Informativity-based Maximality Conditions*

Von Fintel, Fox and Iatridou 2005/2012 argue that 'the NP' should not be taken to refer to the largest NP-object, as is commonly thought, but rather to the object x such that the proposition 'x satisfies NP' is maximally informative. In particular, they show that in some cases an informativity-based treatment correctly predicts that 'the NP' should refer to the smallest rather than to the largest NP-satisfying object (= 'reversal'). We argue that their informativity-based treatment should be extended to the maximality conditions which, according to recent dynamic semantics, accompany most generalized quantifiers (e.g. Brasoveanu 2008). Specifically, we replicate the argument from 'reversal' with indefinite antecedents: in the discourse A certain amount of plutonium is sufficient to trigger a nuclear explosion. I will obtain it., the pronoun it refers to the smallest rather than to the largest amount of plutonium sufficient to trigger a nuclear explosion. This particular case could be handled in two ways: via dynamic treatments that posit that the antecedent comes with a maximal informativity condition; or via E-type analyses that adopt an informativitybased analysis of definite descriptions and give the pronoun it the semantics of a description. However, the same facts extend to examples with symmetric ('bishop') antecedents that are not easily handled by nondynamic (E-type) treatments; this suggests that the maximality conditions of quantifiers in dynamic semantics must be given an informativity-based definition. The usual lexical entry for the in (1) makes reference to a notion of mereological maximality, as in (2)a (Link 1983; see also Sharvy 1980). Von Fintel, Fox and Iatridou 2005/2012 (= FFI) argue that information-based maximality should be preferred, as in (2)b: (1) [[ the]] (φ) is defined only if there is a unique x such that x is a maximal φ-object (= Mx φ for short).When defined, [[ the]] (φ) refers to the maximal φ-object. (2) a. Link's proposal: Mx φ iff (i) x satisfies φ, (ii) no object x' is such that (a) x' satisfies φ, and (b) x < x', where < is strict mereological inclusion. b. FFI's proposal: Mx φ iff (i) x satisfies φ, (ii) no object x' is such that (a) x' satisfies φ, and (b) the proposition φ(x') asymmetrically entails φ(x). We argue that a similar correction should be made to the maximality conditions introduced by generalized quantifiers in recent dynamic treatments of 'donkey' anaphora (e.g. Brasoveanu 2008). FFI note that when ordering by informativity and ordering by size are inversely correlated, (2)b but not (2)a correctly predicts that the φ should denote the smallest φ-object: (3) I have the amount of flour sufficient to bake a cake. (FFI) In this case (henceforth 'reversal'), 'propositions of the form d-much flour is sufficient to bake a cake become more informative the smaller d is' (FFI) – hence the smallest such amount is denoted. This argument can be replicated with donkey anaphora: (4) A certain amount of plutonium is sufficient to trigger a nuclear explosion. I will obtain it. Here it refers to the minimal rather than to the maximal amount of plutonium sufficient to trigger a nuclear explosion. For an E-type theorist, this fact is unsurprising given FFI's initial observation, since it just stands for: the amount of plutonium sufficient to trigger a nuclear explosion. But other cases require a dynamic treatment: they combine 'reversal' with a context in which two pronouns have semantically symmetric ('bishop'-style) antecedents, as in (5) (the sequence mix it with it is infelicitous, hence we resort to mix it with its counterpart or a French equivalent involving two clitics).