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The philosophical approach of this volume is mainly structuralist, using logical tools to investigate the formal structure of various kinds of objects in our world, as characterised by language and as systematised by philosophy. This volume mainly analyses the structural properties of collections or pluralities (with applications to the philosophy of set theory), homogeneous objects like water, and the semantics and philosophy of events. This book thereby complements algebraic work that has been done on other philosophical entities, i.e. propositions, properties, relations, or situations. Located in the triangle of language, logic and philosophy, this volume is unique in combining the resources of different ?elds in an interdisciplinary enterprise. Half of the fourteen chapters of this volume are original papers, complementing the collection of the author's previously published essays on the subject.
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ALGEBRAIC IN PHILOSOPHY
CSLI Lecture Notes No. 74
ALGEBRAIC SEMANTICS IN LANGUAGE AND PHILOSOPHY
GODEHARD LINK
PUBLICATIONS] CENTER FOR THE STUDY OF LANGUAGE AND INFORMATION STANFORD. CALIFORNIA
Copyright © 1998 CSLI Publications Center for the Study of Language and Information Leland Stanford Junior University Printed in the United States 02 01 00 99 98 54321 Library of Congress Cataloging-in-Publication Data Link, Godehard. Algebraic semantics in language and philosophy / Godehard Link. p. cm. — (CSLI lecture notes ; no. 74) Collection of 14 essays, seven of which have been previously published. Includes bibliographical references (p. ) and index. Contents: The logical analysis of plurals and mass terms — Plural — Hydras : on the logic of relative clause constructions with multiple heads — Generalized quantifiers and plurals — Je drei Apfel = Three apples each : quantification and the German je — First-order axioms for the logic of plurality — Ten years of research on plurals : where do we stand? — Algebraic semantics for natural language — Quantity and number — The French Revolution—a philosophical event? — Algebraic semantics of event structures — The ontology of individuals and events — The philosophy of plurality — Mereology, second-order logic, and set theory — Appendix : a chapter in lattice theory. ISBN 1-57586-091-0 (alk. paper). — ISBN 1-57586-090-2 (pbk. : alk. paper) 1. Grammar, Comparative and general—Number. 2. Grammar, Comparative and general—Quantifiers. 3. Semantics (Philosophy) 4. Language and logic. 5. Language and languages—Philosophy. I. Title. II. Series. P240.8.L56 1997 415—dc21 97-46523 CIP oo The acid-free paper used in this book meets the minimum requirements of the American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ANSI Z39.48-1984. CSLI was founded early in 1983 by researchers from Stanford University, SRI International, and Xerox PARC to further research and development of integrated theories of language, information, and computation. CSLI headquarters and CSLI Publications are located on the campus of Stanford University. CSLI Publications reports new developments in the study of language, information, and computation. In addition to lecture notes, our publications include monographs, working papers, revised dissertations, and conference proceedings. Our aim is to make new results, ideas, and approaches available as quickly as possible. Please visit our web site at http://csli-www.stanford.edu/publications/
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Contents Preface
ix
Introduction
1
1 The Logical Analysis of Plurals and Mass Terms: A Latticetheoretical Approach 1.1 Introduction 1.2 The Logic of Plurals and Mass Terms (LPM) 1.3 Applications to Montague Grammar 2 Plural 2.1 Intro