Oddness, modularity, and exhaustification

Abstract

According to the ‘grammatical account’, scalar implicatures are triggered by a covert exhaustification operator present in logical form. This account covers considerable empirical ground, but there is a peculiar pattern that resists treatment given its usual implementation. The pattern centers on odd assertions like #Most lions are mammals and #Some Italians come from a beautiful country, which seem to trigger implicatures in contexts where the enriched readings conflict with information in the common ground. Magri (Nat Language Semant 17(3):245–297. https://doi.org/10.1007/s11050-009-9042-x, 2009; Semant Pragmat 4(6):1–51. https://doi.org/10.3765/sp.4.6, 2011) argues that, to account for these cases, the basic grammatical approach has to be supplemented with the stipulations that exhaustification is obligatory and is based on formal computations which are blind to information in the common ground. In this paper, I argue that accounts of oddness should allow for the possibility of felicitous assertions that call for revision of the common ground, including explicit assertions of unusual beliefs such as Most but not all lions are mammals and Some but not all Italians come from Italy. To adequately cover these and similar cases, I propose that Magri’s version of the Grammatical account should be refined with the novel hypothesis that exhaustification triggers a bifurcation between presupposed (the negated relevant alternatives) and at-issue (the prejacent) content. The explanation of the full oddness pattern, including cases of felicitous proposals to revise the common ground, follows from the interaction between presupposed and at-issue content with an independently motivated constraint on accommodation. Finally, I argue that treating the exhaustification operator as a presupposition trigger helps solve various independent puzzles faced by extant grammatical accounts, and motivates a substantial revision of standard accounts of the overt exhaustifier only.

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Notes

  1. 1.

    For readability, I use symbols like ‘\(\phi \)’ to stand for both components of LFs and their interpretations. When this is potentially confusing, I use \(\llbracket \phi \rrbracket ^{}\) to refer to the interpretation of \(\phi \). Unless otherwise noted, I will assume that propositions are represented as sets of possible worlds, and that the common ground in a particular context c is the set of possible worlds (or pairs of possible worlds and assignment functions) compatible with the information that is taken for granted by interlocutors for purposes of the conversation in c.

  2. 2.

    For an overview of the ‘grammatical’ account of scalar implicatures, see Chierchia et al. (2012). For an overview of a neo-Gricean approach, see Horn (2006). Recent empirical work on implicatures is summarized and discussed in Chemla and Singh (2014a, 2014b).

  3. 3.

    To be sure, there are various neo-Gricean-friendly accounts of oddness which do not appeal to the existence of implicatures/enriched readings that are inconsistent with the common ground. My main goal in this paper is not to directly argue against each of those neo-Gricean accounts (that is my focus in Del Pinal 2020), although I will discuss what I think is the most reasonable alternative account. My goal here is to defend a Magri-style account of oddness, based on implicatures/enriched readings which mismatch with the common ground, given a broadly grammatical approach to covert exhaustification.

  4. 4.

    For interesting refinements of the basic oddness patterns see also Magri (2014), Pistoia-Reda (2017), and Pistoia-Reda and Romoli (2017).

  5. 5.

    Some semanticists adopt a more complex formulation of ‘excludable alternatives’, \(\textit{Excl}\), than the one used in (6b) (see Sauerland 2004; Fox 2007; Chierchia et al. 2012). The revised formulation of \(\textit{Excl}\) is presented in (i), where an alternative \(\psi \) of \(\phi \) is ‘innocently excludable’ (\(\textit{IE}\)) just in case (i) we can consistently negate \(\psi \) while asserting \(\phi \), and (ii) accepting both \(\phi \) and \(\lnot \psi \) doesn’t entail any other alternatives of \(\phi \) (not already entailed by \(\phi \) alone).

    figuref

    One motivation for this revision comes from cases in which each disjunct is a relevant alternative of disjunctions, which can create problems for the simpler formulation (but see Chierchia 2013). In this paper, we will not focus on these kinds of cases. What is important here is just that the version of \(\textit{Excl}\), defined in terms of ‘innocent exclusion’ (\(\textit{IE}\)) as in (ib), still uses the notion of logical entailment, and is extensionally equivalent to our simpler version in most of the cases we consider here. For these reasons, in this paper I use the simpler formulation of \(\textit{Excl}\) in (6b) unless otherwise noted, with the understanding that the core results presented here still hold if we use the more complex \(\textit{IE}\) formulation of \(\textit{Excl}\) instead.

  6. 6.

    From a neo-Gricean perspective, the (potential) obligatoriness of Exh is hard to accept. For the point of triggering a scalar implicature, from a pragmatic perspective, is to make utterances more informative, or appropriate, given the common ground. This suggest that implicatures should not be triggered precisely when the resulting enriched reading clashes with the common ground while the unenriched (‘literal’) reading is at least consistent with it.

  7. 7.

    If Exh is indeed obligatory, how can we explain the well-known phenomenon that, in standard cases, scalar implicatures are cancellable? For example, that John did some of the HW triggers the usual ‘not all’ implicature in \(C_1\) but not in \(C_2\)?

    figurep

    Magri appeals to Relevance (for a detailed defense, see Magri 2011). Suppose that (iiia) is obligatorily parsed as in (iiib). Consider the comprehensive set of alternatives in (iiic). Arguably, alternative (iii) is irrelevant in \(C_1\), while alternative (ii) is irrelevant in \(C_2\) (both suggestions are compatible with the minimal conditions on relevance specified in (6c) above).

    figureq

    As a result, the output of Exh[John did some of the HW] is different in each context, as captured in (iva)–(ivb), with the result that the ‘not all’ implicature is observed only in \(C_1\):

    figurer
  8. 8.

    This incorrect prediction holds for (17b) even if the negation of the \(\forall \)-alternative is not added to its enriched reading (say, because the \(\forall \)-alternative is ignored or taken as non-relevant). For since (17b) conflicts with C even when its exhaustification is vacuous, the mismatch hypothesis in (16) incorrectly predicts that, given C, it should be as odd as (17a).

  9. 9.

    Simplified cases of oddness like (17a) are subtly different from standard Magri-style cases, repeated in (18a), (20a), and (21a) below. This is because, given normal (shared) background beliefs, (17a) is intuitively redundant, which could affect its acceptability, whereas the main predications in cases like (18a), (20a), and (21a) are modeled so as to convey new information relative to their corresponding common ground. Accordingly, examples like (17a) should not be used to motivate an account of oddness based on mismatching implicatures, although it is also not a problem for that account—assuming it is motivated by standard Magri-style examples—if oddness is in this specific case over-determined. Still, I begin with simpler examples like (17a) because, when compared with the variations in (17b) and (17c), they shed light on more complex oddness cases like (18a), (20a), and (21a) and on the problem of over-generation of oddness that their corresponding variations pose for Magri’s blindness package. Having said that, it is arguable that the degree of oddness exhibited by (17a) can’t be fully explained by appealing to its redundancy; for in that case, expressions like Lions are mammals and All lions are mammals should be equally odd, relative to normal shared beliefs. Yet although the generic and universally quantified variants are also usually uninformative, (17a) is substantially more degraded (for discussions of the specific conditions under which redundancy results in oddness see Mayr and Romoli 2016 and Sudo 2018). A reviewer notes that the generic might be preferred over the quantified variants because it arguably is (i) contextually equivalent and (ii) has stronger presuppositions, hence a principle along the lines of ‘Maximize presuppositions’ might entail that choosing a quantified over a generic alternative should lead to oddness. Whether (i)–(ii) hold depends on the specific account of the generic operator. Yet even if this suggestion works in this specific case, it would predict that the ‘some’ and ‘all’ sentences in all the Magri-style oddness patterns in which the generic version is also licensed should be equally degraded. As the reader can test by starting with cases like (18a), this generalization doesn’t seem correct; and as we will see in Sect. 6, the cases in which it does seem to hold can be explained by a revised version of the blindness package combined with independent principles concerning good questions and answers. Finally, some standard examples of Magri-style oddness, such as (20a) (see also (81)), do not plausibly have a generic reading (e.g., in (20a), Sue’s assigning an A to some of her students is a one-time event, which doesn’t have a generic/dispositional/habitual reading), hence also fall outside the scope of this competing account of oddness.

  10. 10.

    I’m grateful to an anonymous reviewer for discussion of this issue and for suggesting the use of examples like those in (19).

  11. 11.

    The following discussion was greatly aided by conversations with Itai Bassi, Gennaro Chierchia, Jacopo Romoli, and Uli Sauerland.

  12. 12.

    This is not to suggest, of course, that the \(\phi _{\exists \wedge \lnot \forall }\) and \(\textit{Only} (\phi _{\exists })\) assertions always succeed in making L, the listener, revise \(C_L\). In particular, if S, the speaker, has just made it very clear (e.g., via an explicit assertion), that he accepts the part of \(C_L\) which causes the conflict with S’s subsequent assertion, revision of \(C_L\) will probably not take place, and the infelicity or oddness of the assertion markedly increases. Many examples of incoherent sequential assertions, such as (ia)–(ib), are of this kind. At the same time, when there is even a small opening to revise the default interpretation of the first assertion so as to make it coherent with the subsequent assertion, we can observe, again, that \(\textit{Only} (\phi _{\exists })\) and \(\phi _{\exists \wedge \lnot \forall }\) assertions are much more effective than their \(\textit{Exh}(\phi _{\exists })\) counterpart, as illustrated by the contrast between (iia) and (iib)–(iic) (this holds even though the use of ‘yet’ suggests to L that some kind of revision/caveat is about to follow):

    figurey
  13. 13.

    Heim (1992, p. 212): “Assumptions to be accommodated are supposed to be uncontroversial and unsurprising. One may explicitly assert controversial and surprising things (in fact one should) but to expect one’s audience to accept them by way of accommodation is not good conversational practice.”

  14. 14.

    Some proponents of the grammatical approach might want to refine these entries to ensure that while covert exhaustification may be vacuous (which would be especially attractive for those who stipulate that it is obligatory, but see Chierchia 2013), overt exhaustification with only is infelicitous if no alternatives can be excluded.

  15. 15.

    To be clear, this is not to say that any assertion whose at-issue content clashes with the common ground is felicitous so long as its presuppositions are consistent with the common ground. This depends, i.a., on whether one can figure out how to accommodate the target information (see von Fintel 2008), and whether the assertion can be construed as a coherent call for revision of the common ground, given such information as what the speaker has previously asserted. This presumably rules out as infelicitous sequences in which a speaker generates a series of assertions whose at-issue contents are inconsistent (see footnote 12).

  16. 16.

    This revised ps-mismatch hypothesis is intended as an implementation of the Lewis/Heim/von Fintel insight about constraints on what can be accommodated, which says roughly that you can introduce controversial information into conversations, but such information should in general be fully contained in the assertive part of your assertions. Independent evidence for both components of the ps-mismatch hypothesis is reviewed in Sect. 5.1.

  17. 17.

    If we were to combine the strong presuppositional entry for only in (26) with the revised version of the ps-mismatch hypothesis in (31), we would incorrectly predict that (30a) is odd. For given these assumptions, the presupposed and at-issue content of (30a) is as in (30d). Crucially, while neither content is itself inconsistent with the common ground, when the ad hoc common ground incorporates the presupposition, the result is inconsistent with the at-issue content. This is precisely the kind of case that the revised ps-mismatch hypothesis was designed to filter out; hence this combination of assumptions incorrectly predicts that (30a) is odd. More generally, this combination of assumptions predicts that, in contexts in which \(\textit{Exh}^p(\phi )\) is filtered out because it violates the second clause of the revised ps-mismatch hypothesis in (31), a matching sentence of the form only\((\phi )\) should also usually be filtered out (and vice versa). One of our key and novel observations, however, is that \(\textit{Exh}\) and only don’t generate the same oddness patterns in these kinds of cases, as illustrated also by patterns like (20)(21).

  18. 18.

    If we assume instead Russell’s original non-presuppositional analysis of the definite article, (42a) is not predicted to be odd by our oddness filter, and is expected to pattern, in terms of its degree of felicity, with other superficial contradictions, such as Triangles have four sides and This book has exactly one author but that author is not its main author. Such surface contradictions may seem absurd, ridiculous, or obviously false; but they don’t seem to be strictly odd or infelicitous in the way our target examples are (of course, whether explicitly asserted contradictions are ultimately also ruled out as infelicitous depends on what additional oddness filters one adopts). Simplifications aside, this illustrates that the ps-mismatch hypothesis may be used—if reasonably confirmed—to discriminate between competing analyses of (potential) presuppositions triggers, given a range of oddness patterns involving those triggers.

  19. 19.

    For a detailed defense of presuppositional exhaustification on independent grounds, see Bassi et al. (2020) and Del Pinal et al. (2020). In those papers, we argue that (blind) presuppositional \(\textit{Exh}^p\) has various empirical advantages over standard non-presuppositional accounts of exhaustification (and some recent presuppositional proposals) by examining how the predicted projection patterns of its presupposed content (the negated excludable alternatives) help solve various extant puzzles concerning the strange behavior of embedded scalar implicatures. Some of the cases discussed in this subsection are pursued more thoroughly in those papers, including a discussion of the possible advantages of implementing \(\textit{Exh}^p\) in a trivalent strong Kleene system.

  20. 20.

    Some caveats: First, this formulation leaves open the possibility that, when the licensing condition is satisfied, we sometimes accommodate a presupposition \(\underline{p}\) by adding more information than is strictly contained in \(\underline{p}\). Second, it also leaves open the possibility that accommodation sometimes triggers some degree of belief revision to increase total coherence. Finally, licensing conditions might have to be relativized to particular kinds of presupposition triggers, since some triggers (such as \(\textit{Exh}^p\) on the view defended here) are much more liberal than others in allowing for default accommodation.

  21. 21.

    There is another interesting prediction, in light of the connection between the contradiction contour and licensing of local accommodation, for accounts of oddness. Global accommodation and local accommodation at matrix level should be strictly distinguished. Now consider examples like those of Magri-style oddness but with an intonation pattern that normally licenses local accommodation at the matrix level, roughly along the lines of \(\setminus \) some lions/ are mammals and \(\setminus \) some italians/ come from a beautiful country. Given our current assumptions, that would in turn arguably license the parses in (ia) and (ib) with matrix-level local accommodation:

    figureax

    The result is that, under these conditions, the corresponding expressions no longer fall under the ps-mismatch hypothesis (again, assuming a licensing distinction between global accommodation and matrix-level local accommodation), and are thus predicted to feel less odd and more adequate as ways to signal to the listener that the common ground should be revised, compared to the original examples without such intonation. This prediction seems to me to be roughly correct, but is admittedly subtle and requires further empirical investigation.

  22. 22.

    This observation can also be used to account for related results reported in the experimental literature. Potts et al. (2016) report that Exacly one player made some of his shots was endorsed by around half of the subjects in a scenario where exactly one player made some but not all shots and one or both of the other players made all shots. Why don’t we get the universal projection here that none of the players made all of the shots? The availability of an LF analogous to the one in (56) helps answer this question, at least given some reasonable story for why it might be preferred in the experimental task/context.

  23. 23.

    Although the strong presuppositional account is still popular, various theorists have defended, on independent grounds, a weak or even non-presuppositional entry for \(\textit{Only}\) (e.g., Ippolito 2007; van Rooij and Schulz 2007).

  24. 24.

    The result that we get vacuous exhaustification when \(\textit{Exh}^p\) associates with a non-negative only-clause is the reason why I didn’t consider, in the discussion of the full oddness pattern in Sect. 4, parses for the only-sentences with matrix \(\textit{Exh}^p\). In those cases, widest scope/matrix \(\textit{Exh}^p\) is vacuous.

  25. 25.

    It is easy to check that this account derives appropriate overall truth conditions for (65b). For simplicity, suppose that the other relevant students are Sue and Peter. Given a flat entry, the embedded only-claim reduces to ‘John passed \(\wedge \) \(\lnot \)at least one of Sue or Peter passed’; when that conjunction is negated, we get ‘\(\lnot \)John passed \(\vee \) at least one of Sue or Peter passed’. Since (65b) presupposes that John passed, the first disjunct can’t hold without triggering presupposition failure. As a result, (65b) is defined iff John passed, and when defined, is true if Sue or Peter passed and false if neither Sue nor Peter passed. These are the appropriate truth conditions for (65b), given the focus/information structure under consideration.

  26. 26.

    Two observations further support the core assumptions of the revised blindness package. First, consider what would happen if the LFs in (71a) and (71b) were formulated with standard \(\textit{Exh}\), rather than presuppositional \(\textit{Exh}^p\). In (71b) both the prejacent and the excluded alternatives would be at-issue; so the reading we would get, when \(\textit{Exh}\) associates with only, is instead the non-default one that John’s having passed the exam is part of the content of what Mary realized. Since this is perfectly consistent given information like that in (69), we would lose the explanation of the contrast in acceptability between the continuations in (69a) and (69b). Second, consider what would happen if exhaustification was not obligatory. Then the embedded only-clause in (68b) would not need to be exhaustified, and we would lose the explanation for why (69b) is odd as a continuation of (69). Of course, even if we fixed the focus structure, the obligatory exhaustification operation in (71b) could also be trivialized by the effect of relevance—but we are assuming, plausibly, that in most contexts where ‘\(\lnot \hbox {only}\) John passed’ (which, given the flat only, amounts to ‘\(\lnot \hbox {John}\) passed \(\vee \) at least one other student passed) is relevant, so is ‘\(\lnot \hbox {John}\) passed’.

  27. 27.

    Matrix \(\textit{Exh}^p\) in (72a) doesn’t change the target result, namely, that (72a) doesn’t presuppose that John can speak French. This is easy to check (e.g., if it associates with possible we get a ‘\(\lnot \)certain’ enrichment), but let me illustrate by considering one potentially relevant parse. Suppose matrix \(\textit{Exh}^p\) associates with only. The prejacent of \(\textit{Exh}^p\) in this case would be \(\Diamond \phi _{\text {only}}\), which, given the flat entry for only, entails that \(\Diamond \phi \). But this in turn entails that the \(\Diamond \phi \)-alternative to the prejacent is again not excludable. To be sure, matrix \(\textit{Exh}^p\) is in some cases very important. For example, (i) arguably implies that Sue believes that John passed:

    figurebr

    On the blindness account, embedded exhaustification of the bare only doesn’t predict that. In this case matrix \(\textit{Exh}^p\) is crucial. Suppose matrix \(\textit{Exh}^p\) associates with only. The prejacent of \(\textit{Exh}^p\) is ‘Sue doubts that only John passed’ and the excludable alternative (obtained via deletion) is ‘Sue doubts that John passed’. Given this parse, then, (i) presupposes that it is not the case that Sue doubts that John passed, and asserts that Sue doubts that only John passed. The presupposition may in turn be strengthened via a general or domain-specific (‘opinionated speaker’-style) default assumption that if it’s not the case that S doubts \(\phi \), S believes \(\phi \).

  28. 28.

    My aim here is not to settle the semantics of only, an (in)famously thorny issue (see Horn 1996; Ippolito 2007; van Rooij and Schulz 2007; Xiang 2017, a.o.). Even if we accept the revised oddness package, various details of its semantics are negotiable. I have argued that we should not assume that only \(\phi \) presupposes \(\phi \); but this is compatible with holding that only has other, non-trivial presuppositions. For example, only \(\phi \) could presuppose, roughly, that there is at least one \(\psi \in Alt(\phi )\) such that \(\phi \not \subseteq \psi \) and \(\psi \) has a reasonable chance of holding, given the information in the common ground (thanks to Eric Swanson for this suggestion). The at-issue content of only \(\phi \), on this view, is that \(\phi \) holds and that each excludable \(\psi \in Alt(\phi )\) is false, despite a prior/common ground-based expectation that at least one has a serious chance of being true. This refinement of the semantics of only issues in good predictions for certain simple variations of our basic oddness pattern, and in addition does not negatively affect our original account of standard Magri-style oddness cases. Consider the contrast in (i):

    figurebt

    Sentence (ia) is part of our original oddness pattern: the basic observation, recall, is that a conspiracy theorist aware of normal background information can use the only-claim in (ia) to propose radical belief revision, relative to the common ground. However—and this is the interesting observation here—the related version in (ib) sounds odd, although one could argue that given a non-presuppositional only it should also be usable for a similar purpose, under similar conditions. The explanation for the oddness of (ib), according to our refined entry for only, is based on presupposition failure. (ia) presupposes that the proposition that all lions are mammals is a serious possibility, given the information in C (and asserts that it happens to be false). This presupposition is trivially entailed by normal adult background information. In contrast, (ib) presupposes that the proposition that all lions are robots is a serious possibility, given the information in C (and asserts that it happens to be false). Crucially, this presupposition is not entailed by normal background information, and is even inconsistent with it (recall: presuppositions that are inconsistent with the common ground are hard to globally accommodate). This presupposition failure explains the oddness of (ib). Finally, this refined entry for only does not negatively affect our previous account of the more complicated examples included in the full oddness pattern. Consider:

    figurebu

    The challenge, recall, is to come up with an account of covert exhaustification and only that can explain why only (iib) is a felicitous and suitable way to call for revision of the common ground. According to our revised entry for only, (iib) presupposes that the proposition that all Italians come from a beautiful country is a reasonable possibility, given the common ground C (and asserts that, despite this reasonable expectation, some but not all do). This presupposition is either entailed by the common ground, or can at least be easily accommodated. As a result, (iib) is correctly predicted to be felicitous, even if most interlocutors with normal background information would also hold that it is obviously false.

  29. 29.

    Katzir and Singh (2015) is not the only recent attempt to deal with Magri-style oddness patterns without adopting the hypothesis that covert exhaustification is contextually blind and obligatory. I decided to discuss Katzir and Singh’s 2015 account here mainly because it is prima facie promising and independently motivated. Other important accounts are presented in Schlenker (2012) and Spector (2014). For a critical discussion of the latter, and further defense of the revised blindness package relative to various recent neo-Gricean alternatives, see Del Pinal (2020).

  30. 30.

    By ‘deficient question’ here I mean relative to ‘normal’ background information such as that in (76). How do we square the observation that, out of the blue, (76a) and (76b) are odd because they are taken as addressing such ‘deficient questions’ with the claim that explicitly mentioning these questions improves their acceptability? Arguably, interlocutors are more willing to perform the required costly accommodation of such deficient questions when they are explicitly raised.

  31. 31.

    This combination of choices, however, has a cost (which I will leave for now as an open problem). For it arguably leaves us without a satisfactory explanation of embedded oddness for cases like (ia)–(ib). Although I think their contrast in acceptability is clear, we can’t appeal to mismatching implicatures or to a global answer condition to explain the oddness of (ib), relative to (ia).

    figurece

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Acknowledgements

Versions of this paper were presented at the University of Barcelona and the University of Illinois at Urbana-Champaign. Thanks to audiences at those talks. For very helpful comments/conversations I’m grateful to Itai Bassi, Gennaro Chierchia, Manuel García-Carpintero, Peter Lasersohn, Paul Marty, Josep Macià, Marie-Christine Meyer, Eleonore Neufeld, Jacopo Romoli, Adam Sennet, Brandon Waldon, and Yimei Xiang. I am also indebted to two anonymous reviewers and the editors of Natural Language Semantics for extremely helpful questions, comments, and suggestions, and to Christine Bartels for her amazing copy editing work. I am specially grateful to Uli Sauerland and Eric Swanson for many insightful conversations on versions of this paper and more generally on the topic of neo-Gricean vs. grammatical approaches to implicatures and exhaustification.

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Del Pinal, G. Oddness, modularity, and exhaustification. Nat Lang Semantics (2021). https://doi.org/10.1007/s11050-020-09172-w

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Keywords

  • Scalar implicatures
  • Exhaustification
  • Oddness
  • Presuppositions
  • Accommodation
  • Logical entailment
  • Contextual entailment
  • Pragmatics