Abstract
This paper explores interactions between the alternative semantics of Kratzer and Shimoyama (2002) and the embeddable exhaustive operator Exh proposed to handle embedded implicatures (Chierchia 2004; Fox 2004, 2007). The proposal is that when Exh applies to single alternative propositions (instead of complete, matrix-level sets of alternatives), it can generate correct scalar implicatures while avoiding several problems proposed in prior literature. The problems solved include implicature generation when a quantifier appears in a disjunction (Chierchia 2004) and when a sentence includes complex quantifiers like “more than two” (Krifka 1999).
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Notes
- 1.
Note that if \(\phi \) itself (or another scalar item with the same meaning as \(\phi \)) were a member of \(Alt(\phi )\) the entailment in (2) would have to be asymmetric entailment.
- 2.
- 3.
Lee (2010) points out that there is a reading of a comparative sentence like (10a) where the numeral—three in this case—is accommodated from previous discourse, and the only scalar term is the phrase more than. In this reading, the implicature generated is something like Paul did not read many more than three books. However, there is also a reading where the numeral three is truly new information. For instance, the person uttering (10a) could only have enough information to say for sure that Paul read three, but there is inconclusive evidence that he may have read more books. It is this reading that I will focus on below.
- 4.
- 5.
Kratzer (2005) proposes a similar line of attack, especially for the comparative puzzle, in her 2005 LSA Summer Institute handout. I have tried to expand this analysis to other puzzles and flesh out the technical details.
- 6.
- 7.
- 8.
An anonymous reviewer notes that Geurts (2009) terms this “M-ONLY.”
- 9.
In relation to the focus set in (42), this sentence generates, among others, the implicature that Paul did not read The New York Times, since The New York Times is not a book. Please note that this sentence would be a fine answer to the question How many books did Paul read last night?. However, given this different question, the implicature that Paul did not read The New York Times would not be generated, since the sentence Paul read The New York Times last night would not be in the relevant focus set.
- 10.
An anonymous reviewer points out that there is another system which allows similar existential closure over indefinites without movement: the choice-function analysis of Ruys (1993); Reinhart (1997); Winter (1997). The choice between the Kratzer and Shimoyama system and the choice-function system is not crucial to the analysis presented here.
- 11.
The constituent structure assumed here is simplified for presentation purposes. See Sauerland and Yatsushiro (2004) for a discussion of the true structure of such phrases.
- 12.
This problem appears in Sauerland (2004a). Danny Fox (p.c.) pointed out the application here.
- 13.
Uli Sauerland (p.c.) pointed out this example.
- 14.
It is crucial for this analysis that the existential force of or, like that of the indefinites, be able to scope above the exhaustive operator. See Alonso and Ovalle (2006) for more discussion of disjunction in Alternative Semantics.
- 15.
Notice that as defined above, \(\exists \) returns a set of propositions; the assumption is that the interpretation procedure can handle such singleton sets of propositions.
- 16.
Giannakidou and Quer (2013) criticize this type of approach.
- 17.
Uli Sauerland (p.c.) suggested the addition of this section.
- 18.
An anonymous reviewer suggests an additional wrinkle: the DP three books may also scope above negation. I assume that in that case, the DP raises above negation, and Exh may apply as usual to the transformed structure.
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Acknowledgement
Thanks to Danny Fox, Irene Heim,Gennaro Chierchia, Kai von Fintel, Tamina Stephenson, Uli Sauerland, the members of the MIT Workshop on Syntax and Semantics, Fall 2005, and the participants of SALT 16. A previous version of this paper appears in the proceedings of SALT 16.
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Keshet, E. (2017). Scalar Implicatures with Alternative Semantics. In: Lee, C., Kiefer, F., Krifka, M. (eds) Contrastiveness in Information Structure, Alternatives and Scalar Implicatures. Studies in Natural Language and Linguistic Theory, vol 91. Springer, Cham. https://doi.org/10.1007/978-3-319-10106-4_13
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