2.4 A scalar implicature-based approach
2.5.2 Other embeddings and non-projection
18.104.22.168 Novel inferences
Consider the case of the antecedent of conditionals as in (82a), schematized as in (82b), where I adopt for concreteness a strict conditional semantics for conditionals (von Fintel 1997; see alsoCHAPTER 5). The alternatives wind up being (83a) and the exhaustification of (82a) with respect to such alternatives is in (83b).
(82) a. If Mary believes that it will rain, she will take an umbrella
b. [believe(p) → q] (83) a. Alt = [believe(p) → q] [(believe(p) ∨ believe(¬p)) → q] b. [[EXH]]([believe(p) → q]) =
[believe(p) → q] ∧ ¬[(believe(p) ∨ believe(¬p)) → q] = [believe(p) → q] ∧ ♦[(believe(p) ∨ believe(¬p)) ∧ ¬q]
(83b) claims that it’s possible that Mary has an opinion as to whether it is raining and that she doesn’t take an umbrella. Together with the first conjunct that asserts that if she believes that it is raining she will take an umbrella, the whole conjunction is equivalent to (84): if she believes that it is raining, she will take an umbrella and it is possible that she believes that it is not raining and she won’t take an umbrella.
(84) [believe(p) → q] ∧ ♦[believe(¬p) ∧ ¬q]
In this case, however, it is not easy to argue for this inference, because it is entailed by the so-called “conditional perfection” inference, which conditionals have independently from the presence of neg-raising predicates.17 Let us turn, then, to another non-UE environment like the
17In this case the inference is that if it’s not the case that Mary believes that it’s raining, then she will not take the
umbrella. This entails that if Mary believes that it’s not raining then she will not take the umbrella. I come back to this in Appendix A.
restrictor of a universal quantifier, as in (85a). In this case, exhaustification gives rise to the result in (85b) as shown in (86b).
(85) a. Every student who believes that she was accepted will come to the party.
b. Some student who believes that she wasn’t accepted will not come to the party.
(86) a. ∀x[believexp→ Qx]
b. [[EXH]](∀x[believexp→ Qx]) =
(∀x[believexp→ Qx])∧ ¬∀x[(believexp∨ believex¬p) → Qx] =
(∀x[believexp→ Qx])∧ ∃x[(believexp∨ believex¬p) ∧ ¬Qx]
(86b) claims that every student who believes that she was accepted will come to the party and there is a student who either believes that she was accepted or believes that she wasn’t and won’t come to the party. The two conjuncts are equivalent to (87): every student who believes that she was accepted, will come to the party and there is a student who believes that she wasn’t and won’t come to the party.
(87) ∀x[believexp→ Qx]∧ ∃x[believex¬p ∧ ¬Qx]
Given that the presuppositional account does not predict this inference, if we can argue for its existence we would have an argument for the present proposal.18
An argument for the inference above can be constructed on the basis of the so-called “Hur- ford’s constraint” outlined inCHAPTER1. Chierchia et al. (To appear) use Hurford’s constraint as a diagnostic for scalar implicatures, so we can use it here to test the status of the inference above. For instance, the present proposal predicts that from (89a) we can have the inference in
18To see that the presuppositional account does not predict it, notice that what we can conclude from (88a) depends
on our assumptions about the projection of presuppositions from the restrictors of universal quantifiers. Suppose, for the sake of the argument, that we assume a theory that predicts universal projection from the restrictor of universal quantifiers, what we can conclude from (88a) is (88b).
(88) a. Every student who believes that she was accepted will come to the party. b. Every student has an opinion on the matter.
(89) a. Every student who thinks I am right will support me.
b. Some student who think that I am not right will not support me.
We can then construct the disjunction in (90) to check whether (89b) is an inference from (89a). Notice that given the downward entailingness of the restrictor of every the second disjunct in (90) entails the first one, unless the first one is analyzed as in (91). (91), given the present proposal, gives rise to the inference in (89b), which disrupts the entailment relation.
(90) Either every student who thinks I am right will support me or every student who has an opinion on the matter (at all) will.
(91) EXH[every student who thinks that I am right will support me]
To the extent that (90) is felicitous we have an argument for the inference in (87). The same argument can be reproduced for the inference from (96a) to (96b), given the disjunction in (97). (cf. section 2.6.3, for the predictions relative to neg-raising predicates embedded under negative quantifiers).19
19Notice that this argument is undermined by felicitous disjunctions with no neg-raising predicate like (92), in
which the second disjunct entails the first.
(92) We will either test everyone who smokes Marlboro or we will test everyone who smokes (at all).
If (92) is felicitous, there must be another inference disrupting the entailment relation between disjuncts. Katzir (2007) argues that the restrictor of a universal has its syntactic simplification as alternatives. So in this case the alternative of (93a) would be (93b). Exhaustification would give then rise to the inference in (94), which, in turn, would disrupt the entailment relation between the disjuncts of (92).
(93) a. We wil test everyone who smokes Marlboro. b. We will test everyone who smokes. (94) ¬[we will test everyone who smokes]
This alternative explanation of the felicity of this type of disjunction is not available for cases in which the entailing disjunct is more complex than the entailed one, like in (95). In this case it is not straightforward to see what alternative obtained by syntactically simplify the first disjunct could disrupt the entailment relation between the second disjunct and the first one.
(96) a. No student who thinks that I am wrong will support me. b. Some student who thinks that I am right will support me.
(97) Either no student who thinks that I am wrong will support me or no student who has
an opinion on the matter will.
I proposed that neg-raising predicates have their corresponding excluded middle propositions as alternatives and that neg-raising inferences arise as a scalar implicature via exhaustification of sentences containing such predicates. As we saw, the differences between neg-raising infer- ences and (soft) presuppositions are accounted for straightforwardly in the present approach. Notice that strictly speaking explaining the difference depends also on the account of soft pre- suppositions that we assume. This is because once we have an account of neg-raising in terms of scalar implicatures we do not have to connect neg-raising and soft presuppositions anymore. In particular, if we have an account of soft presuppositions as real presuppositions, like the one proposed in Fox 2012b, explaining the difference with neg-raising inferences becomes ex- tremely easy: one can simply assume that any difference between the two comes from the fact that they are different things. On the other hand, if you have an account of (soft) presupposi- tions as scalar implicatures like the one I propose inCHAPTER 3 and 4 or Chemla 2009a, in preparation, then, like Gajewski (2007), you face the challenge of accounting for the difference
between neg-raising inferences and soft presuppositions. InCHAPTER 3, Appendix A, I show
that, unlike the presuppositional approach, the scalar implicature approach allows us to account for the differences between soft presuppositions and neg-raising inferences, while treating them both as scalar implicatures. InCHAPTER4, Appendix B, I compare the scalar-implicature based theory of soft presuppositions I propose inCHAPTER3 to the one in Fox 2012b.
Finally, notice that the present proposal, like Gajewski’s (2007), can account for the fact
(95) Either every student who wants to invite Philippe will come to the meeting or every student who has a desire on the matter will come.
that neg-raising inferences are characteristics of certain predicates and not others. What dis- tinguishes neg-raising and non-neg-raising predicates is their alternatives: the former has the excluded middle as an alternative but the latter do not.