does not entail. Therefore, given the alternatives in (149), the exhaustification of a sentence witheitheris (i) vacuous ifOapplies to¬[p∨q], and (ii)contradictory(⊥) ifOapplies to[p∨q]directly. To see why this is, consider first the following example without negation.

(150) Exhaustification of*John left either (Ahn, 2015, p. 33)

a. Prejacentp =John left b. Assertion =q∨p

c. Alternatives ={q∨p,q∧p,q,p}

d. O(p either) = [q∨p]∧ ¬[q∧p]∧ ¬q∧ ¬p =⊥

On the exhaustification story, the reason whyeitheris unacceptable when it it is not in the scope of a downward entailing operator, such as negation, is that none of the alternatives to the prejacent p are entailed byp, and hence they are all negated. This, however, results in a contradiction: it cannot be thatp∨qis true while neither disjunct is true.

34Note that in contrast to Szabolcsi (2017), Ahn (2015) includes the scalar conjunctive alternative[p∧q]in the alternative set (see section 3.2.3).

3.3. Anaphoric approaches

A negated disjunction, however, entails the negation of its two disjuncts (by De Morgan’s law), and it also entails the negation of the scalar alternative. Hence, whenO applies to an either-sentence with negation, exhaustification is vacuous: no alternative is negated.

(151) Exhaustification ofJohn did not leave either (Ahn, 2015, p. 33) a. Prejacentp =John left

b. Assertion =¬[q∨p]

c. Alternatives ={¬[q∨p],¬[q∧p],¬q,¬p} d. O¬(peither) =¬[q∨p]

Recall from section 3.2.3 thatOhas elsewhere been argued to only negate innocently excludable alternatives, i.e. those alternatives that are included in each maximal set of alternatives that can be negated without contradicting the prejacent (Fox, 2007). If innocent excludability is used to decide which alternatives are negated, the same result ensues: no alternative in (151c) is a mem-ber of any set of alternatives that can be negated without contradicting the prejacent (assuming that¬¬[q∧p] = [q∧p]).

Although some open questions remain – for example, the question of whyeitheris not li-censed in all contexts where other negative polarity items such asanyare, and how this analysis could be extended to cover cases where the truth value of the antecedent is not settled, as in the polar use of bound additives in Finnish (see section 4.2 for a description of the data) – Ahn (2015) proposes, for the first time, an answer to thewhy-question concerning the status ofeitheras a negative polarity item (cf. Rullmann, 2003):eitheris a negative polarity item because negation is required for the exhaustification process to not be contradictory. The polarity-insensitivity oftoo also receives an explanation: conjunction is equivalent to universal quantification, and univer-sals tend not to be polarity items cross-linguistically.

To conclude this section, let us discuss one last analysis of additivity that incorporates an anaphor-like contextual dependency, namely, that of Beaver and Clark (2008). In Beaver and Clark’s work, the relationship between F-marking and QUDs is particularly important for the analysis of focus-sensitivity (see section 2.2.1). For the authors, different linguistic expressions may associate with focus in different ways. Additives and exclusives, for example, associate with focus conventionally. This means that the operators encode a grammatical dependency to a QUD.

Specifically, for Beaver and Clark, the function of an additive in discourse is to comment on the current QUD (i.e. the question whose resolution has highest priority). The relevant comment is that the current QUD already has a previous salient answer in the common ground (where typically, just-expressed propositions are salient). For example, in the famous Kripke-example John is having dinner in New York tonight, too, the additive signals that the QUDWho is having dinner in New York tonight? – which is identified based on the F-marking of the assertion – has

been previously answered. This in turn means that some salient proposition of the formx is hav-ing dinner in New York tonightis in the common ground. Crucially, Beaver and Clark explicitly reject a simple existential analysis of additivity, where the common ground would simply be re-quired to entail the truth of the existential statement∃x.having-dinner-in-NY-tonight(x)(Beaver and Clark, 2008, p. 73). Their analysis is therefore classified as anaphoric in this dissertation, although it does not involve an overt propositional anaphor per se.

This ends the presentation of anaphoric (or at least non-existential) approaches to additivity.

In the final section of this chapter – which follows the summary in 3.3.3 – I present three more analyses that deal specifically with Finnish additivity.

3.3.3 Summary

This section presented a number of anaphoric (or at least non-existential) approaches to addi-tivity. First, in section 3.3.1, I reviewed the classic anaphoric approaches of Heim (1990, 1992) and Kripke (1990/2009). These three approaches differ in whether they involve individual-level anaphora (Heim, 1990, 1992) or propositional anaphora (Kripke, 1990/2009; see also Asher, 1993).

Section 3.3.2 then reviewed a number of newer non-existential approaches. I begun with Geurts and van der Sandt’s (2004) binding-theoretic approach to additive presuppositions, and noted that although it attempts to answer the question of why additive presuppositions resist

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