Abstract
Magri (MIT dissertation, 2009b; Nat Lang Semant 17(3):245–297, 2009a; Semant Pragmat 4:1–51, 2011) argues that scalar implicatures are blind to any contextual information. Schlenker (Nat Lang Semant 20(4):391–429, 2012, sections 3 and 4) objects that contextual Blindness is too strong an assumption because of the contextually ordered alternatives documented in Hirschberg (A theory of scalar implicature. Garland, New York, 1991). He thus submits that the computation of scalar implicatures is not blind but just contextually “short-sighted”: it can ignore certain pieces of common knowledge, but it is not required to ignore all of it. In this chapter, the author shows that Schlenker’s proposal is a technical mistake: Short-sightedness is provably equivalent to Blindness under natural assumptions on the set of scalar alternatives. Short-sightedness thus provides no new ammunition against Hirschberg’s challenge. The author then takes a closer look at the challenge, through some initial evidence, that contextually ordered alternatives are restricted and dependent on specific lexical choices. He conjectures that these choices share the property of introducing more logical structure than meets the eye, thus possibly providing the logical ordering required by Blindness (or the equivalent Short-sightedness). If this conjecture turns out to be correct, contextual ordering is never relevant to scalar implicatures, as indeed predicted by Blindness (or the equivalent Short-sightedness).
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Notes
- 1.
This chapter is only concerned with the second part of Schlenker’s paper (sections 3 and 4), not with the analysis of Maximize Presupposition developed in the first part (sections 1 and 2) of his paper—although my critical assessment of his principle of Fallibility in section “Gricean Credentials” below extends to the first part of Schlenker’s paper.
- 2.
- 3.
I assume that c is the set of possible worlds consistent with the common knowledge currently available in the context of utterance. Since the examples considered throughout the chapter are all elementary, this parameter c will never be used in the plain semantics. It will only be relevant for the definition of the excluded alternatives; see (5) and (6) below.
- 4.
With abuse of notation, I use the same symbol φ, ψ, … for both a sentence and its plain meaning.
- 5.
More precisely, it suffices that excluded alternatives do not yield a contradictory strengthened meaning [[[φ]]]c. Condition (6), as it stands, does not ensure that. In fact, suppose that φ comes with two alternatives ψ 1 and ψ 2 whose negation does not contradict φ, namely φ ∩c ∩¬ ψ 1 ≠ ∅ and φ ∩c ∩¬ ψ 2 ≠ ∅. Hence, both ψ 1 and ψ 2 belong to the corresponding set Excl c(φ) of excluded alternatives according to definition (6). Yet, the strengthened meaning [[[φ]]]c = φ ∧¬ ψ 1 ∧¬ ψ 2 could still be a contradiction, namely it could still happen that φ ∩c ∩¬ ψ 1 ∩¬ ψ 2 = ∅. The formulation in (6) is therefore too weak and it has indeed been carefully refined in the literature in a number of ways [see Spector (2016) for a review]. I ignore these refinements because all the cases considered in this chapter involve a unique alternative, so that the refinements considered in the literature turn out to be equivalent to the simplified formulation (6).
- 6.
This conclusion is threatened by the following alternative account. Assume instead that the set of excludable alternatives for only in (12) is computed relative to the actual common knowledge c actual. Thus, the alternative ψ all does not belong to the set of excludable alternatives \(Excl^{\mathsf{\mathbf{c}}_{\mbox{ actual}}}(\varphi _{\mbox{ some}})\) of the prejacent φ some, independently of the definition of excludability. The oddness of sentence (11) is thus due not to a contextual contradiction but to the fact that only is vacuous because its set of excluded alternatives is empty. In other words, sentence (11) is ruled out by the same general constraint that bans the vacuous occurrence of only in a sentence such as #Only every boy arrived. Yet, this alternative line of explanation fails for cases with multiple alternatives (for the full argument, see Magri 2011, Sect. 3).
- 7.
As explained in footnote 5, the specific definition of Excl nc provided in (6) is too weak, because it looks at non-contradictoriness of the negation of each individual alternative by itself. This definition needs to be replaced with a more careful restatement, which looks at the non-contradictoriness of the conjunction of the negations of an entire bunch of alternatives. The monotonicity property (25) plausibly carries over to such a refined definition of Excl nc .
- 8.
Short-sightedness does not help either with Schlenker’s original formulation of the challenge of contextually ordered alternatives, recalled in section “Contextually Equivalent Alternatives”. In fact, the two alternatives φ high school and φ college in (14) are contextually equivalent relative to Schlenker’s special context (13). Allowing the oddness filter more context sensitivity thus does not help to explain why only φ high school but not φ college sounds odd in that context.
- 9.
Here I have in mind the European school system, where a music conservatory is not a college and the two degrees can be pursued independently of each other.
- 10.
Danny Fox (personal communication) pointed out to me a solution to this impasse based on relevance. Here is the idea. Consider again the basic case of the odd sentence φ some = Some Italians come from a warm country. Assume that the algorithm for scalar implicatures is indeed blind to common knowledge. The algorithm will thus generate the implicature that ψ all = All Italians come from a warm country is false. But why is that implicature locked in place (condemning the sentence to oddness) rather than automatically canceled (say, because of the contextual contradiction)? In Magri (2011), I propose the following answer: the mismatching implicature is mandatory because ψ all is necessarily relevant due to the fact that φ some is relevant (because it has been uttered), that φ some, ψ all are contextually equivalent, and that relevance is closed relative to contextual equivalence. Fox notes that the sentence φ college = Mary has a college degree is not contextually equivalent to the alternative ψ high school = Mary has a high school degree in the out-of-the-blue context considered in section “Contextually Asymmetrically Entailing Alternatives”. Therefore, the inference ¬ ψ high school is not a mandatory implicature of φ college. In other words, the theory of oddness based on mismatching scalar implicatures does not strictly speaking predict φ college to be odd, as desired. Unfortunately, Fox’s suggestion does not extend to Schlenker’s special context considered in section “Contextually Equivalent Alternatives”, as the two alternatives φ college, ψ high school are indeed contextually equivalent in that case. Furthermore, it does not extend to contrasts such as (39) and (41) discussed below in this section.
- 11.
In (39) and in the rest of this section, I consider sentences containing overt only, which makes the judgments sharper. I submit nonetheless that the relevant judgments extend to the corresponding sentences without overt only. For instance, the contrast in (39) does extend to the corresponding sentences without only, at least when they are construed as answers to a proper question, such as Where did the train arrive/stop yesterday? Furthermore, there is indeed a contrast between sentences (ia) and (ib) relative to the actual world where the train stops are lined up as specified.
-
(i)
-
a.
#Yesterday, the train arrived at A, B, and C.
-
b.
Yesterday, the train stopped at A, B, and C.
-
a.
It is tempting to explain this contrast as follows. Sentence (ia) is deviant because it is equivalent to the shorter sentence The train arrived at C. Sentence (ib) is instead fine because it is not equivalent to the shorter sentence The train stopped at C, as the latter does indeed trigger the inference that the train did not stop at A and B.
-
(i)
- 12.
Two French informants and two Italian informants have confirmed this intuition; the judgment for the English sentence with the predicate attend seems less clear to me.
- 13.
The complementary cases (40b), (42b), and (44b)–(44c), which do not yield Hirschberg pairs, follow straightforwardly from the assumption that the set of excluded alternatives which appears in the definition (4) of the strengthened meaning and the semantics (12) of overt only is blind to contextual information and defined in terms of non-contradictoriness as in (6). Since the two alternatives in (40b), (42b), (44b), and (44c) are logically unordered, the symmetric scalar behavior displayed by these non-Hirschberg pairs follows straightforwardly.
- 14.
Recent advances in the semantics of telic motion predicates support the conjecture that arriving events have the mereological structure depicted in (49b), along the following lines. Building on a large literature (which includes Beavers 2008; Hay et al. 1999; Kennedy and Levin 2008; Krifka 1998), Beavers (2013, Sect. 2) proposes the scalar semantics (i) for a sentence such as John walked to the station with the telic motion predicate walk. Here, s is a variable over path scales. The predicate walk is a three-way relation between an event, a theme, and a path scale, as represented by the first conjunct in (i). This relation encodes the fact that j is the agent of a walking event e along the path scale s. The event and scale arguments are connected through a proper homomorphism between the sub-events of e and the points of the path scale s (e.g., temporal adjacency in e corresponds to degree adjacency in s). The other conjunct in (i) captures the condition that the station is the goal or the end point of the walking event e relative to the path scale s.
-
(i)
\(\exists e\exists s\big[\mathbf{ walk }(e,s,\mathbf{john}) \wedge \text{ GOAL}(e,s,\mathbf{ the \, station})\big]\)
This semantics plausibly extends from walk to to arrive at. The assumption that e B is an event of the train arriving at B thus means that there exists a path scale s B such that arrive(e B , s B , train). Analogously, the assumption that e C is an event of the train arriving at C means that there exists a path scale s C such that arrive(e C , s C , train). The linear ordering of the stops along the railroad entails that s B ⊆ s C . It is not implausible that the homomorphism between events and path scales ensures that s B ⊆ s C entails e B ⊆ e C , yielding the mereological structure depicted in (49b).
-
(i)
- 15.
If this assumption of a wide scope operator \(\exists e\) turns out to be untenable, I would need to make use of variants of (56) such as the equivalent formula in (i), which nonetheless is not as close to the general scheme (4)/(12) for the strengthened meaning and the meaning of overt only.
-
(i)
\(\exists e\big[\mathbf{ stop }(e,\mathbf{ t })\wedge \text{LOC}(e)\! =\! \mathbf{C }\big]\wedge \bigwedge _{e^{{\prime}}}\neg \big[\mathbf{ stop}(e^{{\prime}}\!\!,\mathbf{ t })\wedge \exists e^{{\prime\prime}}[e^{{\prime\prime}}\subsetneq e^{{\prime}}\wedge \mathbf{stop }(e^{{\prime\prime}}\!\!,\mathbf{ t })\wedge \text{ LOC}(e^{{\prime\prime}})\! =\! \mathbf{C}]\big]\)
-
(i)
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Acknowledgements
I would like to thank Gennaro Chierchia, Danny Fox, Salvatore Pistoia-Reda, Paolo Santorio, and Philippe Schlenker for useful comments. The chapter has also benefitted from comments and discussion at the Exhaustivity Workshop held at MIT on September 10, 2016.
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Magri, G. (2017). Blindness, Short-Sightedness, and Hirschberg’s Contextually Ordered Alternatives: A Reply to Schlenker (2012). In: Pistoia-Reda, S., Domaneschi, F. (eds) Linguistic and Psycholinguistic Approaches on Implicatures and Presuppositions. Palgrave Studies in Pragmatics, Language and Cognition. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-50696-8_2
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