**3.2 Alternatives, projection and triggering**

**3.2.2 Chemla (2009): the projection of presuppositions as a scalar phenomenon**

The proposal in Chemla 2009a is based on the idea that presuppositional triggers are identical to strong scalar items like every. In other words, in his approach, an atomic expression φ that intuitively presupposes p has p as its weaker alternative. For instance, (16b) is both an entailment and an alternative of (16a), as shown in (31c).5

(17) a. Bill won. b. Bill participated. c. Alt(17b) = won(b), participated(b)

As Chemla shows, the proposal predicts the apparent projection behavior through negation, since the negation of (17a), in (18a), has the alternatives in (18c). Given that negation inverts entailment relations, the alternative Bill didn’t participate is stronger than the assertion (i.e., Bill didn’t win). Assuming any theory of scalar implicatures, we obtain the negation of Bill didn’t participate(i.e., Bill participated) as an inference of (18a). In other words, we obtain (18b) as a scalar implicature of (18a).6

(19) a. Bill didn’t win.

b. Bill participated.

5_{The fact that (31b) is an entailment of (31a) is shown by (16).}

(16) Bill won #but didn’t participate.

6_{As Chemla (2009a) points out, one could describe the inference of (16a) in (16b) as projecting through negation,}

when (16a) is negated in (17a); however, like in Wilson’s (1975) proposal above, in this account, this inference is a simple entailment in the case of (16a) and a scalar implicature in the one of (17a). Chemla (2009a) also observes that this is entirely parallel to the behavior of scalar implicatures coming from strong scalar terms, like the ones in (33a) and (33b), which both give rise to the inference in (22) (see also Beaver 2001).

(18) a. Every student came. b. Not every student came. c. Some student came

c. Alt(19b) =

¬won(b), ¬participated(b)

In the same way as above, the fact that both (18a) and its negation in (19a) give rise to the same inference is what creates the appearance of projection through negation.

Beyond negation, the proposal also predicts that in the case of quantificational sentences the projection behavior should depend on the quantifier involved. The pattern predicted by this proposal is that a sentence like (20a) gives rise to the universal inference in (20b), while (21a) and (36a) do not give rise to the corresponding inferences in (21b) and (36b). As I discuss below, this is in line with the experimental results reported in Chemla (2009b).

(20) a. Each of these ten students won.

b. Each of these ten students participated.

(21) a. More than three of these ten students won the marathon.

b. Each of these ten students participated in the marathon.

(22) a. Less than three of these ten students won the marathon.

b. Each of these ten students won the marathon.

While successful with the cases above, as Chemla (2009a) observes, the proposal as it is does not make the right predictions for presupposition projection from the scope of negative quan- tifiers. This is because it predicts the existential inference in (23b), while the participants of Chemla’s (2009b) experiment reported the strong universal inference in (23c) for sentences like the one in (23a).

(23) a. None of these ten students won the marathon.

b. Some of these ten students participated in the marathon. c. Each of these ten students participated in the marathon.

More precisely, the inference in (23c) from (23a) was accepted more often than the analogous inference with a scalar implicature in (24c) from (24a).

(24) a. None of these ten students did all of the readings.

b. Some of these ten students did all of the readings. c. All of these ten students did some of the readings.

This difference constitutes a challenge for any proposal that reduces the behavior of soft pre- suppositions to that of scalar implicatures, since it would predict parallel behavior across the board, contrary to the data just discussed.

Chemla (in preparation) following his idea in Chemla 2009a, proposes a novel unified ac- count of presuppositions and scalar implicatures. I refer the reader to his paper for the details of his account, here I want to emphasize three aspects that are relevant for the comparison with the present proposal.

The first aspect regards the fact that he responds to his own challenge about the difference between presuppositions and scalar implicatures by abandoning the idea that presuppositional triggers are identical to strong scalar items, and assuming different alternatives for scalar im- plicatures and presuppositions. In doing so, he can account for the difference between the projection from the scope of negative quantifiers just discussed, because he only predicts exis- tential inferences in the case of scalar implicatures, while universal inferences for the case of presuppositions. In other words, he only predicts the inference in (24b) for a case like (24a), while he predicts the inference in (23c) from (23a). I argue, however, that while there is a dif- ference with the inference in (23c), the universal inference in (24c) from (24a) is also present in some cases and this is not predicted by Chemla (in preparation).7

7_{Chemla himself, in a different paper (Chemla 2008), discusses the example in (25a) and observes that it could}

have the inference in (25b).

(25) a. None of these 10 teachers killed all of their students. b. All of these 10 teachers killed some of their students.

In this chapter, I propose to develop Chemla’s (2009a) idea differently, responding to his challenge about negative quantifiers in a way that allows us to predict the inferences from (23a) to (23c), from (30a) to (30c), and their difference. The proposal has two components: first, I show that if we look carefully at the alternatives of negative quantifiers, we do actually predict the possibility of universal projection from their scope, both for soft presuppositions and for scalar implicatures. Second, I propose a way to account for the difference between soft presup- positions and scalar implicatures in terms of the notion of obligatory implicatures. As a further consequence, the alternatives assumed here allow an account of the projection of soft presup- positions within negative quantifiers and in particular of the asymmetry between nuclear scope and restrictor, which is not accounted for by Chemla (in preparation) and other recent accounts

An argument for the existence of inferences like (25b) comes from the felicity condition on the utterance of disjunc- tive sentences that I presented inCHAPTER1, also known as “Hurford’s constraint” (Hurford 1974; see also Singh 2008b). On the basis of this constraint, Chierchia et al. (To appear) construct a case for the existence of the inference in (26b) from (26a).

(26) a. All of the students did some of the readings b. None of the students did all of the readings

The logic of the argument is as follows: one creates a disjunction, where one of the disjunct entails the other in all readings of (29a) but the one with the scalar implicature in (29b). The case Chierchia et al. (To appear) construct is (27), which is felicitous and is compatible with Hurford’s constraint, only if we interpret (27) as (28).

(27) Every student solved some of the problems, or Jack solved all of them and all the other students solved only some of them.

(28) Every student solved some but not all of the problems, or Jack solved all of them and all the other students solved only some of them.

We can apply the same logic to the case in (29a), repeated from above, and construct a disjunction that is felicitous under Hurford’s constraint only if we assume that the first disjunct has the scalar implicature in (29b).

(29) a. None of the students did all of the readings. b. All of the students did some of the reading.

The disjunction in (30) is such that the second disjunct entails the first one unless the latter has the implicature in (29b).

(30) None of my professors failed all of their students or Gennaro failed none and all of the others failed just some.

To my ears, while a little involved as a sentence, (30) is felicitous, thereby supporting the existence of the inference in (29b).

I am aware of.

The second aspect that distinguishes the present proposal from Chemla’s (in preparation) account is that the former is not a theory of presuppositions in general but it is restricted to soft presuppositions. As I discuss below, this can account for the differences between soft and hard presuppositions in terms of ease of suspension and projection in quantificational sentences.8

The third relevant difference regards the fact that the present proposal is based on the gram- matical theory of scalar implicature, which postulates the presence of a syntactically realized exhaustivity operator. As I show below, this operator in the syntax predicts the intervention effects of soft presuppositions in the licensing of NPIs.

Summing up, the present proposal develops the idea proposed in Chemla (2009a), differ- ently from the alternative route proposed in Chemla in preparation. As I show below in detail, the contributions of the present proposal are: first, the alternatives for negative quantifiers pro- posed here make better predictions both for the case of scalar implicatures and for the one of soft presuppositions from scopes and restrictors of negative quantifiers. Second, restricting the theory to soft presuppositions, we can account for the differences between them and hard presuppositions. Furthermore, assuming a difference between scalar implicatures and soft pre- suppositions in terms of obligatoriness, we can account for their different behavior. Finally, the fact that the proposal here is based on an exhaustivity operator in the syntax allows an account of the intervention effects of soft presuppositions. I turn now to the triggering problem for the case of soft presuppositions.

— The proposal in Chemla 2009a is based on the idea that presuppositional triggers are identical to strong scalar items like every. In other words, an expression X that intuitively pre- supposes p, has p as its weaker alternative. For instance, (31a), would have (31c) as alternatives, that is, (31b) is, both an entailment and an alternative of (31a).

(31) a. Bill won.

8_{Notice that one could also restrict Chemla’s (in preparation) account to soft presuppositions. If one doesn’t,}

however, one has to provide a different way to account for the differences between soft and hard presuppositions with respect to context dependence and projection (see Chemla in preparation:p.41 for discussion).

b. Bill participated.

c. Alt(31b) =

won(b), participated(b)

As he shows, the proposal immediately predicts the apparent projection behavior through nega- tion, since the negation of (31a), in (32a), has the alternatives in (32c). Given the fact that negation inverts entailment relations, the alternative Bill didn’t participate is stronger than the assertion, Bill didn’t win, hence, assuming any theory of scalar implicatures, we obtain the nega- tion of Bill didn’t participate as an inference of (32a). Now, it is easy to see that the negation of Bill didn’t participateis just (32b). In other words, we obtain (32b) as a scalar implicature of (32a).

(32) a. Bill didn’t win.

b. Bill participated.

c. Alt(32b) =

¬won(b), ¬participated(b)

As Chemla (2009a) points out, one could describe the inference of (31a) in (31b) as projecting through negation, when (31a) is negated as in (32a); however, like in Wilson’s (1975) proposal, in this account, this inference is a simple entailment in the case of (31a) and a scalar implicature in the one of (32a). Chemla (2009a) also observes that this is entirely parallel to the behavior of scalar implicatures coming from strong scalar terms, like the ones in (33a) and (33b), which both give rise to the inference in (22) (see also Beaver 2001).

(33) a. Every student came.

b. Not every student came.

c. Some student came

In the same way as above, the fact that both (33a) and its negation in (33b) give rise to the same inference in (33c) is what creates the appearance of projection through negation.

Beyond negation, the proposal also predicts that in the case of quantificational sentences the projection behavior should depend on the quantifier involved. The pattern predicted by this proposal is that a sentence like (34a) gives rise to the universal inference in (34b), while (35a) and (36a) do not give rise to the corresponding inferences in (35b) and (36b). As I discuss below, this is in line with the experimental results reported in Chemla (2009b).

(34) a. Each of these ten students won.

b. Each of these ten students participated.

(35) a. Some of these ten students won the marathon.

b. Each of these ten students participated in the marathon.

(36) a. Less than three of these ten students won the marathon.

b. Each of these ten students won the marathon.

While successful with the cases above, as Chemla (2009a) observes, the proposal as it is does not make the right predictions for presupposition projection from the scope of negative quan- tifiers. This is because it predicts the existential inference in (37b), while the participants of Chemla’s (2009b) experiment reported the strong universal inference in (37c) for sentences like the one in (37a).

(37) a. None of these ten students won the marathon.

b. Some of these ten students participated in the marathon. c. Each of these ten students participated in the marathon.

More precisely, the inference in (37c) from (37a) was accepted more often than the analogous inference with a scalar implicature in (38c) from (38a).

(38) a. None of these ten students did all of the readings.

b. Some of these ten students did all of the readings. c. All of these ten students did some of the readings.

This is, hence, a challenge for any proposal that reduces the behavior of soft presuppositions to the one of scalar implicatures, since it would predict parallel behavior across the board, contrary to the data just discussed.

In this chapter, I develop Chemla’s (2009a) idea and respond to his challenge about negative quantifiers. First, I argue that while there is a difference with the inference in (37c), the universal inference in (38c) from (38a) is also possible in some cases. Chemla himself, in a different paper (Chemla 2008), discusses the example in (39a) and observes that it could have the inference in (39b).

(39) a. None of these 10 teachers killed all of their students. b. All of these 10 teachers killed some of their students.

The theory that I propose in this chapter can account both for the inference from (39a) to (39b) and for the difference between the latter and the corresponding case involving soft presup- positions like (37a) above. The proposal has two components: first, I show that if we look carefully at the alternatives of negative quantifiers, we do actually predict the possibility of universal projection from their scope, both for soft presuppositions and for scalar implicatures. Second, I propose a way to account for the difference between soft presuppositions and scalar implicatures in terms of the notion of obligatory implicatures. As a further consequence, the alternatives assumed allow an account of the projection of soft presuppositions within negative quantifiers and in particular of an asymmetry between soft presuppositions coming from soft triggers embedded in the nuclear scope on one hand and the one coming from soft triggers embedded in the restrictor on the other; a difference that is not accounted for by alternative accounts in the literature I am aware of. Chemla (in preparation) following his idea, proposes an account of presuppositions as scalar implicatures, responding to his own challenge about the difference between presuppositions and scalar implicatures differently: he abandons the idea that presuppositional triggers are identical to strong scalar items, and assume different alterna- tives for scalar implicatures and presuppositions. I compare his account and the one proposed

In sum, building on Chemla’s (2009a) idea, I propose here a scalar approach to soft pre- suppositions. As I discuss below in detail, the contributions of the proposal are: first, the alternatives for negative quantifiers that I propose here make the right predictions both for the case of scalar implicatures and for the one of soft presuppositions from scopes and restrictors of negative quantifiers. Second, restricting the theory to soft presuppositions, we can account for the difference between them and hard presuppositions. Furthermore, assuming a difference between scalar implicatures and soft presuppositions in terms of the notion of obligatory im- plicatures, we can, in turn, account for their different behavior. I turn now to the triggering problem for the case of soft presuppositions.

3.2.3 Abrusan (2011, to appear): the triggering of soft presuppositions

Abrus´an (2011b,a) proposes a solution to the triggering problem for soft presuppositions, in the form of a selection process among the entailments of a sentence. The intuition, following Stalnaker (1974), is the idea that entailments of a sentence that are not about the main point con- veyed by the sentence are perceived as presupposed. She uses a notion of aboutness formalized by Demolombe and Farinas del Cerro (2000); without going into the detail of the formalization, for which I refer the reader to Abrus´an’s (2011b) paper, the intuition behind this notion is that a sentence is about an entity if and only if its truth value can change if we change the truth value of the facts about that entity. The way this notion is applied to soft presuppositions is as follows: entailments that are about the event time of the matrix predicate of the sentence are part of the main point of the sentence, while the ones that are not about the event time of the matrix predicate are independent and end up being presupposed. Consider the example in (40a) and its entailments in (40b) and (40c).

(40) a. John knows (at t1) that Fred left (at t2)

b. John believes (at t1) that Fred left (at t2)

Intuitively, (40b) is about the time denoted by t1 and (40c) is not: changing the properties of

the world at time t1 won’t change the truth-value of (40c) but might change the one of (40b).

The definition of the triggering of soft presuppositions she proposes is (42).9

(42) Soft presupposition triggering Entailments of a sentence S that can be expressed by

sentences that are not about the event time of the matrix predicate of S are presupposed.

Notice that Abrus´an (2011a) assumes that the definition in (42) only applies to unembedded sentences. Abrus´an (2011b,a) assumes that a separate projection mechanism derives the presup- positions of complex sentences, on the basis of the atomic ones generated by such mechanism. What I do below is modify trivially the definition above, in order to make it an algorithm for selecting which entailments become alternatives and not presuppositions directly. Then, I use Chemla’s (2009a) idea for predicting the projection of soft presuppositions.