In many languages, the same particles build quantifier words and serve as connectives, additive and scalar particles, question markers, existential verbs, and so on. Do the roles of each particle form a natural class with a stable semantics? Are the particles aided by additional elements, overt or covert, in fulfilling their varied roles? I propose a unified analysis, according to which the particles impose partial ordering requirements (glb and lub) on the interpretations of their hosts and the immediate larger contexts, (...) but do not embody algebraic operations themselves. (shrink)

Abstract Proportional quantifiers have played a central role in the development of formal semantics because they set a benchmark for the expressive power needed to describe quantification in natural language (Barwise and Cooper Linguist Philos 4:159–219, 1981). The proportional quantifier most, in particular, supplied the initial motivation for adopting Generalized Quantifier Theory (GQT) because its meaning is definable as a relation between sets of individuals, which are taken to be semantic primitives in GQT. This paper proposes an alternative analysis of (...) most that does not treat it as a lexical item whose meaning is accessible without the help of compositional processes. Instead, proportional most is analyzed as the superlative of many (cf. Bresnan Linguist Inq 4(3):274–344, 1973). Two types of empirical evidence are presented in support of this view, both exploiting the fact that only a decompositional analysis of proportional quantifiers provides the means to generate different logical forms for seemingly equivalent statements of the form most A B and more than half of the A B. (shrink)

We revisit a typological puzzle due to Horn (Doctoral Dissertation, UCLA, 1972) regarding the lexicalization of logical operators: in instantiations of the traditional square of opposition across categories and languages, the O corner, corresponding to ‘nand’ (= not and), ‘nevery’ (= not every), etc., is never lexicalized. We discuss Horn’s proposal, which involves the interaction of two economy conditions, one that relies on scalar implicatures and one that relies on markedness. We observe that in order to express markedness and to (...) account for a bigger typological puzzle, namely the absence of lexicalizations of ‘XOR’ (= exclusive or), ‘all-or-none’, and many other imaginable logical operators, one must restrict the basic lexicalizable elements to a small set of primitives. We suggest that an ordering based perspective, following Keenan and Faltz (Boolean semantics for natural language, 1985), makes the stipulated primitives that we arrive at more natural. We also propose a modification to Horn’s proposal, based on recent work on implicatures, in which only the implicature condition is operative and in which markedness is part of the definition of the alternatives for scalar implicatures rather than an independent condition. (shrink)

The paper discusses a prominent one of Kratzer's (1986, 1991, 2012) arguments against material implication analyses of the denotation of (indicative) conditional sentences. This is the argument based on the sentence _Most of the time, if a man buys a horse, he pays cash for it_. It is shown that material implication makes a prediction that does conform to speakers' intuitions, contrary to Kratzer's claim. The paper also argues that Lewis's (1975) attack on material implication analyses of conditional sentences based (...) on examples where the conditional is embedded under the adverbials _sometimes_ and _never_ does not have much force given that the interpretation of such sentences is subject to inferential pragmatic operations in addition to the recovery of their denotation. (shrink)

This paper investigates the structure of English restrictive relative clauses. It provides support for the view that restrictive relative clauses are structurally ambiguous between two structures: the head-internal, raising structure and the matching structure, which has both an internal and an external head. We present a new test from extraposition facts that distinguishes between the raising and matching structures for relative clauses. Furthermore, this paper presents an account of the semantics of raising relative clauses which is intended to complete the (...) picture of the semantics of relative clauses. In particular, we argue that raising relative clauses are not islands for Quantifier Raising (QR) and that in these clauses there is successive cyclic movement through a CP-adjoined position. (shrink)

The semantic literature takes degree operators like the comparative, but also measure phrases, the equative, the superlative and so on, to be quantifiers over degrees. This is well motivated by their semantic contribution, but leads one to expect far more scope interaction than is actually observed. This paper proposes an alternative-semantic analysis of certain degree constructions, in particular constructions with little and other negative antonyms. Restrictions on scope can then be explained as intervention effects.

It is well known that occurrences of sentences such as “Every bottle is empty” will sometimes be understood relative to a subset of the set of all bottles in the universe. Much has been written about what mechanism should be used to model this phenomenon of domain restriction. However, comparatively little attention has been paid to the question of when domain restriction is triggered. I will begin by challenging a recent partial answer to this question. I will then develop my (...) own partial answer based on observations pertaining to information structure. (shrink)

It has long been observed that the superlative construction, exemplified by John climbed the highest mountain, has two readings. On the absolute reading, the heights of the relevant mountains in a relevant context are compared; on the comparative reading, relevant climbers’ achievements of mountain climbing are compared (Szabolcsi, Comparative superlatives, MIT Working Papers in Linguistics, 1986). Two theories have been proposed regarding this ambiguity. One theory holds that it results from movement of the superlative morpheme -est (movement theory) (Heim, Association (...) with focus, Doctoral Dissertation, 1985, Notes on superlatives, 1999; Szabolcsi 1986).The other theory holds that the ambiguity is derived by assignment of different values to the context variable C, keeping a single LF structure where -est stays in situ (in-situ theory) (Farkas and Kiss, Nat Lang Linguist Theory 18:417–455, 2000; Sharvit and Stateva, Linguist Philos 25:453–504, 2002). As is pointed out by Heim (1999), a choice between these theories is hard to make based solely on English. Through an investigation of Japanese superlative constructions, this paper argues that, in Japanese at least, a movement theory is required. (shrink)

Two theories of implicit domain restriction have gained considerable prominence over the last two decades. According to von Fintel (Restrictions on quantifier domaines, Ph.D. thesis, University of Massachusetts at Amherst, 1994), quantifiers come with covert restrictors and, as a result of this, induce domain restriction; according to Stanley [in Gerhard and Peter (eds) Logical form and language, Clarendon Press, Oxford, 2002; Stanley and Szabó (Mind Lang 15(2–3):2192–2161, 2000)], by contrast, nouns, as opposed to quantifiers, come with covert restrictors. In this (...) article, I do three things. First, I assess the arguments that have been given for and against these two accounts and show that none of them is conclusive. Second, I advance a novel empirical argument based on the observed pragmatic behaviour of bare nouns, an argument that falsifies Stanley’s theory while providing clear evidence in support of von Fintel’s (1994). Finally, I discuss the relevance of the bare noun data in the context of another important debate—namely, whether domain restriction is a local mechanism only, or whether it can also be achieved by global means. (shrink)

This paper argues for a particular semantic decomposition of morphological definiteness. I propose that the meaning of ‘the’ comprises two distinct compositional operations. The first builds a set of witnesses that satisfy the restricting noun phrase. The second tests this set for uniqueness. The motivation for decomposing the denotation of the definite determiner in this way comes from split-scope intervention effects. The two components—the selection of witnesses on the one hand and the counting of witnesses on the other—may take effect (...) at different points in the composition of a constituent, and this has non-trivial semantic consequences when other operators inside the DP take action in between them. In particular, I analyze well-known examples of mutually recursive definite descriptions like ‘the rabbit in the hat’ as examples of definites whose referent-introducing and referent-testing components are interleaved rather than nested. I further demonstrate that this picture leads to a new theory of relative superlative descriptions like ‘the kid who climbed the highest tree’, which explains the previously mysterious role of the definite determiner in licensing such readings. (shrink)

Sentences like _Mary needs to make the fewest mistakes on the upcoming test_ have a ‘split scope’ reading roughly paraphrasable as ‘Mary exceeds all others in terms of how many mistakes she must _not_ make’; that is, her situation is the most precarious. The structural approach to this phenomenon attributes to such sentences a logical form resembling this paraphrase, in which the superlative component of the meaning of _fewest_ scopes above the modal _need to_ and the negative component scopes below (...) it. This paper investigates analogous structures in Syrian Arabic, a language in which superlatives may appear at a distance from their scalar associates in the surface order. The syntax of such expressions in Syrian Arabic, and the range of interpretations available to the various syntactic permutations found there points to two different sources for split scope readings. While some split scope readings are derived by syntactic splitting of _fewest_ across a modal verb, others arise from a semantic ambiguity in the modal verb itself, rather than from a syntactic distinction in logical form. (shrink)

Superlative sentences with modal modifiers like possible give rise to the so-called 'modal superlative reading' . The present paper uses this reading to investigate an open issue in degree constructions: whereas two different lexical entries have been argued to exist for the comparative morpheme -er , it is not clear whether two entries are needed for the superlative morpheme -est. The paper argues that, with 3-place –est, otherwise unmotivated syntactic material would to have to be postulated and that, even with (...) this material, not all modal superlative examples would be assigned correct truth conditions. In contrast, 2-place -est can generate the modal superlative reading in all the cases, as shown in Romero . Modal superlative sentences, thus, provide evidence that 2-place –est is needed in the grammar. (shrink)