The format of this book is unusual, especially for a book about linguistics. The book is meant primarily as a research monograph aimed at linguists who have some background in formal semantics, e. g. Montague Grammar. However, I have two other audiences in mind. Linguists who have little or no experience of formal semantics, but who have worked through a basic mathematics for linguists course, should, perhaps with the help of a sympathetic Montague gramma rian, be able to discover enough (...) of how I have adapted some of the basic ideas in formal semantics to make the developments that I undertake in the rest of the book accessible. Logicians and computer scientists who know about model theoretic semantics and formal systems should be able to glean enough from Chapters I and II about linguistic concerns and techniques to be able to read the remainder of the book, again possibly with the help of a sympathetic Montague grammarian. However, readers should beware. Chapter II is not meant as a general introduction either to formal semantics or to linguistics and while much of the presentation there is going over ground that is already well covered in the literature, the particular formulation and the emphases are very much oriented to the developments to be undertaken later in the book. (shrink)

There is a growing movement towards construing some classic debates in ontology as meaningless, either because the answers seem obvious or the debates seem intractable. In this paper, I respond to this movement. The response has three components: First, the members of the two sides of the ontological debates that dismissivists have targeted are using different quantifiers. Second, the austere ontologist is using a more fundamental quantifier than her opponent. Third, the austere ontologist’s more fundamental quantifier is a restriction of (...) her opponent’s quantifier. This response takes seriously the intuition that there is something wrong with the ontological disputes, but does not entail dismissivism. (shrink)

Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it (...) has been argued that we have good reason to admit among our primitive logical notions also the plural quantifiers ∀xx and ∃xx. More controversially, it has been argued that the resulting formal system with plural as well as singular quantification qualifies as ‘pure logic’; in particular, that it is universally applicable, ontologically innocent, and perfectly well understood. In addition to being interesting in its own right, this thesis will, if correct, make plural quantification available as an innocent but extremely powerful tool in metaphysics, philosophy of mathematics, and philosophical logic. For instance, George Boolos has used plural quantification to interpret monadic second-order logic and has argued on this basis that monadic second-order logic qualifies as “pure logic.” Plural quantification has also been used in attempts to defend logicist ideas, to account for set theory, and to eliminate ontological commitments to mathematical objects and complex objects. (shrink)

Semantic interpretations of both natural and formal languages are usually taken to involve the specification of a domain of entities with respect to which the sentences of the language are to be evaluated. A question that has received much attention of late is whether there is unrestricted quantification, quantification over a domain comprising absolutely everything there is. Is there a discourse or inquiry that has absolute generality? After framing the debate, this article provides an overview of the main (...) arguments for and against the possibility of unrestricted quantification, highlighting some of the broader implications of the debate. (shrink)

The question whether natural language permits quantification over intentional objects as the ‘nonexistent’ objects of thought is the topic of a major philosophical controversy, as is the status of intentional objects as such. This paper will argue that natural language does reflect a particular notion of intentional object and in particular that certain types of natural language constructions (generally disregarded in the philosophical literature) cannot be analysed without positing intentional objects. At the same time, those intentional objects do not (...) come for free; rather they are strictly dependent on intentional acts that generally need to have a presence, in one way or another, in the semantic structure of the sentence. (shrink)

Semantic theories based on a hierarchy of types have prominently been used to defend the possibility of unrestricted quantification. However, they also pose a prima facie problem for it: each quantifier ranges over at most one level of the hierarchy and is therefore not unrestricted. It is difficult to evaluate this problem without a principled account of what it is for a quantifier to be unrestricted. Drawing on an insight of Russell’s about the relationship between quantification and the (...) structure of predication, we offer such an account. We use this account to examine the problem in three different type-theoretic settings, which are increasingly permissive with respect to predication. We conclude that unrestricted quantification is available in all but the most permissive kind of type theory. (shrink)

This book surveys research in quantification starting with the foundational work in the 1970s. It paints a vivid picture of generalized quantifiers and Boolean semantics. It explains how the discovery of diverse scope behavior in the 1990s transformed the view of quantification, and how the study of the internal composition of quantifiers has become central in recent years. It presents different approaches to the same problems, and links modern logic and formal semantics to advances in generative syntax. A (...) unique feature of the book is that it systematically brings cross-linguistic data to bear on the theoretical issues, discussing French, German, Dutch, Hungarian, Russian, Japanese, Telugu (Dravidian), and Shupamem (Grassfield Bantu), and pointing to formal semantic literature involving quantification in around thirty languages. -- -/- 1. What this book is about and how to use it; 2. Generalized quantifiers and their elements: operators and their scopes; 3. Generalized quantifiers in non-nominal domains; 4. Some empirically significant properties of quantifiers and determiners; 5. Potential challenges for generalized quantifiers; 6. Scope is not uniform and not a primitive; 7. Existential scope versus distributive scope; 8. Distributivity and scope; 9. Bare numeral indefinites; 10. Modified numerals; 11. Clause-internal scopal diversity; 12. Towards a compositional semantics of quantifier words. (shrink)

Originally published in 1964. This book is concerned with general arguments, by which is meant broadly arguments that rely for their force on the ideas expressed by all, every, any, some, none and other kindred words or phrases. A main object of quantificational logic is to provide methods for evaluating general arguments. To evaluate a general argument by these methods we must first express it in a standard form. Quantificational form is dealt with in chapter one and in part of (...) chapter three; in the remainder of the book an account is given of methods by which arguments when formulated quantificationally may be tested for validity or invalidity. Some attention is also paid to the logic of identity and of definite descriptions. Throughout the book an attempt has been made to give a clear explanation of the concepts involved and the symbols used; in particular a step-by-step and partly mechanical method is developed for translating complicated statements of ordinary discourse into the appropriate quantificational formulae. Some elementary knowledge of truth-functional logic is presupposed. (shrink)

This paper criticizes George Boolos's famous use of plural quantification to argue that monadic second-order logic is pure logic. I deny that plural quantification qualifies as pure logic and express serious misgivings about its alleged ontological innocence. My argument is based on an examination of what is involved in our understanding of the impredicative plural comprehension schema.

The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in (...) order to specify the truth conditions of certain sentences involving constants or variables that don’t denote, one has to apparently quantify over things that are not identical to anything. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. I argue that although certain names and free variables do not actually refer to anything, in each case there might have been something they actually refer to, allowing one to interpret the contingentist claims without quantifying over mere possibilia. (shrink)

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth (...) and reference. We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege's distinction between sense and reference. (shrink)

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

When viewed as the most comprehensive theory of collections, set theory leaves no room for classes. But the vocabulary of classes, it is argued, provides us with compact and, sometimes, irreplaceable formulations of largecardinal hypotheses that are prominent in much very important and very interesting work in set theory. Fortunately, George Boolos has persuasively argued that plural quantification over the universe of all sets need not commit us to classes. This paper suggests that we retain the vocabulary of classes, (...) but explain that what appears to be singular reference to classes is, in fact, covert plural reference to sets. (shrink)

Alternative readings of quantification are considered. The absence of an unequivocal translation into ordinary speech is noted. Some examples are cited which, in the opinion of the author, are a result of equivocal readings of quantification, or unnecessarily restrictive readings which obscure its primary function.

Nihilism is the thesis that no composite objects exist. Some ontologists have advocated abandoning nihilism in favor of deep nihilism, the thesis that composites do not existO, where to existO is to be in the domain of the most fundamental quantifier. By shifting from an existential to an existentialO thesis, the deep nihilist seems to secure all the benefits of a composite-free ontology without running afoul of ordinary belief in the existence of composites. I argue that, while there are well-known (...) reasons for accepting nihilism, there appears to be no reason at all to accept deep nihilism. In particular, deep nihilism draws no support either from the usual arguments for nihilism or from considerations of parsimony. (shrink)

The standard analysis of quantification says that determiner quantifiers (such as every) take an NP predicate and create a generalized quantifier. The goal of this paper is to subject these beliefs to crosslinguistic scrutiny. I begin by showing that in St'á'imcets (Lillooet Salish), quantifiers always require sisters of argumental type, and the creation of a generalized quantifier from an NP predicate always proceeds in two steps rather than one. I then explicitly adopt the strong null hypothesis that the denotations (...) of quantifiers should be crosslinguistically uniform. Since the Salish data cannot be captured by the usual analysis of English, I pursue the idea that English is reducible to the Salish pattern. Reanalysis of many English constructions is required. I argue that the reanalysis has advantages over the standard analysis for partitives, as well as for non-partitive all- and most-phrases, which I analyze as containing bare plurals of argumental type. Even where the new analysis faces some challenges (for example, with every), the attempt still leads to fruitful results. It forces us to view familiar constructions in a new light, and to redefine, I believe correctly, which quantificational constructions are ‘basic’ and which stand in need of further explanation. (shrink)

We hardly ever mean exactly what we say. I don’t mean that we generally speak figuratively or that we’re generally insincere. Rather, I mean that we generally speak loosely, omitting words that could have made what we meant more explicit and letting our audience fill in the gaps. Language works far more efficiently when we do that. Literalism can have its virtues, as when we’re drawing up a contract, programming a computer, or writing a philosophy paper, but we generally opt (...) for efficiency over explicitness. In.. (shrink)

The use of digital tracking technologies is a widespread phenomenon. Millions of people around the world now track, document, and analyse their physical activities, vital functions, and daily habits through wearable devices, apps, and platforms. The aim is to assess and improve health, productivity, and wellbeing. The current Covid-19 pandemic has accelerated the uptake of tracking technologies. At the heart of this trend lies the quantification of the body, deemed as a key element in medical practice and personal self-care. (...) While often couched in positive promotional terms that highlight its value to users' mental, emotional, and physical health, it is also raising a host of issues and concerns that are at once ontological, ethical, political, social, legal, economic, and aesthetic. The Quantification of Bodies in Health aims to deepen understanding of this growing phenomenon and of the role of self-tracking practices in everyday life. It brings together established and emerging authors working at the intersection of philosophy, sociology, history, psychology, and digital culture, while bridging between philosophical and empirical approaches. A timely topic of extreme relevance and significance, The Quantification of Bodies in Health constitutes a useful and unique companion for anyone interested in the study of body quantification and self-tracking practices. (shrink)

Originally published in 1981. This is a book for the final year undergraduate or first year graduate who intends to proceed with serious research in philosophical logic. It will be welcomed by both lecturers and students for its careful consideration of main themes ranging from Gricean accounts of meaning to two dimensional modal logic. The first part of the book is concerned with the nature of the semantic theorist's project, and particularly with the crucial concepts of meaning, truth, and semantic (...) structure. The second and third parts deal with various constructions that are found in natural languages: names, quantifiers, definite descriptions, and modal operators. Throughout, while assuming some familiarity with philosophical logic and elementary formal logic, the text provides a clear exposition. It brings together related ideas, and in some places refines and improves upon existing accounts. (shrink)

The literature contains a popular argument in favor of the position that conditional attitudes are not simple attitudes with conditional contents but, rather, have a more complex structure. In this paper I show that an analogous argument applies to what we might call quantificational attitudes—like an intention to follow every bit of good advice I receive or a desire to get rabies shots for each bite I incur from an infected bat. The conditions under which these attitudes are satisfied and (...) thwarted are not captured by claiming that they are simple attitudes with quantificational contents. So, the argument supports a novel position—that quantificational attitudes have a more complex structure. After sketching the form of this extra structure, I show how similar considerations count in favor of the existence of genuinely quantificational speech acts. (shrink)

This book addresses a perennial challenge for product planners and designers alike: how to objectively specify and quantify the aesthetics of products. It provides automotive product planners with a framework for the grammar of aesthetics and a tool for quantifying the aesthetics of an intended product. Further, it equips styling designers with a tool for connecting engineering and aesthetics. Given the author’s extensive experience in motorcycle design, the motorcycle has been chosen as the frame of reference for automobiles. Specifically in (...) the field of automobile design, where engineering and aesthetics go hand in hand, it also becomes important to clearly and objectively define the relationship between engineering design and aesthetics. Accordingly, this book clearly establishes the objective parameters of aesthetics, puts forward a method for quantifying aesthetics, identifies the engineering design parameters affecting aesthetics, and determines the relationship between parameters of aesthetics and engineering design. As such, it offers a useful guide not only for design professionals, but also for students and researchers of design. (shrink)

This paper deals with the logical form of quantified sentences. Its purpose is to elucidate one plausible sense in which quantified sentences can adequately be represented in the language of first-order logic. Section 1 introduces some basic notions drawn from general quantification theory. Section 2 outlines a crucial assumption, namely, that logical form is a matter of truth-conditions. Section 3 shows how the truth-conditions of quantified sentences can be represented in the language of first-order logic consistently with some established (...) undefinability results. Section 4 sketches an account of vague quantifier expressions along the lines suggested. Finally, section 5 addresses the vexed issue of logicality. (shrink)

Quine said that the ontological question can be asked in three words, ‘What is there?’, and answered in one, ‘everything’. He was wrong. We need an extra word to ask the ontological question: it is ‘What is there, really?’; and it cannot be answered truthfully with ‘everything’ because there are some things that exist but which don’t really exist (and maybe even some things that really exist but which don’t exist).

This book details how quantification can serve both as evidence and as an instrument of government, whether when dealing with statistics on employment, occupational health and economic governance, or when developing public management or target-driven policies. In the process, it presents a thought-provoking homage to Alain Desrosières, who pioneered ways to study large numbers and the politics underlying them. It opens with a summary of Desrosières's contributions to the field in which several generations of researchers detail how this statistician (...) and historian profoundly influenced them. This tribute, based on personal testimonies, bears witness to the vitality of the school of thought and analytical framework Desrosières initiated. Next, a collection of essays explores the statistical argument in the neoliberal era, examining issues such as counting the homeless in Europe, measuring the performance of public services, and quantifying the effects of public action on the unemployed in France. The third part details the uses of quantification. It reveals that although statistics are frequently used to the advantage of those in power, they can also play a vital role in challenging and resisting both the conventions underlying the measurements as well as the measurements themselves.Featuring the work of economists, historians, political scientists, sociologists, and statisticians, this title provides readers with a thoughtful look at an influential figure in the history of statistics. It also shows how statistics are used to direct public policy, the degree of conflict that is possible in their production, and the disputes that can develop around their uses. (shrink)

Quantifiers, unlike proper names or definite descriptions, cannot be given the semantics of referring expressions. This fact has triggered a long-standing debate in formal semantics and syntax as to the combinatorial means by which quantifiers are integrated into a sentence. The present paper contributes to this debate through an investigation of quantifier comprehension during real-time sentence processing. We present evidence showing that two potentially independent processes—the integration of a quantifier in object position and the resolution of antecedent-contained deletion (ACD)—are linked. (...) Our data show, more specifically, that the resolution of a downstream ACD site is facilitated during real-time sentence processing if the upstream DP hosting the ACD site is quantificational but not if it is definite. We discuss these findings in the context of a QUANTIFIER RAISING-based approach and a type-shifting-based approach to quantifier integration. We argue that facilitation of ACD resolution by an upstream quantifier is only expected by theories, such as the QUANTIFIER RAISING approach, which employ the same mechanism for both processes. We then compare the QUANTIFIER RAISING-based account with a non-grammatical experience-based approach to our data, which attempts to explain the findings in terms of corpus frequencies. Although we cannot rule out such an alternative at this stage, we offer reasons to believe that an account that exploits QUANTIFIER RAISING has an explanatory advantage. (shrink)

Propositional quantifiers are added to a propositional modal language with two modal operators. The resulting language is interpreted over so-called products of Kripke frames whose accessibility relations are equivalence relations, letting propositional quantifiers range over the powerset of the set of worlds of the frame. It is first shown that full second-order logic can be recursively embedded in the resulting logic, which entails that the two logics are recursively isomorphic. The embedding is then extended to all sublogics containing the logic (...) of so-called fusions of frames with equivalence relations. This generalizes a result due to Antonelli and Thomason, who construct such an embedding for the logic of such fusions. (shrink)

I provide a classification of varieties of pantheism. I argue that there are two different kinds of commitments that pantheists have. On the one hand, there is an ontological commitment to the existence of a sum of all things. On the other hand, there is an ideological commitment: either collectively or distributively, the sum of all things is divine.

Call a quantifier ‘unrestricted’ if it ranges over absolutely all objects. Arguably, unrestricted quantification is often presupposed in philosophical inquiry. However, developing a semantic theory that vindicates unrestricted quantification proves rather difficult, at least as long as we formulate our semantic theory within a classical first-order language. It has been argued that using a type theory as framework for our semantic theory provides a resolution of this problem, at least if a broadly Fregean interpretation of type theory is (...) assumed. However, the intelligibility of this interpretation has been questioned. In this paper I introduce a type-free theory of properties that can also be used to vindicate unrestricted quantification. This alternative emerges very naturally by reflecting on the features on which the type-theoretic solution of the problem of unrestricted quantification relies. Although this alternative theory is formulated in a non-classical logic, it preserves the deductive strength of classical strict type theory in a natural way. The ideas developed in this paper make crucial use of Russell’s notion of range of significance. (shrink)

Scientific realism holds that the terms in our scientific theories refer and that we should believe in their existence. This presupposes a certain understanding of quantification, namely that it is ontologically committing, which I challenge in this paper. I argue that the ontological loading of the quantifiers is smuggled in through restricting the domains of quantification, without which it is clear to see that quantifiers are ontologically neutral. Once we remove domain restrictions, domains of quantification can include (...) non-existent things, as they do in scientific theorizing. Scientific realism would therefore require redefining without presupposing a view of ontologically committing quantification. (shrink)

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order counterparts of the original semantics.

Abstract At the time of The Logical Syntax of Language (Syntax), Quine was, in his own words, a disciple of Carnap’s who read this work page by page as it issued from Ina Carnap’s typewriter. The present paper will show that there were serious problems with how Syntax dealt with ontological claims. These problems were especially pronounced when Carnap attempted to deal with higher order quantification. Carnap, at the time, viewed all talk of reference as being part of the (...) misleading material mode of speech, and as such dismissed, rather than addressed, ontological problems. Central to the analysis in the present paper is the concept of an explication, which was seen by both Carnap and Quine as being of great philosophical importance. It will be shown that the concept of explication played a significant role in how each formulated their mature position on ontology. Both these final positions on ontology can also be seen as a evolving in reaction to Carnap’s flawed handling of ontological matters at the time of Syntax. Carnap, influenced by Tarski’s work on semantics, comes to believe that the concept of reference can be given an acceptable explication, and that by doing so we can see reference to abstract objects as unobjectionable. As a result, Carnap develops a position very different from the one presented in Syntax. Quine strongly rejected the instrumentalism of Syntax, and sought to give an explication of ontological questions that was language independent. This paper closes with a discussion of each’s understanding of the other’s position. (shrink)

We demonstrate how to validly quantify into hyperintensional contexts involving non-propositional attitudes like seeking, solving, calculating, worshipping, and wanting to become. We describe and apply a typed extensional logic of hyperintensions that preserves compositionality of meaning, referential transparency and substitutivity of identicals also in hyperintensional attitude contexts. We specify and prove rules for quantifying into hyperintensional contexts. These rules presuppose a rigorous method for substituting variables into hyperintensional contexts, and the method will be described. We prove the following. First, it (...) is always valid to quantify into hyperintensional attitude contexts and over hyperintensional entities. Second, factive empirical attitudes validate, furthermore, quantifying over intensions and extensions, and so do non-factive attitudes, both empirical and non-empirical , provided the entity to be quantified over exists. We focus mainly on mathematical attitudes, because they are uncontroversially hyperintensional. (shrink)

In addition to full beliefs, agents have attitudes of varying confidence, or credences. For instance, I do not believe that the Boston Red Sox will win the American League East this year, but I am at least a little bit confident that they will – i.e. I have a positive credence that they will. It is also common to think that agents have conditional credences. For instance, I am very confident – i.e. have a conditional credence of very-likely strength – (...) that the Red Sox will win the AL East this year given that their pitching staff stays healthy. There are good reasons to think that conditional credences are neither credences nor some combination of credences. In this paper, I show that similar reasons support thinking that agents have what we can call quantificational credences – attitudes like, thinking that each AL East team with a healthy pitching staff is at least a little bit likely to win the division – which are neither credences, conditional credences, nor some combination thereof. I provide a framework for assessing the rationality of credal states which involve quantificational credences. And I give a general picture of credal states that explains the similarities and differences between ordinary, conditional, and quantificational credences. (shrink)

This paper is about avoiding commitment to an ontology of possible worlds with two primitives: a hyperintensional connective like ‘in virtue of’, and primitive quantification into predicate position. I argue that these tools (which some believe can be independently motivated) render dispensable the ontology of possible worlds needed by traditional anaylses of modality. They also shed new light on the notion of truth-at-a-world.

Identity is a modally inflexible relation: two objects are necessarily identical or necessarily distinct. However, identity is not alone in this respect. We will look at the relation that one object bears to some objects if and only if it is one of them. In particular, we will consider the credentials of the thesis that no matter what some objects are, an object is necessarily one of them or necessarily not one of them.

Next SectionWe discuss the thesis formulated by Hintikka (1973) that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.

This paper argues for the thesis that, roughly put, it is impossible to talk about absolutely everything. To put the thesis more precisely, there is a particular sense in which, as a matter of semantics, quantifiers always range over domains that are in principle extensible, and so cannot count as really being ‘absolutely everything’. The paper presents an argument for this thesis, and considers some important objections to the argument and to the formulation of the thesis. The paper also offers (...) an assessment of just how implausible the thesis really is. It argues that the intuitions against the thesis come down to a few special cases, which can be given special treatment. Finally, the paper considers some metaphysical ideas that might surround the thesis. Particularly, it might be maintained that an important variety of realism is incompatible with the thesis. The paper argues that this is not the case. (shrink)

Attempts to clarify some issues about the use of hidden arguments to predicates of personal taste, and motivate an analysis which does not make use of such arguments.

A challenge to the orthodoxy, which shows that quantificational accounts are not only as effective as direct reference accounts but also handle a wider range of ...

Quantification, Negation, and Focus: Challenges at the Conceptual-Intentional Semantic Interface Tista Bagchi National Institute of Science, Technology, and Development Studies (NISTADS) and the University of Delhi Since the proposal of Logical Form (LF) was put forward by Robert May in his 1977 MIT doctoral dissertation and was subsequently adopted into the overall architecture of language as conceived under Government-Binding Theory (Chomsky 1981), there has been a steady research effort to determine the nature of LF in language in light of (...) structurally diverse languages around the world, which has ultimately contributed to the reinterpretation of LF as a Conceptual-Intentional (C-I) interface level between the computational syntactic component of the faculty of language and one or more interpretive faculties of the human mind. While this has opened up further possibilities of research in phenomena such as quantifier scope and scope interactions between negation, quantification, and focus, it has also given rise to a few real challenges to linguistic theory as well. Some of these are: (i) the split between lexical meaning – a matter supposedly belonging to the phase-wise selection of lexical arrays – and issues of semantic interpretation that arise purely from binding and scope phenomena (Mukherji 2010); (ii) partially relatedly, the level at which theta role assignment can be argued to take place, an issue that is taken up by me in Bagchi (2007); and (iii) how supposedly “pure” scopal phenomena relating to quantifiers, negation, and emphasizing expressions such as only and even (comparable to, e.g., Urdu/Hindi hii and bhii, Bangla –i and –o) also have dimensions of both focus and discourse reference. While recognizing all of these challenges, this talk aims to highlight particularly challenge (iii), both in terms of scholarship in the past and for the rich prospects for research on languages of south Asia with the semantics of quantification, negation, and focus in view. The scholarship of the past that I seek to relate this issue to is where, parallel to (and largely independently of) the research on LF that had been happening, Barwise and Cooper were developing their influential view of noun phrases as generalized quantifiers, culminating in their key 1981 article “Generalized Quantifiers and Natural Language” while, independently, McCawley, in his 1981 book Everything that Linguists have Always Wanted to Know about Logic, established through argumentation that all noun phrases semantically behave like generalized quantified expressions (further elaborated by him in the second – 1994 – revised edition of his book). I seek to demonstrate, based on limited data analysis from selected languages of south Asia, that our current understanding of quantification, negation, and focus under the Minimalist view owes something significant to the two major, but now largely marginalized, works of scholarship, and that for the way forward it is essential to adopt a more formal-semantic approach as adopted by them and also by later works such as Denis Bouchard’s (1995) The Semantics of Syntax, Mats Rooth’s work on focus (e.g., Rooth 1996, “Focus” in Shalom Lappin’s Handbook of Contemporary Semantic Theory), Heim and Kratzer’s Semantics in Generative Grammar (1998), and Yoad Winter’s (2002) Linguistic Inquiry article on semantic number, to cite just a few instances. (shrink)

Realist theories about fictional entities must explain the fact that, in ordinary contexts people deny, apparently in all seriousness, that there are such things as the Big Bad Wolf and Santa Claus. The usual explanation treats these denials as involving restricted quantification: The speaker is said to be denying only that the Big Bad Wolf and Santa Claus are to be found among real or actual things, not that there are no such things at all. This is unconvincing. The (...) denials may just as naturally be phrased as “The Big Bad Wolf and Santa Claus don't exist”, and claims of nonexistence seem not to admit of interpretations corresponding to statements of restricted quantification. Ordinary denials of the existence of fictional entities constitute a severe difficulty for realist theories. (shrink)

I argue that academic psychology’s quest to achieve scientific respectability by reliance on quantification and objectification is deeply flawed. Specifically, psychological theory typically cannot support prognostication beyond the binary opposition of “effect present/effect absent”. Accordingly, the “numbers” assigned to experimental results amount to little more than affixing names (e.g., more than, less than) to the members of an ordered sequence of outcomes. This, in conjunction with the conceptual under-specification characterizing the targets of experimental inquiry, is, I contend, a primary (...) reason why psychologists find it difficult to discriminate between competing, explanations of the effects of mind on behavior. Absent well-specified theory capable of enabling precise and detailed quantitative prediction, inferring underlying mental mechanisms from experimental outcomes becomes a difficult, if not impossible, task. (shrink)