Ambiguous than-clauses and the mention-some reading

Linmin Zhang, Jia Ling


This paper addresses the ambiguity of comparatives that contain a permission-related existential modal in their than-clause. For example, given the context that the interval of permitted speed is between 35 and 50 mph, the sentence Lucinda is driving less fast than allowed is ambiguous between two readings: (i) her speed is below the minimum (i.e., 35 mph); (ii) her speed is below the maximum (i.e., 50 mph). Previously, this ambiguity has been attributed to either the scopal interaction between a negation element and a modal (Heim 2006a) or the optional application of a silent operator (Crnic 2017). Here we show that these two lines of accounts under- or over-generate. Instead, we propose that the source of this ambiguity is located in the ambiguous answerhood for wh-questions corresponding to this kind of than-clauses (e.g., how fast is Lucinda allowed to drive). The current proposal consists of three parts. First, based on Zhang & Ling (2015, 2017a,b), we adopt a generalized interval-arithmetic-based recipe for computing the semantics of comparatives. Second, the semantics of than-clauses is considered equal to that of short answers to corresponding wh-questions. Third, since the use of existential priority modals in wh-questions leads to the ‘mention-some/mention-all’ ambiguity for answerhood, we propose that this ambiguity projects in further derivation and leads to the two readings for comparatives like the Lucinda sentence. 

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Alrenga, Peter & Christopher Kennedy. 2014. No more shall we part: Quantifiers in English comparatives. Natural Language Semantics 22(1). 1–53.

Barker, Chris. 2010. Free choice permission as resource-sensitive reasoning. Semantics and Pragmatics 3. 10–1.

Barker, Chris. 2016. Why relational nominals make good concealed questions. Lingua 182. 12–29.

Beck, Sigrid. 2010. Quantifiers in than-clauses. Semantics and Pragmatics 3(1). 1–72.

Beck, Sigrid. 2013. Lucinda driving too fast again – the scalar properties of ambiguous than-clauses. Journal of Semantics 30(1). 1 – 63 (ffr011).

Beck, Sigrid. 2014. Plural predication and quantified ‘than’-clauses. In Luka Crnic & Uli Sauerland (eds.), The art and craft of semantics: A Festschrift for Irene Heim 1, 91–115. MIT Working Papers in Linguistics 70.

Beck, Sigrid & Hotze Rullmann. 1999. A flexible approach to exhaustivity in questions. Natural Language Semantics 7(3). 249–298.

Büring, Daniel. 2007a. Cross-polar nomalies. In T. Friedman & M. Gibson (eds.), Proceedings of Semantics and Linguistic Theory 17, 37–52. Ithaca, NY: Cornell University.

Büring, Daniel. 2007b. More or less. In Proceedings of the 43th Annual Regional Meeting of Chicago Linguistic Society, 3–17. Chicago Linguistic Society.

Crnic, Luka. 2017. More on less. In Andrew Lamont and Katerina A. Tetzloff (eds.), NELS 47: Proceedings of the 47th Meeting of the North East Linguistic Society.

Dayal, Veneeta. 2004. The universal force of free choice any. Linguistic Variation Yearbook 4(1). 5–40.

Dayal, Veneeta. 2016. Questions. Oxford University Press.

Dotlacil, Jakub & Rick Nouwen. 2016. The comparative and degree pluralities. Natural Language Semantics 24(1). 45–78.

Fox, Danny. 2013. Mention-some readings of questions. MIT seminar notes.

Fox, Danny. 2016. Mention some, reconstruction, and free choice. “Attitudes and Questions” Workshop notes.

Ginzburg, Jonathan & Ivan Sag. 2000. Interrogative investigations. Stanford: CSLI publications.

Girard, Jean-Yves. 1987. Linear logic. Theoretical computer science 50(1). 1–101.

Greenberg, Yael. 2010. Additivity in the domain of eventualities (or: Oliver Twist’s more). In Martin Prinzhorn, Viola Schmitt & Sarah Zobel (eds.), Proceedings of Sinn und Bedeutung 14, 151–167.

Groenendijk, Jeroen & Martin Stokhof. 1984. Studies on the semantics of questions and the pragmatics of answers: Universiteit van Amsterdam PhD dissertation.

Guerzoni, Elena & Yael Sharvit. 2007. A question of strength: on npis in interroga- tive clauses. Linguistics and Philosophy 30(3). 361–391.

Hacquard, Valentine. 2005. Aspect and actuality entailment: Too and enough con- structions. In Emar Maier, Corien Bary & Janneke Huitink (eds.), Proceedings of Sinn und Bedeutung 9, 116–130.

Hacquard, Valentine. 2006. Aspects of too and enough constructions. In Proceedings of Semantics and Linguistic Theory 15 15, 80–96. Citeseer.

Hausser, Roland & Dietmar Zaefferer. 1978. Questions and answers in a context- dependent Montague grammar. In Formal semantics and pragmatics for natural languages, 339–358. Springer.

Hausser, Roland R. 1983. The syntax and semantics of english mood. In Questions and answers, 97–158. Springer.

Heim, Irene. 2006a. Little. In M. Gibson & J. Howell (eds.), Proceedings of Semantics and Linguistic Theory 16, 35–58. Ithaca, NY: Cornell University.

Heim, Irene. 2006b. Remarks on comparative clauses as generalized quantifiers. Manuscript, MIT.

Krasikova, Sveta. 2008. Quantifiers in comparatives. In Atle Grønn (ed.), Proceedings of Sinn und Bedeutung 12, 337–352. Oslo: ILOS 2008 (ISBN 978-82-92800-00-3).

Krasikova, Svetlana. 2011. Modals in comparatives: Universität Tübingen PhD dissertation.

Krifka, Manfred. 2011. Questions. In Klaus Heusinger, Claudia Maienborn & Paul Portner (eds.), Semantics: An international handbook of Natural Language Meaning 2, 1742–1785. Berlin: Mouton de Gruyter.

Lokhorst, Gert-Jan C. 1997. Deontic linear logic with Petri net semantics. Erasmus University, Department of Philosophy.

Meier, Cécile. 2002. Maximality and minimality in comparatives. In Graham Katz, Sabine Reinhard & Philip Reuter (eds.), Proceedings of Sinn und Bedeutung 6, 275 – 287.

Meier, Cécile. 2003. The meaning of too, enough, and so... that. Natural Language Semantics 11(1). 69–107.

Moore, Ramon E. 1979. Methods and Applications of Interval Analysis. SIAM.

van Rooij, Robert. 2008. Comparatives and quantifiers. In O. Bonami & P. Cabredo Hofherr (eds.), Empirical Issues in Syntax and Semantics 7, 423–444.

Ross, Alf. 1944. Imperatives and logic. Philosophy of Science 11(1). 30–46.

Rullmann, Hotze. 1995. Maximality in the semantics of wh-constructions: University of Massachusetts Amherst PhD dissertation.

Schwarzchild, Roger & Karina Wilkinson. 2002. Quantifiers in comparatives: A semantics of degree based on intervals. Natural language semantics 10(1). 1–41.

Schwarzschild, Roger. 2008. The semantics of comparatives and other degree constructions. Language and Linguistics Compass 2(2). 308–331.

Seuren, Pieter A. M. 1979. Meer over minder dan hoeft. De nieuwe taalgids 72(3). 236–239.

Thomas, Guillaume. 2010. Incremental more. In Proceedings of Semantics and Linguistic Theory 20, 233–250.

Thomas, Guillaume. 2011. Another additive particle. In Proceedings of Semantics and Linguistic Theory 21, 634–651.

Von Stechow, Arnim. 1984. Comparing semantic theories of comparison. Journal of semantics 3(1). 1–77.

Von Stechow, Arnim & Thomas Ede Zimmermann. 1984. Term answers and con- textual change. Linguistics 22(1). 3–40.

Xiang, Yimei. 2016. Interpreting questions with non-exhaustive answers: Harvard University PhD dissertation.

Zhang, Linmin. In prep.a. Convex set and answerhood. Manuscript.

Zhang, Linmin. In prep.b. The semantics of sufficiency and excess. Manuscript (Sinn und Bedeutung 22).

Zhang, Linmin & Jia Ling. 2015. Comparatives Revisited: Downward-Entailing Differentials Do Not Threaten Encapsulation Theories. In Thomas Brochhagen, Floris Roelofsen & Nadine Theiler (eds.), Proceedings of the 20th Amsterdam Colloquium, 478 – 487.

Zhang, Linmin & Jia Ling. 2017a. LITTLE: Not a dichotomy-based negation operator, but a trivalence-based polar opposition operator. In Aaron Kaplan, Abby Kaplan, Miranda K. McCarvel & Edward J. Rubin (eds.), Proceedings of the 34th West Coast Conference on Formal Linguistics, Cascadilla Press.

Zhang, Linmin & Jia Ling. 2017b. The semantics of English clausal comparatives: An interval-arithmetic-based approach. Manuscript.