# What the presuppositional approach gets right

In document Soft but Strong. Neg-Raising, Soft Triggers, and Exhaustification (Page 45-51)

## 2.3 Predictions

### 2.3.1 What the presuppositional approach gets right

The presuppositional approach can successfully account for four aspects of the behavior of neg- raising predicates. In the following, I summarize each of them and briefly show how they are predicted by the presuppositional account.

The first aspect, observed by Gajewski (2005), regards the fact that the inference associated with a neg-raising predicate in the scope of negation is hard to suspend, in a way that resembles the markedness of presupposition cancellation in such environments. For instance, there is a contrast between (24a) and (24b)/(24c), which shows that canceling neg-raising requires a special intonation, like stress on the auxiliary or on the predicate.

(24) a. John doesn’t think that it is raining, #he is not sure. b. John DOESN’T think that it is raining, he is not sure. c. John doesn’t THINK that it is raining, he is not sure.

The second aspect regards the inferences that neg-raising predicates give rise to when embed- ded in the scope of negative quantifiers and negated universals: from a sentence like (25a) we typically draw the universal inference in (25b), while in the case of a negated universal sentence like (26a), the inference that we draw is (26b).10

10Homer (2012a) calls the inference in (26b) “wide-scope existential quantification reading” and takes it as char-

(25) a. No student thinks that Mary passed. b. Every student thinks that Mary didn’t pass.

(26) a. Not every student thinks that Mary passed.

b. There are some students who think that Mary didn’t pass.

The third aspect has to do with the licensing of certain NPIs. NPI licensing is a useful tool in the analysis of neg-raising predicates, as it backs up the often subtle judgements about neg- raising inferences. The standard assumption about NPIs is that they are licensed in downward

entailing (DE) environments (Ladusaw 1979; cf.CHAPTER 4). A DE environment is the scope

of a DE function, which can be defined as in (27).11

(27) A function f is downward entailing iff for any a, b in the domain of f such that a ⊆ b, then f(b) ⊆ f(a).

Negation is a DE function, as shown by the fact that (28a) entails (28b) and (29b) entails (29a).

(28) a. It rained hard.

b. It rained.

(29) a. It didn’t rain hard.

b. It didn’t rain.

A subset of NPIs, so-called “strict” or “strong” NPIs, are licensed only in some DE environ- ments. Zwarts (1998) proposes that the characteristic property of the members of such the en- vironments that license strong NPIs is anti-additivity (but see appendix C for a different, more recent, hypothesis on the licensing of strict NPIs, defended in Gajewski 2011 and Chierchia to appear). An anti-additive environment is the scope of an anti-additive function, defined in (30).

(30) A function f is anti-additive iff for any a, b in the domain of f, f(a)∧ f(b) ⊆ f(a ∨ b)

11from Gajewski 2007, where ⊆ indicates cross-categorial entailment as defined in

As shown by the validity of the inference from (31a) to (31b), negation is also an anti-additive function.

(31) a. It didn’t rain and it didn’t snow.

b. It didn’t rain or snow.

It was noticed in Lakoff 1969 that strict NPIs show a difference between neg-raising and non- neg-raising predicates, in that they are licensed when embedded under a negated neg-raising predicate, like in (32a), but they are not when in the scope of a non-neg-raising one, like in (32b).

(32) a. John doesn’t think that Mary will arrive until tomorrow.

b. *John isn’t certain that Mary will arrive until tomorrow.

Furthermore, strict NPIs are licensed in the scope of neg-raising predicates embedded under negative quantifiers, as in (33).

(33) No student thought that Mary would arrive until tomorrow.

The fourth aspect regards the behavior of stacked neg-raising predicates. Fillmore (1963) orig- inally observed that neg-raising operates cyclically. In other words, a sentence like (34a), in which negation appears before a sequence of stacked neg-raising predicates, gives rise to the neg-raising inference in (34b).

(34) a. I don’t imagine Bill thinks Mary wants Fred to leave.

b. I imagine Bill thinks Mary wants Fred not to leave.

Horn (1971), however, observes that the cyclicity is only partial: the generalization appears to be that neg-raising belief predicates embedding neg-raising desire ones allow cyclicity, while desire-predicates embedding belief-ones do not.

(35) a. I don’t believe Bill wanted Harry to die. b. I believe Bill wanted Harry not to die.

(36) a. I don’t want Bill to believe Harry died 6

b. I want Bill to believe Harry didn’t die.

The NPI licensing also reveals this pattern as shown by (37a) and (37b) (from Gajewski 2007).12

(39) a. I don’t believe John wanted Harry to die until tomorrow.

b. *I don’t want John to believe Harry died until yesterday.

In sum, there are four aspects of the behavior of neg-raising predicates, which, as I discuss below, can be accounted for if we treat them as presuppositional triggers: (a) the fact that the neg-raising inferences are hard to cancel (b) the inferences they give rise to from the scope of negative quantifiers and negated universals, (c) the licensing of strong NPIs, and (d) the behavior of stacked neg-raising predicates. Gajewski (2007) shows that the presuppositional approach can account for these four aspects of the behavior of neg-raising predicates. Let us go through each of them in the following.

First, the fact that presuppositions are hard to cancel under negation appears to be parallel to what happens with neg-raising inferences.13 (40b) appears parallel to the case of a presuppo- sitional triggers like discover, as (41a) and (41b) show.

(40) a. John doesn’t think that it is raining, #he is not sure. b. John DOESN’T think that it is raining, he is not sure.

12Other doxastic and bouletic/deontic predicates behave similarly.

(37) a. Mary doesn’t think Bill should have left until yesterday. b. *Mary shouldn’t think Bill left until yesterday.

(38) a. Bill doesn’t imagine Sue ought to have left until yesterday. b. *Bill ought not imagine Sue left until yesterday.

13Notice that this applies even if Gajewski (2007) argues that neg-raising predicates are soft triggers, since also

(41) a. John didn’t discover that he was accepted, #he wasn’t.

b. John DIDN’T discover that he was accepted, he wasn’t.

Second, if we assume that presuppositions in the scope of negative quantifiers project univer- sally (see Heim 1983 and Chemla 2009a for discussion), the prediction for the meaning of a sentence like (42a) are (43a) with the presupposition in (43b). (43a) and (43b) together entail (43c). In other words, Gajewski (2007) can derive the universal inference in (42b) (=(43c)).

(42) a. No student thinks that he was accepted.

b. Every student thinks that he wasn’t accepted.

(43) a. ¬∃x[student(x) ∧ thinksx(p)]

b. ∀x[student(x) → (thinksx(p)∨ thinkx(¬p))]

c. ∀x[student(x) → thinkx(¬p)]

The presuppositional account also makes the right predictions in the case of negated universal sentences: (44a), schematized as in (45a), together with the presupposition in (45b), entails (45c), which is the intuitively correct inference in (44b).

(44) a. Not every student thinks that he was accepted.

b. Some student thinks that he wasn’t accepted.

(45) a. ¬∀x[student(x) → thinksx(p)]

b. ∀x[student(x) → (thinksx(p)∨ thinkx(¬p))]

c. ∃x[student(x)∧ thinkx(¬p)]

Third, it can be shown that the presuppositional approach predicts that cases like (49) and (50) are anti-additive environments, thus the fact that strong NPIs are licensed in these environments is predicted.14

14As Gajewski (2007:p.304) discuss, consider the meaning of a neg-raising predicate P as in (46) (where

 has to be understood to range over the modal base of the neg-raising predicate P, see fn.3 above).

(49) John doesn’t think that Mary would arrive until tomorrow.

(50) No student thinks that Mary would arrive until thursday.

Finally, Gajewski (2007) shows that the presuppositional account can also derive the behavior of partial cyclicity. The reason why it predicts it lies in the different way presuppositions project from belief- versus from desire-predicates. Consider embedding a sentence, like (51a), which presupposes (51b), into think and want, as in (52a) and (52b), respectively. The observation is that both (52a) and (52b) appear to presuppose (52c) and crucially (52b) does not presuppose (52d) (see Heim 1992 and Beaver and Geurts To appear for discussion).

(51) a. Bill will sell his cello.

b. Bill has a cello.

(52) a. Bill thinks he will sell his cello. b. Bill wants to sell his cello. c. Bill thinks he has a cello. d. Bill wants to have a cello.

This asymmetry in projection between think and want is what allows Gajewski (2007) to derive (46) [[not P]](p)(x) =

a. presupposes: [p ∨ ¬p] b. asserts:¬p

c. together (46a) and (46b) entail:¬p (47) [[not P]](q)(x) =

a. presupposes: [q ∨ ¬q] b. asserts:¬q

c. together (47a) and (47b) entail:¬q (48) [[not P]](p∨ q)(x) =

a. presupposes: [(p ∨ q) ∨ ¬(p ∨ q)] b. asserts:¬(p ∨ q)

c. together (48a) and (48b) entail:¬(p ∨ q)

(46) and (47) entails that no world is a (p∨ q)-world, hence the presupposition of (48) is satisfied and (48) must be true. The presuppositional account, then, predicts that negated neg-raising predicates create anti-additive contexts.

the pattern above (see Gajewski 2007 and Homer 2012a for detail).

In sum, the presuppositional account successfully accounts for the four aspects of the be- havior of neg-raising predicates presented above. However, as I discuss now, the presuppo- sitional account does not predict any difference between soft presuppositions and neg-raising inferences, contrary to what appears to be the case.

In document Soft but Strong. Neg-Raising, Soft Triggers, and Exhaustification (Page 45-51)