AGAINST CHIERCHIA’S COMPUTATIONAL ACCOUNT OF SCALAR IMPLICATURES
    OWEN GREENHALL
    Recent theories of scalar implicature, such as that proposed by Gennaro Chierchia, have sought to bring them within the domain of compositional semantic theory. These approaches contrast with standard pragmatic explanations of the phenomena in that implicatures are calculated by default and are computed locally. One motivation for Chierchia’s approach, the purported connection between the computation of scalar implicatures and ‘any’-licensing polarity items, is shown to be weak. Difficulties are then presented for his approach which are not shared by the pragmatic theory.
    
    I
    Introduction. Despite not playing a large role in Paul Grice’s own writing, scalar implicatures are often viewed as paradigmatic cases of conversational implicature1. A semantic scale is an ordered set of lexical items of the same syntactic category. The ordering is that induced by the semantic entailments of simple sentences containing the item. If P and Q are members of a semantic scale {P Q} (with ordering shown by ‘ ’), and f(P) is a sentence in which there is a unique occurrence of P (and P does not fall within the scope of a sentential operator), then f(P) entails f(P/Q).2 Entailments between the (a) and (b) sentences in (1) and (2) generate the orderings shown:
    Grice’s own work on this area does not explicitly discuss any of the example implicatures contained in this paper, though he does discuss the implication from ‘I think that p’ to the speaker not having justification for ‘I know that p’ (Grice 1967, p. 141) and the implication from disjunctive statements to the speaker not knowing that either disjunct is true (Grice 1961, pp. 130–2; 1967, pp. 46–7). Both of these are cases that have been analysed as scalar implicatures by subsequent theorists, for example Stephen Levinson (2000). 2 ‘f(P/Q)’ is shorthand for ‘the sentence obtained by replacing all occurrences of P in f(P) with Q’. ©2008 The Aristotelian Society Proceedings of the Aristotelian Society, Vol. cviii, Part 3 doi: 10.1111/j.1467-9264.2008.00252.x
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    (1) (a) Paul drank tea and coffee. (b) Paul drank tea or coffee. (c) {and or} (2) (a) It’s hot outside. (b) It’s warm outside. (c) {hot warm} A scalar alternative of a sentence f(P1, …, Pn) containing scalar terms P1 to Pn is a sentence formed by replacing one or more of P1 to Pn with another item from the semantic scale to which it belongs. Often an utterance of a sentence f(P1, …, Pn) will imply that the logically stronger scalar alternatives to it are false. For example, an utterance of (1b) typically implies the negation of (1a). Similarly, using the scale {all some}, the classic implicature in (3) can be predicted (using ‘ ’ for ‘implicates’ 3): (3) Some of the students came to the party. It’s not the case that all of the students came to the party. However, such a simple account of implicature generation will not work in general. It will not capture the implicature in (4) because the implied sentence is not a scalar alternative of the sentence uttered. (4) Kai had the broccoli or some of the peas last night. Kai did not have all of the peas last night. As formal theories of implicature generation become more sophisticated in order to handle cases such as this, the reliance on contextual assumptions to derive scalar implicatures is obscured.4 A theory treating scalar implicatures as inferences computed by default during semantic interpretation, without regard to contextual assumptions, has been proposed by Gennaro Chierchia (2004).5 This contrasts with a pragmatic account that explicitly treats scalar implicatures as a variety of conversational implicature.
    
    3 4
    
    ‘ / ’ is used to indicate ‘does not implicate’. Uli Sauerland (2004) presents an illuminating history of formal accounts of scalar implicatures from the early work of Larry Horn (1972) and Gerald Gazdar (1979) through that of Julia Hirschberg (1991) to Sauerland’s own account. 5 Stephen Levinson (2000) and Danny Fox (2007) also propose default theories; however, their theories are significantly different to Chierchia’s (and to one another). ©2008 The Aristotelian Society Proceedings of the Aristotelian Society, Vol. cviii, Part 3 doi: 10.1111/j.1467-9264.2008.00252.x
    
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    II
    The Pragmatic Account. From the hearer’s perspective, a standard Gricean account of the inference involved in the conversational implicatures relies on the following contextual assumptions: (i) The speaker has expressed the proposition P in a context in which more information than just P is required (i.e., what is said violates the maxim of quantity). (ii) The speaker is not being uncooperative. (iii) The speaker knows whether or not Q for any proposition Q concerning the matter at hand. Assumptions (i) and (ii) prompt the hearer to search for some further information which the speaker intended to communicate. Together with (iii), this allows an abductive inference to the conclusion:6 (iv) The speaker wishes to imply that P is the informationally strongest true proposition concerning the matter at hand.7 If informational strength is equated with logical strength, and it is assumed that the other propositions concerning the matter at hand are the scalar alternatives to P, then the conclusion of the Gricean reasoning is that the speaker wishes to imply that logically stronger scalar alternatives to P are false. The pragmatic account only licenses this conclusion under specific circumstances; thus, it differs from accounts on which scalar implicatures are derived by default.8 It is clear that, on the pragmatic account, scalar implicatures are merely a subspecies of those conversational implicatures which exploit the maxim of quantity, and, like all conversational implicatures, they
    6 7
    
    The details of the chain of reasoning are suppressed. It is assumed that the set of propositions concerning the matter at hand is constrained so that all its members are of limited complexity. 8 Initial evidence that default accounts are mistaken arises from the behaviour of scalar terms in cases where the assumptions used in the Gricean inference do not hold. Clearly, cases in which it is known that the speaker is in a less than perfect epistemic position will not fit the pattern above, since assumption (iii) will not hold. Instead, the abductive reasoning delivers the following conclusion. (iv ) The speaker wishes to imply that P is the (informationally) strongest proposition concerning the matter at hand that they know. Such epistemic modification of implicatures has been highlighted by Scott Soames (1982), amongst others. ©2008 The Aristotelian Society Proceedings of the Aristotelian Society, Vol. cviii, Part 3 doi: 10.1111/j.1467-9264.2008.00252.x
    
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    make essential use of assumptions about the context of utterance.9 As with standard Gricean implicatures, the input to the inferential process includes the semantic value of the entire utterance.
    
    III
    ‘Any’-Licensing and Implicature. In contrast to the pragmatic account, Chierchia (2004) develops a theory of scalar implicatures on which they are derived during the compositional semantic interpretation of a sentence. Scalar implicatures are computed at specific points in the syntactic structure of a sentence from the meaning of the sub-sentential expressions local to those points, rather than after the interpretation of the whole sentence, as on traditional, global, Gricean theories. Chierchia’s positive account is presented in a wideranging paper, in which he argues against global theories in two significant ways: in an attempt to support the computational basis for scalar implicatures, he argues for an intimate connection between scalar implicatures and the grammatical feature ‘any’-licensing,10 and he presents a range of cases of scalar implicature which, he claims, cannot be accounted for on global theories of implicature. He concludes from this that:
    9
    
    This reliance on contextual assumptions is shown in one of Grice’s first examples of conversational implicature: [T]he spokesman who announces, ‘The next conference will be in Geneva or New York’ perhaps does not imply that he does not know which; for he may well be just not saying which. (Grice 1961, p. 131) For the spokesman’s conversational interests, providing maximal information is not the aim. Recent empirical work suggests that certain presumptions concerning speakers’ knowledge and reliability are made by hearers unless evidence is given to the contrary, and that these assumptions can have a range of effects on pragmatic inferences. See Grodner and Sedivy (forthcoming). 10 In English, ‘any’ functions either as a free choice item or a negative polarity item. A free choice item signals that the choice of an element from a given group is unconstrained: for example, ‘any’ as it occurs in ‘Pick any card’. A negative polarity item (NPI) is one that must occur within the scope of a negation or other negative environment. For present concerns, it suffices to identify negative environments with downward entailing contexts: the contexts formed by monotone decreasing elements. Thus NPIs are those which must occur within downward entailing contexts. A predicate P occurs in a downward entailing context in a sentence f if whenever P is semantically entailed by P then f(P) entails f(P/P ). Negative polarity ‘any’ is a model NPI, hence NPI-‘any’-licensing will be taken as a syntactic test for the positions an NPI may hold. Examples of contexts which are not downward entailing but which do license NPI-‘any’ are those formed by ‘only’ (e.g. ‘Only John ate any apples’). Kai von Fintel (1999) provides a sophisticated discussion of NPI-licensing and downward entailment. ©2008 The Aristotelian Society Proceedings of the Aristotelian Society, Vol. cviii, Part 3 doi: 10.1111/j.1467-9264.2008.00252.x
    
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    … some of the Grice-inspired pragmatics is probably part of the computational system of grammar. (Chierchia 2004, p. 59)
    
    However, the connection, if any, between scalar implicatures and ‘any’-licensing is not as tight as Chierchia claims. Moreover, his positive proposal faces several difficulties not shared by the pragmatic account.11 Chierchia states that ‘any’-licensing is connected to the derivation of scalar implicatures because:
    (Ordinary) scalar implicatures are suspended in the contexts that license any (as a Neg Pol or Free-Choice Item). (Chierchia 2004, p. 55)12
    
    This generalization does not hold up to scrutiny. It is held by Chierchia that standard scalar implicatures are suspended under modalities of permission, which are ‘any’-licensing: witness (5a). The standard implicature associated with ‘or’ is lost in (5b) and (5c). (5) (a) John may bring anyone to the party. (*John brought anyone to the party.) (b) John is permitted to smoke or drink. / John is not permitted to smoke and drink. (c) John may smoke or drink.13 / John may not smoke and drink. Although, (5b) and (5c) are typically interpreted without the indicated implicatures, there is a pragmatic explanation for the lack of implicature. Whilst the speaker of (5b) or (5c) has not told the hearer explicitly whether or not John is allowed to smoke and drink, in most scenarios, it is assumed that if he can do either then he can do both. Indeed, in parallel contexts where this assumption is dropped the implicature resurfaces. Consider an utterance of (6) by a father to his daughter before a birthday meal.
    11
    
    The purportedly difficult cases Chierchia presents for global accounts may be handled with a suitably sophisticated pragmatic approach, though there is not space to discuss these issues here. 12 This generalization is closely related to Horn’s (1989) observation that standard implicatures are typically reversed in downward entailing contexts. 13 This must be understood with ‘may’ taking wide scope over ‘or’. As Chierchia (2004, p. 54) states, ‘intonation matters’: ‘smoke or drink’ must form an intonational phrase. ©2008 The Aristotelian Society Proceedings of the Aristotelian Society, Vol. cviii, Part 3 doi: 10.1111/j.1467-9264.2008.00252.x
    
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    (6) You may eat some of the biscuits. You may not eat all of the biscuits. The implicature is present here because it is contextually relevant whether or not she may eat all of the biscuits, and there is no assumption that permission to eat some biscuits entails permission to eat all of them. Another case Chierchia presents in favour of his generalization is that of imperatives. These also license free choice ‘any’, for example (7a), and sometimes implicatures are removed, as in (7b). (7) (a) Get me anyone from IT support. (*He got me anyone from IT support.) (b) Get me Paul or Bill. / Don’t get me Paul and Bill.14 Again, it is possible to explain the lack of implicature in (7b) on a pragmatic account. The background assumption is that, whatever purpose the speaker has for requesting Paul or Bill, it will equally well be served by both of them. When the assumption that satisfying a logically weaker member of a set of scalar alternatives is just as good for the speaker as satisfying a logically stronger member is dropped, implicatures are present in imperatives. (8) Take some of the biscuits. Don’t take all of the biscuits. These counterexamples to Chierchia’s generalization involve contexts which only license free choice ‘any’ and not ‘any’ as a negative polarity item (NPI).15 Thus, it is plausible that Chierchia ought to move to the restricted generalization that implicatures are suspended in contexts which license ‘any’ as an NPI. However, many instances of this restricted generalization are easily explained on the
    14 15
    
    It seems clear that this implicature is only blocked in certain contexts and not in all. Chierchia’s other examples in support of the restricted generalization include questions and the irrealis mood in Italian. The latter is not a topic on which I am qualified to comment. Evidence provided by the former is inconclusive. Some implicatures are cancelled. (a) Did John or Paul arrive? (b) / Did John or Paul but not both arrive? However, empirical work by Ira Noveck (2001) suggests that adults interpret questions like (c) as asking (d), which indicates that the implicature remains. (c) Did some of the horses jump the fence? (d) Did some but not all of the horses jump the fence? ©2008 The Aristotelian Society Proceedings of the Aristotelian Society, Vol. cviii, Part 3 doi: 10.1111/j.1467-9264.2008.00252.x
    
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    pragmatic account. Since most contexts in which ‘any’ is licensed as an NPI are downward entailing contexts, in such contexts the replacement of a weaker member of a semantic scale with a stronger one does not generate a sentence that expresses a stronger proposition. Thus, the pragmatic account predicts that the standard implicature is lost. In fact, for simple cases the pragmatic account makes accurate predictions beyond the mere suspension of implicatures.16 (9) (a) John doubts that anyone is in the room. (*Anyone is in the room.) (b) John doubts that Paul or Bill is in the room. / John doesn’t doubt that Paul and Bill are in the room. (c) John doubts that Paul and Bill are in the room. John doesn’t doubt that Paul or Bill is in the room. Given that ‘doubt’ forms a downward entailing context, that John doubts that both Paul and Bill are in the room follows from (9b). Thus, an assertion of (9b) is not predicted to carry the implicature marked, since the relevant information has already been provided. However, given an utterance of (9c), the speaker has not asserted whether or not John doubts that Paul or Bill are in the room, and since this proposition is informationally stronger, its negation will be implied in suitable contexts.17 Contrary to Chierchia’s claim, there is no interesting connection between contexts which license ‘any’ as a free choice item and the suspension of implicatures. In fact, the genuine cases of suspension (or recalibration) of implicatures can be explained on the pragmatic account. Moreover, problems arise for his positive account of scalar implicatures.
    These predictions were noted by Atlas and Levinson (1981) and Horn (1989). Chierchia’s generalization regarding NPI licensing may be of more interest for accounts which assume that implicatures are computed locally, but that does not include the pragmatic account. 17 Cases not considered here are those in which ‘any’ is licensed as an NPI, but which are not straightforwardly downward entailing. Matters here are complex, but it does not seem that all implicatures are suspended. In appropriate contexts (a) may imply (b), particularly when information is requested about both Gemma’s individual performance on a given test and how it relates to her classmates or other salient group. The precise derivation of this implicature and its relation to (c) is unclear. (a) Only Gemma answered most of the questions. (b) Gemma did not answer all of the questions. (c) ? Only Gemma answered most but not all of the questions. Benjamin Russell (2006) provides a more comprehensive criticism of Chierchia’s claims concerning scalar implicatures and NPI licensing. ©2008 The Aristotelian Society Proceedings of the Aristotelian Society, Vol. cviii, Part 3 doi: 10.1111/j.1467-9264.2008.00252.x
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    IV
    Chierchia’s Computational Account. Chierchia adopts a multidimensional version of standard type-driven intensional logic to formalize his theory of scalar implicatures. During the recursive process of semantic interpretation, each node, a, has both a plain semantic value, ||a||, and a set of strengthened or scalar values, ||a||s (this may include the plain value). The strengthened values are computed from the semantic value of English expressions together with their scalar alternatives. The details of Chierchia’s system are complex, but essentially scalar implicatures are introduced at scope sites, where the strong semantic value equals the conjunction of the plain semantic value and the negation of all logically stronger scalar alternatives. These strong semantic values then enter recursive derivation in the standard way, unless they enter a downward entailing context in which case they are recalibrated. Outside of downward entailing contexts, recalibration of implicatures does not occur. The mechanism and its difficulties are demonstrated by the example in (10).18 (10) (a) Somebody smokes or drinks. (b) LF: somebodyi [ti smokes or ti drinks]. (c) ||[ti smokes or ti drinks]||s =[[smoke (x)∨drink (x)]∧¬[smoke (x)∧drink (x)]] (d) ||somebodyi [ti smokes or ti drinks]||s ={somebody (lx [[smoke (x)∨drink (x)]∧ ¬[smoke (x)∧drink (x)]]), somebody (lx[smoke (x)∨drink (x)])∧ ¬everybody (lx[smoke (x)∨drink (x)])} Translated into English, the theory predicts that (11a) has the implicatures given in (11b) and (11c). (11) (a) Somebody smokes or drinks. (b) Somebody smokes or drinks but not both. (c) Not everybody smokes or drinks.
    18
    
    This formalization includes the correction of a minor typographical error in the appendix to Chierchia (2004, p. 97).
    
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    However, an utterance of (11a) will often also imply (12). (12) Nobody smokes and drinks. Chierchia’s mechanism for generating scalar implicatures is too inflexible to generate (12) from (11a). In contrast, a pragmatic account that is more permissive in combining scalar items predicts that ‘Someone smokes and drinks’ is a relevant alternative to (11a) in appropriate contexts. Since this sentence is more informative than (11a), its negation, (12), is implied by (11a). The reason that (12) cannot be derived on Chierchia’s account is that once the scalar implicature associated with ‘or’ has been introduced, in (11b), it is ignored by other scalar terms higher in the tree structure of LF. As Chierchia writes:
    Now, since the plan is to deal with each implicature as soon as possible, I will define a alt [the scalar alternatives of a node, a] in such a way that it yields the alternatives induced solely by the last scalar element in the tree (i.e. the highest or topmost one). The rationale for this is that scalar terms below the topmost (if present) will have already been taken care of (by the terms below the topmost). This is a locality constraint driven by the guiding idea of our attempt (namely, that implicatures are processed locally in the order in which their triggers appear). (Chierchia 2004, p. 60)
    
    Applying this locality constraint in example (10) entails that, whilst ‘[smoke (x)∧drink (x)]’ is a scalar alternative of ‘[smoke (x)∨ drink (x)]’ at the node on which ‘somebody ’ operates, ‘somebody (lx[smoke (x)∧drink (x)])’ is not a scalar alternative of ‘somebody (lx[smoke (x)∨drink (x)])’ at the highest point in the tree. Hence, the fact that (12) is not a predicted implicature from (11a) follows directly from the locality constraint.19 Chierchia’s claim that the locality constraint follows from the ‘guiding idea’ behind his account is correct. Therefore, his account cannot be adapted to handle the implication of (12) without abandoning its central aim. Without the locality constraint, Chierchia’s formal apparatus is merely a means to model the global derivation of scalar alternatives and the motivation for a default account is lost.20 Finally, Chierchia’s account cannot adequately predict the impli19
    
    That the inability to derive (12) from (11a) follows from the locality constraint has been independently noted by Jaegyun Song (2005); however, Song fails to see this as an inadequacy of Chierchia’s account.
    
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    catures arising from (13a) when the speaker is in a strong epistemic position. If it is known that the speaker knows the professions of everyone at a particular party last night and he utters (13a), then the implicatures (13b) to (13d) follow. (13) (a) Everyone was a linguist or a philosopher. (b) Not everyone was a linguist and a philosopher. (c) Not everyone was a linguist. (d) Not everyone was a philosopher. Chierchia’s account predicts (13b) as an implicature, but does not predict (13c) or (13d). Since his account is semantically driven, in order to generate (13c) and (13d) as part of the strong meaning of (13a), Chierchia would have to alter the interpretation of ‘or’ throughout his theory so that ‘P or Q’ would always imply both ‘Not P’ and ‘Not Q’. The difficulties of such a modification are clear. On a pragmatic account, the implicatures in (13) are predicted as long as ‘Everyone was a linguist’ is taken to be a relevant alternative to (13a). Provided the speaker is assumed to have relevant knowledge about the group in question, the negation of ‘Everyone was a linguist’, (13c), will be implied by an utterance of the weaker (13a) and similarly for (13d). This case and the previous one show that Chierchia’s theory is significantly inferior to the pragmatic account.
    
    V
    Conclusion. Computational and default theories of implicature blur the distinction between the semantic and pragmatic content of an utterance. The fact that Chierchia’s approach is unsuccessful sug20
    
    The scalar terms in (11a) are not far removed in the LF tree. However, even if Chierchia relaxed his locality constraint to allow access to alternatives introduced by scalar terms that are merely near the top of the tree (rather than topmost) his account would remain inadequate, since there is no principled limit to the number of embeddings within which a scalar term may appear and still introduce implicatures. In order to generate implicatures such as that in (12) Chierchia must combine his account with a general theory of global implicature generation. However, provided that a suitably sophisticated general theory is able to handle all the cases Chierchia’s account can predict, a requirement already noted in footnote 11, it would seem that there is little work left for Chierchia’s computational account to perform. It should be noted that this paper has not sought to separate the defaultness and locality properties of Chierchia’s theory; the viability of approaches which abandon only one of these properties remains to be seen. ©2008 The Aristotelian Society Proceedings of the Aristotelian Society, Vol. cviii, Part 3 doi: 10.1111/j.1467-9264.2008.00252.x
    
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    gests that the traditional Gricean distinction between conversational implicatures and semantic content should be of fundamental importance to contemporary linguistic theorists.21 Moreover, the comparative success of the pragmatic account suggests that this is a fertile avenue for further research.22 Centre for the Study of Mind in Nature University of Oslo Blindern n-0315, Oslo Norway owengr@ifikk.uio.no REFERENCES
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    Further difficulties for default theories have been raised by cognitive scientists investigating scalar implicatures from an empirical perspective: for example, Breheny, Katsos and Williams (2006). 22 I am grateful to Napoleon Katsos, Nathan Klinedinst and audiences at Oxford University, University College London and the 2007 Joint Session for helpful comments on the material in this paper. They are not responsible for any errors that may remain. ©2008 The Aristotelian Society Proceedings of the Aristotelian Society, Vol. cviii, Part 3 doi: 10.1111/j.1467-9264.2008.00252.x
    
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    vard University Press, 1989. Grodner, Daniel and Julie Sedivy forthcoming: ‘The Effect Of Speaker-Specific Information on Pragmatic Inferences’. In E. Gibson and N. Perlmutter (eds.), The Processing and Acquisition of Reference. Cambridge, ma: MIT Press. Hirschberg, Julia 1991: A Theory of Scalar Implicature. New York: Garland. Horn, Larry 1972: ‘On the Semantic Properties of Logical Operators in English’. Ph.D. thesis, University of California, Los Angeles. ——1989: A Natural History of Negation. Chicago: University of Chicago Press. Levinson, Stephen C. 2000: Presumptive Meanings: The Theory of Generalized Conversational Implicature. Cambridge, ma: MIT Press. Noveck, Ira A. 2001: ‘When children are more logical than adults: experimental investigations of scalar implicature’. Cognition, 78(2), pp. 165– 88. Russell, Benjamin 2006: ‘Against Grammatical Computation of Scalar Implicatures’. Journal of Semantics, 23(4), pp. 361–82. Sauerland, Uli 2004: ‘Scalar Implicatures in Complex Sentences’. Linguistics and Philosophy, 27, pp. 367–91. Soames, Scott 1982: ‘How Presuppositions are Inherited: A Solution to the Projection Problem’. Linguistic Inquiry, 13, pp. 483–545. Song, Jaegyun 2005: ‘Local Computation of Scalar Implicatures’. Korean Journal of English Language and Linguistics, 5(1), pp. 95–114.
    
    ©2008 The Aristotelian Society Proceedings of the Aristotelian Society, Vol. cviii, Part 3 doi: 10.1111/j.1467-9264.2008.00252.x

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