Back to the case of scalar implicatures

In document Soft but Strong. Neg-Raising, Soft Triggers, and Exhaustification (Page 152-158)

4.2 Soft presuppositions and intervention effects

4.2.2 The proposal Back to the case of scalar implicatures

As we saw above, NPIs are grammatical in cases like (7a) but not in a simple positive sentence like (7b). Chierchia’s (to appear) exhaustivity-based theory of NPI licensing sketched above is based on three components: first, an NPI like any has the same basic lexical entry as that of a plain indefinite: an existential quantifier over some pragmatically determined domain of individuals, indicated asD, like in (22).

(22) [[any]] = λPλQ[∃x ∈D[P(x)∧ Q(x)]]

Second, any is associated with a particular set of alternatives, so called domain alternatives. Domain alternatives are obtained by replacing the variableDwith variablesD0of the same type ranging over smaller non-empty domains, as illustrated in (23).8

(23) AltD([[any]]) ={λPλQ[∃x ∈D0[P(x)∧ Q(x)]] :D0⊆D}

Third, domain alternatives are assumed to be obligatorily active, in the same way as we assume for the alternatives of soft presuppositions. This means that any bears a domain alternative feature [D], in addition to the feature [σ] and the combination of σ andD can only be assigned value “+”. As a result, NPIs must enter into an agree relation with a higher operator carrying the same feature, i.e. EXHand hence they must be exhaustified.

(24) EXH¬[Mary make any[+σ],[+D]mistake]

8I indicate domain alternatives asAlt

This set of ingredients derives the distribution and interpretation of NPIs, in that it correctly predicts a contradictory meaning, unless the NPI lies in a DE environment.9 Furthermore, this account of NPIs licensing can be extended to provide a treatment of intervention effects by scalar implicatures, and as I propose below, by soft presuppositions as well.

The Intervention effects of scalar implicatures Chierchia (to appear) offers an analysis of intervention effects caused by conjunction and quantifiers, both scalar terms endowed with alternatives. An example of an intervention effect case is (28b), versus its minimal variant (28a).

(28) a. Theo didn’t play the guitar or drink any coffee

b. ??Theo didn’t play the guitar and drink any coffee

Accounting for contrasts such as the on in (28) is done by appealing to both a semantic and syntactic requirement. Semantically, the intervention effect arrises as a result of the scalar implicature which comes about as a result of having the conjunction in the scope of negation. Syntactically, the relation between the exhaustifying operatorEXHand NPIs or scalar terms is subject to minimality, in the sense above. Let’s look at each of these requirements in detail below.

9To illustrate, consider how this account can explain why (7a) is grammatical, while (7b) is not: if we exhaustify

(7b) in (25a) with respect to its domain alternatives in (25b), we get (26). (25) a. ∃x ∈D[mistake(x)∧ make(m, x)]

b. {∃x ∈D0[mistake(x)∧ make(m, x)] : ∅ 6=D0⊆D}

(26) [[EXH]](26a) = ∃x ∈D[mistake(x)∧ make(m, x)] ∧ ¬∃y ∈ D0[mistake(y)∧ make(m, y)] for all non emptyD0such thatD0⊆D

(26) says is that there is at least one mistake in some domainDthat Mary made, but that for all non-empty subsets

D0ofD, there is no mistake that Mary made. This is clearly impossible, hence we end up with a meaning that can never be true. In the case of (7a), instead, represented in (27a) with its alternatives in (27b), the domain alternatives are all entailed by (27a). If there is no mistake in some domain D that Mary made, there won’t be any mistake in all subdomainsD0ofD. Hence, given the definition ofEXH, it will turn out to be vacuous in this case.

(27) a. ¬∃x ∈D[mistake(x)∧ make(m, x)]

The semantic side of the intervention effects can be illustrated in three steps. First step: consider two variants of (28a) and (28b) without NPIs, like (29a) and (29b), and notice that a difference between the two is that (29a) gives rise to the inference in (29c), while (29b) does not.

(29) a. Theo didn’t play the guitar and dance.

b. Theo didn’t play the guitar or dance.

c. Theo played the guitar or danced

Second step: as we saw in the last section, a sentence like (30) is predicted to be felicitous in Chierchia’s (to appear) account, because exhaustification of an NPI in the scope of a DE function is just vacuous (it does not result in a contradictory meaning).

(30) Theo didn’t drink any coffee

Third step: putting these two pieces together and going back to the contrast in (28a) versus (28b), we can now see that the scalar implicature makes it so that the NPI any does not lie in a DE environment anymore and thus it cannot be licensed. Consider (28a) first. Following Chierchia (to appear), I assume the LF in (31), where the NPI and the scalar term each have their own exhaustivity operator, as indicated by the co-indexing.10

(31) EXHiEXHj[¬[Theo play the guitar andj[+σ][drink anyi[+σ,+D]coffee ]]]

In the interpretation of (31) we first exhaustify (32a) with respect to its alternatives in (32b) and we obtain (33).

(32) a. ¬[play-guitar(t) ∧ ∃x ∈D[coffee(x)∧ drink(t, x)]

b. Alt(32a) =     

¬[play-guitar(t) ∨ ∃x ∈D[coffee(x)∧ drink(t, x)] ¬[play-guitar(t) ∧ ∃x ∈D[coffee(x)∧ drink(t, x)]

    

10See Chierchia (to appear:ch. 7) for arguments in favor of separate exhaustification of the scalar and domain

(33) ¬[play-guitar(t) ∧ ∃x ∈D[coffee(x)∧ drink(t, x)] ∧[play-guitar(t)∨ ∃x ∈ D[coffee(x)∧ drink(t, x)]]

One can see that once the scalar implicature is added the second conjunct (in blue) in (33) is positive making the conjunction as a whole no longer DE. This means that when we exhaustify with respect to the domain alternatives of any in (34b), all alternatives are logically independent. Since they are all logically independent, the exhaustification negates them all and a contradic- tion ensues (I show this in Appendix C).

(34) a. ¬[play-guitar(t) ∧ ∃x ∈D[coffee(x)∧ drink(t, x)]

∧[play-guitar(t) ∨ ∃x ∈D[coffee(x)∧ drink(t, x)]]

b. AltD(34a) ={¬[play-guitar(t)∧∃x ∈D0[coffee(x)∧drink(t, x)]∧[play-guitar(t)∨

∃x ∈ D[coffee(x)∧ drink(t, x)]] :D0⊆D}

On the other hand, in (28a), since or is in the scope of negation, it does not give rise to any scalar implicatures and thus the exhaustification of the NPI proceeds as if it were directly under negation.

(35) EXHiEXHj[¬[Theo play the guitar orj[+σ][drink anyi[+σ,+D] coffee ]]]

In sum, the approach can account for the contrast in (28a) versus (28b); there are, however, two open issues at this point: the first regards the order between exhaustification of the scalar term and exhaustification of the NPI; to obtain the intervention effect above, the order of exhaustifi- cation between scalar and domain alternatives is crucial. To illustrate, consider the LF in (36), where we first exhaustify the NPI and then the scalar term and.

(36) EXHjEXHi[¬[Theo play the guitar andj[+σ][drink anyi[+σ,+D] coffee ]]]

Notice that at the point of the first exhaustification the NPI lies in a downward entailing en- vironment, thus exhaustification is just vacuous; then we exhaustify again and add the scalar

implicature and the result is obviously non-contradictory: Theo didn’t both played the guitar and drink coffee, but he did one or the other. The first question is, then, what rules out the LF in (36).

The second issue regards the fact that, as we saw above, scalar terms can have the alterna- tives inactive, so why can’t we have the LF in (37), where and has no active alternatives? In this case the scalar term and would not be exhaustified and would thus not create intervention.

(37) EXHi[¬[Theo play the guitar and[−σ][drink anyi[+σ,+D]coffee ]]]

These two issues are resolved on syntactic grounds. Recall that we are assuming that NPIs bear the feature [σ] and the feature [D] and that the combination [σ,D] can only get the value “+” (the alternatives of NPIs are obligatorily active). This means that an exhaustivity operator C-commanding them has to be present or the derivation will crash. A precise formulation of minimality is (38).11

(39) Minimality:EXHmust target the closest potential alternative bearer a. A bearer XP of [σ]/[D] is closest toEXHiff:

(i) EXHasymmetrically C-commands XP

(ii) There is no other bearer YP of the relevant features (σ,D) such that EXH asymmetrically C-commands YP and YP C-commands XP

We can now see that this notion of minimality rules out the first problematic case in (36), repeated in (40), in which the order of exhaustification makes it so that the result is not contra- dictory.

(40) EXHjEXHi[¬[Theo play the guitar andj[+σ][drink anyi[+σ,+D] coffee ]]]

11The notion of C-command assumed here is (39).

(38) C-command: A C-commands B iff A doesn’t dominate B and the first relevant branching node that domi- nates A dominates B

Notice that in (40) the first exhaustivity operator is not targeting the closest potential alter- native bearer, in the sense in (39) above, thus the configuration turns out to be syntactically ill-formed.12 Finally, the second problematic case in (42) is also ruled out in the way above: the exhaustivity operator has to target the closest potential bearer, thus it cannot skip it and target any.

(42) EXHi[¬[Theo play the guitar and[−σ][drink anyi[+σ,+D]coffee ]]]

Summing up, the scalar implicature based approach, together with a syntactic constraint of minimality, can account for the intervention effects in a case like (28b), repeated below in (43).

(43) ??Theo didn’t play the guitar and drink any coffee

(43a) can be analyzed as (44a), (44b) or (44c). However, (44a) and (42) are ruled out on syntactic grounds via minimality above, while (44c) is syntactically well-formed, but it gives rise to a contradictory meaning.

(44) a. EXHjEXHi[¬[Theo play andj[+σ][drink anyi[+σ,+D]coffee ]]]

b. EXHi[¬[Theo play and[−σ][drink anyi[+σ,+D]coffee ]]]

c. EXHiEXHj[¬[Theo play andj[+σ][drink anyi[+σ,+D]coffee ]]]

In the following, I show how we can extend this approach straightforwardly to the case of soft presuppositions.

12Notice that minimality allows the configuration with the opposite order in (41), repeated from above. However,

as we saw, (41) gives rise to a contradiction, thus it is ruled out by the semantic side of the account. (41) EXHiEXHj[¬[Theo play the guitar andj[+σ][drink anyi[+σ,+D]coffee ]]]

In document Soft but Strong. Neg-Raising, Soft Triggers, and Exhaustification (Page 152-158)