How Much Can We Weaken Downward Entailment?

This paper discusses the occurrence of certain polarity items (PIs) in the complements of factive verbs and only, which are not downward entailing (DE). Two solutions in the direction of weakening classical monotonicity are discussed: Strawson DE, von Fintel 1999; and weak DE, Hoeksema 1986. Both rely on the idea that monotonicity is computed only after the inference to the subset is made part of the background knowledge. We see that this weakening systematically either overgeneralizes or undergeneralizes, in either case failing to characterize the correct set of licensers. It is proposed that a more promising account must rely on the notion of nonveridicality (Giannakidou 1998, 1999), augmented with the premise that certain PIs, i.e. the liberal class represented by any, are subject to a weaker polarity dependency identified as anti-licensing by veridicality. 1 The problem and the suggested remedies The main observation, which goes back to Linebarger 1980 (see also Atlas 1993, 1996, Horn 1996, to appear, Giannakidou 1998, von Fintel 1999) is that polarity items (PIs) like any and English minimizers occur in the scope of only, and in the complements of negative factive verbs: (1) a Only Larry ate anything. b Only Larry slept a wink. (2) a Larry regrets that he said {anything/a word}. b * Larry is glad that he said {anything/a word}. The fact in (1) as well as the grammaticality of (2a) and its contrast with (2b) do not follow from Ladusaw’s classical thesis that PIs are licensed in the scope of expressions that denote downward entailing functions: (3) Ladusaw’s (1979) licensing condition α is a trigger for NPIs in its scope iff α is downward entailing. (4) Downward entailing function A function f is downward entailing iff for every arbitrary element X,Y such that X⊆Y: f(Y) → f(X).