Alternatives for soft presuppositions and the triggering problem

Following Chemla (2009a), I assume that soft triggers are strong scalar items: they are associ- ated with a set of lexical alternatives, of which they are the strongest elements.10 _{For instance,}

we associate soft triggers like win, know and stop with lexical alternatives as in (43b), (44b) and (45b).

(43) a. [[win]] = λx[win(x)]

b. Alt(43a) = {λx[win(x)], λx[participate(x)]}

(44) a. [[know]] = λpλx[knowx(p)]

b. Alt(44a) = {λpλx[knowx(p)], λpλx[p]}

(45) a. [[stop]] = λPλx[stop(x, P)]

b. Alt(45a) = {λPλx[stop(x, P)], λPλx[used-to(x, P)]}

I assume that these alternatives become sentential alternatives in the way outlined in CHAP- TER 1, so that for instance, in (46a), the alternatives are the ones in (46b) and similarly the alternatives of (47a) are the ones in (47b) and the ones of (48a) are in (48b).

(46) a. John won.

b. {won(j), participated(j)}

(47) a. John doesn’t know that it is raining

b. {¬know_j,w(p),¬p(w)}

(48) a. Mary didn’t stop smoking.

10_{I am assuming the notion of generalized entailment defined in}

b. {¬stop(m, smoke), ¬used-to(m, smoke)}

The question at this point is of course where these alternatives come from. Notice that this is once again the triggering problem (i.e., where presuppositions come from) but this time in a different guise. This is because theories of presuppositions that are based on alternatives do not automatically solve the triggering problem, but rather reframe it so as to question the origin of the alternatives instead: where the alternatives come from and why those alternatives and not others (see Schlenker 2010 for discussion). Here is where I adopt Abrus´an’s (2011b) idea and propose that these alternatives represent a subset of their lexical entailments which can be characterized systematically. Her notion of aboutness gives us a way to characterize this subset of lexical entailments. Specifically, it tells us why, for instance, John believes that it is raining is not an alternative of (49a). Recall that her idea is that a lexical entailment of a sentence is not about the event time of the matrix predicate if it does not co-occur with it. As seen above, (49a) entails (49b) and (49c), but only (49c) is not about the matrix event time in Abrus´an’s (2011b) system.

(49) a. John knows that it is raining.

b. John believes that it is raining. c. It is raining.

While she argues that (49c) becomes a presupposition of (49a), I propose to trivially modify her procedure so that (49c) becomes an alternative of (49a), while (49b) does not. Her notion can systematically distinguish the entailments that I assume are among the alternatives from the ones that are not. In other words. For instance, it tells us that (50b), but not (50c), should be an alternative of (50a).11

11_{One might ask at this point why we should treat certain entailments as alternatives in the case of soft triggers}

but not do the same in the case of hard triggers (see also Abbott 2006 for a similar criticism of Abusch’s (2002) system). Notice that Abrus´an’s (2011b) algorithm can only apply to presuppositional verbs, or triggers for which the presupposition can be traced back to the presence of a verb in the sentence. Hence, if she is right, the proposed algorithm is indeed expected to apply only to soft triggers. There is an open question here about the status of definite descriptions or possessives (see footnote 3 above). Thanks to Marta Abrusan (p.c.) for discussion on this point.

(50) a. John stopped smoking.

b. John used to smoke.

c. John doesn’t smoke.

Finally, there appears to be a difference between the alternatives of strong scalar items like every and soft triggers like win which is worth emphasizing: while the alternatives of strong scalar items appears to be symmetric, in that, for instance, some is an alternative of every and every is an alternative of some, the ones of soft triggers do not. In other words, I am assuming that win has participate as an alternative but not that participate has win as an alternative. This in turn predicts that we should not expect participate to behave like a weak scalar item, a prediction that is confirmed by the pattern of win and participate in certain disjunctions. In CHAPTERS 1 and 2, I discussed the so-called “Hurford’s constraint”, a felicity condition on the utterance of disjunctive sentences (Hurford 1974; see also Chierchia et al. To appear and Singh 2008c). Chierchia et al. (To appear) use Hurford’s constraint as a diagnostic for scalar implicatures, so given the present proposal, we can use it here to explore soft presuppositions. In particular, the present proposal expects soft triggers like win to behave like a strong scalar term like all. As (51a) and (52a) show this prediction is borne out: in both cases the second disjunct would entail the first, unless we analyze them as (51b) and (52b), which are equivalent to (51c) and (52c), respectively, with no entailment relation between the disjuncts.

(51) a. Either John didn’t do all of the readings or he didn’t do any of them.

b. EitherEXH[not[John did all of the readings] or not[he did any of the readings] c. Either John did some but not all of the readings or he didn’t do any.

(52) a. Either John didn’t win or he didn’t participate.

b. EitherEXH[not[John win] or not[he participate]

c. Either John participated and didn’t win or he didn’t participated.

On the other hand, given that we are not assuming that participate has any alternative, we do not expect expressions like participate to behave like (weak) scalar terms. This prediction again

is borne out. To see this, consider (53a) and (54): in both cases the second disjunct entails the first, however if we analyze (53a) as (53b), we predict the reading in (53c), with no entailment relation between the disjuncts. On the other hand, given that we are assuming that participate has no alternative, we cannot exhaustify the first disjunct and obtain an inference from the first disjunct of (54), thus the infelicity is expected.

(53) a. Either John did some of all of the readings.

b. EitherEXH[John did some] or all of the readings. c. Either John did some but not all or all of the readings.

(54) #John participated or he won.

I turn now to a reminder on the theory of scalar implicatures that I am assuming outlined in CHAPTER 1.