Logic, Meaning and Computation Essays in Memory of Alonzo Church
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SYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE
Managing Editor:
JAAKKO HINTIKKA, Boston University, U.S.A.
Editors : DIRK VAN DALEN, University of Utrecht, The Netherlands DONALD DAVIDSON, University of California, Berkeley, U.S.A. THEO A.F. KUIPERS , University of Groningen, The Netherlands PATRICK SUPPES, Stanford University, California, U.S.A. JAN WOLENSKI, Jagiellonian University, Krakow, Poland
VOLUME 305
LOGIC, MEANING AND COMPUTATION Essays in Memory of Alonzo Church Edited by
C. ANTHONY ANDERSON University of California, Santa Barbara, U.S.A.
and MICHAEL ZELENY P7YX, Los Angeles, California, U.S.A.
" ~.
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-3891-1 ISBN 978-94-010-0526-5 (eBook) DOI 10.1007/978-94-010-0526-5
Printed on acid-free paper
AII Rights Reserved © 200 1 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2001 Softcover reprint of the hardcover lst edition 200 1 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.
TABLE OF CONTENTS
C . ANTHONY ANDERSON DAVID KAPLAN
and MICHAEL
and TYLER
BURGE
I
ZELENY
I
Preface
RememberingAlonzoChurch
vii xi
PART I LOGIC PETER APOSTOLI
of arithmetic JOHN CORCORAN
I
Logic, truth and number: The elementary genesis
I
Second-order logic
3
I A representation of relation algebrasusing Routley-Meyer frames
61
J. MICHAEL DUNN
I
THOMAS FORSTER ROBIN O. GANDY
I
Church's settheorywitha universal set Axioms of infinityin Church'stypetheory
EDWARD L . KEENAN
I
SAUNDERS MAC LANE
77 109 139
Logicalobjects
149
I
181
The lambdacalculus andadjointfunctors
I Atomic Booleanalgebrasa ndclassical propositional logic
GERALD J . MASSEY
ROBERT K. MEYER
relevant logic STEWART SHAPIRO
185
I
Improved decision proceduresfor pure
I
The "triumph"of first-order languages
219
I
261
191
RAYMOND SMULLYAN
Equivalencer elations andgroups PART II COMPUTATION
HENK BARENDREGT KLAUS GRUE
I
I
Discriminatingcodedlambdaterms
A-calculus as a foundation formathematics
275 287
vi
TABLE OF CONTENTS Peano'slambdacalculus:The functional abstraction implicitin arithmetic
DANIEL LEIVANT /
RALPH LOADER /
The undecidability of >'-definability
313 331
A construction of the provable wellorderings of thetheoryof species
343
Semanticsfor first and higher orderrealizability
353
PER MARTIN-LOF /
COLIN MCLARTY /
JOHN C . SHEPHERDSON /
Languageand equalityt heoryin logic
programming
365
PART III PHILOSOPHY, MEANING , AND INTENSIONAL LOGIC C . ANTHONY ANDERSON /
Alternative (1*): A criterionof identity
forintensional entities
395
Nominalistparaphraseand ontological
JOHN P. BURGESS /
commitment
429
Peace,justiceand computation
