Intensional Logic and The Metaphysics of Intentionality Author's Preprint Author's Preprint Intensional Logic and The Metaphysics of Intentionality Edward N. Zalta Stanford University Author's Preprint Author's Preprint Copyright c 1988 by Edward N. Zalta (This work is forthcoming at MIT Press/Bradford Books.) All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the author. This book was typeset in Computer Modern Roman using the LATEX document preparation system. It was printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Zalta, Edward N., 1952{ Intensional logic and the metaphysics of intentionality Bibliography: p. Includes index. 1. Intentionality (Philosophy) 2. Logic, Symbolic and mathematical. I. Title XXXX.XXXXX 1988 110{dc19 87-32171 ISBN X-XXX-XXXXX-X Author's Preprint To Melissa Author's Preprint Author's Preprint Contents Preface xi I Introduction 1 1 Intensionality and Intentionality 3 1.1 Intensional Logic . .3 1.2 Intentional States . 10 2 An Overview of the Theory 15 2.1 The Insight Behind the Theory . 15 2.2 The Presentation of the Theory . 19 2.3 The Explanation of the Theory . 22 2.4 Some ObservationsAuthor's . Preprint. 33 II Strong Extensionality 39 3 The Basic Theory of Relations 41 3.1 Taking Relations as Primitive . 41 3.2 The Semantic Conception of the Language of Encoding . 45 3.3 Conditions Under Which There Are Relations . 46 3.4 Identity Conditions for Relations . 51 4 Propositions, Situations, Worlds, and Times 56 4.1 The Basic Theory of Propositions . 57 4.2 Situations, Worlds, and Times . 61 4.3 Other Theories of Worlds and Times . 68 4.4 The Challenge for Other Logics . 75 vii viii Contents 5 Definite Descriptions 78 5.1 A Simple View of Descriptions . 78 5.2 The Semantics of Rigid Descriptions . 81 5.3 Descriptions, Propositions, and Relations . 83 5.4 The Logic of Descriptions . 86 5.5 Non-rigid Descriptions . 91 5.6 Final Comments . 97 III Existential Generalization 99 6 The Turn-of-the-Century Debate About Intentionality 101 6.1 Two Kinds of Existence . 102 6.2 Brentano, Meinong, and Husserl . 105 6.3 Mally, A-Objects, and Noemata . 108 6.4 A-Objects and Meinong . 113 7 The Analysis of Existential Generalization 115 7.1 Russell's Objections to Meinong's Views . 115 7.2 A Clear Response to Russell's Objections . 120 7.3 Names, Descriptions, and Fiction . 123 7.4 The Principles of Generalization . 127 8 Meinong's Recent Resurrection 130 8.1 Parsons' TheoryAuthor's of Meinongian Preprint Objects . 131 8.2 A Strict Understanding of Meinong . 135 8.3 Did Meinong Have to Commit Himself to Principle (G)? . 138 8.4 The Principle of Independence . 143 IV Substitutivity and Existential Generalization151 9 Direct Reference, Fregean Senses, and The Propositional Attitudes 153 9.1 Roles Senses Play in the Philosophy of Language . 154 9.2 A-Objects as Senses: The General Picture . 159 9.3 Sense1, Sense4, and Sense7 .................. 161 9.4 Sense2, Sense5, and Direct Reference . 164 9.5 Sense3, Sense6, and the Propositional Attitudes . 166 9.6 Summary . 172 Contents ix 10 Further Issues Concerning the Attitudes 174 10.1 Possible Objections to the Theory . 174 10.2 The Triadic Theory of Belief . 181 10.3 Existential Generalization . 184 11 Other Substitutivity Puzzles 187 11.1 Russell's Puzzle About George IV . 187 11.2 Kripke's Puzzles . 189 11.3 Indexical Belief . 196 V Conclusion 203 12 A Comparison with Montague's Intensional Logic 205 12.1 General Comparison . 206 12.2 Montague and Nonexistence . 216 12.3 Propositional Attitudes . 220 12.4 Modality, Descriptions, and Intensionality . 223 Appendix The Formal Intensional Logic 231 A.1 The Language . 232 A.2 The Semantics . 236 A.3 The Logic . 240 A.4 The Proper Axioms . 243 Bibliography 245 IndexAuthor's Preprint 253 Author's Preprint Preface In writing this book, I have had three goals in mind: (1) to develop a new, expanded conception of intensionality, (2) to explain clearly how the theory and technical apparatus developed in my first book is sensitive to this conception, and (3) to extend and apply the theory in new ways. The expanded conception of intensionality occurred to me while thinking about the differences among intensional logics. There is a wide variety of such logics, and some of them have very little in common. Though most of them were designed to explain apparent failures of the principle of substitution, each system focuses on a somewhat different body of data. And each breaks down when faced with intensional data outside its focus. It seemed important to try to collate and classify the entire range of data that occasioned the development of these intensional logics. And as a result of doing this, it became clear that there was a wider group of inferential principles thatAuthor's appeared to Preprint fail in various situations. So the expanded conception of intensionality is tied essentially to this expanded set of inferential principles. My second goal has been to show that the system described in my first book, Abstract Objects: An Introduction to Axiomatic Metaphysics, can represent the entire range of intensional data. In that book, I de- veloped a theory of abstract objects and tried to construct, by means of the theory, a progressive explanation of certain sentences that had puz- zled metaphysicians and philosophers of language. But there was little attempt to state explicitly the puzzles that surrounded these sentences. There was almost no attempt to argue for the theory or compare it with alternatives. And little mention was made either of the philosophical presuppositions of the theory or of a host of traditional issues in the philosophy of language. This situation is rectified in the present work. But more importantly, the system is reconceptualized in terms of the ex- panded conception of intensionality. Let me note that familiarity with xi xii Preface my first book is not presupposed, and reference to it has been kept to a minimum. My third goal has been to expand the theory. Three new areas of application are: (a) the addition of tense operators and the identifica- tion of moments of time, (b) the attempt to make some of Husserl's ideas precise, and (c) the inclusion of indexicals and contexts to explain substitutivity failures affecting indexicals. The system described right at the outset includes some of the new additions. These, then, are the principal goals that have directed this project. I have had one other, more practical, goal. And that is to make the book accessible to philosophers with little training in logic. I have tried to motivate and explain all of the technical material and logical nota- tion. For example, numerous instances of comprehension schemata are constructed, to show how the schemata work. The formal semantics of the system is developed only insofar as it helps one to picture what the theory asserts. The structure of the book is rather simple. It contains five parts. One of the parts is the Introduction, and another is the Conclusion. The three parts in the middle each deal with one or more of the principles that are used to identify intensional contexts. There is also an Appendix, the only part of the book that focuses entirely on technical definitions. The Appendix contains the most highly evolved incarnation of the system, with all of the new additions and modifications. The following typographical conventions have been employed. Single quotes are used to mention subsentential words or phrases of English, as well as to mention expressions of the formal language, whether they are terms, formulas, or otherAuthor's symbols. Sometimes, Preprint when it is too obvious that I am talking about an expression of the language, the single quotes are omitted. Double quotes are used to mention entire sentences of English. This makes it easier to distinguish them from the surrounding sentences. However, double quotes serve a variety of other purposes. They are used for quotation, as scare-quotes, to give readings of formal expressions in English, and to introduce symbols and abbreviations. The context should make the meaning of the double quotes clear. There are also conventions concerning typefaces. Italics serve several purposes. Certain symbols and expressions of the formal language (for example, the primitive terms) are always written in italic. Italic is used for emphasis, and for the introduction and definition of new or technical terms. It is also used for most foreign, especially Latin, words. Greek letters, with the exception of λ and ι, are usually used as metalinguistic variables that range over expressions of the object language. The two just mentioned are part of the object language, however. Finally, bold- face is used for one purpose, namely, to identify items associated with Preface xiii the semantics of the object language. The names of interpretations, as- signment functions, denotation functions, extension functions, etc., are all written in boldface. When I use boldface variables to range over worlds and times, therefore, I am talking about entities that are prim- itive in the semantics. But when I use regular italic variables to range over worlds and times, I am talking about entities that are defined in the object language, using only the primitives of the theory. Finally, let me acknowledge my indebtedness. I am indebted first and foremost to the people at Stanford's Center for the Study of Language and Information (CSLI). The first draft of this work was written while I was a postdoctoral fellow at CSLI.