The notion of measurement plays a central role in human cognition. We measure people’s height, the weight of physical objects, the length of stretches of time, or the size of various collections of individuals. Measurements of height, weight, and the like are commonly thought of as mappings between objects and dense scales, while measurements of collections of individuals, as implemented for instance in counting, are assumed to involve discrete scales. It is also commonly assumed that natural language makes use of (...) both types of scales and subsequently distinguishes between two types of measurements. This paper argues against the latter assumption. It argues that natural language semantics treats all measurements uniformly as mappings from objects (individuals or collections of individuals) to dense scales, hence the Universal Density of Measurement (UDM). If the arguments are successful, there are a variety of consequences for semantics and pragmatics, and more generally for the place of the linguistic system within an overall architecture of cognition. (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)

In the study of natural language quantification, much recent attention has been devoted to the investigation of verification procedures associated with the proportional quantifier most. The aim of these studies is to go beyond the traditional characterization of the semantics of most, which is confined to explicating its truth-functional and presuppositional content as well as its combinatorial properties, as these aspects underdetermine the correct analysis of most. The present paper contributes to this effort by presenting new experimental evidence in support (...) of a decompositional analysis of most according to which it is a superlative construction built from a gradable predicate many or much and the superlative operator -est. Our evidence comes in the form of verification profiles for sentences like Most of the dots are blue which, we argue, reflect the existence of a superlative reading of most. This notably contrasts with Lidz et al.’s results. To reconcile the two sets of data, we argue, it is necessary to take important differences in task demands into account, which impose limits on the conclusions that can be drawn from these studies. (shrink)

This squib presents two puzzles related to an ambiguity found in for-infinitival relative clauses (FIRs). FIRs invariably receive a modal interpretation even in the absence of any overt modal verb. The modal interpretation seems to come in two distinct types, which can be paraphrased by finite relative clauses employing the modal auxiliaries should and could. The two puzzles presented here arise because the availability of the two readings is constrained by factors that are not otherwise known to affect the interpretation (...) of a relative clause. Specifically, we show, first, that “strong” determiners require the FIR to be interpreted as a SHOULD-relative while “weak” determiners allow both interpretations (the Determiner-Modal Generalization). Secondly, we observe that the COULD-interpretation requires a raising (internally headed) structure for the FIR, while the SHOULD-interpretation is compatible with either a raising or a more standard matching (externally headed) structure (the Raising/Matching Generalization). (shrink)

This squib presents two puzzles related to an ambiguity found in for-infinitival relative clauses (FIRs). FIRs invariably receive a modal interpretation even in the absence of any overt modal verb. The modal interpretation seems to come in two distinct types, which can be paraphrased by finite relative clauses employing the modal auxiliaries should and could. The two puzzles presented here arise because the availability of the two readings is constrained by factors that are not otherwise known to affect the interpretation (...) of a relative clause. Specifically, we show, first, that “strong” determiners require the FIR to be interpreted as a SHOULD-relative while “weak” determiners allow both interpretations (the Determiner-Modal Generalization). Secondly, we observe that the COULD-interpretation requires a raising (internally headed) structure for the FIR, while the SHOULD-interpretation is compatible with either a raising or a more standard matching (externally headed) structure (the Raising/Matching Generalization). (shrink)

This paper brings a developmental perspective to the discussion of a longstanding issue surrounding the proper characterization of presuppositions. On an influential view (Stalnaker in Synthese 22(1–2):272–289, 1970; Stalnaker, in Milton, Unger (eds) Semantics and philosophy, New York University Press, New York, 1974; Karttunen in Theor Linguist 1:181–194, 1974), formal presuppositions reflect admittance conditions: an utterance of a sentence which presupposes _p_ is admitted by a conversational context _c_ only if _p_ is common ground in _c_. The theory distinguishes two (...) modes of satisfying this formal requirement: (i) presuppositions may have common ground status prior to utterance, or (ii) they may achieve common ground status post hoc, via accommodation, an adjustment of the common ground by cooperative listeners so as to meet the requirements of an uttered sentence. While intuitive and general, the theory has been criticized (among other things) on methodological grounds (see e.g. Gazdar in Pragmatics: implicature, presupposition and logical form, Academic Press, New York, 1979): the availability of accommodation makes it difficult to empirically examine the notion of presupposition as admittance conditions because a central tenet—pragmatic infelicity results whenever _c_ does not entail _p_—may be masked due to the pragmatic sophistication of language users. In this paper, we argue that child language presents an opportunity to avoid this intrinsic difficulty. In a series of behavioral experiments, we show that young children generate a default expectation that the presuppositions of an asserted sentence have common ground status prior to utterance. Furthermore and more tellingly, we also find that even when accommodation is the preferred option for adults, children fail to accommodate presuppositions in an adult-like manner. This pattern of behavior, we argue, is expected under the admittance theory: in a population where the interference from accommodation is reduced, the impact of failing to satisfy the formal admittance conditions becomes directly observable. (shrink)