Directions in Relevant Logic

449 Pages·1989·17.211 MB·English

by  Jean Norman, Richard Sylvan (auth.), Jean Norman, Richard Sylvan (eds.)

DIRECTIONS IN RELEVANT LOGIC
REASON AND ARGUMENT
VOLUME 1
General Editor: Jan T. J. Srzednicki
Editors: E. M. Barth, Groningen. N. C. A. DaCosta, Sao Paulo. P. T. Geach,
Cambridge, U.K. K. Lorenz, Saarbrucken. W. Marciszewski, Warsaw. S. J. Surma,
Auckland. R. Sylvan, Canberra. R. R. Verma, Lucknow.
Editorial Board: J. Bochenski, Freibourg. J. L. Cohen, Oxford. J. Grattan, Guiness,
Middlesex. A. Grzeqorczyk, Warsaw. R. Harre, Oxford. L. Kielkopf, Columbus,
Ohio. D. Scott, Pittsburgh, Pennsylvania. K. Segerberg, Auckland. P. Suppes,
Stanford, California. K. Szaniawski, Warsaw. P. Weingartner, Salzburg.
R. Wojcicki, Lodz.
Directions
•
In
Relevant Logic
edited by
Jean Norman
and
Richard Sylvan
The Australian National University
KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON
IS BN-13:978-94 -010-6942-7 e-ISBN -13:978-94-009-1005-8
DOl: 10.1007/978-94-009-1005-8
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
© 1989 by Kluwer Academic Publishers
Softcover reprint of the hardcover 1st edition 1989
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.
CONTENTS
Preface. Jean Nonnan and Richard Sylvan vii
Foreword. Nuel D. Belnap, Jr.: Dedicatory Note on Alan Anderson ix
List of Contributors xii
CHAPTER 1. Introduction: Routes in Relevant Logic 25
PART I. RELEVANCE AND THE CONNECTION REQUIREMENT
CHAPTER 2. Teun A. van Dijk: "Relevance" in Logic and Grammar 25
CHAPTER 3. John Parks-Clifford: Literal Relevance 59
CHAPTER 4. John Woods: The Relevance of Relevant Logics 77
CHAPTERs. Charles F. KieJkopf: The Classical Logic of Relevant Logicians 87
CHAPTER 6. Larisa Maksimova: Relevance Principles and Fonnal Deducibility 95
PART II. THE GRANDER SWEEP OF RELEVANT LOGICS
CHAPTER 7. William T. Parry: Analytic Implication; Its History, Justification and Varieties 101
CHAPTER 8. R. B. Angell: Deducibility, Entailment and Analytic Containment 119
CHAPTER 9. Nuel D. Belnap, Jr.: Conjunctive Containment 145
CHAPTER 10. John Myhill: Real Implication 157
CHAPTER 11. Alasdair Urquhart: What is Relevant Implication? 167
PART ill. TECHNICAL INVESTIGATIONS AND PRESENT LIMITATIONS
CHAPTER 12. Dolph Ulrich: The NonExistence of Finite Characteristic Matrices for
Subsystems of R 177
j
CHAPTER 13. Zane Parks and Michael Byrd: Relevant Implication and Leibnizian Necessity 179
CHAPTER 14. Nuel D. Belnap, Jr.: Which Entailments Entail Which Entailments? 185
CHAPTER 15. John Bacon: Categorical Propositions in Relevance Logic 197
CHAPTER 16. Kit Fine: Im;ompleteness for Quantified Relevance Logics 205
PART IV. WIDER APPLICATIONS OF RELEVANT LOGICS
CHAPTER 17. J. Michael Dunn and Robert K. Meyer: Gentzen' s Cut and Ackennann' s Gamma 229
CHAPTER 18. Charles G. Morgan: Semantic Discovery for Relevance Logics 241
CHAPTER 19. Richard Routley: Philosophical and Linguistic Inroads: Multiply Intensional
Relevant Logics 269
CHAPTER 20. James B. Freeman: Quantification, Identity, and Opacity in Relevant Logic 305
VI
CHAPTER 21. John Barker: Relevance Logic and Inferential Knowledge 305
CHAPTER 22. Richard Routley: Semantics Unlimited I: A Rclevant Synthcsis of Implication
with Higher Intensionality 327
CHAPTER 23. Graham Priest and Jan Crosthwaite: Relevance, Truth and Meaning 377
CHAPTER 24. Conclusion: Further Directions in Relevant Logics 399
Bibliography 439
PREFACE
Relevance logics came of age with the one and only International Conference on relevant
logics in 1974. They did not however become accepted, or easy to promulgate. In March
1981 we received most of the typescript of
IN MEMORIAM: ALAN ROSS ANDERSON
Proceedings of the International Conference of Relevant Logic
from the original editors, Kenneth W. Collier, Ann Gasper and Robert G. Wolf of Southern
Illinois University.1 They had, most unfortunately, failed to find a publisher - not, it appears,
because of overall lack of merit of the essays, but because of the expense of producing the
collection, lack of institutional subsidization, and doubts of publishers as to whether an
expensive collection of essays on such an esoteric, not to say deviant, subject would sell.
We thought that the collection of essays was still (even after more than six years in the
publishing trade limbo) well worth publishing, that the subject would remain undeservedly
esoteric in North America while work on it could not find publishers (it is not so esoteric in
academic circles in Continental Europe, Latin America and the Antipodes) and, quite
important, that we could get the collection published, and furthermore, by resorting to local
means, published comparatively cheaply. It is indeed no ordinary collection. It contains work
by pioneers of the main types of broadly relevant systems, and by several of the most
innovative non-classical logicians of the present flourishing logical period.
We have slowly re-edited and reorganised the collection and made it camera-ready.
While we have retained all the completed essays from the Conference sent to us with the
exception of essays that have, in the interval, been published elsewhere, we have not limited
ourselves to these essays but have, so far as space permitted, invited newer essays. As well we
have included overviews, which provide introductions to current directions of research on
broadly relevant logics and to many general problems in the area.
In an effort, then, to ensure that the book was rather newer and more up-to-date -and
not simply a rather dated collection of papers from a conference more than a decade ago - we
decided to
1. Remove all papers from the Conference that had been published in the interim or that
were to be published elsewhere. As a result the following papers given at the Conference, and
included in earlier unpublished collections of the proceedings have been deleted: Allen 82, Fine
79, Gupta, Belnap and Dunn 80, Hanson 80, Pottinger 79.
For different reasons, two papers delivered at the Conference were never received by any
editors, namely Woodruff's on three-valued relevance logic and Stephenson's 'Law and
explanation in the new regime'. These it was easy not to include. A final paper, Anderson and
Meyer's 'Open problems II', we managed to obtain only in very incomplete form; moreover,
owing to substantial progress in relevant problem solving, it is conspicuously out-of-date.
Accordingly, we decided against including what we had of it; but we have offered a partial,
though very different substitute, in the conclusion.
2. Update all the papers remaining from the Conference. Somewhat to our disappointment,
not many authors took much advantage of this opportunity; but perhaps this only reflects the
lack of recent movement in some parts of the field, not always sloth. An exception is van
Dijk, who replaced his original paper by a substantially new one.
3. Invite some newer significant papers in the area. So resulted the papers now included by
VII
VlIl
Belnap, Fine, and Priest and Crosthwaite.
4. Delete the long introduction by the original editors, which summarised the original papers,
and which tied the text to the Conference and to the state of relevant logics a decade ago.
We have in fact removed most allusions to the Conference from the body of the work. In
place of the original introduction we initially included, dispersed throughout the book,
introductory surveys, including historical and other guide material. But as a result of these
scholarly additions, the text became much too long. Eventually these seemingly integral
additions were removed to a companion volume, A Bystanders' Guide to Sociative Logics;
then remaining blockages impeding production were quickly dissolved.
For the long delays in the final production of this scheme the present editors do accept a
due measure of responsibility. It is some little excuse that production of camera-ready copy of
a text of this magnitude and symbolic complexity proves to be a remarkedly slow business,
especially when it is slotted into the press of other departmental and personal activities. The
delays have understandably worried some contributors, and have undoubtedly cost others, less
worried but more damaged, proper credit for their original ideas.
Notes on citations, etc. We have adopted modes of referencing that are now fairly standard in
texts on relevant logic (that used in RLR, which is a straightforward modification of that of
ENT). Most work is indicated by author (or first author) and date (or abbreviated date in the
case of twentieth century work). But a few frequently cited works, such as ENT (i.e
Entailment) are referred to by mnemonics, which are listed alphabetically at the beginning of
the bibliography. All work cited will be found in the bibliography at the end.
Acknowledgements. We are much indebted to Lois Newman and especially Frances Redrup
who succeeded in producing a fine camera-ready copy from a typographically difficult text. In
early 1986 Jean Norman left the employment of the Australian National University, the
institution which generously, if largely unwittingly, supplied the infrastucture for production
of the camera-ready script. She was succeeded by Debbie Trew who carried on the complex
and not always rewarding editorial task. We want also to thank Con all O'Connell and David
Bennett, for their effort in proof reading, bibliographical excursions, and research into
sociative logics. In the final debugging of the typescript, we have beer. greatly assisted by
Arnold Gunther, who much surpasses ordinary mortals like us in his ability to discern
typographical errors and infelicities.
Jean Norman and Richard Sylvan
NOTES
1. The Conference itself, organised from Southern Illinois University, was held at nearby St
Louis, Missouri. Only Wolfremains at Southern Illinois University, Edwardsville, which
was an important centre for relevant logics and source of the valuable, but regrettably
now defunct, Relevance Logic Newsletter. Collier and Gasper have both left academic
life, Collier for a ministry in the Unitarian Church, Gasper for parts unknown.
In fact, the drop-out rate of relevantly-disposed thinkers appears disconcertingly high.
The Conference gathering indicates a trend. There, not only have original editors left
academia and many others involved turned away to safer topics; one of the speakers,
G.H. Stephenson, seems to have disappeared without a trace. We have been unable to
obtain a copy of the paper he presented, despite much effort at a distance. Other
speakers, who submitted papers and whose papers are included, we have not heard from,
namely Myhill (now dead) and Parks, who is also out of academia.
FOR~WORD
DEDICATORY NOTE
ON
ALAN ANDERSON
Nnel D. Belnap, Jr.
I'd like to share with you how I first got to know Alan and how we started working
together. Alan and I were at Yale, I as a graduate student and he teaching, for nearly two
years before we ever met. This is fully explained by the hypothesis that Yale is Yale.
In the spring of 1957, towards the end of these two years, I was taking a course from
Fred Fitch on Godel's incompleteness theorem when in strode Alan to explain that Fitch was
out of town and to show us what those marvelous alpha and beta functions really amount to
and how they work. It was my first experience of Alan's teaching, and let me just say that his
performance was beautifully typical. Though we may have said a few words of greeting after
class, I did not see him again for a year and a half. In the meantime I had gone to Belgium on
a Fulbright to study with Canon Robert Feys. Feys was interested both in Ackermann and in
Gentzenj he had written a little paper on Ackermann's Strenge Implikation for Logique et
Analyse, and he gave me the problem of finding a Gentzen formulation of Ackermann's
calculus. By the time the tenure of my fellowship was up, I had formulated an inordinately
complex conjecture as to what might count as the Gentzen formulation for a part of
Ackermann's system, and I asked Feys for suggestions as to how I might go about proving the
conjecture. Though 1 now no longer recall the details, nothing seemed to work; so, since 1 was
about to return to the States, I asked Feys if anyone there knew anything about Ackermann.
He said he didn't know of anybody, but recommended that 1 try Godel on the grounds that he
was the only one that Feys knew that could contribute to the solution of a problem, with
which he was totally unfamiliar, after ten minutes' explanation.
My hopes dimmed, but when I got back to Yale I went in to see Alan to ask him if he
knew anyone who knew anyone who knew anything about Ackermann. His eyes lit up as
upon finding a long lost friend. He leapt from his chair, held his hand up high aloft, and said
"I do!" He had reviewed the Ackermann article for the Journal of Symbolic Logic and had
become deeply interested in the topic; but not knowing anybody else that was, he was equally
delighted to find a fellow Strengenite. He patiently listened to my enthusiastic Gentzenizing
and was able to suggest some generalized strategies, one of which ultimately worked. He also
proposed we take a leaf from Ruth Marcus' research notebook and try to prove an appropriate
deduction theorem for Ackermann's calculus. This was the germ of the "dependence" analysis
of relevance.
We began meeting an hour or two a week, but the deduction theorem project and
related Ackermann studies rapidly began to take up the lion's share of both of our working
times.
Especially in those early years we worked together extremely closely. We spent hours
and hours and hours together, usually in Alan's office in Saybrook College, black boarding or
talking sometimes between ourselves but equally often with some of the first-rate
undergraduates such as Levin and Wallace, Gallagher, Snavely and Barwise. Our method of
composition was absolutely joint. We used to hammer out every sentence together while one
or the other of us, but mostly Alan, inscribed the words on paper. We both enjoyed our work
together enormously. Over the years never did we have anything remotely resembling an
IX