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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.
Edwin Mellen Press Ltd
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