Scalar implicatures: exhaustification operators

Another important phenomenon concerning the interaction of semantics and context that has received much recent attention is that of scalar implicatures. A scalar implicature derives from the assertion of a sentence containing an expression that belongs to a quantity scale.

Grice (1975) was the first to discuss the calculation of implicatures. Horn (1972) formulated an influential approach to scalar implicature proposing the existence of conventionalized scales (often called Horn scales) that give rise to implicatures. The general idea is that when a speaker uses an item from a scale (see 51b), their use of that item is automatically compared with statements they could have made with the item’s scalemates.

(51) a Bill read some of the articles.

b <some, many, most, all> Scale

c Bill didn’t read all of the articles. Scalar implicature

If they could have chosen an item that would have resulted in a stronger statement (all in 51c), they should have used that item (if the additional information is relevant). Given that they did not choose to make the stronger statement (and it was relevant), hearers are entitled to infer that the speaker does not know the stronger statement to be true – or even that the speaker knows it to be false. This line of reasoning relies on Horn’s (1972) scales and Grice’s (1975) rules for conversation including maxims enjoining speakers to make their contributions as informative as appropriate and to say only that for which they have adequate evidence.

Another perspective has arisen suggesting that, in fact, scalar implicatures are calculated in parallel with the recursive compositional rules of semantics. Here I will discuss only one argument that has been given in favour of this view (cf. Chierchia et al. 2010). Hurford

(1974) observed that disjunctive statements are infelicitous when one of the disjuncts entails the other. Since being a dog entails being an animal, the following sentence is infelicitous.

(52) ^#Mary saw an dog or an animal.

It has been noticed, however, that in some cases that involve scalar items, disjunctions that have one disjunct entailed by the other can indeed be felicitous. Consider the case of “some or all”. Solving all of the problems means solving some of them, and yet (53) is felicitous.

(53) Bill solved some or all of the problems.

Chierchia et al. 2010 argue that this sentence is felicitous because it does in fact satisfy Hurford’s constraint. They argue that this is so because there is a reading for the first con-junct that is not entailed by the second. Typical uses of some result in a “not all” implicature.

Chierchia et al. suggest that a grammatical mechanism is able to apply that makes this impli-cature part of the meaning of the first disjunct. They propose, specifically, that there is an exhaustification operator O, similar in meaning to only that introduces implicatures. Under such a view, it is possible to embed O under the scope of other operators.

(54) Bill read (only) some of the articles.

(55) [O[Bill solved some of the problems] or [Bill solved all the problems]]

“Bill solved only some of the problems or he solved all of them.”

The proposal is controversial and has been the topic of much recent debate. Alternative pro-posals that do not make use of exhaustification operators have been advanced. For criticisms of this approach and more Gricean alternative see Geurts (2009).

6 Conclusion

In this brief point, I have attempted to give a sketch of the tools and concerns of formal approaches to semantics. Many issues remain to be resolved: the appropriate character of the syntactic input, the dividing line between semantics and pragmatics, the role of models in semantic theory. On the last point, see Zimmermann (2012). One important development within the field of formal semantics has been the attempt to extend the use of these tools to the analysis of less well-studied languages. Important contributions in this domain include Matthewson (2008) et seq. on the cross-linguistic study of the semantics-pragmatics inter-face and Schlenker et al. (2013) on the formal semantics of sign languages.

Further reading

Jacobson, Pauline 1999. Towards a Variable-Free Semantics. Linguistics and Philosophy 22: 117–184.

Strong statement of the benefits of a surface compositional approach to natural language semantics.

Heim, Irene and Kratzer, Angelika 1998. Semantics in Generative Grammar. Oxford: Blackwell. Now classic textbook that has established a lingua franca among formal semanticists, with special atten-tion paid to the rules of interpretaatten-tion.

Landman, Fred 1991. Structures for Semantics. Kluwer: Dordrecht. Still the best introduction to the intricacies of the structure of models for different domains, including events, times and plural individuals.

Dekker, Paul 2011. Dynamic Semantics. In C. Maienborn, K. Von Heusinger and P. Portner (eds) Semantics: An International Handbook of Natural Language Meaning, vol. 1. Mouton de Gruyter:

Berlin, 229–254. Very clear and up-to-date introduction to the central concepts of dynamic seman-tics. Includes discussion of the historical development of these concepts.

Chierchia, G., D. Fox and B. Spector 2010. The Grammatical View of Scalar Implicatures and the Relationship between Semantics and Pragmatics. http://semanticsarchive.net/Archive/

WMzY2ZmY/CFS_EmbeddedSIs.pdf. To appear in Handbook of Semantics, Paul Portner, Claudia Maienborn et Klaus von Heusinger (Eds), Mouton de Gruyter. Important guide to recent develop-ments at the interface of semantics and pragmatics. An emphasis on the analysis of implicatures and their interpretation when embedded.

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Related topics

Chapter 1, (Descriptive) Externalism in semantics; Chapter 16, The semantics of nominals; Chapter 17, Negation and polarity; Chapter 18, Varieties of quantification.