Noun phrases (NPs) beginning with the or a/an are prototypical definite and indefinite NPs in English. The two main theories about the meaning of definiteness are uniqueness and familiarity. Both properties characterize most occurrences of definite descriptions although there are examples which defy one or the other or both theories. Existential sentences have become criterial for distinguishing indefinites from definites, and have led to broadening of both categories to include a variety of other NP forms. Information status approaches propose a (...) hierarchy of NP types, rather than a simple binary distinction. The expression of definiteness varies from language to language. (shrink)

This paper sets forth a new theory of quantifiers and term connectives, called shadow theory , which should help simplify various semantic theories of natural language by greatly reducing the need of Montagovian proper names, type-shifting, and λ-conversion. According to shadow theory, conjunctive, disjunctive, and negative noun phrases such as John and Mary , John or Mary , and not both John and Mary , as well as determiner phrases such as every man , some woman , and the boys (...) , are all of semantic type e and denote individual-like objects, called shadows — conjunctive , disjunctive , or negative shadows, such as John-and-Mary, John-or-Mary, and not-(John-and-Mary). There is no essential difference between quantification and denotation: quantification is nothing but denotation of shadows. Individuals and shadows constitute a Boolean structure. Formal language LSD (Language for Shadows with Distributivity), which takes compound terms to denote shadows, is investigated. Expansions and enrichments of LSD are also considered toward the end of the paper. (shrink)

This extended collection of papers is the result of putting recent ideas on quantification to work on a wide variety of languages.

In this paper, we discuss some rather puzzling facts concerning the semantics of Warlpiri expressions of cardinality, i.e. the Warlpiri counterparts of English expressions like one,two, many, how many. The morphosyntactic evidence, discussed in section 1, suggests that the corresponding expressions in Warlpiri are nominal, just like the Warlpiri counterparts of prototypical nouns, eg. child. We also argue that Warlpiri has no articles or any other items of the syntactic category D(eterminer). In section 2, we describe three types of readings— (...) "definite", "indefinite" and "predicative"—which are generally found with Warlpiri nouns, including those which correspond to English common nouns and cardinality expressions. A partial analysis of these readings is sketched i n section 3. Since Warlpiri has no determiner system, we hypothesize that the source of (in)definiteness in this language is semantic. More specifically, we suggest that Warlpiri nominals are basically interpreted as individual terms or predicates of individuals and that their three readings arise as a consequence of the interaction of their basic meanings, which are specific to Warlpiri, with certain semantic operations, such as type shifting (Rooth and Partee 1982, Partee and Rooth 1983, Partee 1986, 1987), which universally can or must apply in the process of compositional semantic interpretation. (shrink)

In this paper I revisit the main arguments for a predicate analysis of descriptions in order to determine whether they do in fact undermine Russell's theory. I argue that while the arguments without doubt provide powerful evidence against Russell's original theory, it is far from clear that they tell against a quantificational account of descriptions.

In his groundbreaking Grundlagen, Frege (1884) pointed out that number words like ‘four’ occur in ordinary language in two quite different ways and that this gives rise to a philosophical puzzle. On the one hand ‘four’ occurs as an adjective, which is to say that it occurs grammatically in sentences in a position that is commonly occupied by adjectives. Frege’s example was (1) Jupiter has four moons, where the occurrence of ‘four’ seems to be just like that of ‘green’ in (...) (2) Jupiter has green moons. On the other hand, ‘four’ occurs as a singular term, which is to say that it occurs in a position that is commonly occupied by paradigmatic cases of singular terms, like proper names: (3) The number of moons of Jupiter is four. Here ‘four’ seems to be just like ‘Wagner’ in (4) The composer of Tannhäuser is Wagner, and both of these statements seem to be identity statements, ones with which we claim that what two singular terms stand for is identical. But that number words can occur both as singular terms and as adjectives is puzzling. Usually adjectives cannot occur in a position occupied by a singular term, and the other way round, without resulting in ungrammaticality and nonsense. To give just one example, it would be ungrammatical to replace ‘four’ with ‘the number of moons of Jupiter’ in (1): (5) *Jupiter has the number of moons of Jupiter moons. This ungrammaticality results even though ‘four’ and ‘the number of moons of Jupiter’ are both apparently singular terms standing for the same object in (3). So, how can it be that number words can occur both as singular terms and as adjectives, while other adjectives cannot occur as singular terms, and other singular terms cannot occur as adjectives? (shrink)

talk presented at On Linguistic Interfaces, Ulster, June 2007.

In this note I provide an answer to an apparently technical query by van Benthem (1986; 67) concerning denotations of English expressions. The answer turns out to be revealing of some systematic semantic differences associated with certain categories of expression. The categories of interest to us are illustrated in (1a) and given an extensional type theoretic analysis in (1b).

I will assume (without explicitly argue for it here) that the verb’s external argument is not an argument of the verb root itself, but is introduced by a separate head in a neo-Davidsonian way. The content argument can be saturated by DPs denoting the kinds of things that can be believed or reported.

In 1905, Bertrand Russell published 'On Denoting' in which he proposed and defended a quantificational account of definite descriptions. Forty-five years later, in 'On Referring', Peter Strawson claimed that Russell was mistaken: definite descriptions do not function as quantifiers but (paradigmatically) as referring expressions. Ever since, scores of theorists have attempted to adjudicate this debate. Others have gone beyond the question of the proper analysis of definite descriptions, focusing instead on the complex relations between definites, indefinites, and pronouns. These relations (...) are often examined with attention to the phenomena of scope and anaphora. This collection assembles nineteen new papers on definite descriptions and related topics. The contributors include both philosophers and linguists, many of whom have been active participants in the various debates concerning descriptions. The volume contains a brief general introduction and is divided into six sections, each of which is accompanied by a detailed introduction of its own. Several of the sections concern issues associated with the Russell/Strawson debate. These include the sections on incomplete descriptions, the referential/attributive distinction, and presupposition and truth value gaps. There is also a section on the representation of definites and indefinites in semantic theory, containing papers that reject certain core assumptions of the Russellian paradigm. Linguists interested in definites have traditionally been concerned with how such expressions interact with other expressions, including pronouns and indefinites. They have explored, and continue to explore, these interactions through the complex phenomena of scope and anaphora. In the section dealing with anaphoric pronouns and descriptions, indefinites and dynamic syntax/semantics, five linguists propose and defend their views on these and related issues. Finally, there is a section that concerns the relation between proper names and descriptions and, more particularly, the idea that some names, those introduced into the language by description, are semantically equivalent to definite descriptions. (shrink)

It is not a common practice to postulate meaning entities treated as objects of some kind. The paper demonstrates two ways of introducing meaning-objects in two logics of natural language, Tichy’s Transparent Intensional Logic and Zalta’s Intensional Logic of Abstract Objects. Tichy’s theory belongs to the Fregean line of thinking, with what he calls ‘constructions’ as Fregean senses, and ‘determiners’ as object-like meaning entities constructed by the senses. Zalta’s theory belongs to Meinongian logics and he postulates a rich realm of (...) abstract Meinongian objects to play the role of meanings. The paper analyses the mechanisms of reference in both conceptions and it offers a comparison of the mediating meaning-objects and the framework designed to expose this mediation in both theories. An attempt is made to expose how the treatment of the meaning entities depends upon the theory of meaning which is assumed. (shrink)

Possessive DPs are “complex” in the sense that they involve two distinct nominal expressions as components.1 In this paper I address the issue of characterizing the nature of the syntactic relation holding between these two nominal expressions in possessives whose possessum is arguably not a syntactic argument-taking category. This amounts to providing an account of what licenses the insertion of the possessor in the derivation of possessive DPs and in accounting for any further steps in the syntactic derivation which lead (...) to the structure which undergoes Spell-Out. (shrink)

Possessives are “complex” DPs: they involve two distinct nominal expressions as components.1 In this paper I address the issue of characterizing the nature of the syntactic relation holding between these two nominal expressions in possessives whose possessum is arguably not a syntactic argument-taking category. This task can be divided into two parts: (i) providing an account of what licenses the insertion of the possessor in the derivation of possessive DPs and (ii) accounting for any further steps in the syntactic derivation (...) which lead to the structure which undergoes Spell-Out. With respect to (i), I argue in favor of the proposal in (den Dikken, 1998) that in possessive DPs of the type considered here the possessor is licensed as complement of an empty preposition in the PP predicate of a small clause whose subject is the possessum. I provide some empirical support for this position using agreement data from Maasai. With respect to (ii), I depart from den Dikken’s proposal. I argue that prenominal possessors in English are not derived by DP-internal Predicate Inversion and outline two alternative analyses for the derivation of possessives in languages with prenominal possessors. Finally, I address the issue whether the postnominal position of possessors in Maasai is the product of further movement operations preceding Spell-Out or rather reflects the absence of overt syntactic derivation. (shrink)

Dayal's (2004) theory of kind terms accounts for the definiteness and number marking patterns in kind terms in many languages. Brazilian Portuguese has been claimed to be a counter-example to her theory as it seems to allow bare ``singular'' kind terms, which are predicted to be impossible according to her theory. However, the empirical status of the relevant data has not been clear so far. This paper presents a new data point from Singlish and confirms the existence of bare ``singular'' (...) kind terms. A modified theory of kind terms is proposed that accounts for it. The proposed theory puts forth a number system with three basic categories, i.e. singular, plural and general. It is claimed that bare ``singular'' kind terms are in fact derived from general NPs, which are associated with number-neutral properties. The paper also discusses why bare ``singular'' kind terms are not perfectly acceptable in Brazilian Portuguese. (shrink)

Languages that have determiners often have a rich inventory of them. In English, indefinite determiners include a(n), some, a certain, this, one, another, cardinals, partitives, the zero determiner of bare plurals (in some analyses), and, according to Horn 1999 and Giannakidou 2001, any. Despite the attention indefinites have received in the literature, characterizing what is common to all of them and what is specific to each is still an elusive task. This paper investigates the first three determiners in this list, (...) attempting to provide a semantic characterization that accounts for their distribution. (For pertinent discussion of issues that overlap to some extent with those taken up below, see Kamp and Bende-Farkas 2002, and for a discussion of the French versions of some and a certain, see Jayez and Tovena (this volume).) The Ds that concern us here share two characteristics: (i) they are indefinite, and (ii) they are existential when not in the scope of any operator or quantifier. As seen in [1], they may occur as pivots in existential there constructions, and therefore all three form weak DPs. (shrink)

It has been generally assumed that certain categories of numerical expressions, such as ‘more than n’, ‘at least n’, and ‘fewer than n’, systematically fail to give rise to scalar implicatures in unembedded declarative contexts. Various proposals have been developed to explain this perceived absence. In this paper, we consider the relevance of scale granularity to scalar implicature, and make two novel predictions: first, that scalar implicatures are in fact available from these numerical expressions at the appropriate granularity level, and (...) second, that these implicatures are attenuated if the numeral has been previously mentioned or is otherwise salient in the context. We present novel experimental data in support of both of these predictions, and discuss the implications of this for recent accounts of numerical quantifier usage. (shrink)

The relationship between language and conceptual thought is an unresolved problem in both philosophy and psychology. It remains unclear whether linguistic structure plays a role in our cognitive processes. This special issue brings together cognitive scientists and philosophers to focus on the role of language in numerical cognition: because of their universality and variability across languages, number words can serve as a fruitful test case to investigate claims of linguistic relativism.

A realist view of numbers often rests on the following thesis: statements like ‘The number of moons of Jupiter is four’ are identity statements in which the copula is flanked by singular terms whose semantic function consists in referring to a number (henceforth: Identity). On the basis of Identity the realists argue that the assertive use of such statements commits us to numbers. Recently, some anti-realists have disputed this argument. According to them, Identity is false, and, thus, we may deny (...) that the relevant statements commit us to numbers. The present paper argues that the correct linguistic analysis of the relevant number statements supports the anti-realist view that Identity is false. However, as will further be shown, pace the anti-realist, this analysis does not establish that such statements do not commit us to numbers after all. (shrink)

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event (...) depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS. (shrink)

The question whether numbers are objects is a central question in the philosophy of mathematics. Frege made use of a syntactic criterion for objethood: numbers are objects because there are singular terms that stand for them, and not just singular terms in some formal language, but in natural language in particular. In particular, Frege (1884) thought that both noun phrases like the number of planets and simple numerals like eight as in (1) are singular terms referring to numbers as abstract (...) objects. (shrink)

Abstract A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets , eight , as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily (...) treated abstract objects, but rather ‘aspects’ of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. Content Type Journal Article Pages 1-38 DOI 10.1007/s11098-011-9779-1 Authors Friederike Moltmann, IHPST (Paris1/ENS/CNRS), Paris, France Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116. (shrink)

Dayal's (2004) theory of kind terms accounts for the definiteness and number marking patterns in kind terms in many languages. Brazilian Portuguese has been claimed to be a counter-example to her theory as it seems to allow bare ``singular'' kind terms, which are predicted to be impossible according to her theory. However, the empirical status of the relevant data has not been clear so far. This paper presents a new data point from Singlish and confirms the existence of bare ``singular'' (...) kind terms. A modified theory of kind terms is proposed that accounts for it. The proposed theory puts forth a number system with three basic categories, i.e. singular, plural and general. It is claimed that bare ``singular'' kind terms are in fact derived from general NPs, which are associated with number-neutral properties. The paper also discusses why bare ``singular'' kind terms are not perfectly acceptable in Brazilian Portuguese. (shrink)

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic (...) mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)

Developing earlier studies of the system of numbers in Mundurucu, this paper argues that the Mundurucu numeral system is far more complex than usually assumed. The Mundurucu numeral system provides indirect but insightful arguments for a modular approach to numbers and numerals. It is argued that distinct components must be distinguished, such as a system of representation of numbers in the format of internal magnitudes, a system of representation for individuals and sets, and one-to-one correspondences between the numerosity expressed by (...) the number and its metrics. It is shown that while many-number systems involve a compositionality of units, sets and sets composed of units, few-number languages, such as Mundurucu, do not have access to sets composed of units in the usual way. The nonconfigurational character of the Mundurucu language, which is related to a property for which we coin the term 'low compositionality power', accounts for this and explains the curious fact that Mundurucus make use of marked one-to-one correspondence strategies in order to overcome the limitations of the core system at the perceptual/motor interface of the language faculty. We develop an analysis of a particular construction, parallel numbers, which has not been studied before, elucidating the whole system. This analysis, we argue, sheds new light on classical philosophical, psychological and linguistic debates about numbers and numerals and their relation to language, and more particularly, sheds light on few-number languages. (shrink)

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 (...) or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic. (shrink)

We propose that the restrictive/non restrictive distinction found in relative clauses corresponds to the Inalienable vs Alienable distinction of the Nominal Possessive constructions. We propose to extend this distinction to adjectives suggesting that is not construction specific.

Yang (2004) observes that in Mandarin, an initial possessor phrase (PossessorP) may be followed by a bare noun as in (1), or by a possessee phrase that can be headed by a numeral and classifier, [Numeral + CL + N], as in (2) or by a demonstrative, [Dem + (Numeral) + CL + N] as in (3). (In all the examples in this section, we begin with Yang’s own initial glosses and translations3. The interpretation of the examples will be probed (...) after they have been presented.). (shrink)

It is claimed that the English genitive marker 's' suprisingly mirrors- at least in some dialects of English - the three main different usage of the mono-morphemic reflexives such as 'se' in French. A solution to this paradox already noted by Jespersen (1918) is proposed drawing on Watkins paradox according to which the study of what looks like 'social' parameters might be relevant for linguistics.