Table Of ContentTRUTH OR CONSEQUENCES
Nuel Belnap
"Photo by Jonas"
Copyright 1989-All Rights Reserved JONAS PHOTOGRAPHY
TRUTH OR
CONSEQUENCES
Essays in Honor of
Nuel Belnap
edited by
J. MICHAEL DUNN
Department of Philosophy and Department of Computer Science,
Indiana University, Bloomington, U.S.A.
and
ANILGUPTA
Department of Philosophy, Indiana University,
Bloomington, U.S.A.
KLUWER ACADEMIC PUBLISHERS
DORDRECHT I BOSTON I LONDON
Library of Congress Cataloging-in-Publication Data
Truth or consequences essays in honor of Nuel Belnap / edited by J.
Mlchael Dunn and Ani 1 Gupta.
p. cm.
Inc 1u des bib 1 i ograph i ca 1 references and indexes.
ISBN-I3:978-94-010-6791-1 e-ISBN-13:978-94-009-0681-5
DOl: 10.1007/978-94-009-0681-5
1. Logic. 2. Truth. 3. Mathematics--Philosophy.
4. Probabilities. I. Dunn. J. Michael. 1941- II. Gupta. Anil.
1949- III. Belnap. Nuel D. • 1930-
BC71.T78 1990
160--dc20 90-5141
ISBN-J3:978-94-010-6791-1
Published by Kluwer Academic Publishers,
P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
Kluwer Academic Publishers incorporates
the publishing programmes of
D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press.
Sold and distributed in the U.S.A. and Canada
by Kluwer Academic Publishers,
101 Philip Drive, Norwell, MA 02061, U.S.A.
In all other countries, sold and distributed
by Kluwer Academic Publishers Group,
P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
Printed on acid-free paper
All Rights Reserved
© 1990 Kluwer Academic Publishers
Softcover reprint of the hardcover 1st edition 1990
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system. without written permission from the copyright owner.
For
Nuel and Gillian Belnap
TABLE OF CONTENTS
PREFACE ix
ACKNOWLEDGEMENTS xi
LIST OF CONTRIBUTORS xii
DOROTHY GROVER / On Two Deflationary Truth Theories 1
W. KENT WILSON / Some Reflections On The Prosentential
Theory of Truth 19
MICHAEL KREMER / Paradox and Reference 33
ANIL GUPTA / Two Theorems concerning Stability 49
ALASDAIR URQUHART / The Complexity of Decision Procedures
in Relevance Logic 61
J. MICHAEL DUNN /RelevantPredication 3: Essential Properties 77
JAY L. GARFIELD / The Dog: Relevance and Rationality 97
JON BARWISE / Consistency and Logical Consequence 111
DANIEL COHEN / On What Cannot Be 123
RUTH MANOR / Durations: Temporal Intervals with Gaps
and Undetermined Edges 133
JAMES W. GARSON / Categorical Semantics 155
A. P. HAZEN / The Myth of the Intuitionistic "Or" 177
VIRGINIA KLENK / What Mathematical Truth Need Not Be 197
GARREL POTTINGER / A Tour of the Multivariate Lambda Calculus 209
STORRS McCALL / Choice Trees 231
ALDO BRESSAN / The Extensional but Hyper-Intensional Calculus Co:
with Orderless Constants and Variables 245
JOHN F. HORTY / A Skeptical Theory of Mixed Inheritance 267
ROBERT L. BIRMINGHAM / The Logic of Mitchill v. Lath 283
HUGUES LEBLANC and PETER ROEPER / What are Absolute
Probabilities a Function of? 307
PATRICK MAHER I How Prediction Enhances Confirmation 327
BAS C. VAN FRAAS SEN / Figures in a Probability Landscape 345
NUEL BELNAP: CURRICULUM VITAE 357
NUEL BELNAP: DOCTORAL STUDENTS 359
NUEL BELNAP: PUBLICATIONS 361
INDEX OF NAMES 369
INDEX OF SUBJECTS 373
vii
PREFACE
The essays in this collection are written by students, colleagues, and friends of Nuel
Belnap to honor him on his sixtieth birthday. Our original plan was to include pieces
from fonner students only, but we have deviated from this ever so slightly for a
variety of personal and practical reasons.
Belnap's research accomplishments are numerous and well known: He has
founded (together with Alan Ross Anderson) a whole branch of logic known as
"relevance logic." He has made contributions of fundamental importance to the
logic of questions. His work in modal logic, fonnal pragmatics, and the theory of
truth has been highly influential. And the list goes on. Belnap's accomplishments
as a teacher are also distinguished and well known but, by virtue of the essential
privacy of the teaching relationship, not so well understood. We would like to reflect
a little on what makes him such an outstanding teacher.
The following, though true, can only be a partial answer: He understands his
subject through and through; he is smart, perceptive, and penetrating. There are
two more factors that should be taken into account, if one is to understand Belnap's
teaching accomplishments. The first is his attitude towards logic and philosophy:
he approaches the subject with a sense of play and a sense of humor. He does not
work with ideas, he plays with them. He doesn't get mired in complicated fonnulas,
he draws pictures. He doesn't construct convoluted proofs, he "arm waves," as he is
fond of saying. When things take an unexpected turn, he doesn't fret, he laughs. To
do logic and philosophy with Nuel is not like carrying a heavy stone up a steep hill.
It is more like exploring an exotic city. He is not content to stay on the main drag;
he wants to explore all the alleys and byways. And exploration with him is fun. For
he has such infectious enthusiasm, and he is smart, perceptive, and penetrating.
The second factor we need to consider to understand Belnap's teaching accom
plishments consists of some of his personal qualities. One important aspect is his
infonnality. In the early sixties, when he first came to Pittsburgh, he even had a
nickname "Nuel, call me Nuel" because of his penchant for being on a first name
basis with his students. Remember this was well before everyone became a "hippy"
and such things became common.
Even more important than this infonnality, we think, are his intellectual courage,
honesty, open-mindedness, and generosity. His office door is always open, and
students do not feel silly bothering him with "silly" questions. Never, in all his play
and experimentation with ideas, does he exhibit dogmatism. Never is he dismissive
or disrespectful of views that are contrary to his own. To play with ideas with such a
person is bound to be fun. And when that person is quick to credit you with having
taught him something, when he makes you feel part of the enterprise, he becomes
an irresistible teacher.
ix
PREFACE
The qualities that make Nuel such a great teacher make him also such an
adorable man. It is to this beloved man that these essays are dedicated.
J. Michael Dunn
AnilGupta
x
ACKNOWLEDGEMENTS
We wish to acknowledge the help of many people in producing this volume, not the
least of whom are our contributors. This book was produced from a camera-ready
copy which, in turn, was prepared using Donald Knuth's excellent program TEX.
Almost all of our contributors helped by producing either a TEX file or another elec
tronic version of their document that could be massaged (in a few cases "wrestled"
is the more appropriate word) into TEX.
Andre Chapuis deserves special thanks not only for overseeing the entire
project, but also for his tireless, skillful, and conscientious work in producing the
camera-ready copy. Others who helped in this process are Nancy Garrett, Luzia
Martins, and Shirley Roper. Indiana University provided support that was crucial to
the preparation of the volume.
We want to take this opportunity to give special thanks to Collie Henderson,
Belnap's secretary for many years. The immediate occasion is for her giving to
us Belnap's vita, list of publications, and a list of his doctoral students. But more
generally she has not just been a constant support to Belnap's own work, but a friend
and helper to many of his students.
We want to thank the people at Kluwer, particularly Martin Scrivener, for
taking on this project. We also wish to thank Scrivener for his helpful cooperation
and for his understanding and patience during the delay caused by our complete
underestimate of the time needed to perfect the camera-ready copy.
Thanks to Gillian Belnap for the photograph that appears as the frontpiece to
this volume.
xi
LIST OF CONTRmUTORS
Jon Barwise is College Professor of Philosophy, Mathematics, and Logic at Indiana
University.
Robert L. Birmingham is Professor of Law at the University of Connecticut.
Aldo Bressan is Professor of Physics at the University of Padua
Daniel Cohen is Assistant Professor of Philosophy at Colby College.
J. Michael Dunn is Oscar Ewing Professor of Philosophy, and Professor of Computer
Science at Indiana University.
Jay L. Garfield is Associate Professor of Philosophy at Hampshire College.
James W. Garson is Professor of Philosophy at the University of Houston.
Dorothy Grover is Professor of Philosophy at the University of illinois, Chicago.
Anil Gupta is Professor of Philosophy at Indiana University.
A. P. Hazen is Lecturer in Philosophy at the University of Melbourne.
John F. Horty is Assistant Professor of Philosophy at the University of Maryland.
Virginia Klenk is Professor of Philosophy at West Virginia University.
Michael Kremer is Assistant Professor of Philosophy at the University of Notte
Dame.
Hugues Leblanc is Professor of Philosophy at Temple University.
Patrick Maher is Assistant Professor of Philosophy at the University of Illinois at
Urbana-Champaign.
Ruth Manor is Professor of Philosophy at San Jose State University.
Storrs McCall is Associate Professor of Philosophy at McGill University.
Garrel Pottinger is a Researcher at Odyssey Research Associates Inc.
Peter Roeper is Senior Lecturer in Philosophy in The Faculties at the Australian
National University, Canberra.
Alasdair Urquhart is Professor of Philosophy at the University of Toronto.
W. Kent Wilson is Associate Professor of Philosophy at the University of Illinois,
Chicago.
Bas C. van Fraassen is Professor of Philosophy at Princeton University.
xii
