Don’t scope your universal quantifier over negation!

DOČEKAL, Mojmír and Hana STRACHOŇOVÁ. Don’t scope your universal quantifier over negation! In Formal Approaches to Slavic Linguistics 22. 2013.

Basic information

• Original name: Don’t scope your universal quantifier over negation!
• Authors: DOČEKAL, Mojmír and Hana STRACHOŇOVÁ.
• Edition: Formal Approaches to Slavic Linguistics 22, 2013.

Other information

• Original language: English
• Type of outcome: Presentations at conferences
• Field of Study: 60200 6.2 Languages and Literature
• Country of publisher: Canada
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Organization unit: Faculty of Arts
• Keywords in English: negation; scope; universal quantifier

Abstract

In this paper we propose that the scope of universal quantifier and negation in a natural language (particularly Czech) should be analyzed as fixed despite superficial examples against this claim. More specifically, we argue that universal quantifier is semantically always in the scope of negation. For example, the sentence in (1) has two theoretical interpretations – either the numeral out-scopes the negation and the sentence is understood as that John saw all Jarmusch movies with the exception of two, or it means that John saw less than two Jarmusch movies (one or zero). The second reading can be formally represented as negation having wider scope than the numeral 2. But as was observed already by Jackendoff (1972), Büring (1997) and Kadmon (2001) among others, if we replace the numeral with the universal quantifier, one of the readings disappears. For example, consider the example (2), for which the only reading is: John saw some but not all Jarmusch movies, the wide scope of negation. The other logically possible reading: John didn’t see any of Jarmusch movies seems to be absent. (1) John hasn’t seen two Jarmusch movies. (2) John hasn’t seen all Jarmusch movies. Majority of recent approaches to the lack of ambiguity in examples like (2), such as Büring (1997) and Kadmon (2001), all make use of information structure mechanisms where usually some sort of ‘wide scope for focused element’ rule is applied to explain the lack of ambiguity. Our work aims to improve on their work by deriving the preference for wide scope interpretation of negation from another source, namely from the idea of grammatical concurrence between universal quantifier and negative noun phrases. In our use of the concurrence explanation we build very much upon the ideas of Hoekstra (1998) and Horn (1990).