To Mock a Mockingbird and Other Logic Puzzles: Including an Amazing Adventure in Combinatory Logic

262 Pages·1985·3.99 MB·English

by  Raymond M. Smullyan

FPT $14.95
In this entertaining and challenging new collection
of logic puzzles, Raymond Smullyan- author of
What Is the Name of This Book> and Tile Lady or the
Tiger?- continues to delight and astonish us with
his gift for making available, in the thoroughly
pleasurable form of puzzles, some of the most im
portant mathematical thinking of our time.
In the first part of the book, he transports us once
again to that wonderful realm where knights,
knaves, twin sisters, quadruplet brothers, gods,
demons, and mortals either always tell the truth or
always lie, and where truth-seekers are set a variety
of fascinating problems. The section culminates in
an enchanting and profound metapuzzle (a puzzle
about a puzzle), in which Inspector Craig of Scot
land Yard gets involved in a search for the Fountain
of Youth on the Island of Knights and Knaves.
In the second and larger section, we accompany
the Inspector on a summer-long adventure into the
field of combinatory logic (a branch of logic that
plays an important role in computer science and ar
tificial intelligence). His adventure, which includes
enchanted forests, talking birds, bird sociologists,
and a classic quest, provides for us along the way the
pleasure of solving puzzles ofi ncreasing complexity
until we reach the Master Forest and-thanks to
Godel's famous theorem-the final revelation.
To Mork a Mork;t1gbird will delight all puzzle lov
ers-the curious neophyte as well as the serious stu
dent oflogic, mathematics, or computer science.
\
\
Raymond Smullyan, a well-known mathematician
and logician, is Oscar Owing Professor of Philos o
phy at Indiana University and Professor Emeritus
of the City University of New York- Lehman
College and Graduate Center, His many writings
include three previous volumes of recreational
logic and math problems, What Is the Name of This
Book?, The Lady or the Tiger', and Alice in Puzzle
land; two studies of deductive logic in chess, The
Chess Mysteries of Sherlock Holmes and The Chess
Mysteries of the Arabian Knights; and three collec
tions of philosophical essays and aphorisms, The Tao
Is Silent, This Book Needs No Title, and 5000 B. C.
Jacket illustration and design by Steven Max Singer
~
Alfred A. Knopf, Publisher, New York
6/8S

TO MOCK
A MOCKINGBIRD
ALSO BY RAYMOND SMULLYAN
Theory of Formal Systems
First Order Logic
The Tao Is Silent
What Is the Name of This Book?
This Book Needs No Title
The Chess Mysteries of Sherlock Holmes
The Chess Mysteries of the Arabian Knights
The Lady or the Tiger?
Alice in Puzzle-Land
5000 B.C.
TO MOCI(
A MOCI(INGBIRD
And Other Logic Puzzles
Including an Amazing Adventure
in Combinatory Logic
by Raymond Smullyan
ALFRED A. KNOPF
NEW YORK 1985
To the memory of HASKELL CURRY
an early pioneer in combinatory lo.f?!c
and an avid bird-watcher
THIS IS A BORZOI BOOK
PUBLISHED BY ALFRED A. KNOPF, INC.
Copyright © 1985 by Raymond Smullyan
All rights reserved under International and Pan-American
Copyright Conventions. Published in the United States by Alfred
A. Knopf, Inc., New York, and simultaneously in Canada by
Random House of Canada Limited, Toronto. Distributed by
Random House, Inc., New York.
Library of Congress Cataloging in Publication Data
Smullyan, Raymond M. To mock a mockingbird.
1. Philosophical recreations. 2. Puzzles. 3. Logic.
I. Title.
GV1507.P43S68 1985 793.73 84-48737
ISBN 0-394-53491-3
Manufactured in the United States of America
FIRST EDITION
A NOTE ON THE TYPE
This book has been set in a digitized version of the well-known
Monotype face, Bembo. The roman is a copy of a letter cut for the
celebrated Venetian printer Aldus Manutius by Francesco Griffo,
and first used in Cardinal Bembo's De Aetna of 1495. The
companion italic is an adaption of the chancery script type designed
by the Roman calligrapher and printer Lodovico degli Arrighi,
called Vincentino, and used by him during the 1520's.
Composed by Maryland Composition Company, Inc.,
Glen Burnie, Maryland. Printed and bound by Fairfield Graphics,
Fairfield, Pennsylvania.
Based on a design by Judith Henry.
Contents
Acknowledgments vii
Preface ix
PART I' LOGIC PUZZLES' I
1 The Prize-and Other Puzzles 3
2 The Absentminded Logician 9
3 The Barber of Seville 18
4 The Mystery of the Photograph 28
PART II' KNIGHTS, KNAVES, AND THE
F 0 UN T A I N 0 F YOU T H • 37
5 Some Unusual Knights and Knaves 39
6 Day-Knights and Night-Kni~hts 48
7 Gods, Demons, and Mortals 56
8 In Search of the Fountain of Youth 63
PAR T I I I • TOM 0 C K A M 0 C KIN G B I RD' 71
9 To Mock a Mockingbird 73
10 Is There a Sage Bird? 89
11 Birds Galore 93
CONTENTS
12 Mockingbirds, Warblers, and Starlings 117
13 A Gallery of Sage Birds 128
PAR T I V • SIN GIN G B I R D S • 141
14 Curry's Lively Bird Forest 143
15 Russell's Forest 151
16 The Forest Without a Name ISS
17 Godel's Forest 158
PAR TV· THE MAS T E R FOR EST • 165
18 The Master Forest 167
19 Aristocratic Birds 179
20 Craig's Discovery 187
PAR T V I • THE G RAN D QUE S T ION! • 191
21 The Fixed Point Principle 193
22 A Glimpse into Infinity 199
23 Logical Birds 208
24 Birds That Can Do Arithmetic 215
25 Is There an Ideal Bird? 229
Epilogue 241
Who's Who Among the Birds 244