What is the relationship between the structure of existential sentences and their meaning? How do hearers interpret existential sentences using pragmatic assumptions? This study attempts to account for the relationship between the structure of existential sentences (ES) and their meaning. The study of ES has received a great deal of attention because the construction has complex syntactic properties, is associated with restrictions of a semantic nature, and provides an interesting area for...

This revised and considerably expanded 2nd edition, published in 2008, brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are exp...

Perhaps the most important work of philosophy written in the twentieth century, Tractatus Logico-Philosophicus was the only philosophical work that Ludwig Wittgenstein published during his lifetime. Written in short, carefully numbered paragraphs of extreme brilliance, it captured the imagination of a generation of philosophers. For Wittgenstein, logic was something we use to conquer a reality which is in itself both elusive and unobtainable. He famously summarized the book in the...

First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic.

Published in 1953, Wittgenstein's Philosophical Investigations had a deeply unsettling effect upon our most basic philosophical ideas concerning thought, sensation and language. Its claim that philosophical questions of meaning necessitate a close analysis of the way we use language continues to influence Anglo-American philosophy today. However, its compressed and dialogic prose is not always easy to follow. This collection of essays deepens but also challenges our understanding of the wo...

If you keep removing single grains of sand from a heap, when is it no longer a heap? From discussions of the heap paradox in classical Greece, to modern formal approaches like fuzzy logic, Timothy Williamson traces the history of the problem of vagueness. He argues that standard logic and formal semantics apply even to vague languages and defends the controversial, realist view that vagueness is a form of ignorance - there really is a grain of sand whose removal turns a heap into a non-hea...

"The best introduction to logic you will find."—Martin Gardner"Professor Bennett entertains as she instructs," writes Publishers Weekly about the penetrating yet practical Logic Made Easy. This brilliantly clear and gratifyingly concise treatment of the ancient Greek discipline identifies the illogical in everything from street signs to tax forms. Complete with puzzles you can try yourself, Logic Made Easy invites readers to identify and ...

It seems reasonable to believe that there might have existed things other than those that in fact exist, or have existed. But how should we understand such claims? Standard semantic theories exploit the Leibnizian metaphor of a set of all possible worlds: a proposition might or must be true if it is true in some or all possible worlds. The actualist, who believes that nothing exists except what actually exists, prefers to talk of possible states of the world, or of ways that a world might ...

From the point of view of psychology and cognitive science, much of modern linguistics is too formal and mathematical to be of much use. The newly emerging approaches to language termed, "Functional and Cognitive Linguistics," however, are much less formally oriented. Instead, functional and cognitive approaches to language structure are typically couched in terms already familiar to cognitive scientists: perception, attention, conceptualization, meaning, symbols, categories, schemas, pers...

The central concern of this title, first published in 1994, is the syntactic nature of negation in Universal Grammar, and its relation to other functional elements in the Syntax. The study argues that negation is not a syntactic category on its own; rather, it is one of the values of a more abstract syntactic category, named Σ, which includes other sentence operators, such as affirmation and emphasis. This title will be of interest to students of language and linguistics.