This paper presents an analysis of the sorites paradox for collective nouns and gradable adjectives within the framework of classical logic. The paradox is explained by distinguishing between qualitative and quantitative representations. This distinction is formally represented by the use of a different mathematical model for each type of representation. Quantitative representations induce Archimedean models, but qualitative representations induce non-Archimedean models. By using a non-standard model of \ called \, which contains infinite and infinitesimal numbers, the two paradoxes are shown (...) to have distinct structures. The sorites paradox for collective nouns arises from the use of infinite numbers, whereas the sorites paradox for gradable adjectives arises from the use of infinitesimal numbers. Each paradox can be traced to a different source of vagueness. The sorites paradox for collective nouns is caused by \, and the sorites paradox for gradable adjectives is caused by \ \. If correct, this analysis implies that infinite and infinitesimal numbers are cognitively real, and that they play a role in the semantic interpretation of natural language. (shrink)

The idea that the form of a word reflects information about its meaning has its roots in Platonic philosophy, and has been experimentally investigated for concrete, sensory-based properties since the early 20th century. Here, we provide evidence for an abstract property of ‘boundedness’ that introduces a systematic, iconic bias on the phonological expectations of a novel lexicon. We show that this abstract property is general across events and objects. In Experiment 1, we show that subjects are systematically more likely to (...) associate sign language signs that end with a gestural boundary with telic verbs (denoting events with temporal boundaries, e.g., die, arrive) and with count nouns (denoting objects with spatial boundaries, e.g., ball, coin). In Experiments 2–3, we show that this iconic mapping acts on conceptual representations, not on grammatical features. Specifically, the mapping does not carry over to psychological nouns (e.g. people are not more likely to associate a gestural boundary with idea than with knowledge). Although these psychological nouns are still syntactically encoded as either count or mass, they do not denote objects that are conceived of as having spatial boundaries. The mapping bias thus breaks down. Experiments 4–5 replicate these findings with a new set of stimuli. Finally, in Experiments 6–11, we explore possible extensions to a similar bias for spoken language stimuli, with mixed results. Generally, the results here suggest that ‘boundedness’ of words' referents (in space or time) has a powerful effect on intuitions regarding the form that the words should take. (shrink)

In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We identify four (...) main objections and show how each can be addressed. Finally, we compare the strengths and shortcomings of the mereological approach and plural logic. Our conclusion is that the former remains a viable and well-motivated framework for the analysis of plurals. (shrink)

A vagueness-based approach to the mass/count distinction was developed in Chierchia. Liebesman argues against Chierchia’s proposal developing four arguments against it. He furthermore tries to make a case that regardless of the details of C’s proposal no vagueness-based account of the distinction is viable. In this paper I show that Liebesman’s arguments against C don’t go through and that a line of investigation on the mass count contrast in terms of vagueness is not only viable but also perhaps a source (...) of insight on the nature of this much debated distinction and on the relations between grammar and metaphysics in general. The outcome of the present discussion is of interest beyond the question of who is right in this debate, as it puts into sharper focus several issues pertaining to mass vs. count, plural vs. singular, and the role of vagueness in natural language semantics. (shrink)

Does vagueness underlie the mass/count distinction? My answer is no. I motivate this answer in two ways. First, I argue against Chierchia’s recent attempt to explain the distinction in terms of vagueness. Second, I give a more general argument that no such account will succeed.

Portioning-out and individuation are two important semantic properties for the characterization of countability. In Mandarin, nouns are not marked with count-mass syntax, and it is controversial whether individuation is encoded in classifiers or in nouns. In the present study, we investigates the interpretation of a minimal pair of non-interrogativewh-pronominal phrases, includingduo-shao-N andduo-shao-ge-N. Due to the presence/absence of the individual classifierge, these twowh-pronominal phrases differ in how they encode portioning-out and individuation. In two experiments, we used a Truth Value Judgment Task (...) to examine the interpretation of these twowh-pronominal phrases by Mandarin-speaking adults and 4-to-6-year-old children. We found that both adults and children are sensitive to their interpretative differences with respect to the portioning-out and individuation properties. They assign either count or mass readings to the barewh-pronominal phraseduo-shao-N depending on specific contexts, but only count readings to the classifier-bearingwh-pronominal phraseduo-shao-ge-N. Moreover, the portioning-out and individuation properties associated with the individual classifiergeemerge independently in the course of language development, with the portioning-out property taking precedence over the individuation property. Taken together, the present study provides new evidence for the view that the portioning-out and individuation properties in Mandarin are encoded in classifiers rather than in nouns, and these two semantic properties are two distinct components in our grammar. (shrink)

The distinction between abstract and concrete concepts is fundamental to cognitive linguistics and cognitive science. This distinction is commonly operationalized through concreteness ratings based on the aggregated judgments of many people. What is often overlooked in experimental studies using this operationalization is that ratings are attributed to words, not to concepts directly. In this paper we explore the relationship between the linguistic properties of English words and conceptual abstractness/concreteness. Based on hypotheses stated in the existing linguistic literature we select a (...) set of variables and verify whether they are statistically associated with concreteness ratings. We show that English nouns are rated as more concrete compared to other parts of speech, but mass nouns are rated as less concrete than count nouns. Furthermore, a more complex morphological structure is associated with abstractness, and as for etymology, French- and Latin-derived words are more abstract than words of other origin. This shows that linguistic properties of words are indeed associated with the degree of concreteness that we attribute to the underlying concepts, and we discuss the implications that these findings have for linguistic theory and for empirical investigations in the cognitive sciences. (shrink)

That words express a conceptual content is uncontroversial. This does not entail that their content should break down neatly into a grammatical part, relevant for language and to be analyzed in linguistic terms, and a conceptual part, relevant for cognition and to be analyzed in psychological terms. Various types of empirical evidence are reviewed, showing that the conceptual content of words cannot be isolated from their linguistic properties, because it is affected and shaped by them. The view of words as (...) labels or containers for a non-linguistic conceptual content stems from a naive disregard of the complex and structured nature of lexical knowledge. On the contrary, knowledge of language is shown not just to organize and categorize conceptual content in a way not reducible to non-linguistic cognition, but also to affect its scope, as the range of verbalized concepts is both limited by abstract templates and expanded by productive word formation. This suggests that lexical knowledge is a distinctively linguistic dimension of conceptualization, and that words do not so much label or package concepts, as provide an inner form for conceptual knowledge. (shrink)

The primary argument against mereological singularism—the view that definite plural noun phrases like ‘the students’ refer to “set-like entities”—is that it is ultimately incoherent. The most forceful form of this charge is due to Barry Schein, who argues that singularists must accept a certain comprehension principle which entails the existence of things having the contradictory property of being both atomic and non-atomic. The purpose of this paper is to defuse Schein’s argument, by noting three necessary and independently motivated restrictions on (...) the metalinguistic predicates ‘atom’ and ‘non-atom’: both are sort, property, and context-relative. With these restrictions in place, Schein’s problematic assumption becomes evident: his presumed singularist analysis of ‘non-atom’ conflates the metalanguage with the meta-metalanguage, i.e. the language used to talk about the metalanguage. (shrink)

In Word and Object, Quine proposed that names be treated as the predicate elements of covert descriptions, expressing the property of being identical to the named individual. More recently, many theorists have proposed a predicativist view according which a referential name expresses the property of being called by that name. Whereas this Being-Called Predicativism has received much attention in the recent literature, Quinean Predicativism has not. This neglect is undeserved. In this paper, I argue, first, that close appositive constructions suggest (...) that names can function as predicates expressing identifying properties of the sort proposed by Quine, and, second, that a predicativist analysis which extends this view to referential names overcomes some of the central objections that have been raised against Being-Called Predicativism. (shrink)

ASL can express plurals by repeating a noun, in an unpunctuated fashion, in different parts of signing space. We argue that this construction may come with a rich iconic component: the geometric arrangement of the repetitions provides information about the arrangement of the denoted plurality; in addition, the number and speed of the repetitions provide information about the size of the denoted plurality. Interestingly, the shape of the repetitions may introduce a new singular discourse referent when a vertex can be (...) inferred to denote a singular object. Thus one may point towards the first or last iteration of a horizontal repetition of BOOK to denote the left- or right-edge of the corresponding row. This yields a remarkable interaction between iconic semantics and standard logical semantics. We show that our analysis extends to ‘punctuated’ repetitions, which involve clearly individuated iterations of a singular noun. While these may initially look like coordinated indefinites, they are better handled by the same iconic framework as plural, unpunctuated repetitions. Some repetition-based mass terms also give rise to iconic effects, and to different readings depending on whether the repetition is continuous, unpunctuated, or punctuated. Our analysis highlights the need for a formal semantics with iconicity to study the integration of such iconic and logical conditions. It also raises a question: can similar facts be found in spoken language when gestures are taken into account? We suggest that several effects can be replicated, especially when one considers examples involving ‘pro-speech gestures’. (shrink)

To what extent are countability distinctions subject to systematic semantic variation? Could there be a language with no countability distinctions—in particular, one where all nouns are count? I argue that the answer is no: even in a language where all NPs have the core morphosyntactic properties of English count NPs, such as combining with numerals directly and showing singular/plural contrasts, countability distinctions still emerge on close inspection. I divide these distinctions into those related to sums and those related to parts. (...) In the Sahaptian language Nez Perce, evidence can be found for both types of distinction, in spite of the absence of anything like a traditional mass–count division in noun morphosyntax. I propose an extension of the Nez Perce analysis to Yudja, analyzed by Lima as lacking any countability distinctions. More generally, I suggest that at least one countability distinction may be universal and that languages without any countability distinctions may be unlearnable. (shrink)

This paper analyzes argument formation in Nuosu Yi, a language that is typologically unusual in having classifiers as well as a definite determiner. Also unusual is the fact that demonstratives do not combine directly with nouns in this language but require the mediation of classifiers. Properties such as these are shown to pose a challenge to current accounts of argument formation. The Neocarlsonian approach of Chierchia explains the absence of definite articles in classifier languages as resulting from considerations of economy. (...) If nouns in classifier languages are names of kinds, they can occur directly as arguments of verbs, thereby obviating the need for extra structure to host a determiner. The data from Nuosu Yi alters the empirical generalization and calls for a modification of the explanation. The specific account of Nuosu Yi that is presented bears on current discussions about the nature of argument formation. Must arguments necessarily occur with overt or covert determiners or is it possible for languages to differ in this respect? Must bare nominal arguments necessarily denote kinds or can they denote properties? In this sense, the discovery of a new type of classifier language contributes to a theory of language variation and argument formation in general. (shrink)

Predicates like gather and ones like be numerous have both been described as ‘collective predicates,’ since they predicate something of a plurality. The two classes of predicates differ, however, with respect to plural quantifiers, which are grammatical with gather-type predicates but ungrammatical with numerous-type predicates. Here, I show that the gather/numerous opposition derives from mereological properties that are familiar from the domains of telicity and mass/count. I address problems of undergeneration and overgeneration with two technical innovations: first, I weaken the (...) property of divisibility to Champollion’s concept of stratified reference; second, I provide mechanisms to rule out accidental satisfaction of the logical property. More broadly, I place collective predication in a larger context by building empirical connections to mass/count and collectivity across semantic domains. (shrink)

Esta investigación indaga sobre el procesamiento de la contabilidad nominal. De hecho, añade más evidencia a favor de una posible influencia del número semántico en el procesamiento de los sustantivos incontables en cuatro pacientes diagnosticadas con afasia de Broca, siendo su lengua materna es el inglés. Esto sugiere que el procesamiento de estos sustantivos sería un híbrido tanto sintáctico como semántico. Además, corrobora al igual que estudios previos, un déficit específico en la gramática de los sustantivos incontables.

Schwarzschild (Nat Lang Semant 7:141–177, 1999)’s account of givenness elaborates a notion of complementarity of givenness and focus in an intricate way: while givenness is semantically interpreted, focus is grammatically marked. It has been noticed, however, that under certain circumstances givenness in English is grammatically marked as well. Movement plays a role in this process. This paper provides further evidence for givenness marking. I present a case study of three Slavic languages (Czech, Russian, and Serbo-Croatian) in which givenness is always (...) grammatically marked. In these languages, given elements must linearly precede new elements. If this relative ordering cannot be achieved by base generation, the ordering can be achieved by movement. I offer an account of the data in terms of givenness and the Maximize Presupposition principle of Heim (1991). In particular, I argue for an operator that marks elements in its scope as given. The operator divides the structure between a given and a new part. The role of Maximize Presupposition is to enforce that every given element is in the scope of the operator. The operator and Maximize Presupposition work in tandem with an economy condition on movement that licenses movement only if it yields an otherwise unavailable semantic interpretation. The proposal thus provides independent evidence for competition in grammar and for the role of Maximize Presupposition in the process. (shrink)

Although there is no consensus about what kinds are, there is a common understanding that kinds can be regarded as collections of objects that share certain properties. What these properties exactly are is often left unspecified. This paper explores the semantics of ad hoc kind-referring terms, where the determination of the relevant set of shared properties does not rely on “natural” properties or world knowledge. Rather, information provided by a nominal modifier, typically a relative clause, is used to impute the (...) required regular behavior on the kind-referring NP. Building on Carlson’s disjointness condition, I show that we can not only account for the ubiquity of these expressions, but we can also extend the analysis to other constructions that have traditionally not been taken to be kind referring, such as Amount and Degree Relative constructions. (shrink)

The primary argument against mereological singularism—the view that definite plural noun phrases like ‘the students’ refer to “set-like entities”—is that it is ultimately incoherent. The most forceful form of this charge is due to Barry Schein, who argues that singularists must accept a certain comprehension principle which entails the existence of things having the contradictory property of being both atomic and non-atomic. The purpose of this paper is to defuse Schein’s argument, by noting three necessary and independently motivated restrictions on (...) the metalinguistic predicates ‘atom’ and ‘non-atom’: both are sort, property, and context-relative. With these restrictions in place, Schein’s problematic assumption becomes evident: his presumed singularist analysis of ‘non-atom’ conflates the metalanguage with the meta-metalanguage, i.e. the language used to talk about the metalanguage. (shrink)

This paper develops a semantic account of morphological number marking, specifically in the presence of numerals. In addition to accounting for number marking on basic nouns like _book_ in English, the account handles variation in patterns of number marking along two dimensions: cross-linguistically, between languages that either necessitate or prohibit singular morphology in the presence of numerals greater than ‘one’; and within one and the same language on the various nominal elements in English. Building off the presuppositional approach to morphological (...) number from Sauerland (Proc SALT 13:258–275, 2003), the proposed semantics accounts for both sorts of variation by assuming flexibility in the selection of the measure relevant to the one-ness presupposition of the morphological singular form. (shrink)

This paper presents a new logical analysis of quantity comparatives (i.e. More linguists than philosophers came to the party.) within the Delineation Semantics approach to gradability and comparison (McConnell-Ginet in Comparison constructions in English. PhD thesis, University of Rochester, Rochester, 1973; Kamp in Formal semantics of natural language. Cambridge University Press, Cambridge, 1975; Klein in Linguist Philos 4:1–45, 1980) among many others. Along with the Degree Semantics framework (Cresswell in Montague grammar. Academic Press, New York, 1976; von Stechow in J (...) Semant 3:1–77, 1984; Kennedy in Projecting the adjective. PhD thesis. University of California, Santa Cruz, 1997, among many others) Delineation Semantics is one of the dominant logical frameworks for analyzing the meaning of gradable constituents of the adjectival syntactic category; however, there has been very little work done investigating the application of this framework to the analysis of gradability outside the adjectival domain. This state of affairs distinguishes the Delineation Semantics framework from its Degree Semantics counterpart, where such questions have been investigated in great deal since the beginning of the twenty-first century. Nevertheless, it has been observed [for example, by Doetjes (Seventeenth amsterdam colloquium. University of Amsterdam, Amsterdam, 2011); van Rooij (The vagueness handbook. Springer, Dordrecht, 2011c)] that there is nothing inherently adjectival about the way that the interpretations of scalar predicates are calculated in Delineation Semantics, and therefore that there is enormous potential for this approach to shed light on the nature of gradability and comparison in the nominal and verbal domains. This paper is a first contribution to realizing this potential within a Mereological extension of a simple version of the DelS system. (shrink)

In this paper we explore the interpretation of quantity expressions in Yudja, an indigenous language spoken in the Amazonian basin, showing that while the language allows reference to exact cardinalities, it does not generally allow reference to exact measure values. It does, however, allow non-exact comparison along continuous dimensions. We use this data to argue that the grammar of exact measurement is distinct from a grammar allowing the expression of exact cardinalities, and that the grammar of counting and the grammar (...) of measurement may use numerals with different, though related interpretations. As Yudja shows, the language of measurement is not automatically acquired along with the knowledge of exact numeral expressions. We show that the ‘gap’ between prelinguistic intuitions about quantity in terms of numerosity and counting, which is bridged by the learning of language expressing exact cardinality, is paralleled by a similar gap between prelinguistic intuitions about quantity on a continuous dimension and measuring: this gap too must be bridged by language which expresses exact measure values. Our results suggest that the enculturation process by which we develop skills to perform abstract operations in the domain of measurement is (1) language dependent and (2) distinct from the process by which we learn to perform abstract calculations in the cardinal domain. (shrink)

This paper explores the idea that scalar implicatures are computed with respect todiscourse referents. Given the general consensus that a proper account of pronominal anaphora in natural language requires discourse referents separately from the truth-conditional meaning, it is naturally expected that the anaphoric information that discourse referents carry play a role in the computation of scalar implicatures, but the literature has so far mostly exclusively focused on the truth-conditional dimension of meaning. This paper offers a formal theory of scalar implicatures (...) with discourse referents couched in dynamic semantics, and demonstrates its usefulness through a case study on the plurality inferences of plural nouns in English. (shrink)