A Typology of Negative Indefinites

Abstract

Chapter 3 investigated ways in which languages convey negation by means of an expression that corresponds to the first-order logic connective ¬. In English this would be not. Negation can also be attracted to other expressions in the sentence, particularly indefinites in argument or adjunct position (Section 1). Negative attraction creates negative indefinites. The class of negative indefinites includes both negative quantifiers (English nobody, nothing, nowhere, never) and n-words. Negative attraction is extended to multiple indefinites under negation in Section 2. Sentences involving a range of negative indefinites raise problems for the principle of compositionality of meaning, because some languages assign a double negation reading to such a sequence, and others a single negation reading. Chapter 1 argued that the compositionality problem cannot be solved in the lexicon, and exploited the polyadic quantifier analysis proposed by de Swart and Sag (2002) to offer a grammatical analysis. The argumentation is briefly summarized in Section 3, in preparation of the typology of double negation and negative concord languages. The polyadic quantifier analysis developed by de Swart and Sag (2002) works well for French because it displays ambiguities between single and double negation readings in sentences that combine two negative expressions. However, in most other languages there is a strong bias toward either the double negation or the negative concord reading. Section 4 builds a bidirectional optimality theory (OT) built on top of the polyadic quantifier analysis in order to account for the systematic contrast between negative concord and double negation languages. In negative concord languages, the functional motivation that favors marking of ‘negative variables’ in the syntax wins out. Double negation languages value first-order iteration in the semantics. Languages that display ambiguities have an overlapping range of constraints in a stochastic extension of the model developed in Chapter 6 (Section 3). As Section 4 emphasizes, the bidirectional setup is essential, for syntactic and semantic variation go hand in hand. Section 5 returns to the relation between negative concord and negative polarity, and offers a diachronic perspective while Section 6 concludes the chapter.