Suspension of scalar implicatures vs suspension of soft presuppositions

In document Soft but Strong. Neg-Raising, Soft Triggers, and Exhaustification (Page 128-133)

3.4 Soft versus hard triggers and soft triggers versus strong scalar terms

3.4.2 Suspension of scalar implicatures vs suspension of soft presuppositions

Returning to the difference in defeasibility between soft triggers and strong scalar terms, I ar- gue that we can account for this phenomenon if we take into account the varying availability of the activated alternatives. The feature-based implementation, adopted from Chierchia (2006, to appear), provides us with the option of having the alternatives of certain elements obligatorily active. I propose that soft triggers are such elements. The way to capture this is by assuming that soft triggers are endowed with the feature [σ], which is, however, necessarily valued as “+”. As a consequence, the alternatives of soft triggers are always active and require exhaustifica- tion. Furthermore, I am assuming that when alternatives are always active, the question under discussion plays no role. In other words, the alternatives of strong scalar terms are subject to

relevance while the ones of soft triggers are not.24,25

Taking the alternatives of soft triggers to be obligatory predicts prima facie that their pre- suppositions should never be suspendable. However, we observed earlier that this is not always the case. If we want to maintain that alternatives are always active and yet that they don’t always give rise to presuppositions, we need to appeal to a different source for this suspendabil- ity. I argue that the difference source of suspension is the scope ofEXH. This is because in the case of strong scalar items local exhaustification is always vacuous and thus represent a way of suspending their inference. To illustrate consider (113).

(113) If Mary won, she is celebrating.

Given the hypothesis above, the alternatives of win are always active, exhaustification always occurs and there are in principle two sites at which this can happen: at the global level as in (114a), or within the antecedent of the conditional as in (114b).

(114) a. EXH[if Mary won[+σ]she is celebrating]

b. [If [EXH[Mary won[+σ]] she is celebrating]

(114a) gives rise to the soft presupposition that Mary participated in the way proposed in section 3.3.2. (114b), on the other hand, does not give rise to any inference, since the exhaustification of the embedded complement is vacuous.26 Notice that given the principle do not weaken! in

24Simons et al. (2010) propose a theory of the projection of presuppositions (and other inferences) which is also

connected to the notion of questions under discussions. Roughly, they propose that presuppositions project when they are not at issue relative to the question under discussion. I leave the comparison between the present account and theirs for further research. See Abrus´an 2011a for detailed criticism of their proposal.

25Notice that, as an anonymous reviewer points out, a prediction of this feature-based account is that there might

be languages in which strong scalar terms like every would only have a [+σ], while soft triggers could have [+σ] or [−σ], thus we expect their behavior to change accordingly.

26To see this notice that exhaustification at that scope site is like exhaustifying the unembedded sentence in (115a),

with respect to the alternatives in (115b). (115) Mary won.

(57), (114b) is dispreferred, as it is equivalent to the meaning withoutEXH. The inference that Mary participated is, then, predicted to be the default unless we make it clear in the context that it should be suspended; more precisely, we do not insert exhaustification locally unless information in the context contradicts the result of global exhaustification, like in (116).

(116) I don’t know whether Mary ended up participating, but if she won, she is celebrating.

In sum, contrary to scalar implicatures which can be suspended by virtue of there not being active alternatives to exhaustify, soft presuppositions can only be suspended via local exhaus- tification.27 Let us now go through to how this mechanism can account for the differences between scalar implicatures and soft presuppositions.

I proposed above that scalar implicatures are subject to relevance while soft presuppositions are not. I argue now that it is precisely this difference that gives rise to the different behavior that they exhibit. Consider the case of negation first, where we saw that both scalar implicatures and soft presuppositions seem to project robustly. A possible question under discussion for a sentence like (118a) appears to be (119a), which corresponds to the partition in (119b), which divides the logical space in a cell in which John did all of the readings, one in which John did some but not all of the readings, and one in which John didn’t do any of the readings.

(118) a. John didn’t do all of the readings

b. {¬[John did all], ¬[John did some]}

(119) a. How much of the readings didn’t John do?

b. {c1= all, c2=¬all ∧ some, c3=¬some}

27Notice that in principle also scalar implicatures coming from strong scalar items could be suspended via local

exhaustification: in fact, in principle the scalar implicature of (117a) could be suspended as in (117b) but also as in (117c). This creates a redundancy in the system; I come back to this below.

(117) a. John didn’t do all of the readings b. ¬[John did all[−σ]of the readings]

Both the alternatives in (118b) correspond to a cell or a union of cell in (119b), hence they are both relevant.28 When we then exhaustify (118a), we obtain the inference that John did some of the readings.

Consider, instead, what happens in somewhat more complex cases involving scalar terms embedded under the antecedent of a conditional like (120a) or (120b). The question here is whether we predict the inference in (120c).

(120) a. If John did all of the readings, he will go out tonight. b. John will go out tonight, if he did all of the readings.

c. John did some of the readings.

Natural questions under discussion for (119a) and (119b) are (122a) and (122b), respectively.29

(121) a. What will John do if he did all of the readings?

b. Under what conditions will John go out?

It can be shown that in both of these cases the alternatives that would give rise to the inference in (120c) are not relevant. By way of illustration, consider the case of (121b) Recall that the alternatives assumed above for cases like (120a) or (120b) are the ones in (122).

(122) Alt =     

[all → go-out(j)], [some → go-out(j)]

♦¬all,♦¬some,♦¬go-out(j), ♦go-out(j)

    

The partition corresponding to (121b) is in (123), where p and q are propositions that represent

possible conditions under which John will go out. It is easy to see that ♦¬some does not

correspond to any cell or union of cells of (123) and it is then irrelevant.

(123) {c1= go-out(j) if and only if p, c2= go-out(j) if and only if q, ....}

28Namely¬[John did some] corresponds to c

3, while¬[John did all] corresponds to c2∪ c3 29See von Fintel (1994) for discussion.

Therefore, in the case of scalar terms embedded in the antecedents of conditionals like (120b) or (120a), given reasonable questions under discussion, the alternatives that would give rise to the inference in (120c) are not going to be relevant. This is the reason why (120c) is not predicted as an inference from (120a) and (120b).

In sum, we can account for the suspendability difference between scalar implicatures and soft presuppositions by postulating a difference in terms of their being subject to relevance or not, as modeled with the obligatoriness of activation of the alternatives.

3.5

Novel Predictions for Projection in Quantificational Sentences

As Chemla (2009a) points out, one motivation for the scalar approach to presuppositions is that it makes fine-grained predictions for quantificational sentences, which map nicely to Chemla’s (2009b) empirical results. In particular, as shown below, it predicts that the projection in quan- tificational sentences should be sensitive to the type of determiner involved in the sentence. The present proposals makes three novel contributions with respect to quantificational sentences: first, by being restricted to soft presuppositions, together with any theory of hard presupposi- tions which predicts that they project universally, it can account for the differences between triggers observed by Charlow (2009). Second, by assuming independently justified alternatives for negative quantifiers, it correctly predicts both universal projection from the scopes of nega- tive quantifiers and non-universal projection from their restrictors, a combination of predictions that is not made by any account that I am aware of. Furthermore, these new alternatives also pre- dict universal inferences like (124b) for strong scalar terms embedded in the scope of negative quantifiers like all in (124a).

(124) a. None of these professors failed all of their students.

b. All of these professors failed some of their students.

Finally, given the differences in obligatoriness of alternatives, it can also account for the dif- ference in robustness between the inference from (124a) to (124b) and the corresponding cases

involving soft presuppositions like (125a) and (125b).

(125) a. None of these students won.

b. All of these students participated.

In document Soft but Strong. Neg-Raising, Soft Triggers, and Exhaustification (Page 128-133)