Presuppositionality

3.1.7.1 Presuppositional status of additive meaning

In most – but not all, as this chapter will show – of current work on additivity, the nature of the meaning contributed by additives is assumed to be presuppositional. Two arguments for this classification come from the non-cancellability and the non-deniability of additive meaning. The first property is illustrated in (99). As (99a) shows, the scalar implicature triggered bysomemay be explicitly cancelled. The same remark does not apply to the additive presupposition in (99b).

4Not all languages in Forker’s sample make use of additives for all of the core functions. Forker proposes an im-plicational map that relates the presence of one function to the presence of others in a given language.

5In chapter 4, I show that in Finnish, bound additives have all of Forker’s main functions except for the ones listed under 6 and 7 (although scalar additivity is not discussed in this dissertation); moreover, they have the "extended"

function of expressing surprise and/or disappointment.

(99) Cancellation

a. Some chess players are good [ not all chess players are good] ... in fact, all of them are

b. Mary plays chess too [ someone distinct from Mary plays chess]

# ... in fact, no one besides Mary plays chess

Presuppositions are not at-issue, and may therefore not be directly denied or rejected (Beaver et al., 2009). This is illustrated in (100), where only the at-issue content of the sentence falls into the scope of the negative operator: the non-at-issue additive presupposition cannot be targeted byno. Indeed, as (100c) shows, only indirect denial of the additive meaning (here, the antecedent is assumed to be roughlythat Mary likes cheese) usingHey! Wait a minute...is possible.

(100) Direct denial

Mary likes olives, too

a. No, she doesn’t (like olives)!

b. # No, she doesn’t (like cheese)!

c. Wait a minute... she never said she likes cheese!

Further support for the presuppositionality (or, more widely speaking, non-at-issueness) of addi-tive meaning comes from its projection properties (Roberts et al., 2009; Simons et al., 2010). Addi-tive meaning projects through presupposition holes such as modal operators and negation with-out being modified (Karttunen, 1973). Thus, in (101a), the presupposition remains the same re-gardless of whether the host sentence is modalised or not; the same comment applies to (101b).⁶

6Note that with respect to projection, additive presuppositions behave in a way that is partly unlike other presup-positions. For example, additive presuppositions that arise from complement clauses of non-factive attitude verbs such asbelieveorthinkdo not project in the expected way. The expected way, in this case, is projection to the attitude holder, but not to the speaker (Karttunen, 1974). For this reason, non-factive attitude verbs have been termed presup-position plugs. That presuppresup-positions fail to reach the level of the speaker is illustrated in (i), where the presuppresup-position due tomy– that there is a cat that the speaker owns – does not have to hold of the common ground, and specifically, the speaker may well not have a cat, and know it. The presupposition ofmymust instead hold of the belief context anchored to the attitude holderMary.

(i) Projection under attitude verbs Mary thinks that my cat is sick

As (ii) shows, this projection pattern does not apply to additive presuppositions under attitude verbs (Heim, 1992;

van der Sandt and Geurts, 2001); the felicity of Mary’s remark does not require that her parents think that someone else besides herself is in bed.

(ii) Projection under attitude verbs (van der Sandt and Geurts, 2001) [John and Mary are on the phone]

John: I am already in bed

Mary: My parents think that I am in bed too

In sum, the projection properties of additive presuppositions are partly as expected, and partly unexpected.

3.1. Review of the main issues concerning additivity

(101) Projection through presupposition holes

a. Mary might like chess too [ Someone distinct from Mary likes chess] b. Mary does not like chess too [ Mary likes something distinct from chess] In some recent approaches, additives have been argued to contribute both at the level of at-issue meaning and presupposition (Abrusán, 2014), and even essentially only at the level of at-issue meaning (Ahn, 2015; Gaji´c, 2016). The question of whether additive meaning is (only) presup-positional is thus still debated in the literature. Moreover, as this chapter will show, analyses of additivity differ in which approach to presupposition they take: while the majority assume that presuppositions are definedness or admittance conditions, some also use the binding and speaker presupposition approaches (see section 2.2.2).

3.1.7.2 Accommodation

Under the view that presuppositions impose certain requirements on the context – or more specif-ically, the common ground – it is also possible to maintain that when those requirements are not met on the get-go, they may beaccommodated. Accommodation consists in ‘repairing’ the con-text by spontaneously adding the required piece of information or proposition to the common ground, so as to satisfy the presupposition (cf. section 2.2.1) (Lewis, 1979). As was noted in the section concerning the antecedency question (section 3.1.2), additive presuppositions are noto-rious for resisting accommodation (Heim, 1990; Kripke, 1990/2009; Beaver and Zeevat, 2007).

Besides explaining why accommodation from additives is generally not possible, it must also be explained why and how some contexts in fact productively allow accommodation. The rele-vant examples are not recognised as cases of accommodation in the previous literature (Kaplan, 1984; Krifka, 1998). For example, Kaplan (1984) notes that in (102a), the additivetoois infelici-tous, because interpreting the example leads to "a feverish attempt to re-interpret the sentence with Jo equaling Mo, or fish equaling soup; anything to reduce the two differences into one" (p.

511). What is interesting is that when the sentence receives a different intonational pattern – one where the subject is a (contrastive) topic (signalled with double-underlining) and the object is focused – the use oftoois in fact felicitous. As a whole, the conjunction presupposes that Mo had fish (in addition to soup, as the assertion states). Crucially, the propositionthat Mo had fishneed not be part of the common ground at the time of utterance of (102b) fortooto be felicitous. In fact, it seems to be introduced as new information into the common ground. In other words, this proposition is accommodated.⁷

7The accommodation process only takes place in the presence of the additive, as (i-a) withouttooillustrates. The projection test shown in (i-b) further supports the argument that the inference is indeed a presupposition; in contrast to (i-a), (i-b) presupposes that Mo had fish.

(i) a. Jo had fish, and Mo had soup

b. Jo had fish, and Mo might have had soup too

(102) a. Jo had fish, and Mo had soup #too

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

In sum, theories of additivity should address the question of when additive presuppositions can and cannot be accommodated. It seems clear that the surrounding context plays an important role in making the accommodation process possible for additive presuppositions.

3.1.7.3 Suspension

As was mentioned in section 2.2.2, additives arehardpresupposition triggers in the terminology of Abusch (2010). As such, they contrast withsoftpresupposition triggers. This difference – what-ever lies at its root – can be illustrated by the pair of examples in (103). The verbwinpresupposes that a preparatory phase of participation preceeds the winning (Abusch, 2010). In (103a), the first discourse segment explicitly expresses ignorance as to whether this presupposition holds. Nev-ertheless,wincan be used felicitously. The same has been argued not to apply to additivetoo (103b): when the first segment expresses ignorance as to whether the presupposition is satisfied, the use oftoois judged infelicitous. In both examples below, the presupposition trigger is in bold.

(103) Soft (a) and hard (b) presupposition triggers (Abusch, 2010)

a. I have no idea whether John ended up participating in the Road Race yesterday. But if hewonit, then he has more victories than anyone else in history

b.?? I have no idea whether John read that proposal. But if Bill read ittoo, let’s ask them to confer and simply give us a yes-no response

The question of whether additive presuppositions are soft or hard is closely related to the ques-tions of of what kind of antecedents additives may refer to (if they are assumed to do so), and where those antecedents may be found, i.e. the antecedency question.