# A condition on EXH

In document Soft but Strong. Neg-Raising, Soft Triggers, and Exhaustification (Page 74-81)

## 2.6 Explaining what the presuppositional approach can explain

### 2.6.4.2 A condition on EXH

The idea in informal terms is that the exhaustification of a sentence should leave untouched the presupposition of its prejacent. As I show below, if we were to exhaustify a sentence like (138) we would end up strengthening its presuppositions and thus we cannot do it.

(138) I don’t want Bill to believe Harry died.

Before formulating the condition, let us make some explicit assumptions about what hap-

pens when EXH applies to a presuppositional prejacent. First, we need to adopt the notion

of strawson-entailment, as defined in (139) (Gajewski 2011, von Fintel 1999).

(139) Strawson entailment

a. For p, q of type t, p⊆sq iff p → q

b. For f, g of type hσ, τi,

The notion of Strawson entailment allows us to look at entailment relations by ignoring presup- positions. We can, hence, defineEXHas in (140).25

(140) a. [[EXH]](φ)(w) =∀ψ ∈Excl(φ)[¬ψw]

b. Excl(φ) = {ψ ∈ Alt(φ) : φ *sψ}

The presuppositions of an exhaustified sentence are, hence, going to be those of the prejacent and those of the negated alternatives. We can now formulate the condition in (141), which requiresEXHto leave the presuppositions of its prejacent untouched. In other words, the ex- haustivity operator should be just a “hole” in Karttunen’s (1973) sense and not add anything to the presuppositions of the prejacent. The condition is formulated as a presupposition ofEXH as in (141) (to be revised in Appendix B, to accommodate cases not involving only neg-raising predicates).

(141) EXH[φ] is defined only if π(φ) = π(EXH[φ])

(where for any α, π(α) indicates the presuppositions of α)

I show now that (141) blocks exhaustification in the case of want embedding believe, but before that let us go through a semantics for want that I adopt.

A semantics for want I adopt the doubly-relative modal semantics of want proposed by von

Fintel (1999), and defended further in Crnic 2011.26 A sentence like a wants p roughly says

that among a’s doxastic alternatives, the most desirable to a are p-worlds. von Fintel (1999) formalizes this intuition with a modal semantics, relativized to two conversational backgrounds: the first is the modal base, that is the set of a’s doxastic worlds, and the second is a set of propositions, representing a’s desires and used to impose an ordering on the modal base. These two conversational backgrounds are obtained through the use of the two functions in (142a) and

25We can define the notion of innocent exclusion on the basis of Strawson entailment. I just use the simpler notion

here for the sake of presentation.

(142b).

(142) a. f(a, w) ={w0∈ W : w0is compatible with what a believes in w}

b. g(a, w) ={p ⊆ W : p is (the content of) a desire of a in w}

We now define a strict partial ordering on f(a, w) using the set of propositions g(a, w), as in (143): w0 is better than w00 relative to P iff all propositions in P that hold in w00also hold in w0and some that hold in w0do not hold in w00.

(143) for any set of propositions P, worlds w0, w00:

w0<pw00iff ∀p ∈ P : p(w00)→ p(w0)∧ ∃q ∈ P : p(w0)∧ ¬p(w00)

Then we define a selection functionBESTP, which picks the worlds in the modal base that are best according to <p

(144) given a partial ordering <p,BESTPselects the best P worlds in any set of worlds X:

∀X ⊆ W :BESTP(X) ={w ∈ X : ¬∃w0 ∈ X : w0<pw}

Finally, we can define the meaning of want as in (145).

(145) [[want]](f)(g)(p)(a) = λw . ∀w0 ∈BESTg(a,w)(f(a, w))[p(w0)]

The semantics above has to be refined, because as Heim (1992) and von Fintel (1999) notice, it has some unwanted consequence in relation to what the attitude holder believes. In particular, if a believes that p, it follows that a wants that p is automatically true (if all a’s belief worlds are p-worlds, then the most desirable worlds to a among them will also be). Analogously, if a believes that p is false, it follows automatically that a wants that p is false (if none of a’s belief worlds are p-worlds, then none of the most desirable to a among them are p-worlds). To avoid this problem, von Fintel (1999), following Heim (1992), postulates that the semantics above also has a presupposition that the attitude holder neither believes that the propositional

argument of want is true nor believes that it’s false.27

(147) [[want]](f)(g)(p)(a) =

λw : ∅ 6= f(a, w) ∩ p 6= f(a, w) . ∀w0∈BESTg(a,w)(f(a, w))[p(w0)]

Back to partial cyclicity Let us go back to the case of want embedding believe like in (148).

(148) Mary doesn’t want John to believe that Fred left.

I am assuming that the meaning of (148) is (149a) with the presuppositions in (149b). I show now that if we were to exhaustify (149) we would strengthen the presuppositions in (149b).

(149) a. ¬∀w0∈BESTg(m,w)(f(m, w))[belj,w0(p)]

b. ∃w0 ∈ f(m, w)[belj,w0(p)]∧ ∃w00∈ f(m, w)[¬belj,w00(p)]

Let us simplify the notation and write (149b) as (150), where♦m[p] indicates that p is possible

according to Mary’s beliefs.

(150) ♦m[belj(p)]∧ ♦m[¬belj(p)]

Consider now what would happen if we were to exhaustify (148) as in (151) with respect to its alternatives in (152).

(151) EXH[Mary doesn’t want John to believe that Fred left]

27Notice that this has to be further refined to accommodate examples such as (146) from Heim (1992), where the

attitude holder does not appear to have doubts about where he will be tonight. (146) (John hired a baby-sitter) because he wants to go to the movies tonight.

Heim (1992:p.199) proposes that what (146) teaches us is that “when we assess someone’s intention [...] we don’t take into account all his beliefs, but just those that he has about matters unaffected by his own future actions”. In other words, in the semantic adopted here, we should not consider in f(α, w) the set of doxastically accessible worlds, but rather the set of worlds compatible with what α believes to be the case no matter how he or she chooses to act. For our purposes, this modification is immaterial, so I will just ignore it.

(152)                  ¬[wantm[belj(p)]]

¬[wantm[belj(p)∨ belj(¬p)]]

¬[wantm[belj(p)]∨ wantm[¬[belj(p)]]]

¬[wantm[belj(p)∨ belj(¬p)] ∨ wantm[¬[belj(p)∨ belj(¬p)]]]

                

The result of exhaustification is the conjunction of (153a), (153b), and (153c).

(153) a. ¬wantm(belj(p))

b. wantm(belj(p))∨ wantm¬(belj(p))

c. wantm(belj(p)∨ belj(¬p))

As for the assertion part, in parallel to the case of believe embedding want, from (154a) and (154b) we could conclude (154c) and from (155a) and (155b) we could conclude (155c). In other words, we would obtain the reading equivalent to negation taking scope below both neg- raising predicates.

(154) a. ¬wantm(belj(p))

b. wantm(belj(p))∨ wantm¬(belj(p))

c. wantm(¬(belj(p))

(155) a. wantm(¬belj(p))

b. wantm(belj(p)∨ belj(¬p))

c. wantm(belj(¬p))

However, I show now that the presupposition of the exhaustified sentence is stronger than that of the prejacent, thus exhaustification is blocked by the condition in (141). To see this, let us go through the presupposition of each conjunct of the exhaustified assertion. The first conjunct in (153a) is simply the prejacent so its presupposition in (156a) is just that of the prejacent. The presupposition of the second conjunct in (153b) is the same as the one in (156a) as shown in

(156b).28Finally, that of the third conjunct (153c) is the one in (156c).

(156) a. ♦m[beljp]∧ ♦m[¬beljp]

b. ♦m[beljp]∧ ♦m[¬beljp]

c. ♦m[beljp∨ belj¬p] ∧ ♦m[¬[beljp∨ belj¬p]]

The presupposition of the exhaustified assertion would, hence, be (157a), that is the conjunction of the presuppositions in (156a), (156b) and (156c).

(157) a. ♦m[beljp]∧ ♦m[¬[beljp∨ belj¬p]]

b. ♦m[beljp]∧ ♦m[¬beljp]

It is easy to see that (157a) is stronger than the presupposition of the prejacent repeated in (157b), thus exhaustification is blocked by the condition in (141) above.

Notice that the case of unembedded want is not blocked by (141). To see this consider the exhaustification of a sentence like (158a), which gives rise to the meaning in (158b): the presuppositions is that in (159), which is identical to that of the prejacent.

(158) a. EXH[John doesn’t want that p]

b. ¬wantjp∧ wantjp∨ wantj¬p =

wantj¬p

(159) ♦jp∧ ♦j¬p

Furthermore, the case of believe embedding want like (164a) repeated from above is also al- lowed by (141) because believe is non-presuppositional, so we predict thatEXHcan apply and thus gives rise to the inference in (164b).

Notice that by blockingEXHin (160a) we not only predict that negation cannot take scope below think, but we also seem to incorrectly predict that it should not even take scope below

28Notice that this is the case regardless of the assumptions about the projection of presuppositions in disjunctive

want. In other words, we do not predict the inference from (160a) to (160b)

(160) a. John doesn’t want that Mary think that p

b. John wants that it’s not true that Mary think that p

However, we have a way to predict the inference from (160a) to (160b), through the LF in (161). In fact, the most embedded EXHis vacuous, as think is the strongest among its alternatives, however it “eats” the alternatives of think. Hence, at the global level we are free to exhaustify again only over the alternatives of want in (162), thereby getting the reading that we want, as shown in (163). This reduces to the case of want not embedding other scalar terms above, which is allowed by (141).

(161) EXH[¬[wantsj[EXH[thinkm(p)]]]]

(162)      ¬[wantm[thinkmp]]

¬[wantm[thinkmp]∨ wantm[¬[thinkmp]]

     (163) wantj¬[thinkmp]

(164) a. Mary doesn’t believe that John wants that Fred left.

b. Mary believes that John wants that Fred didn’t leave.

In sum, given (141) we correctly predict that, contrary to (164a), (165a) cannot be exhausti- fied and thus cannot give rise to the inference in (165b). Also the last putative argument for the presuppositional status of neg-raising predicates can, hence, be accounted for in the scalar implicature-based proposal here.

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

In document Soft but Strong. Neg-Raising, Soft Triggers, and Exhaustification (Page 74-81)