In this paper, we outline and critically evaluate Thomas Hofweber’s solution to a semantic puzzle he calls Frege’s Other Puzzle. After sketching the Puzzle and two traditional responses to it—the Substantival Strategy and the Adjectival Strategy—we outline Hofweber’s proposed version of Adjectivalism. We argue that two key components—the syntactic and semantic components—of Hofweber’s analysis both suffer from serious empirical difficulties. Ultimately, this suggests that an altogether different solution to Frege’s Other Puzzle is required.

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) is (...) high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (shrink)

In this paper I focus on a recently discussed phenomenon illustrated by sentences containing predicates of taste: the phenomenon of " perspectival plurality " , whereby sentences containing two or more predicates of taste have readings according to which each predicate pertains to a different perspective. This phenomenon has been shown to be problematic for (at least certain versions of) relativism. My main aim is to further the discussion by showing that the phenomenon extends to other perspectival expressions than predicates (...) of taste and by proposing a general solution to the problem raised by it on behalf of the relativist. The core claim of the solution (" multiple indexing ") is that utterances of sentences containing perspectival expressions should be evaluated with respect to (possibly infinite) sequences of perspective parameters. (shrink)

This paper provides a formal pragmatic analysis of precision which accounts for its essential properties, but also for Lewis’s :339–359, 1979) observation of asymmetry in how standards of precision may shift due to normal discourse moves: Only up, not down. I propose that shifts of the kind observed and discussed by Lewis are in fact cases of underlying disagreement about the standard of precision, which is only revealed when one interlocutor uses an expression which signals their adherence to a higher (...) standard than the one adhered to by the other interlocutor. This paper shows that a modest formal pragmatic analysis along the lines of many prior optimality-theoretic and game-theoretic accounts can easily capture the natural asymmetry in standard-signaling that gives rise to Lewis’s observation, so long as such an account is dynamic and enriched with a notion of relevance. (shrink)

In this article, we describe and attempt to solve a puzzle arising from the interpretation of modified numerals like less than five and between two and five. The puzzle is this: such modified numerals seem to mean different things depending on whether they combine with distributive or non-distributive predicates. When they combine with distributive predicates, they intuitively impose a kind of upper bound, whereas when they combine with non-distributive predicates, they do not. We propose and explore in detail four solutions (...) to this puzzle, each involving some notion of maximality, but differing in the type of maximality involved and in the source of maximality. While the full range of data we consider do not conclusively favor one theory over the other three, we do argue that overall the evidence goes against the view that modified numerals lexically encode a ‘standard’ maximality operator, and suggests the need for a pragmatic blocking mechanism that filters out readings of sentences that are generated by the grammar but intuitively unavailable. (shrink)

This paper presents a novel semantic analysis of unit names and gradable adjectives, inspired by measurement theory (Krantz et al 1971). Based on measurement theory's typology of measures, I claim that different predicates are associated with different types of measures whose special characteristics, together with features of the relations denoted by unit names, explain the puzzling limited distribution of measure phrases.

Winter (2000) argues that so-called co-distributive or cumulative readings do not involve polyadic quantification (contra proposals by Krifka, Schwarzschild, Sternefeld, and others). Instead, he proposes that all such readings involve a hidden anaphoric dependency or a lexical mechanism. We show that Winter's proposal is insufficient for a number of cases of cumulative readings, and that Krifka's and Sternefeld's polyadic **-operator is needed in addition to dependent definites. Our arguments come from new observations concerning dependent plurals and clause-boundedness effects with cumulative (...) readings. (shrink)

This is the first in a pair of papers that aim to provide a comprehensive analysis of the semantic phenomenon of distributivity in natural language. This paper investigates and formalizes different sources of covert distributivity. Apart from lexical distributivity effects, which are modeled by meaning postulates, phrasal distributivity is captured via two covert operators: (i) a D operator distributing over atoms only (Link 1987), and (ii) a cover-based Part operator, which can also distribute over non-atomic pluralities under contextual licensing (Schwarzschild (...) 1996). The resulting theory surpasses accounts in which nonatomic distributivity is freely available, or not available at all; furthermore, it correctly predicts differences between lexical and phrasal nonatomic distributivity. D and Part are reformulated in Neo-Davidsonian algebraic event semantics, so that they apply to event predicates and make the sum event available for further modification by arguments and adjuncts. This paves the way for an account of the context-dependency of distributivity phenomena under for-adverbials, which improves on theories that predict indefinites to either always or never covary with for-adverbials. The paper and its companion include an explicit proposal for the compositional process in event semantics. (shrink)

Davidsonian event semantics is often taken to form an unhappy marriage with compositional semantics. For example, it has been claimed to be problematic for semantic accounts of quantification Proceedings of the 16th Amsterdam Colloquium, 2007), for classical accounts of negation Semantics and contextual expression, 1989), and for intersective accounts of verbal coordination. This paper shows that none of this is the case, once we abandon the idea that the event variable is bound at sentence level, and assume instead that verbs (...) denote existential quantifiers over events. Quantificational arguments can then be given a semantic account, negation can be treated classically, and coordination can be modeled as intersection. The framework presented here is a natural choice for researchers and fieldworkers who wish to sketch a semantic analysis of a language without being forced to make commitments about the hierarchical order of arguments, the argument-adjunct distinction, the default scope of quantifiers, or the nature of negation and coordination. (shrink)

This paper proposes that both weak and strong NPIs in English are sensitive to the downward entailingness of their licensers. It is also proposed, however, that these two types of NPIs pay attention to different aspects of the meaning of their environment. As observed by von Fintel and Chierchia, weak NPIs do not attend to the scalar implicatures of presuppositions of their licensers. Strong NPIs see both the truth-conditional and non-truth-conditional (scalar implications, presuppositions) meaning of their licensers. This theory accounts (...) for the puzzling inability, noted by Rullmann and Gajewski, of Strawson anti-additive operators to license strong NPIs, as well as for the effects of Zwarts’s hierarchy of negative strength. Additional issues concerning comparative quantifiers, few, and proportional quantifiers are addressed. (shrink)

In Shona , bare plurals and bare singulars seem to have different scope possibilities with respect to a class of modifiers which I term “scopeless quantity words” few’, and ose ‘all’). I argue that this is due to two factors. First, the scopeless quantity words are intersective modifiers rather than quantifying determiners, so that DPs containing them denote entities rather than generalised quantifiers. Second, transitive sentences involving plural arguments are usually interpreted using the **-operator, which gives a cumulative reading; the (...) apparent wide and narrow scope readings of bare plurals are both subcases of this reading, but a narrow scope reading for bare singulars cannot be subsumed by the cumulative reading. I also discuss the scope behaviour of a quantifying determiner, oga-oga ‘every’, which shows a subject/object asymmetry: in subject position, it appears to show the expected scopal ambiguity, but in object position, it appears to have the same readings as a scopeless quantity word; I argue that this is because of the location of existential closure. This adds to the evidence suggesting that many words giving quantity are intersective modifiers rather than quantifying determiners or adverbial quantifiers. (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)

Hurford’s Constraint (Hurford, Foundations of Language, 11, 409–411, 1974) states that a disjunction is infelicitous if its disjuncts stand in an entailment relation: #John was born in Paris or in France. Gazdar (Pragmatics, Academic Press, NY, 1979) observed that scalar implicatures can obviate the constraint. For instance, sentences of the form (A or B) or (Both Aand B) are felicitous due to the exclusivity implicature of the first disjunct: A or B implicates ‘not (A and B)’. Chierchia, Fox, and Spector (...) (Handbook of semantics, 2008) use the obviation of Hurford’s Constraint in these cases to argue for a theory of local implicature. I present evidence indicating that the constraint needs to be modified in two ways. First, implicatures can obviate Hurford’s Constraint only in earlier disjuncts, not later ones: #(Both A and B) or (A or B). Second, the constraint rules out not only disjuncts that stand in an entailment relation, but also disjuncts that are even mutually consistent: #John is from Russia or Asia. I propose to make sense of these facts by providing an incremental evaluation procedure which checks that each new disjunct to the right is inconsistent with the information to its left, before the disjunct can be strengthened by local implicature. (shrink)

Aspectual particles (the term is due to (König 1991)) appear to come in groups, related by negation, and therefore have attracted the attention of formal semanticists. The following examples list the particles of English, German and Hebrew; they show that the system is semantically transparent in various degrees.

The term ‘ellipsis’ can be used to refer to a variety of phenomena: syntactic, semantic, and pragmatic. In this article, I discuss the recent comprehensive survey by Stainton 2006 of these kinds of ellipsis with respect to the analysis of nonsententials and try to show that despite his trenchant criticisms and insightful proposal, some of the criticisms can be evaded and the insights incorporated into a semantic ellipsis analysis, making a ‘divide-and-conquer’ strategy to the properties of nonsententials feasible after all. (...) -/- Editor's comment: To find the contribution, please go to item 16 of the URL, which contains the full text. Professor Merchant has permitted this. (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.

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)

Recent research has shown that the superlative quantifiers at least and at most do not have the same type of truth conditions as the comparative quantifiers more than and fewer than. We propose that superlative quantifiers are interpreted at the level of speech acts. We relate them to denegations of speech acts, as in I don’t promise to come, which we analyze as excluding the speech act of a promise to come. Calling such conversational acts that affect future permissible speech (...) acts “meta-speech acts,” we introduce the meta-speech act of a GRANT of a proposition as a denial to assert the negation of that proposition. Superlative quantifiers are analyzed as quantifiers over GRANTS. Thus, John petted at least three rabbits means that the minimal number n such that the speaker GRANTs the proposition that John petted n rabbits is n = 3. We formalize this interpretation in terms of commitment states and commitment spaces, and show how the truth conditions that are derived from it are partly entailed and partly conversationally implicated. We demonstrate how the theory accounts for a wide variety of distributional phenomena of superlative quantifiers, including the contexts in which they can be embedded. (shrink)

This article describes a novel pattern of interpretations associated with universal determiners like ‘each’ and ‘every’. It is demonstrated that these canonically distributive quantifiers can give rise to surprising collective readings when they quantify into sub-clausal constituents, especially other Determiner Phrases. For instance, ‘two cards from each player’ can be understood to pick out a single assorted deck of cards, one whose contents co-vary with the players. Yet this deck as a whole may be said to participate in a range (...) of collective activities (being shuffled together, being traded en masse, not fitting into a standard pack, etc.). Such examples are shown to differ from more familiar _cumulative_ readings of the same quantifiers. A compositional analysis is offered that generalizes Krifka’s ( 2001 ) method of quantification into speech acts in order to accommodate quantification into a larger class of non-truth-denoting semantic objects, including in these cases, entities. (shrink)

The 2007 edition of the Amsterdam Colloquium is the Sixteenth in a series which started in 1976. Originally, the Amsterdam Colloquium was an initiative of the Department of Philosophy of the University of Amsterdam. Since 1984 the Colloquium is organized by the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam.

This paper revisits intervention effects in Mandarin Chinese why-questions. I present a novel empirical generalization, in which it is shown that the ability for quantifiers to induce intervention hinges upon their monotonicity and their ability to be interpreted as topics. I then propose a semantic account of intervention that correlates topicality with the monotone properties of intervening operators. A crucial assumption in this account is that why-questions in Chinese are idiosyncratic, in that the Chinese equivalent of why directly merges at (...) a high scope position that stays above a propositional argument. Combining the semantic idiosyncrasies of why-questions with the theory of topicality, I conclude that a wide range of intervention phenomena can be explained in terms of interpretation failure. (shrink)

The goal of this paper is to propose a unified approach to the split scope readings of negative indefinites, comparative quantifiers, and numerals. There are two main observations that justify this approach. First, split scope shows the same kinds of restrictions across these different quantifiers. Second, split scope always involves low existential force. In our approach, following Sauerland, natural language determiner quantifiers are quantifiers over choice functions, of type <<,t>,t>. In split readings, the quantifier over choice functions scopes above other (...) operators (such as intensional verbs like must or can). Determiner quantifiers leave a choice-function trace when they move and this trace combines with the noun restriction, which is interpreted low. That split scope always involves low existential force is derived, without stipulation, from Kratzer’s idea that low existential force can be achieved via binding (into the noun restriction). (shrink)

The existential and universal quantifiers in Japanese both consist of two morphemes: an indeterminate pronoun and a quantificational suffix. This paper examines the distributional characteristics of these suffixes (ka for the existential quantifier and mo for the universal quantifier). It is shown that ka can appear in a wider range of structural positions than mo can. This difference receives explanation on semantic grounds. I propose that mo is a generalized quantifier. More specifically, I assume that the phrase headed by mo (...) is of type ${\langle\langle\alpha, t\rangle, t}$ . Because of its type, mo cannot appear in certain structural positions without causing type mismatch. Ka, on the other hand, is a choice function variable of type ${\langle\alpha/t, \alpha\rangle}$ , and due to its type, its distribution is not as restricted. One of the consequences of this analysis is that there are no quantifier raising or type shifting operations in Japanese that would adequately obviate type mismatch. (shrink)

The paper concerns the expression of non-strict comparison, focusing in particular on constructions of the form [no(t) . . .-er than] in modified numerals. The main empirical finding is the observation that negated comparatives contrast with regular comparatives in that the former but not the latter can give rise to (scalar) implicatures. It is shown that such a contrast falls out of theories of exhaustive interpretation that claim alternatives to form dense scales. An important result is that the paper sharpens (...) the desiderata for theories of exhaustification. (shrink)

We carry out the Karttunen-Stalnaker pragmatic account of presupposition projection within a state-of-the art version of dynamic epistemic logic. It turns out that the basic projection facts can all be derived from a Gricean maxim ‘be informative’. This sheds light on a recent controversy on the appropriateness of dynamic semantics as a tool for analysing presupposition.