Contemporary Readings in Logical Theory

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Contents Part 1 THE HISTORY OF LOGIC Introduction 1 The Development of Symbolic Logic C. 1. LEWIS AND C. H. LANGFORD 3 The Place of Logic Among the Sciences W. c. KNEALE AND M. H. KNEALE 21 Part 2 THE FORMAL APPROACH Introduction 27 On FormaIization HAO WANG 29 On the Ontological Significance of the L6wenheim-Skolem Theorem JOHN R. MYHlLL 40 ~G6del's Proof ERNEST NAGEL AND JAMES R. NEWMAN 51 Part 3 MEANING AND REFERENCE Introduction 73 On Sense and Nominatum GOTTLOB FREGE 75 On Denoting BERTRAND RUSSELL 93 On Referring PETER FREDERICK STRAWSON 105 Mr. Strawson on Referring BERTRAND RUSSELL 127 Part 4 THE THEORY OF TYPES Introduction 133 Mathematical Logic as Based on the Theory of Types BERTRAND RUSSELL 135 Sejf-Reference in Philosophy FREDERIC B. FITCH 154 Part 5 LOGIC AND ONTOLOGY Introduction 163 On What There Is WILLARD VAN ORMAN QUlNE 165 Empiricism, Semantics, and Ontology RUDOLF CARNAP 178 The Need for Abstraet Entities in Semantie Analysis ALONZO CHURCH 194 A W orld of Individuals NELSON GOODMAN 204 Part 6 LOGle AND ORDINARY LANGUAGE I ntroduction 217 Formal and Informal Logie GILBERT RYLE 219 Logieal Theory PETER FREDERICK STRAWSON 226 Mr. Strawson on Logieal Theory WILLARD VAN ORMAN QUINE 236 Mr. Strawson on Symbolie and Traditional Logie PETER T. GEACH 252 Part 7 MODAL LOGle lntroduction 257 The Strueture of the System of Strict Implieation CLARENCF. lRVING LEWIS 259 The Problem of Interpreting Modal Logie WILLARD VAN ORI\IAN QUlNE 267 The Problem of the Morning Star and the Evening Star FREDERIC B. FITCH 273 Modalities and Intensional Languages RUTH BARCAN MARCUS 278 Reply to Professor Mareus WILLARD VAN ORMAN QUlNE 293 Part 8 DEONTle LOGle lntroduction 301 Deontie Logie GEORG HENRIK VON WRIGHT 303 A Note on Deontie Logie and Derived Obligation GEORG HENRIK VON WRIGHT 316 The Formal Analysis of Normative Coneepts ALAN ROSS ANDERSON AND OMAR KHAYYAM MOORE 319 Part 9 MANY VALUED LOGleS I ntroduction 333 Many Valued Logies JOHN BARKLEY ROSSER AND ATWELL R. TURQUETTE 335 Index 343 .

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Paraconsistent Extensional Propositional Logics.* 1
PARACONSISTENT EXTENSIONAL PROPOSITIONAL LOGICS.* Diderik BATENS 1. Introduction In this paper I develop some logics that are as close as possible to the classical propositional calculus (PC) but do not presuppose that the world is consistent. It will turn out that there is one obvious basic logic of this sort, which may be extended in several ways into richer systems. 1 shall study the main formal properties of these systems and offer some philosophical remarks about them. The logics studied in this paper are material (and quasi-material) paraconsistent logics. 1 refer the reader to section 2 for a definition of «material logic» and oquasi-material logic». By a paraconsistent logic I mean, following Ayda I . Arruda (1980), a logic that «can be employed a s underlying lo g ic f o r inconsistent b u t non-trivial theories...» Incidently, the name 'paraconsistent logic' was coined recently by F. Mirô Quesada, but the definition of this kind of logics was offered years ago by Newton C.A. da Costa. Quite some results on paraconsistent logics have been published recently, and it is one of the aims of the present paper to order the domain of those paracon- sistent logics that are extensions o f the full positive propositional calculus. A first embrionic version of this paper was written in 1973. I got interested in the subject because I believed, and still believe, it to be relevant to several problems dealt with by Alan Ross Anderson and Nue! D. Be!nap in connection with their systems E and R. to the problem o f meaning relations (see my (1975a)), to the deduction problem (see my (1975b)), etc.
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The Oberlin Colloquium in Philosophy: Program History
The Oberlin Colloquium in Philosophy: Program History 1960 FIRST COLLOQUIUM Wilfrid Sellars, "On Looking at Something and Seeing it" Ronald Hepburn, "God and Ambiguity" Comments: Dennis O'Brien Kurt Baier, "Itching and Scratching" Comments: David Falk/Bruce Aune Annette Baier, "Motives" Comments: Jerome Schneewind 1961 SECOND COLLOQUIUM W.D. Falk, "Hegel, Hare and the Existential Malady" Richard Cartwright, "Propositions" Comments: Ruth Barcan Marcus D.A.T. Casking, "Avowals" Comments: Martin Lean Zeno Vendler, "Consequences, Effects and Results" Comments: William Dray/Sylvan Bromberger PUBLISHED: Analytical Philosophy, First Series, R.J. Butler (ed.), Oxford, Blackwell's, 1962. 1962 THIRD COLLOQUIUM C.J. Warnock, "Truth" Arthur Prior, "Some Exercises in Epistemic Logic" Newton Garver, "Criteria" Comments: Carl Ginet/Paul Ziff Hector-Neri Castenada, "The Private Language Argument" Comments: Vere Chappell/James Thomson John Searle, "Meaning and Speech Acts" Comments: Paul Benacerraf/Zeno Vendler PUBLISHED: Knowledge and Experience, C.D. Rollins (ed.), University of Pittsburgh Press, 1964. 1963 FOURTH COLLOQUIUM Michael Scriven, "Insanity" Frederick Will, "The Preferability of Probable Beliefs" Norman Malcolm, "Criteria" Comments: Peter Geach/George Pitcher Terrence Penelhum, "Pleasure and Falsity" Comments: William Kennick/Arnold Isenberg 1964 FIFTH COLLOQUIUM Stephen Korner, "Some Remarks on Deductivism" J.J.C. Smart, "Nonsense" Joel Feinberg, "Causing Voluntary Actions" Comments: Keith Donnellan/Keith Lehrer Nicholas Rescher, "Evaluative Metaphysics" Comments: Lewis W. Beck/Thomas E. Patton Herbert Hochberg, "Qualities" Comments: Richard Severens/J.M. Shorter PUBLISHED: Metaphysics and Explanation, W.H. Capitan and D.D. Merrill (eds.), University of Pittsburgh Press, 1966. 1965 SIXTH COLLOQUIUM Patrick Nowell-Smith, "Acts and Locutions" George Nakhnikian, "St. Anselm's Four Ontological Arguments" Hilary Putnam, "Psychological Predicates" Comments: Bruce Aune/U.T.
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What Does It Mean to Say That Logic Is Formal?
WHAT DOES IT MEAN TO SAY THAT LOGIC IS FORMAL? by John Gordon MacFarlane A.B., Philosophy, Harvard College, 1991 M.A., Philosophy, University of Pittsburgh, 1994 M.A., Classics, University of Pittsburgh, 1997 Submitted to the Graduate Faculty of Arts and Sciences in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2000 i Robert Brandom, Distinguished Service Professor of Philosophy (Director) Nuel Belnap, Alan Ross Anderson Distinguished Professor of Philosophy (Second Reader) Joseph Camp, Professor of Philosophy Danielle Macbeth, Associate Professor of Philosophy, Haverford College (Outside Reader) Kenneth Manders, Associate Professor of Philosophy Gerald Massey, Distinguished Service Professor of Philosophy ii WHAT DOES IT MEAN TO SAY THAT LOGIC IS FORMAL? John Gordon MacFarlane, PhD University of Pittsburgh, 2000 Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a pri- ori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal? Three things: logic is said to be formal (or “topic-neutral”) (1) in the sense that it provides constitutive norms for thought as such, (2) in the sense that it is indiﬀerent to the particular identities of objects, and (3) in the sense that it abstracts entirely from the semantic content of thought.
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Introduction: at the Intersection of Truth and Falsity
Introduction: At the Intersection of Truth and Falsity JC Beall ‘Now we will take another line of reasoning. When you follow two separate chains of thought, Watson, you will ﬁnd some point of intersection which should approximate to the truth.’—Sherlock Holmes, in ‘The Disappearance of Lady Frances Carfax’. 1. TOWARDS THE INTERSECTION Suppose that we have (at least) two categories X and Y for any meaningful, declarative sentence A of our language.É Pending further information about X and Y, there seem to be four options for an arbitrary sentence A: » A is only in X » A is only in Y » A is in both X and Y » A is in neither X nor Y Whether each such ‘option’ is logically possible depends not only on our logic (about which more below) but on the details of X and Y. Suppose that X comprises all (and only) sentences composed of exactly six words, and Y those with exactly nineteen words. In that case, only the third option is ruled out: X and Y are exclusive—their intersection X ∩ Y is empty—since no A can be composed of exactly six words and also be composed of exactly nineteen words.Ê Despite being exclusive, X and Y are not exhaustive—their union X ∪ Y does not exhaust all sentences—since some A may fall into neither X nor Y. (Just consider ‘Max sat on Agnes’.) Consider another example. Let X comprise all sentences of your favourite novel and Y your all-time favourite sentences. In that case, exclusion is not ruled out; the intersection of X and Y may well be non-empty.
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Two Entries from the Dictionary of Modern American Philosophers Edited by John R
Two entries from the Dictionary Of Modern American Philosophers edited by John R. Shook, Thoemmes Continuum, 2005 belnap, nuel dinsmore jr. (1930– ) Nuel Belnap was born on 1 May 1930 in Evanston, Illinois. He received an Illinois BA in 1952, and moving to Yale for postgraduate study in logic under the supervision of Alan Anderson, he received an MA in 1957 and a PhD in 1960. After graduation, Belnap continued to work at Yale as an Assistant Professor until 1963, whereupon he moved to the Department of Philosophy at the University of Pittsburgh to take up a position as an Associate Professor. He remains there to this day, where he is now the Alan Ross Anderson Distinguished Professor of Philosophy, in addition to holding positions in Sociology, History and Philosophy of Science, and in the Intelligent Systems Program. Belnap’s research covers logic and related fields such as the philosophy of language and metaphysics and philosophy of science. His name is most often associated with his teacher and colleague Alan Anderson and their research program in relevance logic. Belnap’s research, with Anderson, and their colleagues and students, first at Yale, and then at Pittsburgh, provided a rigorous formal theory of logical consequence and implication that takes account of relevance. The two volumes Entailment (1975, 1992) provide a survey of work in this field, which has continued since the 1950’s. Belnap’s contributions to relevance logic are too numerous to list here, but many have gone on to shape a thriving, if not quite orthodox, research community. A good example of Belnap’s contributions here is his paper “Display Logic” (1982), which develops a new way of seeing the structure of proof, encompassing classical, intuitionistic, modal and relevance logic.
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Alan Ross Anderson and Nuel D.Belnap, Jr. Entailment the Logic
(", , ENTAILMENT ,l THE LOGIC OF RELEVANCE AND NECESSITY by ALAN ROSS ANDERSON and I i--' NUEL D. BELNAP, JR. wUh contributions by J. MICHAEL DUNN j ROBERT K. MEYER Ii l and further contributions by JOHN R. CHIDGEY STORRS MCCALL J. ALBERTO COPPA ZANE PARKS DOROTHY L. GROYER GARREL POTTINGER BAS YAN FRAASSEN RICHARD ROUTLEY HUGUES LEBLANC ALASDAIR URQUHART ROBERT G. WOLF i J VOLUME I PRINCETON UNIVERSITY PRESS Dedicated to the memory of WILHELM ACKERMANN (1896-1962) whose insights in BegrUndung einer strengen Implikatiol1 (Journal of symbolic logic, 1956) provided the impetus for this enterprise COPYRIGHT © 1975 BY PRINCETON UNIVERSITY PRESS Published by Princeton University Press Princeton and London All Rights Reserved LCC: 72-14016 ISBN: G-691-07192-6 Library of Congress cataloging in Publication Data will be found on the last printed page of this book Printed in the United States of America by Princeton University Press Princeton, New Jersey CONTENTS VOLUME I Analytical Table of Contents IX Preface xxi Acknowledgments xxix I. THE PURE CALCULUS OF ENTAILMENT 3 II. ENTAILMENT AND NEGATION 107 III. ENTAILMENT BETWEEN TRUTH FUNCTIONS 150 IV. THE CALCULUS E OF ENTAILMENT 231 V. NEIGHBORS OF E 339 Appendix: Grammatical propaedeutic 473 Bibliography for Volume I 493 Indices to Volume I 517 VOLUME II (tentative) VI. THE THEORY OF ENTAILMENT VII. INDIVIDUAL QUANTIFICATION VIII. ACKERMANN'S Strengen Implikation IX. SEMANTIC ANALYSIS OF RELEVANCE LOGICS X. ASSORTED TOPICS Comprehensive Bibliography (by Robert G. Wolf) Combined Indices vii ANALYTICAL TABLE OF CONTENTS VOLUME I I. THE PURE CALCULUS OF ENTAILMENT §1. The heart of logic 3 § 1.1.
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QUANTIFYING OVER PROPOSITIONS in RELEVANCE LOGIC: NONAXIOMATISABILITY of PRIMARY INTERPRETATIONS of Vp and 3P*
THE JOURNAL OF SYMBOLIC LOGIC Volume 58, Number 1, March 1993 QUANTIFYING OVER PROPOSITIONS IN RELEVANCE LOGIC: NONAXIOMATISABILITY OF PRIMARY INTERPRETATIONS OF Vp AND 3p* PHILIP KREMER A typical approach to semantics for relevance (and other) logics: specify a class of algebraic structures and take a model to be one of these structures, a, together with some function or relation which associates with every formula A a subset of a. (This is the approach of, among others, Urquhart, Routley and Meyer and Fine.) In some cases there are restrictions on the class of subsets of a with which a for mula can be associated: for example, in the semantics of Routley and Meyer [1973], a formula can only be associated with subsets which are closed upwards. It is nat ural to take a proposition of a. to be such a subset of a, and, further, to take the propositional quantifiers to range over these propositions. (Routley and Meyer [1973] explicitly consider this interpretation.) Given such an algebraic semantics, we call (following Routley and Meyer [1973], who follow Henkin [1950]) the above- described interpretation of the quantifiers the primary interpretation associated with the semantics.1 Received April 11, 1991; revised December 18, 1991. *I am much indebted to Nuel Belnap for his constant help and encouragement, and, not least of all, for rather closely inspecting the proofs. I thank Aldo Antonelli for asking me whether the systems studied here fail to be arithmetical (in the recursion theoretic sense of Hinman [1978], Odifreddi [1989] and others) as well as recursively enumerable. Not only are the systems here nonarithmetical, they are recursively isomorphic to full second-order logic.
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There Is No Logical Negation: True, False, Both and Neither
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NUEL BELNAP: CURRICULUM VITAE PRESENT POSITION: Alan Ross Anderson Distinguished Professor of Philosophy, Professor of Sociology, Professor of History and Philosophy of Science, and Professor of the Intelligent Systems Program, University of Pittsburgh. PERSONAL: born Evanston, Illinois, May 1, 1930. EDUCATION: B. A., University of Illinois, 1952; M. A., Yale University, 1957; Ph. D., Yale University, 1960. EMPLOYMENT: Yale University, Department of Philosophy, Instructor, 1958-1960; Assistant Professor, 1960--1963. University of Pittsburgh, Department of Philosophy, Associate Professor, 1963- 1966; Professor, 1966 to date; Professor of Sociology, 1967 to date; Professor of History and Philosophy of Science, 1971 to date; Alan Ross Anderson Lecturer, 1983-84; Alan Ross Anderson Distinguished Professor, 1984 to date; Professor in the Intelligent Systems Program, 1988 to date. University of California at Irvine, Visiting Professor of Philosophy, Winter, 1973. Indiana University, Visiting Oscar R. Ewing Professor of Philosophy, Fall, 1977, Fall, 1978, and Fall, 1979. PROFESSIONAL ASSOCIATIONS: American Philosophical Association; Associa tion for Symbolic Logic (Program Committee Chairman, 1961; Executive Com mittee, 1970--1973; representative to Section L ofthe AAAS, 1974-84; Commit tee on reviews policy, 1974-1976; Oversight Committee 1988-1989; Nomination Committee 1989); American Association for the Advancement of Science; So ciety for Exact Philosophy (Vice president, 1971-1974; President, 1974-1976; Program coordinator, 1978; treasurer,
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Af7fb205-44E1-4410-99Eb-77Fb56b2d124.Pdf
ENTAILMENT ENTAILMENT THE LOGIC OF RELEVANCE AND NECESSITY by ALAN ROSS ANDERSON and NUEL D. BELNAP, JR. and J. MICHAEL DUNN with contributions by KIT FINE ALASDAIR URQUHART and further contributions by DANIEL COHEN GLEN HELMAN STEVE GIAMBRONE ERROL P. MARTIN DOROTHY L. GROVER MICHAEL A, MCROBBIE ANIL GUPTA STUART SHAPIRO and including a Bibliography of Entailment by ROBERT G. WOLF VOLUME II PRINCETON UNIVERSITY PRESS COPYRIGHT © 1992 BY PRINCETON UNIVERSITY PRESS Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, Oxford All Rights Reserved Library of Congress Cataloging-in-Publication Data (Revised for vol. 2) Anderson, Alan Ross. Entailment: the logic of relevance and necessity. Vol. 2. written by Alan Ross Anderson, Nuel D. Belnap and J. Michael Dunn with contribution by Kit Fine ... et al. Includes bibliographical references. 1. Entailment (Logic). I. Belnap, Nuel D., 1930- —joint author. II. Dunn, J. Michael, 1941- III. Fine, Kit. IV. Title. BC199.E58A53 1975 160 72-14016 ISBN 0-691-07192-6 (v. 1) ISBN 0-691-07339-2 (v. 2) This book has been composed in Monotype Times Roman by Syntax International Pte Ltd Princeton University Press books are printed on acid-free paper, and meet the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources Printed in the United States of America by Princeton University Press Princeton, New Jersey 10 987654321 Dedicated to six generous parents SELMA WETTELAND ANDERSON ROSS ELMER ANDERSON ELIZABETH DAFTER BELNAP · NUEL DINSMORE BELNAP PHILOMENA LAUER DUNN · JON HARDIN DUNN CONTENTS VOLUME I Analytical Table of Contents ix Preface xxi Acknowledgments xxix I.
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