**3.3 An exhaustivity-based theory of soft presuppositions**

**3.3.3 First predictions**

**3.3.3.3 Conditionals**

The case of a soft trigger embedded in the consequent like (72) is analogous to the correspond- ing case of disjunction in the preceding section: the conditional inference that if John wasn’t sick he participated in the marathon is predicted as an entailment. In the same way as in the case of disjunction, we can rely on a solution to the proviso problem and obtain the non-conditional inference that he participated in the marathon.

(72) If John wasn’t sick, he won the marathon.

Let us now look at the predictions of the present proposal for the case of a soft trigger embedded in the antecedent of a conditional, like (73a). The inference that we want to obtain, at least in some cases is (73b).

(73) a. If Jane won, she is celebrating right now.

b. Jane participated.

I first show that we predict the weaker inference in (74) and then suggest two ways to strengthen (74) to (73b).

(74) It’s possible that Jane participated.

Weak projection There are a number of possible analysis of conditionals on the market, so

first we need to decide which one to adopt. One such analysis of conditionals is the material implication, p → q, which states that a conditional is false only if the antecedent is true and the consequent is false. As I show now, this analysis can account for the cases of projection of soft presuppositions from antecedents of conditionals. However, it also make wrong predic- tions about the consequent. By way of illustration, consider the case in (75a), schematically represented in (75b).

(75) a. If Jane won, she is celebrating right now.

b. won(j) → cel(j)

c. Alt =

won(j) → cel(j), par(j) → cel(j)

When we exhaustify (75b) as in (76a), over its alternatives in (75c), we negate the non-weaker alternative part → cel(j) and we obtain two inferences: first, given that the falsity of a condi- tional analyzed as material implication entails the truth of its antecedent, we obtain the inference that Jane participated. This could account for the apparent projection behavior of the presup- position of Jane won embedded in the the antecedent. Second, however, we also obtain the non-attested inference to the negation of the consequent, that is she isn’t celebrating right now.

(76) a. [[EXH]](won(j) → cel(j)) =

(won(j) → cel(j))∧ ¬(par(j) → cel(j)) =

(won(j) → cel(j))∧ (par(j) ∧ ¬cel(j))

Material implication combined with the theory of soft presuppositions given here gives rise to a problematic prediction. Notice, however, that since this prediction carries over to cases involv- ing “regular” scalar implicatures, a solution for this problem is needed independently. Indeed for a case like (77a), involving the scalar term all, we obtain in the same way the prediction that

John corrected some of the assignment but also that he will not go out tonight. Again the latter is certainly not an attested inference of (77a).

(77) a. If John corrected all of the assignments, he will go out tonight. b. John corrected some of the assignments and he won’t go out tonight.

If we move to a different theory of conditionals, like strict implication,(p → q), we do not make this incorrect prediction anymore: we only predict that it is possible that Jane participated and that she is not celebrating right now. This is illustrated in (78a)-(78d).

(78) a. If Jane won, she is celebrating right now.

b. [won(j) → cel(j)]

c. Alt =

[won(j) → cel(j)], [par(j) → cel(j)]
d. [[EXH]](_{[won(j) → cel(j)]) =}

(_{[won(j) → cel(j)]) ∧ (¬[par(j) → cel(j)]) =}

(_{[won(j) → cel(j)]) ∧ (♦[par(j) ∧ ¬cel(j)])}

Furthermore, it is easy to see that (78d) is equivalent to the claim that it is possible that Jane participated and did not win and that she is not celebrating right now. This appears an attested inference for conditionals like (78a). Indeed, it is entailed by an inference that we generally draw from conditionals, the so-called “conditional perfection” inference, which in this case would be (79) (see von Fintel 2001 and references therein; see alsoCHAPTER2, Appendix A).

(79) [¬win(j) → ¬cel(j)]

I come back to the inferences predicted in this non-upward entailing contexts like antecedent of conditionals in section 3.6, when I talk about the restrictors of universal sentences. Now let us discuss instead the issue that, while on one hand we solved the problem of the non- attested inference to the negation of the consequent, now the projection out of the antecedent is weakened: we only get that it’s possible that Jane participated, which seems too weak, at least

in some cases. In the next paragraph, I sketch two possible ways to strengthen this inference to Jane participated.

Strong projection A first strategy to account for the strong inference in (80c) from (80a) in the present account would be to say that the prediction from a conditional like (80a) to the weak inference in (80b), is another instance of the proviso problem.

(80) a. If Jane won, she is celebrating right now.

b. It’s possible that Jane participated. c. Jane participated.

In particular, Singh (2009) argues that we should analyze also cases like (81) and (82) as giving rise to another instances of the proviso problem and propose a way to derive the inferences from (81b) to (81c) and from (82b) to (82c).

(81) a. John believes that Bill’s brother will come.

b. John believes that Bill has a brother. c. Bill has a brother.

(82) a. It’s possible that John won.

b. It’s possible that John participated. c. John participated.

It is conceivable, then, that the inference from (80b) to (80c) is of the same nature and should be solved by an account of the proviso problem, which accounts for the inference from (81b) to (81c) and from (82b) to (82c).

In Romoli 2011, I propose a different solution by postulating that conditionals also introduce their own alternatives. I adopted a strict conditional semantics of conditionals, with the (hard) presupposition that the antecedent must be compatible with the modal base (von Fintel 1999).

The proposal is that conditionals like (83a) are associated with the alternatives in (83b).14 (83) a. [[if p, q]] is defined if♦p when defined =[p → q] b. Alt = [p → q], ♦¬p, ♦q, ♦¬q

One can show that in simple cases, where no scalar item appears in the antecedent, none of the three alternatives is excludable, hence exhaustification is predicted to be vacuous. On the other hand, if we go back to the crucial case involving a scalar item embedded in the antecedent, we end up with more alternatives. In these cases, with (84) as an example, exhaustification is no longer vacuous and we end up with the right prediction, namely that Jane participated.15,16

(86) a. If Jane won, she is celebrating right now

b. Alt =

[won(j) → cel(j)], [par(j) → cel(j)] ♦¬won(j), ♦¬par(j), ♦¬cel(j), ♦cel(j)

c. [[EXH]]([won(j) → cel(j)]) = [won(j) → cel(j)] ∧¬♦¬par(j)=

14_{Where these alternatives come from is left open in Romoli 2011. I leave this open here as well, noting that one}

direction for future exploration might be to observe that the alternatives of conditionals posited here are what they are generally thought as the clausal implicatures, minus the one that is missing,♦p, which is already presupposed (cf. Gazdar 1979). The hope is that a theory of clausal implicatures will motivate independently the alternatives here.

15_{More precisely, we obtain that it is true that Jane participated in all worlds in the relevant modal base, which I}

take to be epistemic in these cases. I leave for further research to explore the predictions for cases of non-epistemic conditionals.

16_{Notice that at this point the present system predicts that also scalar implicatures coming from strong scalar items}

should “project” out of the antecedents of conditionals. In other words, it predicts that (84b) can be an inference of (84a).

(84) a. If John failed all of his students, the dean will be upset. b. John failed some of his students.

It is unclear whether (84a) can ever have (84b) as an inference, but if it can, it is intuitively much weaker than the inference from (85a) to (85b), repeated from above. Below, when I discuss the differences between soft presuppo- sitions and scalar implicatures I show that we can account for the difference between (84a) and (84b), on one hand, and (85a) and (85b) on the other, via the notion of obligatory scalar implicature.

(85) a. If Jane won, she is celebrating right now b. Jane participated

[won(j) → cel(j)] ∧par(j)

In the following, I tentatively adopt the second strategy from Romoli 2011 to account for the projection of soft presuppositions from the antecedents of conditionals and leave for further research the exploration of the first one based on an account of the proviso problem.

In the next section, I sketch the predictions for the case of polar questions and then I turn to the behavior of stacked soft triggers, which as discussed in CHAPTER 2 is problematic for Abusch’s (2010) account, and show how the present proposal can straightfowardly predict their behavior.