Quantifier Raising usually exhibits finite-clause boundedness due to the syntactic and semantic constraints it is subject to (Fox 1995, 2000, Cecchetto 2004, a.o.). In this paper, I argue that QR out of a Mandarin prenominal pre-determiner RC is not only properly licensed, obeying both syntactic and semantic constraints, but also needed to account for the exceptional-scope effects observed across relative clause boundaries (Huang 1982, Aoun and Li 1993, a.o.). I further consider constructions where the exceptional-scope effects are not (...) present, including relative clauses containing the focus-sensitive operator _dou_ and full-sized subject RCs, and show that the absence of the exceptional-scope effects in these constructions follows directly from the proposed analysis. (shrink)

This paper addresses the question of whether the preverbal even (VP-even) embedded in a nonfinite clause can take wide scope (e.g., Bill refused to even drink WATER). The paper presents novel evidence for wide scope VP-even that is independent of the presuppositions of even. The evidence is based on examples of antecedent-contained deletion (ACD), where embedded VP-even associates with a nominal constituent (or part of it) that raises out of the embedded clause via quantifier raising. Assuming that even (...) must c-command the focus that it associates with, the case at issue forces VP-even to have wide scope, and further shows that VP-even in NPI-licensing contexts is not necessarily an NPI. (shrink)

The growth of self-tracking and personal surveillance has given rise to the Quantified Self movement. Members of this movement seek to enhance their personal well-being, productivity, and self-actualization through the tracking and gamification of personal data. The technologies that make this possible can also track and gamify aspects of our interpersonal, romantic relationships. Several authors have begun to challenge the ethical and normative implications of this development. In this article, we build upon this work to provide a detailed ethical analysis (...) of the Quantified Relationship. We identify eight core objections to the QR and subject them to critical scrutiny. We argue that although critics raise legitimate concerns, there are ways in which tracking technologies can be used to support and facilitate good relationships. We thus adopt a stance of cautious openness toward this technology and advocate the development of a research agenda for the positive use of QR technologies. (shrink)

On the Fregean view of NP's, quantified NP's are represented as operator-variable structures while proper names are constants appearing in argument position. The Generalized Quantifier approach characterizes quantified NP's and names as elements of a unified syntactic category and semantic type. According to the Logicality Thesis, the distinction between quantified NP's, which undergo an operation of quantifier raising to yield operator-variable structures at Logical Form and non-quantified NP's, which appear in situ at LF, corresponds to a difference (...) in logicality status. The former are logical expressions while the latter are not. Using van Benthem's [2, 3] criterion for logicality, I extend the concept of logicality to GQ's. I argue that NP's modified by exception phrases constitute a class of quantified NP's which are heterogeneous with respect to logicality. However, all exception phrase NP's exhibit the syntactic and semantic properties which motivate May to treat quantified NP's as operators at LF. I present a semantic analysis of exception phrases as modifiers of GQ's, and I indicate how this account captures the central semantic properties of exception phrase NP's. I explore the consequences of the logically heterogeneous character of exception phrase NP's for proof theoretic accounts of quantifiers in natural language. The proposed analysis of exception phrase NP's provides support for the GQ approach to the syntax and semantics of NP's. (shrink)

In this paper I discuss two objections raised against von Fintel’s (1994) and Stanley and Szabó’s (2000a) hidden variable approach to quantifier domain restriction (QDR). One of them concerns utterances of sentences involving quantifiers for which no contextual domain restriction is needed, and the other concerns multiple quantified contexts. I look at various ways in which the approaches could be amended to avoid these problems, and I argue that they fail. I conclude that we need a more flexible account (...) of QDR, one that allows for the hidden variables in the LF responsible for QDR to vary in number. Recanati’s (2002; 2004) approach to QDR, which makes use of the apparatus of “variadic functions”, is flexible enough to account successfully for the two phenomena discussed. I end with a few comments on what I take to be the most promising way to construe variadic functions. (shrink)

The phenomenon of the quantified self, which is especially addressed by sociology and medical humanities, is still quite disregarded by philosophy. Yet, the philosophical issues it raises are various and meaningful, from the realm of epistemology to the realm of ethics. Moreover, it may be read as a key symptom to investigate the complex technological era in which we live, starting from the meaning of contemporary technology itself from a philosophical perspective. I shall focus on one of the epistemological issues (...) raised by the phenomenon of the quantified self by arguing that it may be read in terms of epistemological anarchism, which also leads to other epistemological issues, such as a possibly detectable crisis of the notions of knowledge in general and science in particular as founded on the relationship between particularity and universality, as well as between reality and ideality. I shall select cases that are peculiarly representative of the founding epistemological stance I shall focus on. Yet, the reason why they deserve special attention is that they are also representative of an increasingly widespread attitude characterising not only the community of the quantified self but also, at least to some extent, anyone of us who may happen to use technologies to try to self-diagnose. (shrink)

* This work has been evolving for a while now. Some parts trace back to the few pages on the context-dependency of quantifiers in my dissertation. Reading Recanati’s paper on domains of discourse made me rethink some of my earlier conclusions without in the end actually changing them much. Other parts formed the material for several discussions in my seminar on context-dependency at MIT in the fall of 1995, which included several sessions exploring the issues raised in an early version (...) of Kratzer. Connecting the choice function approach to indefinites with a general analysis of contextual domain restriction was an idea that I considered then without however working out any details. Conversations with Lisa Matthewson and studying her paper inspired me to tackle the problem again. Connections to questions about the context-dependency of conditional sentences also tickled my fancy, since I have been working on conditionals for a while now. Having the opportunity to present this material at the Vilem Mathesius Series provided the impetus to flesh out some of my vague thoughts. Major influences come from the work done in recent years at MIT by Lisa Matthewson, Philippe Schlenker, Julie Legate, and Uli Sauerland. I thank Irene Heim, Lisa Matthewson, Orin Percus, Philippe Schlenker, and Jason Stanley for illuminating discussions about this material. At this point, I see this talk as a report on the state of the art, exploring an intriguing possible connection, but I do not claim substantial intellectual property rights. Mistakes are certainly mine, achievements are probably not. (shrink)

This paper presents and discusses a range of counterexamples to the common view that quantifiers cannot take scope over epistemic modals. Some of the counterexamples raise problems for ‘force modifier’ theories of epistemic modals. Some of the counterexamples raise problems for Robert Stalnaker’s theory of counterfactuals, according to which a special kind of epistemic modal must be able to scope over a whole counterfactual. Finally, some of the counterexamples suggest that David Lewis must countenance ‘would’ counterfactuals in which a covert (...) ‘would’ scopes over the whole consequent of the counterfactual, including an overt ‘might.’. (shrink)

In a mathematical perspective, neighborhood models for modal logic are generalized quantifiers, parametrized to points in the domain of objects/worlds. We explore this analogy further, connecting generalized quantifier theory and modal neighborhood logic. In particular, we find interesting analogies between conservativity for linguistic quantifiers and the locality of modal logic, and between the role of invariances in both fields. Moreover, we present some new completeness results for modal neighborhood logics of linguistically motivated classes of generalized quantifiers, and raise new (...) types of open problem. With the bridges established here, many further analogies might be explored between the two fields to mutual benefit. (shrink)

Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the (...) framework will permit us to address a puzzle raised by Elizabeth Barnes and Robert Williams. (shrink)

We here examine the expressive power of first order logic with generalized quantifiers over finite ordered structures. In particular, we address the following problem: Given a family Q of generalized quantifiers expressing a complexity class C, what is the expressive power of first order logic FO(Q) extended by the quantifiers in Q? From previously studied examples, one would expect that FO(Q) captures L C , i.e., logarithmic space relativized to an oracle in C. We show that this is not always (...) true. However, after studying the problem from a general point of view, we derive sufficient conditions on C such that FO(Q) captures L C . These conditions are fulfilled by a large number of relevant complexity classes, in particular, for example, by NP. As an application of this result, it follows that first order logic extended by Henkin quantifiers captures L NP . This answers a question raised by Blass and Gurevich [Ann. Pure Appl. Logic, vol. 32, 1986]. Furthermore we show that for many families Q of generalized quantifiers (including the family of Henkin quantifiers), each FO(Q)-formula can be replaced by an equivalent FO(Q)-formula with only two occurrences of generalized quantifiers. This generalizes and extends an earlier normal-form result by I. A. Stewart [Fundamenta Inform. vol. 18, 1993]. (shrink)

We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable elements are (...) disjoint. We formulate general criteria that allow one to conclude that a distributive upper semi-lattice has a decidable two-quantifier theory. These criteria are applied not only to the weak truth-table degrees of the recursively enumerable sets but also to various substructures of the polynomial many-one (pm) degrees of the recursive sets. These applications to the pm degrees require no new complexity-theoretic results. The fact that the pm-degrees of the recursive sets have a decidable two-quantifier theory answers a question raised by Shore and Slaman in [21]. (shrink)

In “Complex Demonstratives: A Quantificational Account” (MIT Press 2001) (henceforth CD), I argued that complex demonstratives are quantifiers. Many philosophers had held that demonstratives, both simple and complex, are referring terms. Since the publication of CD various objections to the account of complex demonstratives I defended in it have been raised. In the present work, I lay out these objections and respond to them.

We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engström, comparing them with a more general, higher order definition of team quantifier. We show that Engström’s definitions can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engström’s quantifiers only range over the latter. We further argue that Engström’s (...) definitions are just embeddings of the first-order generalized quantifiers into team semantics, and fail to capture an adequate notion of team-theoretical generalized quantifier, save for the special cases in which the quantifiers are applied to flat formulas. We also raise several doubts concerning the meaningfulness of the monotone/nonmonotone distinction in this context. In the appendix we develop some proof theory for Engström’s quantifiers. (shrink)

This paper reexamines some examples, discussed by Mates and others, of sentences containing both definite descriptions and quantifiers. It has frequently been claimed that these sentences provide evidence for the view that definite descriptions themselves are quantifiers. The main goal of this paper is to argue this is not so. Though the examples are compatible with quantificational approaches to definite descriptions, they are also compatible with views that treat definite descriptions as basically scopeless. They thus provide no reason to see (...) definite descriptions as quantifiers. Even so, this paper shows that the examples do raise a surprising range of complex issues about how quantifier scope works, and where it occurs. Thus, a clear picture of how these examples work will help us to understand better where definite descriptions fit into the larger picture of quantifiers and related phenomena. (shrink)

This paper investigates the effects of (surface) DP-internal quantifying expressions on semantic interpretation. In particular, I investigate two syntactic constructions in which an adjective takes scope out of its embedding DP, thus raising an interesting question for strict compositionality. Regarding the first construction, I follow Larson (1999) and assume that the adjective incorporates into the determiner of its DP, forming a complex quantifier [D+A]. I present new evidence in favor of this analysis. Since Larson's semantic analysis of complex (...) quantifiers [D+A] makes a wrong prediction, I propose an alternative, empirically more adequate analysis that treats D+A compounds as pluractional quantifiers in the sense of Lasersohn (1995). Finally, I turn to the second construction, arguing that – despite superficial similarities to the first construction - it should not be analyzed in terms of complex quantifier formation, but in terms of LF-movement of the adjective to Spec,DP. The discussion suggests that there is more than one way for DP-internal modifiers to take DP-external scope in natural language. (shrink)

This paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the toolkit of Janin and Marcinkowski [JM01].We introduce an operation existsn on properties S that says "there are n components having S". We use this operation to show that under natural strictness conditions, adding a first order quantifier word u to the beginning of a prefix class V increases the expressive power monotonically in u. As a (...) corollary, if the first order quantifiers are not already absorbed in V, then both the quantifier alternation hierarchy and the existential quantifier hierarchy in the positive first order closure of V are strict.We generalize and simplify methods from Marcinkowski [Mar99] to uncover limitations of the expressive power of an additional first order quantifier, and show that for a wide class of properties S, S cannot belong to the positive first order closure of a monadic prefix class W unless it already belongs to W.We introduce another operation alt on properties which has the same relationship with the Circuit Value Problem as reach has with the Directed Reachability Problem. We use alt to show that Πn⊈ FO, Σn⊈ FO, and Δn+1⊈ FOB, solving some open problems raised in [Mat98]. (shrink)

I am a friend of supervaluationism. A statement lacks a definite truth value if, and only if, it comes out true on some admissible ways of precisifying the semantics of the relevant vocabulary and false on others. In this paper, I focus on the special case of identity statements. I take it that such statements, too, may occasionally suffer a truth-value gap, including philosophically significant instances. Yet there is a potentially devastating objection that can be raised against the supervaluationist treatment (...) of such cases—in fact two objections. Luckily, both can be resisted. But seeing how requires that we take a closer look at the ontological presuppositions of supervaluationism, allowing for more leeway than is usually supposed. (shrink)

Pietroski’s model of semantic composition is introduced and compared to the standard type hierarchy. Particular focus is then given to Pietroski’s account of quantifi cation. The question is raised of how the model might account for the weak/strong distinction in natural language quantifi cation. A number of options are addressed and one proposal is tentatively recommended.

In two of the earliest papers on extending modal logic with propositional quantifiers, R. A. Bull and K. Fine studied a modal logic S5Π extending S5 with axioms and rules for propositional quantification. Surprisingly, there seems to have been no proof in the literature of the completeness of S5Π with respect to its most natural algebraic semantics, with propositional quantifiers interpreted by meets and joins over all elements in a complete Boolean algebra. In this note, we give such a proof. (...) This result raises the question: For which normal modal logics. (shrink)

The growth of self-tracking and personal surveillance has given rise to the Quantified Self movement. Members of this movement seek to enhance their personal well-being, productivity, and self-actualization through the tracking and gamification of personal data. The technologies that make this possible can also track and gamify aspects of our interpersonal, romantic relationships. Several authors have begun to challenge the ethical and normative implications of this development. In this article, we build upon this work to provide a detailed ethical analysis (...) of the Quantified Relationship. We identify eight core objections to the QR and subject them to critical scrutiny. We argue that although critics raise legitimate concerns, there are ways in which tracking technologies can be used to support and facilitate good relationships. We thus adopt a stance of cautious openness toward this technology and advocate the development of a research agenda for the positive use of QR technologies. (shrink)

In two of the earliest papers on extending modal logic with propositional quantifiers, R. A. Bull and K. Fine studied a modal logic S5Π extending S5 with axioms and rules for propositional quantification. Surprisingly, there seems to have been no proof in the literature of the completeness of S5Π with respect to its most natural algebraic semantics, with propositional quantifiers interpreted by meets and joins over all elements in a complete Boolean algebra. In this note, we give such a proof. (...) This result raises the question: For which normal modal logics L can one axiomatize the quantified propositional modal logic determined by the complete modal algebras for L? (shrink)

Quantification over individuals, times, and worlds can in principle be made explicit in the syntax of the object language, or left to the semantics and spelled out in the meta-language. The traditional view is that quantification over individuals is syntactically explicit, whereas quantification over times and worlds is not. But a growing body of literature proposes a uniform treatment. This paper examines the scopal interaction of aspectual raising verbs (begin), modals (can), and intensional raising verbs (threaten) with quantificational (...) subjects in Shupamem, Dutch, and English. It appears that aspectual raising verbs and at least modals may undergo the same kind of overt or covert scope-changing operations as nominal quantifiers; the case of intensional raising verbs is less clear. Scope interaction is thus shown to be a new potential diagnostic of object-linguistic quantification, and the similarity in the scope behavior of nominal and verbal quantifiers supports the grammatical plausibility of ontological symmetry, explored in Schlenker (2006). (shrink)

In paper [5] it was shown that a great part of model theory of logic with the generalized quantifier Q x = there exist uncountably many x is reducible to the model theory of first order logic with an extra binary relation symbol. In this paper we consider when the quantifier Q x can be syntactically defined in a first order theory T. That problem was raised by Kosta Doen when he asked if the quantifier Q x (...) can be eliminated in Peano arithmetic. We answer that question fully in this paper. (shrink)

In order to know what a belief is, we need to know when it is appropriate to say that two subjects (or the same subject at two different times) believe(s) the same or entertain the same thought. This is not entirely straightforward. Consider for instance1. Tom thinks that he himself is the smartest and Tim believes the same2. In 2001, Bill believed that some action had to be taken to save the rain forest and today he believes the same.What does (...) Tim think? That he, Tim, is the smartest, or that Tom is? And what does Bill believe today? That action had to be taken in 2001 or that it has to be taken now? Both answers are intuitively acceptable. This has to be accounted for somehow.Building on Mark Richard's work on tense, Scott Soames 1 claims that the substitutional interpretation of the quantifiers is unable to account for the intended meaning of such statements as (2) and the validity of some inferences involving them. I will show that his argument is not convincing. Not only does the substitutional interpretation fare no worse than the objectual one, but it seems to be able to avoid a problem which could be seriously damaging for any account of the sameness of thoughts based on the notion of structured proposition. In the first section, I state the problem allegedly raised by tensed belief ascriptions to the substitutional interpretation of the quantifiers. In the second, Soames's argument is shown to be flawed. I also show that the content of the that-clause in (2) is not faithfully represented by any kind of structured proposition. Finally, I show how the substitutional interpretation can handle all such statements as (1) and (2) and the inferences involving them. (shrink)

This chapter explores parsing and grammar in children, with an emphasis on how children resolve sentences with ambiguous scope. It focuses on an ambiguity involving the universal quantifier every in subject position along with a negated main predicate, as in the sentence “Every horse didn’t jump over the fence.” One interpretation of this sentence is the “surface-scope” interpretation, which views the expression every horse as a reference to all the horses in the set; thus, each horse in the set (...) did not jump over the fence. Another interpretation is the “inverse-scope” interpretation, whereby some horses jumped over the fence while others did not. The chapter presents evidence suggesting that children tend to prefer the surface-scope interpretation and cannot obtain the inverse-scope interpretation. In other words, children systematically use the surface position of the relevant quantificational elements to determine scope relations. The chapter also discusses negation and quantified noun phrases, along with isomorphism. Finally, it discusses the implications of these findings for language development and sentence processing. (shrink)

I propose the first strictly compositional semantic account of same. New data, including especially NP-internal uses such as two men with the same name, suggests that same in its basic use is a quantificational element taking scope over nominals. Given type-lifting as a generally available mechanism, I show that this follows naturally from the fact that same is an adjective. Independently-motivated assumptions extend the analysis to standard examples such as Anna and Bill read the same book via a mechanism I (...) call PARASITIC SCOPE, in which the scope of same depends on the scope of some other scopetaking element in the sentence. Although I will initially discuss the analysis in terms of a familiar Quantifier Raising framework, I go on to implement the analysis within an innovative continuation-based Type-Logical Grammar. The empirical payoff for dealing in continuations is that a simple generalization of the basic analysis gives the first ever formal account of cases in which same distributes over objects other than NP denotations, as in the relevant interpretation of John hit and killed the same man. (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)

This squib presents a rebuttal to two of King’s (Complex demonstratives: A quantificational account. Cambridge, Mass.: MIT Press, 2001) arguments that complex demonstratives are quantifier phrases like every man. The first is in response to King’s argument that because complex demonstratives induce weak crossover effects, they are quantifier phrases. I argue that unlike quantifier phrases and like other definite determiner phrases, complex demonstratives in object position can corefer with singular pronouns contained in the subject DP. Although complex (...) demonstratives could undergo LF-movement, the ruling out by weak crossover is empirically undetectable. The second rebuttal is in response to King’s argument that because complex demonstratives allow antecedent-contained deletion, they are quantifier phrases. I present data showing that along with quantifier phrases, complex demonstratives pattern with proper names in allowing ACD with restrictive modification, but usually not with non-restrictive modification. (shrink)

This paper proposes that the meanings of some natural language expressions should be thought of as functions on their own continuations. Continuations are a well-established analytic tool in the theory of programming language semantics; in brief, a continuation is the entire default future of a computation. I show how a continuation-based grammar can unify several aspects of natural language quantification in a new way: merely stating the truth conditions for quantificational expressions in terms of continuations automatically accounts for scope displacement (...) and scope ambiguity. To prove this claim, I exhibit a simple finite context-free grammar with a strictly compositional semantics in which quantificational NPs are interpreted in situ but take semantic scope over larger constituents. There is no Quantifier Raising (nor any use of a level of Logical Form distinct from overt syntax), no Cooper Storage (or similar mechanisms used in many recent HPSG, Categorial, or Type-logical treatments), and no need for type-shifting (as in Hendriks' Flexible Types account). Continuations also provide a natural account of generalized coordination that does not require either type-shifting or type polymorphism. Compositionality issues are discussed in some detail. (shrink)

Branching quantifiers were first introduced by L. Henkin in his 1959 paper ‘Some Remarks on Infmitely Long Formulas’. By ‘branching quantifiers’ Henkin meant a new, non-linearly structured quantiiier-prefix whose discovery was triggered by the problem of interpreting infinitistic formulas of a certain form} The branching (or partially-ordered) quantifier-prefix is, however, not essentially infinitistic, and the issues it raises have largely been discussed in the literature in the context of finitistic logic, as they will be here. Our discussion transcends, however, (...) the resources of standard lst-order languages and we will consider the new form in the context of 1st-order logic with 1- and 2-place ‘Mostowskian` generalized quantifiers.2.. (shrink)

This paper argues that “covert” operations like Quantifier Raising (QR) can precede “overt” operations. Specifically we argue that there are overt operations that must take the output of QR as their input. If this argument is successful there are two interesting consequences for the theory of grammar. First, there cannot be a “covert” (i.e. post-spellout) component of the grammar. That is, what distinguishes operations that affect phonology from those that do not cannot be an arbitrary point in the (...) derivation (“spellout”) before which the former apply and after which the latter do; all syntactic operations apply in the same component (henceforth ‘single component grammar’). Second, there must be some alternative means for distinguishing “overt” from “covert” operations. One such alternative, which we can call the ‘phonological theory of QR’, was suggested by Bobaljik (1995), Pesetsky (1998), Groat and O’Neil (1994). These authors proposed that the distinguishing property has to do with principles of the syntax-phonology interface. Assume that movement is a copying operation with phonology targeting one copy in a chain for pronunciation. The distinction between “overt” and “covert” movement, these authors suggest, is this: “overt” movements are the result of phonology targeting the head of a chain for.. (shrink)

This paper argues in favor of two claims: (a) that Scope Shifting Operations (Quantifier Raising and Quantifier Lowering) are restricted by economy considerations, and (b) that the relevant economy considerations compare syntactic derivations that end up interpretively identical. These ideas are shown to solve several puzzles having to do with the interaction of scope with VP ellipsis, coordination, and the interpretation of bare plurals. Further, the paper suggests a way of dealing with the otherwise puzzling clause-boundedness of (...) Quantifier Raising. (shrink)

Lambek elegantly characterized part of natural language. As is well-known, his substructural logic L, and its non-associative version NL, handle basic function/argument composition well, but not scope taking and syntactic displacement—at least, not in their full generality. In previous work, I propose $$\text {NL}_\lambda $$, which is NL supplemented with a single structural inference rule (“abstraction”). Abstraction closely resembles the traditional linguistic rule of quantifier raising, and characterizes both semantic scope taking and syntactic displacement. Due to the unconventional (...) form of the abstraction inference, there has been some doubt that $$\text {NL}_\lambda $$ should count at a legitimate substructural logic. This paper argues that $$\text {NL}_\lambda $$ is perfectly well-behaved. In particular, it enjoys cut elimination and an interpolation result. In addition, perhaps surprisingly, it is decidable. Finally, I prove that it is sound and complete with respect to the usual class of relational frames. (shrink)

Lambek elegantly characterized part of natural language. As is well-known, his substructural logic L, and its non-associative version NL, handle basic function/argument composition well, but not scope taking and syntactic displacement—at least, not in their full generality. In previous work, I propose \, which is NL supplemented with a single structural inference rule.ion closely resembles the traditional linguistic rule of quantifier raising, and characterizes both semantic scope taking and syntactic displacement. Due to the unconventional form of the abstraction (...) inference, there has been some doubt that \ should count at a legitimate substructural logic. This paper argues that \ is perfectly well-behaved. In particular, it enjoys cut elimination and an interpolation result. In addition, perhaps surprisingly, it is decidable. Finally, I prove that it is sound and complete with respect to the usual class of relational frames. (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)

With the aid of some results from current linguistic theory I examine a recent anti-Fregean line with respect to hybrid talk of numbers and ordinary things, such as ‘the number of moons of Jupiter is four’. I conclude that the anti-Fregean line with respect to these sentences is indefensible.

Quotation exhibits characteristics of both use and mention. I argue against the recently popular pragmatic reductions of quotation to mere language use (e.g. Recanati 2001), and in favor of a truly hybrid account synthesizing and extending Potts (2007) and Geurts & Maier (2005), using a mention logic and a dynamic semantics with presupposition to establish a context-driven meaning shift. The current paper explores a `quotebreaking' extension to solve the problems posed by non-constituent quotation, and anaphora, ellipsis and quantifier (...) class='Hi'>raising across quotation marks. (shrink)

This paper presents an argument based on evidence from experiments featuring Antecedent-Contained Deletion sentences situated in carefully-manipulated discourse contexts, that covert movement is not grammatically constrained by tense. ACD is a form of Verb Phrase Ellipsis in which ellipsis is embedded in its antecedent. Under an account appealing to Quantifier Raising, the quantificational phrase containing the ellipsis site raises to a VP-external position, allowing the VP to become the antecedent. When ACD is embedded in a non-finite clause, such (...) sentences are ambiguous, since multiple VPs can serve as an antecedent. However, when ACD is embedded in a finite clause, the range of interpretations has been claimed to be restricted, because of an independent ‘clause-bounded’ movement constraint on Quantifier Raising. However, there are exceptions to this generalization. I present evidence from an experimental investigation of finite-clause-embedded ACD sentences, relying on Cecchetto, to demonstrate that under the right discourse conditions, the supposedly unavailable Matrix reading surfaces robustly, at a percentage that is surprising if the constraint were rooted in the grammar. I argue that these results call into question the source of this locality restriction, and propose that it has nothing to do with an arbitrary grammatical constraint on movement. (shrink)

The phenomenon of inverse linking, where a noun phrase embedded within another behaves with respect to binding as though it were structurally independent, has proven challenging for theories of the syntax–semantics interface. In this paper I show that, using an LF-movement style approach to the syntax–semantics interface, we can derive all and only the appropriate meanings for such constructions using no semantic operations other than function application and composition. The solution relies neither on a proliferation of lexical ambiguity nor on (...) abandoning the idea that pronouns denote variables, but rather on a straightforward (and standard) reification of assignment functions, which allows us to define abstraction operators within our models. (shrink)

Focusing on cases which involve binding into epistemic modals with definite descriptions and quantifiers, I raise some new problems for standard approaches to all of these expressions. The difficulties are resolved in a semantic framework that is dynamic in character. I close with a new class of problems about de re readings within the scope of modals.

Generics exhibit genericity, and though a theory of generics is closely connected to a theory of genericity, the two are distinct. They raise a host of interesting linguistic and philosophical issues, both separately and in their interaction. This chapter begins with a fairly manifest phenomenon one can observe in natural language. There is a range of sentences that, speaking intuitively, one can use to talk about kinds. It argues that there's no simple statistical criterion that systematically captures the patterns of (...) the truth and falsity of generics. Generics seem to not just be substantially independent of statistical facts in the world and at the time with respect to which they are evaluated. The chapter points‐out a likely form of context dependence in generics, and argues that on a quantificational approach to generics, the restrictor of the generic quantifier must be determined at least in part by the predicate at issue. (shrink)

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in metaphysics, and indicate a (...) number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them. (shrink)

We make a proposal for formalizing simultaneous games at the abstraction level of player’s powers, combining ideas from dynamic logic of sequential games and concurrent dynamic logic. We prove completeness for a new system of ‘concurrent game logic’ CDGL with respect to finite non-determined games. We also show how this system raises new mathematical issues, and throws light on branching quantifiers and independence-friendly evaluation games for first-order logic.

This paper introduces a new Ehrenfeucht-Fraïssé type game that is played on two classes of models rather than just two models. This game extends and generalizes the known Ajtai-Fagin game to the case when there are several alternating moves played in different models. The game allows Duplicator to delay her choices of the models till the very end of the game, making it easier for her to win. This adds on the toolkit of winning strategies for Duplicator in Ehrenfeucht-Fraïssé type (...) games and opens up new methods for tackling some open problems in descriptive complexity theory. As an application of the class game, it is shown that, if m is a power of a prime, then first order logic augmented with function quantifiers F1n of arity 1 and height n < m can not express that the size of the model is divisible by m. This, together with some new expressibility results for Henkin quantifiers H1n gives some new separation results on the class of finite models among various F1n on one hand and between F1n and H1n on the other. Since function quantifiers involve a bounded type of second order existential quantifiers, the class game solves an open problem raised by Fagin, which asks for some inexpressibility result using a winning strategy by Duplicator in a game that involves more than one coloring round. (shrink)