Universal Quantification with Skolemization as Evidenced in Chinese and English

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This book is concerned with the formal definition of universal quantification. The central claim advanced here is that the formal definition of EVERY, which stands for any distributive universal quantifier, ought to incorporate a skolem function to capture the paired reading that for every x there is a y. We claim that this paired reading is present in all universal quantifier sentences. This definition of EVERY requires a variable in the scope of the universal quantifier word. This is so because the skolem function facilitates the paired reading by linking the choice of the value for y with the choice of the value for x. Under this view, securing a variable in the scope of a universal quantifier word becomes a make-or-break requirement of universal quantification. The issues dealt with in this book are highly theoretical and formal, but we approach them almost entirely from an empirical perspective, supporting the skolemized definition of EVERY with evidence drawn exclusively from natural language data, mostly from Chinese, but with some crucial data from English as well. This book makes a contribution to the study of universal quantification, scoping properties of indefinites in Chinese, semantic properties of the Chinese adverb dou and a number of conjunction and additive words, and event semantics. It also offers a novel way of explaining the interaction of dou with interrogative Wh-phrases.


“This is an important book. It is mainly concerned with the revision of the formal definition of universal quantification and in order to do so, it delves deeply into the semantics of dou and in the structuring of (Davidsonian) events. The Mandarin element dou is generally regarded as a universal quantifier, but Shi-Zhe Huang shows that that is only part of the story, since dou may also occur in contexts with no universal quantification. On top of that, the alternative view that dou is a distributor, i.e., more like each in English does not cover the whole array of facts either … The nicest thing about this book is that it is inspiring. It is about old problems but it is full of new ideas. It deals with long-standing issues, but the claims made are fresh and original.” – (from the Commendatory Preface)Professor Rint Sybesma, Universiteit Leiden, Department of Chinese Studies, Leiden, The Netherlands

“This study is an exciting, satisfying, and important book. It offers not just elegant and convincing solutions of long-standing puzzles in Chinese, such as the meaning and behavior of the particle dou and the apparent almost complete absence in Chinese of scope ambiguity; it also offers important contributions to semantic methodology and theory. In a style clear and readable even to those unfamiliar with Chinese, Dr. Huang marshals fascinating data from Chinese as well as English to prove that universal quantification in natural language must be modeled with the addition of skolem functions to traditional Generalized Quantifiers. While there have been several recent suggestions from other scholars about the use of skolem functions in accounting for scope and existential quantification, most of these arguments have emphasized the possibility or formal economy of such accounts. Dr. Huang, however, in her open-minded and theoretically broad-ranging work, uses the exquisite detail of a wide variety of Chinese examples, as well as English tenseless sentences, to argue that the data absolutely requires a skolemized account of universal quantification. Skolem function operators require a second variable within their scope, which can come from the variable inherent in an indefinite or from an event variable. Dr. Huang shows us that, unexpectedly, dou represents a sum operator on events, and that, as such, it actually plays a role similar to that of tense in English in licensing an event variable, which, in the absence of indefinites, can be seen to make universal quantification possible by providing the variable required by the skolem function. Dr. Huang’s deft discussion of tenseless sentences in English adds weight to the important generalizations that cross-linguistic EVERY involves skolemization and that the variables required for this skolemized quantification must be licensed morphologically or lexically. In a field in which scholars sometimes focus more on problems generated within their own theories than on explaining real language phenomena, Dr. Huang’s study represents a model of linguistic research. It combines careful attention to language data with a broad mastery of issues in formal semantics to bring forward proposals of great interest to those working in both Chinese linguistics and formal semantics.” – Professor Muffy Siegel, Temple University

Table of Contents

Preface by Dr. Sybesma
1. Introduction
2. EVERY with Skolemization: Every and Mei
3. Dou and Partial Order
4. Constraining the Event Variable

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